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\\href{http://cronfa.swan.ac.uk/Record/cronfa49707}{http://cronfa.swan.ac.uk/Record/cronfa49707}\n\nUse policy:\n\nThis item is brought to you by Swansea University. Any person downloading material is agreeing to abide by the terms of the repository licence: copies of full text items may be used or reproduced in any format or medium, without prior permission for personal research or study, educational or non-commercial purposes only. The copyright for any work remains with the original author unless otherwise specified. The full-text must not be sold in any format or medium without the formal permission of the copyright holder. Permission for multiple reproductions should be obtained from the original author.\n\nAuthors are personally responsible for adhering to copyright and publisher restrictions when uploading content to the repository.\n\nPlease link to the metadata record in the Swansea University repository, Cronfa (link given in the citation reference above.)\n\n\\href{http://www.swansea.ac.uk/library/researchsupport/ris-support/}{http://www.swansea.ac.uk/library/researchsupport/ris-support/}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-002}\n\\end{center}\n\n\\section*{Swansea University Prifysgol Abertawe }\n\\section*{Physical Verification of the Melt Pool in Laser Powder-Bed Fusion}\nSubmitted to Swansea University in fulfilment of the requirements for the Degree of Engineering Doctorate\n\nSwansea University\n\nMaterials Research Centre\n\n\\section*{Acknowledgements}\nThe research presented here was funded by my industrial sponsor, Renishaw plc, and MATTER, funded by the EPSRC through Swansea University.\n\nl'd like to thank both my parents for showing me steadfast dedication, as well as my academic supervisors, Dr Nick Lavery and Professor Steve Brown, for showing infinite patience and astute guidance. l'd like to give them all special thanks for helping me get this far. I want to say thanks as well to all my friends and colleagues who've helped me out and been there for me.\n\n\\section*{Declaration }\nThis work has not previously been accepted in substance for any degree and is not being concurrently submitted in candidature for any degree.\n\nSigned (candidate)\n\nDate\n\n\\section*{STATEMENT 1}\nThis thesis is the result of my own investigations, except where otherwise stated. Where correction services have been used, the extent and nature of the correction is clearly marked in a footnote(s).\n\nOther sources are acknowledged by footnotes giving explicit references. A bibliography is appended.\n\n$$\n\\text { Signed .................................................................. (candidate) }\n$$\n\nDate\n\n\\section*{STATEMENT 2}\nI hereby give consent for my thesis, if accepted, to be available for photocopying and for inter-library loan, and for the title and summary to be made available to outside organisations.", "start_char_idx": 0, "end_char_idx": 3554, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5a2448ec-c374-4181-b3f4-9cc1d586bf6d": {"__data__": {"id_": "5a2448ec-c374-4181-b3f4-9cc1d586bf6d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8416d6bc-4bae-47a8-b4f2-2ad9966e1ba3", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a52b8934bca22bee3636b18161621a021879354ed945068b2526e7b4224a3a00", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9143e7ba-b863-49ec-8c20-181bb1030f17", "node_type": "1", "metadata": {}, "hash": "a536169e5ce5c48203b5a90af7a2e690d2e2794a7d6d1bd2eded34db1385a61d", "class_name": "RelatedNodeInfo"}}, "text": "I want to say thanks as well to all my friends and colleagues who've helped me out and been there for me.\n\n\\section*{Declaration }\nThis work has not previously been accepted in substance for any degree and is not being concurrently submitted in candidature for any degree.\n\nSigned (candidate)\n\nDate\n\n\\section*{STATEMENT 1}\nThis thesis is the result of my own investigations, except where otherwise stated. Where correction services have been used, the extent and nature of the correction is clearly marked in a footnote(s).\n\nOther sources are acknowledged by footnotes giving explicit references. A bibliography is appended.\n\n$$\n\\text { Signed .................................................................. (candidate) }\n$$\n\nDate\n\n\\section*{STATEMENT 2}\nI hereby give consent for my thesis, if accepted, to be available for photocopying and for inter-library loan, and for the title and summary to be made available to outside organisations.\n\nDate\n\n\\section*{Table of Contents}\nAcknowledgements ..... I\\\\\nDeclaration ..... II\\\\\nTable of Contents ..... III\\\\\nList of Figures ..... $\\mathrm{VI}$\\\\\nList of Tables ..... XII\\\\\nAbstract ..... 13\\\\\nChapter 1 Introduction ..... 15\\\\\n1.1 An Introduction to Additive Manufacturing ..... 15\\\\\n1.2 Limitations and Issues concerning Powder-Bed Fusion ..... 17\\\\\n1.3 State-of-the-Art in Generating Process Maps ..... 18\\\\\n1.4 Objectives of this work ..... 20\\\\\n1.5 Publications ..... 21\\\\\nChapter 2 Overview of Additive Manufacturing Systems ..... 22\\\\\n2.1 Introduction ..... 22\\\\\n2.2 Electron Beam Melting ..... 22\\\\\n2.3 Laser Metal Deposition ..... 24\\\\\n2.4 Selective Laser Melting ..... 25\\\\\n2.5 Lasers ..... 30\\\\\n2.6 Renishaw Systems ..... 33\\\\\n2.7 AM250 Specifications ..... 33\\\\\n2.8 Conclusions ..... 36\\\\\nChapter 3 Thermo-Mechanics of melt pool formation ..... 37\\\\\n3.1 Introduction ..... 37\\\\\n3.2 The Physical Model.", "start_char_idx": 2609, "end_char_idx": 4475, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9143e7ba-b863-49ec-8c20-181bb1030f17": {"__data__": {"id_": "9143e7ba-b863-49ec-8c20-181bb1030f17", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5a2448ec-c374-4181-b3f4-9cc1d586bf6d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7c31c84bd557d5b7fe88e3ced265cee9385f081c409dc4d60294618fb3df4b8b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5fe24d35-eef1-48a2-86cf-51533d81ffe5", "node_type": "1", "metadata": {}, "hash": "cef91e56cfaa011e76ce6c4c55c279a66561cf76cee6291c08659c669a6d5eff", "class_name": "RelatedNodeInfo"}}, "text": "..... 38\\\\\n3.2.1 The Powder Bed ..... 38\\\\\n3.2.2 The Laser Beam ..... 39\\\\\n3.2.3 Melting of the Powder Bed ..... 40\\\\\n3.3 Effects ..... 41\\\\\n3.3.1 Wetting and Balling ..... 41\\\\\n3.3.2 Plateau-Rayleigh Instability ..... 43\\\\\n3.3.3 Marangoni Convection ..... 44\\\\\n3.3.4 Keyholing ..... 46\\\\\nChapter 4 Experimental Methods and Materials ..... 48\\\\\n4.1 Optimal Density Parameters ..... 48\\\\\n4.1.1 Introduction ..... 48\\\\\n4.1.2 General Method ..... 49\\\\\n4.1.3 Stainless Steel 316L Powder (Experiments A and B) ..... 50\\\\\n4.1.4 Stainless Steel 316L Powder (Experiments C and D) ..... 51\\\\\n4.1.5 Titanium Ti6Al4V Powder (Experiment E) ..... 53\\\\\n4.2 Experiment A - Direct Base Plate Method ..... 54\\\\\n4.2.1 Objectives ..... 54\\\\\n4.2.2 Experimental Design ..... 54\\\\\n4.3 Experiment B - Single-Lines on Recessed Plates Method ..... 56\\\\\n4.3.1 Objectives ..... 56\\\\\n4.3.2 Experimental Design ..... 56\\\\\n4.4 Crucible Method (CM) ..... 59\\\\\n4.4.1 Introduction ..... 59\\\\\n4.4.2 Crucible Design ..... 60\\\\\n4.4.3 Experiment C - Verification of Single-Track Crucible Methodology ..... 62\\\\\n4.4.4 Experiment D - Single-Tracks on Crucible Substrates ..... 64\\\\\n4.4.5 Experiment E - Crucible Single-Track experiments using Ti-6Al-4V ..... 65\\\\\nChapter 5 Results ..... 68\\\\\n5.1 Optimal Density Parameters ..... 68\\\\\n5.1.1 Stainless Steel 316L Powder (Experiments A and B) ..... 68\\\\\n5.1.2 Stainless Steel 316L Powder (Experiments C and D) ..... 69\\\\\n5.1.3 Titanium Ti6Al4V Powder (Experiment E) ..... 70\\\\\n5.2 Experiment A- Direct Base Plate Method ..... 71\\\\\n5.2.1 Results ..... 71\\\\\n5.2.2 Discussion ..... 76\\\\\n5.2.3 Conclusions ..... 76\\\\\n5.3 Experiment B - Single-Lines on Recessed Plates Method ..... 77\\\\\n5.3.1 Results ..... 77\\\\\n5.3.2 Discussion ..... 80\\\\\n5.3.3 Conclusions ..... 92\\\\\n5.4 Experiment C - Verification of Single-Track Crucible Methodology ..... 94\\\\\n5.4.1 Results ..... 94\\\\\n5.4.2 Discussion ..... 103\\\\\n5.4.3 Conclusions ..... 109\\\\\n5.5 Experiment D - Single-Tracks on Crucible Substrates ..... 111\\\\\n5.5.1 Results ..... 111\\\\\n5.5.2 Discussion ..... 114\\\\\n5.5.3 Conclusions ..... 126\\\\\n5.6 Experiment $\\mathrm{E}$ - Crucible Single-Track experiments using Ti-6AI-4V ..... 128\\\\\n5.6.1 Results ..... 128\\\\\n5.6.2 Discussion ..... 141\\\\\n5.6.3 Conclusions ..... 145\\\\\nChapter 6 Discussion ..... 146\\\\\nChapter 7 Conclusions and Further Work ..... 152\\\\\n7.1 Specific Conclusions ..... 152\\\\\n7.2 General Conclusions. ..... 154\\\\\n7.3 Further Work ..... 155\\\\\nReferences ..... 156\\\\\nAppendix 1 - TMS Paper 3026 ..... 163\\\\\nAppendix 2 - Metallographic Preparation for Experiment A ..... 170\\\\\nAppendix 3 - Metallographic Preparation for Experiment $C$ ..... 171\\\\\nAppendix 4 - Beraha II Etchant Preperation ..... 172\\\\\nAppendix 5 - Metallographic Preparation for Experiment E ..... 174\n\n\\section*{List of Figures}\nFigure 1. Laser Metal Deposition Apparatus ..... 25\\\\\nFigure 2. Schematic drawing of SLM process ..... 26\\\\\nFigure 3.", "start_char_idx": 4476, "end_char_idx": 7400, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5fe24d35-eef1-48a2-86cf-51533d81ffe5": {"__data__": {"id_": "5fe24d35-eef1-48a2-86cf-51533d81ffe5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9143e7ba-b863-49ec-8c20-181bb1030f17", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1526c6d6b3cc7860ea029c4d660db7d6e1cf24b2a79a2400e37a9aa363ac1733", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a9008d36-d74c-4611-8f79-a6704b5211e5", "node_type": "1", "metadata": {}, "hash": "e08214787252c86fa1b433330b417f13741199aec4f976ca34c2c01537c875aa", "class_name": "RelatedNodeInfo"}}, "text": "..... 154\\\\\n7.3 Further Work ..... 155\\\\\nReferences ..... 156\\\\\nAppendix 1 - TMS Paper 3026 ..... 163\\\\\nAppendix 2 - Metallographic Preparation for Experiment A ..... 170\\\\\nAppendix 3 - Metallographic Preparation for Experiment $C$ ..... 171\\\\\nAppendix 4 - Beraha II Etchant Preperation ..... 172\\\\\nAppendix 5 - Metallographic Preparation for Experiment E ..... 174\n\n\\section*{List of Figures}\nFigure 1. Laser Metal Deposition Apparatus ..... 25\\\\\nFigure 2. Schematic drawing of SLM process ..... 26\\\\\nFigure 3. Absorption of laser output at different wavelengths ..... 27\\\\\nFigure 4. Laser focus positions with respect to the powder bed. ..... 29\\\\\nFigure 5. Basic Laser Operation, [63] ..... 32\\\\\nFigure 6. AM250 ..... 34\\\\\nFigure 7. Laser parameters in the Renishaw AM250 ..... 35\\\\\nFigure 8. Physical phenomena at play in the powder-bed fusion system. ..... 38\\\\\nFigure 9. Surface Wetting ..... 42\\\\\nFigure 10. Plateau-Rayleigh Instabilities ..... 44\\\\\nFigure 11. Right) Layout of the machine parameter array on the build plate, Left) as-built sample labels ..... 51\\\\\nFigure 12. Left) Density cubes, as they appeared in the assembly diagram, Right) the asbuilt density cube on a base plate. ..... 52\\\\\nFigure 13. Experiment A (SS316L) - Experimental Design ..... 55\\\\\nFigure 14. Experiment B (SS316L) - Experimental design ..... 58\\\\\nFigure 15. The Crucible Design ..... 60\\\\\nFigure 16. Left) CAD drawing of crucibles used during an experiment, Right) Three single track structures placed at the top of the crucibles ..... 61\\\\\nFigure 17. Relative density with laser input energy ..... 68\\\\\nFigure 18. Relative density with input energy measured in DOE experiment for Chapter 5, (SS316L) ..... 69\\\\\nFigure 19. Relative density with input energy measured in DOE experiment for Chapter 6, (Ti-6Al-4V) ..... 70\\\\\nFigure 20. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 1. 72\n\nFigure 21. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 2. 72 Figure 22. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 3. 73 Figure 23. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 4. 73 Figure 24. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 5. 74 Figure 25. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 6. 74 Figure 26. Experiment A (SS316L) - Changes in the track dimensions and gap sizes 75 Figure 27. Experiment B (SS316L) - Topographical process map at 504m layer depth. The red dot shows the shows the parameters used at the Renishaw recommended operating conditions. 78\n\nFigure 28. Experiment B (SS316L) - Cross-sectional process map at 50 4 m layer depth.... 79\n\nFigure 29. Experiment B (SS316L) -The five types of topographical tracks which formed during experiment.\n\nFigure 30. Experiment B (SS316L) - The three types of cross-sectional tracks formed during experiment.\n\nFigure 31. Experiment B (SS316L) - Variation of the melt pool stability with scan speed.\n\nFigure 32. Experiment B (SS316L) - Track width at the 75-125W range compared to results from Bertoli et al 85\n\nFigure 33. Experiment B (SS316L) - Track width at the 150-200W range compared to results from Bertoli et al 85\n\nFigure 34. Experiment B (SS316L) - Track depth at the 75-125W range compared to results from Bertoli et al 86\n\nFigure 35.", "start_char_idx": 6889, "end_char_idx": 10256, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a9008d36-d74c-4611-8f79-a6704b5211e5": {"__data__": {"id_": "a9008d36-d74c-4611-8f79-a6704b5211e5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5fe24d35-eef1-48a2-86cf-51533d81ffe5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "59622c7fdb833ac98034a3c8596dd853390402fc0c2edfbdd84a1ccfb9460257", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "4c8b6892-40f9-470d-87be-79979691dd6d", "node_type": "1", "metadata": {}, "hash": "acb13303e8e65620520c4880a75a65167eddea2d686b1faf94d187f515c17970", "class_name": "RelatedNodeInfo"}}, "text": "Experiment B (SS316L) -The five types of topographical tracks which formed during experiment.\n\nFigure 30. Experiment B (SS316L) - The three types of cross-sectional tracks formed during experiment.\n\nFigure 31. Experiment B (SS316L) - Variation of the melt pool stability with scan speed.\n\nFigure 32. Experiment B (SS316L) - Track width at the 75-125W range compared to results from Bertoli et al 85\n\nFigure 33. Experiment B (SS316L) - Track width at the 150-200W range compared to results from Bertoli et al 85\n\nFigure 34. Experiment B (SS316L) - Track depth at the 75-125W range compared to results from Bertoli et al 86\n\nFigure 35. Experiment B (SS316L) - Track depth at the 150-200W range compared to results from Bertoli et al 86\n\nFigure 36. Experiment B (SS316L) - Comparison of measured and predicted melt pool depths at the 75-125W range according to equation from Gladush and Smurov\n\nFigure 37. Experiment B (SS316L) - Comparison of measured and predicted track depths at the 150-200W range according to equation from Gladush and Smurov\n\nFigure 38. Experiment B (SS316L) - Topographical images of tracks built using parameters similar to the DOE optimal parameters (180W, $433 \\mathrm{mms}^{-1}$ ).... 91\n\nFigure 39. Experiment B (SS316L) - Contours of build ratios of single tracks. 91\n\nFigure 40. Experiment B (SS316L) - Contours of depth to width ratio of single tracks 92\n\nFigure 41. Experiment C (SS316L) - Topographical process map at 504m layer depth 95\n\nFigure 42. Experiment C (SS316L) - Cross-sectional process map at 50 4 m layer depth.... 96\n\nFigure 43. Experiment C (SS316L) - Topographical process map at 1004m layer depth.... 97\n\nFigure 44. Experiment C (SS316L) - Cross-sectional process map at 1004m layer depth.. 98\n\nFigure 45. Experiment C (SS316L) - Topographical process map at 1504m layer depth.... 99\n\nFigure 46. Experiment C (SS316L) - Cross-sectional process map at 150 1 m layer depth. 100\n\nFigure 47. Experiment C (SS316L) - Topographical process map at 2004m layer depth.. 101\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-010}\n\\end{center}\n\nFigure 49. Experiment C (SS316L) - The three types of tracks formed 104\n\nFigure 50. Experiment C (SS316L) - Left) Tracks build on the crucible substrate, with distinctive, flattened tracks appearing on the left-hand side. Right) Cross-sectional image taken using the same parameters. 104\n\nFigure 51. Keyhole formation and fluid flow in the melt pool, taken from Stanciu et al. [113]\n\nFigure 52. Experiment C (SS316L) - Contours of depth-to-width ratios at the different layer depths..... 109\n\nFigure 53. Experiment D (SS316L) - Topographical process map. 112\n\nFigure 54. Experiment D (SS316L) - Cross-sectional process map. 113\n\nFigure 55. Experiment D (SS316L) - Track widths compared with Experiment B (SS316L) at the $75-125 \\mathrm{~W}$ range 115\n\nFigure 56. Experiment D (SS316L) - Track widths compared with Experiment B (SS316L) at the $150-200 \\mathrm{~W}$ range. 115\n\nFigure 57. Experiment D (SS316L) - The three types of tracks formed. 118\n\nFigure 58. Experiment D (SS316L) - Keyhole porosity observed during experiment. 119\n\nFigure 59. Experiment D (SS316L) - Track depths compared with Experiment B (SS316L) at the $75-125 \\mathrm{~W}$ range 120\n\nFigure 60.", "start_char_idx": 9623, "end_char_idx": 12912, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "4c8b6892-40f9-470d-87be-79979691dd6d": {"__data__": {"id_": "4c8b6892-40f9-470d-87be-79979691dd6d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a9008d36-d74c-4611-8f79-a6704b5211e5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cb2457d542f80fb5620fc39496462c918d76bbc0c4bf014eacb0d7cfe055221d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "10ab5e65-d8ed-4f46-b2ce-9f9edeb9fa4a", "node_type": "1", "metadata": {}, "hash": "ffec4b5b108bc5f96a16459723d61a1464e6f559ae6e4c51e9c0fd4520eb0cca", "class_name": "RelatedNodeInfo"}}, "text": "112\n\nFigure 54. Experiment D (SS316L) - Cross-sectional process map. 113\n\nFigure 55. Experiment D (SS316L) - Track widths compared with Experiment B (SS316L) at the $75-125 \\mathrm{~W}$ range 115\n\nFigure 56. Experiment D (SS316L) - Track widths compared with Experiment B (SS316L) at the $150-200 \\mathrm{~W}$ range. 115\n\nFigure 57. Experiment D (SS316L) - The three types of tracks formed. 118\n\nFigure 58. Experiment D (SS316L) - Keyhole porosity observed during experiment. 119\n\nFigure 59. Experiment D (SS316L) - Track depths compared with Experiment B (SS316L) at the $75-125 \\mathrm{~W}$ range 120\n\nFigure 60. Experiment D (SS316L) - Track depths compared with Experiment B (SS316L) at the $150-200 \\mathrm{~W}$ range. 120\n\nFigure 61. Experiment D (SS316L) - Comparison of measured and predicted penetration depths according to equation from Gladush and Smurov 121\n\nFigure 62. Experiment D (SS316L) - Comparison of measured and predicted penetration depths according to equation from Gladush and Smurov\n\nFigure 63. Experiment D (SS316L) - Left) Topographical image of track built using parameters similar to DOE optimal parameters, Right) cross-section taken at the same track. 124\n\nFigure 64. Experiment D (SS316L) - Contours of line build percentage of single tracks 124\n\nFigure 65. Experiment D (SS316L) - Contours of depth-to-width ratio. 125\n\nFigure 66. Experiment D (SS316L) - Cross section of a track, highlighting the type of grain formation. 126\n\nFigure 67. Experiment E (Ti-6Al-4V) - Topographical process map at 504m layer depth.. 128 Figure 68. Experiment E (Ti-6Al-4V) - Cross-sectional process map at 50 4 m layer depth. 129 Figure 69. Left) Experiment E (Ti-6Al-4V) -Single Tracks, produced at 200W, 500mms ${ }^{-1} .130$ Figure 70. Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at 200W, $500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $200 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $50 \\mu \\mathrm{m}$ 131\n\nFigure 71.Experiment E (Ti-6Al-4V) - Track cross-section, taken at 150W, 1000mms ${ }^{-1}$.\n\nNecking occurs between the melt bead and substrate. 132\n\nFigure 72. Experiment E (Ti-6Al-4V) - Topographical process map at 1004m layer depth. 133 Figure 73. Experiment E (Ti-6Al-4V) - Cross-sectional process map at 1004m layer depth.\n\nFigure 74. Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at 200W, $500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $200 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $100 \\mu \\mathrm{m}$ 134\n\nFigure 75. Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at $100 \\mathrm{~W}, 500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $100 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $100 \\mu \\mathrm{m}$ 135\n\nFigure 76. Experiment E (Ti-6Al-4V) - Topographical process map at $150 \\mu$ m layer depth. 136 Figure 77. Experiment E (Ti-6Al-4V) - Cross-sectional process map at $150 \\mu \\mathrm{m}$ layer depth.\n\nFigure 78.", "start_char_idx": 12298, "end_char_idx": 15326, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "10ab5e65-d8ed-4f46-b2ce-9f9edeb9fa4a": {"__data__": {"id_": "10ab5e65-d8ed-4f46-b2ce-9f9edeb9fa4a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "4c8b6892-40f9-470d-87be-79979691dd6d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c3dd708ad2de0d2bb27adcbbb3259d46b06725b94416d232f8c747de33f24c6a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "cad96959-9ca5-47b4-95b1-e9e32858810c", "node_type": "1", "metadata": {}, "hash": "452f35fc2b3fe5b4dade7dac84ef72a66169dcc3b69652fef47315aced688e73", "class_name": "RelatedNodeInfo"}}, "text": "Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at $100 \\mathrm{~W}, 500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $100 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $100 \\mu \\mathrm{m}$ 135\n\nFigure 76. Experiment E (Ti-6Al-4V) - Topographical process map at $150 \\mu$ m layer depth. 136 Figure 77. Experiment E (Ti-6Al-4V) - Cross-sectional process map at $150 \\mu \\mathrm{m}$ layer depth.\n\nFigure 78. Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at 200W, $500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $200 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $150 \\mu \\mathrm{m}$ 137\n\nFigure 79. Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at $150 \\mathrm{~W}, 500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $150 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $150 \\mu \\mathrm{m}$ 138\n\nFigure 80. Experiment E (Ti-6Al-4V) - Topographical process map at $200 \\mu$ m layer depth. 139 Figure 81. Experiment E (Ti-6Al-4V) - Cross-sectional process map at $200 \\mu m$ layer depth.\n\nFigure 82. Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at 200W, $500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $200 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $200 \\mu \\mathrm{m}$\n\nFigure 83. Experiment E (Ti-6Al-4V) - Tracks formed at $200 \\mathrm{~W}, 500 \\mathrm{mms}^{-1}$, at increasing layer thicknesses. 142\n\nFigure 84. Experiment E (Ti-6Al-4V) - Average Track Width at 200W. ............................ 143\n\nFigure 85. Experiment E (Ti-6Al-4V) - Average Track Width at 150W. ............................. 144\n\nFigure 86. Experiment E (Ti-6Al-4V) - Average Track Width at 100W. ............................ 144\n\nFigure 87. Transition of the track geometry in Experiment B (SS316L)........................... 147\n\nFigure 88. The five types of tracks that formed during Experiment B (SS316L)................ 148\n\nFigure 89. Transition of the track geometry in Experiment D (SS316L)\n\n\\section*{List of Tables}\nTable 1. Spot size calibration of the Renishaw AM250 used in this work ..... 34\\\\\nTable 2. Typical laser parameters for the Renishaw AM250 ..... 36\\\\\nTable 3. Design of experiments used for Chapter 4 ..... 50\\\\\nTable 4. Composition, in weight percentage, of the $316 \\mathrm{~L}$ powder used in the study ..... 50\\\\\nTable 5. Laser parameters used for DOE for Chapter 5. ..... 52\\\\\nTable 6. Laser parameters used for DOE ..... 53\\\\\nTable 7. Experiment A (SS316L) - Laser Parameters used ..... 54\\\\\nTable 8. Experiment B (SS316L) - Processing parameters used ..... 57\\\\\nTable 9. Experiment C (SS316L) - Processing parameters ..... 63\\\\\nTable 10. Experiment D (SS316L) - Processing parameters used ..... 65\\\\\nTable 11. Experiment E (Ti-6Al-4V) - Processing parameters used ..... 66\\\\\nTable 12. Experiment A (SS316L) - Average Length, Width, Height and Gap Size taken from surface images ..... 71\\\\\nTable 13.", "start_char_idx": 14871, "end_char_idx": 17887, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "cad96959-9ca5-47b4-95b1-e9e32858810c": {"__data__": {"id_": "cad96959-9ca5-47b4-95b1-e9e32858810c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "10ab5e65-d8ed-4f46-b2ce-9f9edeb9fa4a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7fd3652f1055171273669b871050958c502a39716815ae5f8a7690e8de94498f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b0293187-d6f9-4d80-9610-df83f6c194b8", "node_type": "1", "metadata": {}, "hash": "79c1df3f3a2d6d0c00ac34fb974718e33a74525f4ee298a4f67aa44811a2e632", "class_name": "RelatedNodeInfo"}}, "text": "Laser parameters used for DOE for Chapter 5. ..... 52\\\\\nTable 6. Laser parameters used for DOE ..... 53\\\\\nTable 7. Experiment A (SS316L) - Laser Parameters used ..... 54\\\\\nTable 8. Experiment B (SS316L) - Processing parameters used ..... 57\\\\\nTable 9. Experiment C (SS316L) - Processing parameters ..... 63\\\\\nTable 10. Experiment D (SS316L) - Processing parameters used ..... 65\\\\\nTable 11. Experiment E (Ti-6Al-4V) - Processing parameters used ..... 66\\\\\nTable 12. Experiment A (SS316L) - Average Length, Width, Height and Gap Size taken from surface images ..... 71\\\\\nTable 13. Experiment B (SS316L) - Process Map with line build percentages, divided into\\\\\nsections ..... 80\\\\\nTable 14. Values used to calculate values for penetration depth equation from Gladush and\\\\\nSmurov ..... 87\\\\\nTable 15. Experiment C (SS316L) - Process maps with line build percentages for each layer\\\\\ndepth, given in bold over each table. ..... 103\\\\\nTable 16. Experiment D (SS316L) - Process map with line build percentages ..... 111\\\\\nTable 17. Experiment E (Ti-6Al-4V) - Process map with line build percentages for each layer depth, given in bold over each table. ..... 141\n\n\\section*{Abstract}\nLaser Powder-Bed Fusion (LPBF) is an additive manufacturing process which fuses metal powder on a layer by layer basis to form complex three-dimensional components. As with other additive processes, LPBF is seeing a rapid evolution of machine design, scanning techniques, and materials development which has moved the process well beyond its origins in rapid prototyping to a process which can manufacture fit-for-purpose components. At the heart of the LPBF process lies the melt pool, and the way in which the laser properties, such as speed, power and beam diameter interact to form tracks fused to the substrate is integral to the way in which multiple tracks will fill the contours across each layer in the build sequence.\n\nControlling the as-solidified bead shape is important to ensure optimal mechanical properties. A widespread technique for measuring the effect of laser properties on the mechanical properties and track formation is process mapping. Single-layer or single-track process maps, which measure the behaviour of the melt according to laser properties on a single layer of powder, have been limited to a base plate of same composition, but with a different microstructure, typically resulting from a rolling process. The work in this thesis describes the efforts to standardise a high-throughput method of creating process maps which measure the effects of these process parameters on, in a way which compliments and improves upon the usual technique of deposition of single line tracks directly onto a base plate. One result of this work is a new method where substrates are built using the LPBF process, on which single tracks are deposited with a controlled powder depth. This is done in such a way that the as-built tracks are representative of the process at regions away from the base plate, by building the substrate in-situ, before the forming of the tracks.\n\nIt was found that the crucible single track method could be used quite effectively to control the powder layer depth at which tracks were deposited on. The additional benefit granted by\\\\\nthe crucible substrate was the ease at which high quality topographical and cross-sectional metallography could take place in order to quantify and investigate the effects of changing the parameters. For example, by using the crucible method, it was found that titanium alloy Ti-6Al-4V, at a maximum laser power of $200 \\mathrm{~W}$, could form relatively stable track formations at $100 \\mu \\mathrm{m}$ layer thickness at a scan speed of $500 \\mathrm{mms}^{-1}$. At lower power values, faster scan speeds or larger layer depths, tracks would not form successfully.\n\nAnother important outcome was that the crucible method predicted a much less severe transition between conductive and keyhole modes of melting than direct deposition of single tracks onto a baseplate, with shallower re-melting of lower layers. The crucible method also predicted a more forgiving transition between continuous lines and lines which had broken down due to poor wetting or insufficient temperatures.", "start_char_idx": 17308, "end_char_idx": 21545, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b0293187-d6f9-4d80-9610-df83f6c194b8": {"__data__": {"id_": "b0293187-d6f9-4d80-9610-df83f6c194b8", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "cad96959-9ca5-47b4-95b1-e9e32858810c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7f2bcb50f24898d91f34c8e9d87a63818cba8288000ecce61571d19206ba855f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2ead336d-fadb-4f33-a3cb-bf528dc097ca", "node_type": "1", "metadata": {}, "hash": "11231c4e6247d70714a364824ea0d76dd949f7b62de27a3aec75fc098d6f8684", "class_name": "RelatedNodeInfo"}}, "text": "For example, by using the crucible method, it was found that titanium alloy Ti-6Al-4V, at a maximum laser power of $200 \\mathrm{~W}$, could form relatively stable track formations at $100 \\mu \\mathrm{m}$ layer thickness at a scan speed of $500 \\mathrm{mms}^{-1}$. At lower power values, faster scan speeds or larger layer depths, tracks would not form successfully.\n\nAnother important outcome was that the crucible method predicted a much less severe transition between conductive and keyhole modes of melting than direct deposition of single tracks onto a baseplate, with shallower re-melting of lower layers. The crucible method also predicted a more forgiving transition between continuous lines and lines which had broken down due to poor wetting or insufficient temperatures.\n\n\\section*{Chapter 1 Introduction}\n\\subsection*{1.1 An Introduction to Additive Manufacturing}\nAdditive manufacturing (AM) is an umbrella term to describe a wide number of manufacturing techniques used to build three-dimensional (3D) parts by progressively laying down and binding layers of material to the specification of a digital model, such as a computer-aided design (CAD) model. AM methods have several advantages over traditional, subtractive methods like CNC machining. Instead of having a part made from a mould and have it go through several machining processes, a part can instead be made in a single step. This can reduce the production time and associated costs. Material costs are also limited to the exact material used to create the part, save for if or when support structures are used. AM offers a greater degree of design freedom, as it eliminates many limitations imposed through traditional methods. Parts can be produced on demand and customised easily, allowing features to be modified late in the design cycle if necessary. The origins of additive manufacturing can be traced back to the development of rapid prototyping methods back in the 1980s and 1990s. Initially, these methods were limited to low-strength materials such as polymers and waxes[1], [2]. Eventually, these methods were improved to be able to produce higher quality parts, viable for commercial and industrial use. Other technologies would be developed through the 1990s and early 2000s, such as electron beam melting (EBM) and selective laser melting (SLM), which would introduce metal processing capability to AM. The history, development and capabilities of rapid prototyping and AM technologies are discussed further in Chapter 2.\n\nThe AM market has seen substantial growth, with its worth being estimated to be over $\\$ 4$\n\nbillion in 2014, [3]. It is expected to grow to over $\\$ 21$ billion by 2020 [4]. Whilst a large portion of the market is devoted to polymer-based AM, there has been substantial interest in\\\\\nmetal-based AM methods, and in particular, powder-bed based systems such as EBM and SLM, also called powder-bed fusion additive manufacturing processes.\n\nPowder-bed fusion AM systems use a high energy delivery system, such as a high-power laser or electron beam, to heat and melt sections of a thin bed of evenly spread metal powder, around $20 \\mu \\mathrm{m}$ to $200 \\mu \\mathrm{m}$ in thickness. The powder reaches a high enough temperature to melt, and the resulting melt pool extends to the solid material beneath the powder and binds to it. The melt pool quickly re-solidifies, and the laser moves to other parts of the powder bed to repeat the process. After a layer is completed, the build platform is lowered, and another layer of powder is evenly spread over the previous one, and the process is repeated until the part is completed.\n\nPowder-bed based AM methods have seen widespread use throughout the automotive, aerospace and medical industries, due to their ability to create useable rapid prototyped parts reducing the overall design and production lead costs.\n\nIn both automotive and aerospace industries, any small reduction in time and development cost can result in significant overall savings in the development of a vehicle or aircraft. Automotive manufactures have utilised powder-bed fusion AM methods such as selective laser sintering (SLS), laser beam melting (LBM) and SLM for prototyping, as well as the rapid fabrication or repairing of tooling components, [5]-[7]. Additionally, the need for tool manufacture for a production of a part can be cut out entirely by fabricating the part in a single procedure, shortening the design and production cycle [8], [9]. Aerospace industries utilise powder-bed fusion AM methods to create highly complex products with high performance properties.", "start_char_idx": 20765, "end_char_idx": 25375, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2ead336d-fadb-4f33-a3cb-bf528dc097ca": {"__data__": {"id_": "2ead336d-fadb-4f33-a3cb-bf528dc097ca", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b0293187-d6f9-4d80-9610-df83f6c194b8", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6e40386eb7cb7c7afc944e199f6e8dc1756b0621e7f6da20959d31ba42f70f2d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7147f8c3-2317-4b29-a867-b627761662f3", "node_type": "1", "metadata": {}, "hash": "950b565cb7a3b20fdbb6b399bcefe3bc5fe49e4abe97561c029efaab58072dd4", "class_name": "RelatedNodeInfo"}}, "text": "Powder-bed based AM methods have seen widespread use throughout the automotive, aerospace and medical industries, due to their ability to create useable rapid prototyped parts reducing the overall design and production lead costs.\n\nIn both automotive and aerospace industries, any small reduction in time and development cost can result in significant overall savings in the development of a vehicle or aircraft. Automotive manufactures have utilised powder-bed fusion AM methods such as selective laser sintering (SLS), laser beam melting (LBM) and SLM for prototyping, as well as the rapid fabrication or repairing of tooling components, [5]-[7]. Additionally, the need for tool manufacture for a production of a part can be cut out entirely by fabricating the part in a single procedure, shortening the design and production cycle [8], [9]. Aerospace industries utilise powder-bed fusion AM methods to create highly complex products with high performance properties. The designer freedom offered by AM eliminates the need for assembly features and allows for the addition of features with internal functionality, such as internal honeycomb structures to reduce weight whilst maintaining mechanical strength, [10]. The manufacturing company Siemens claimed to have successfully created and tested gas turbine blades, made with a revised blade design and improved internal cooling channels [11].\n\nMedical industries utilise AM techniques extensively due to the ease in which 3D medical imaging data can be converted into solid objects. Orthopaedic and dental implants can be customised to fit individual patients quite easily using AM techniques [12], [13]. Certain alloys, such as Tantalum, are useful in implants due to their biocompatibility and chemical resistance. However, they are also found to be difficult to process using conventional metal processing techniques due to their high cost and melting temperatures, Powder-bed fusion methods, such as EBM and SLM, are able to process these types of alloys quite readily, and are thus popular and ideal methods to use within the field, [14], [15].\n\n\\subsection*{1.2 Limitations and Issues concerning Powder-Bed Fusion}\nMost powder-bed fusion methods typically have low build rates and small build volumes, although there have been efforts by manufacturers to increase both the build volume and build rate. A typical laser powder-bed fusion system uses one fibre laser, ranging between $200 \\mathrm{~W}$ to $1 \\mathrm{KW}$ capacity, and can achieve build rates of around $5-20 \\mathrm{~cm}^{3}$ per hour, in a build volume limited to $250 \\mathrm{~mm} \\times 250 \\mathrm{~mm} \\times 325 \\mathrm{~mm}$, [16]. Manufacturers of SLM and EBM systems have attempted to address these limitations through implementing multiple laser beams in the process to increase build rate (e.g. the Renishaw RenAM $500 Q^{1}$ ), or continually increasing the build volume offered by their machines (e.g. SLM $500^{2}$ or EOS M $400^{3}$ ). However, the defining limitation, which is often referred to as the Achilles heel of AM, [17], is ensuring part quality and reproducibility, especially for large scale production as desired by the automotive and aviation industries. Laser powder-bed fusion is subject to highly complex and dynamic manufacturing constraints, and it has been estimated that there are nearly 130 influential parameters that can affect the process, [18].\n\nDefects such as porosity within the part, [19],surfaces roughness, [20], and residual stresses [21], [22], cause a reduction in the physical properties of powder-bed fusion based parts. These defects can be attributed to the formation and subsequent solidification of the melt\\\\\n\\textbackslash footnotetext\\{\\\\\n${ }^{1}$ \\href{http://www.metal-am.com/renishaw-introduce-four-laser-system-formnext-2017/}{http://www.metal-am.com/renishaw-introduce-four-laser-system-formnext-2017/}\n\n${ }^{2} \\mathrm{https} / / / \\mathrm{slm}$-solutions.com/products/machines/selective-laser-melting-machine-slm-500\n\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-019}\\\\\npool. The factors affecting the formation include the laser processing parameters, such as the laser power, beam diameter, scanning pattern and scanning speed, which have a direct impact on how energy is delivered to the metal powder particles.", "start_char_idx": 24406, "end_char_idx": 28747, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7147f8c3-2317-4b29-a867-b627761662f3": {"__data__": {"id_": "7147f8c3-2317-4b29-a867-b627761662f3", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2ead336d-fadb-4f33-a3cb-bf528dc097ca", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "330a0a6b9631b74e4498792cf3578f8a29efdde7e51a2312b9c34314a27c5d39", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "206fd717-a444-459e-9afa-3e47aca391ca", "node_type": "1", "metadata": {}, "hash": "6650646e7a8d33fd9f8ff8c863b5329528ce78caf2f611de15edddde1fa53f8c", "class_name": "RelatedNodeInfo"}}, "text": "The factors affecting the formation include the laser processing parameters, such as the laser power, beam diameter, scanning pattern and scanning speed, which have a direct impact on how energy is delivered to the metal powder particles. For example, if there is insufficient melting of the powder due to low energy input from the laser, a phenomenon known as balling may occur, where the scanned laser track breaks into a series of droplets. This can have negative affects the part, such as pore formation and surface roughness, [23]. Detrimental issues could arise from the powder bed itself, from differences in the powder alloy composition, size, morphology, particle size distribution and presence of oxidation. Powder re-use has been found to be a potential liability in powder-bed fusion processes, where repeated cycles of powder reuse can cause a reduction the certain elements within the chemical composition of the part [24]. Powder particle size and distribution can affect the flowability and packing density of the powder bed, [25].\n\n\\subsection*{1.3 State-of-the-Art in Generating Process Maps}\nAs new machines are developed, and new powder materials are introduced, it is important that high throughput methods are developed to identify optimal processing parameters. Such methods should investigate the relationship between the process parameters and formation of the melt pool. Single melt track process maps are a highly utilised method of performing such an investigation, wherein the laser only scans powder in a single, narrow width, consisting of the diameter of the beam.\n\nThe process map provides an in-depth study of the interaction between the laser, the powder and the solid substrate. Two commonly used parameters are the laser power (W) and the laser speed $(\\mathrm{mm} / \\mathrm{s})$. The process map should ideally assist in the selection of optimal laser settings with energy densities which avoid melt-track defects, such as balling. A criticism which has been made of process maps is that they are not general enough, and this is exasperated by a number of factors. One factor is the rapidly developing technology of the AM machines themselves, with changing laser types, beam sizes and powers, powder deposition strategies and gas flow handling. Another factor is the lack of user control of\\\\\nmachine parameters at a fundamental level to control build sequences, particularly the movement and firing of the laser and stage movements. Often the ported software is developed by other companies, not necessarily the machine manufacturer and is more geared towards simplification of the build preparation for full components rather than providing full access to all machine parameters for scientific study.\n\nIn addition to process maps, bulk properties such as density and tensile strength are used to select optimal machine parameters over multiple layers, using Design of Experiments (DOE) and Analysis of Variances (ANOVA). The time taken to determine optimal machine parameters for a new AM powder has come down from 3 to 4 months to a few weeks, and this is typically done looking at bulk density, using optically measured porosity, and mechanical properties. However, this is still too long when multiple iterations are required, for example in the case where multiple new compositions of powders need to be tested and assessed with relatively small amounts of powder.\n\nRecent research has made it possible to envisage in real time the way in which powder particles melt and solidify at the level of the melt-pool, or along tracks [26], [27].\n\nComputational models are being developed and validated, but the complexity of the physics, and the difficulty of observing the melt-pools and limited thermal measurements, makes the modelling of limited use at the moment.\n\nThis means that the traditional way of understanding the interaction between the laser, powder and substrate using physical experimentation persists as the preferred means for new powder alloy development and optimisation of machine parameter. However, the combination of factors described above has led to published process maps often being outof-date by the time of publication, tending to make it difficult to establish empirical relationships between beam sizes and powder depth, and linking results to existing knowledge of larger beam sizes, [28] and outcomes from computational models. However, single track experimental work which results in process maps leads to a better understanding of not just the porosity formation mechanisms, but also the inter-layer penetration and the resulting microstructures which are formed and have a direct effect on\\\\\nthe as-built mechanical properties of the material. Yadroitsev and Smurov, [29], [30], provide examples of the early attempts at generalising rules for melt-pool instabilities, but these were typically done with low laser powers and energy densities. These have been based upon an often-used method of direct melting powder onto base-plates or substrates made through machining traditionally fabricated metal plates.", "start_char_idx": 28509, "end_char_idx": 33593, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "206fd717-a444-459e-9afa-3e47aca391ca": {"__data__": {"id_": "206fd717-a444-459e-9afa-3e47aca391ca", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7147f8c3-2317-4b29-a867-b627761662f3", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d9bdc34b218263c13cf4773ce9442db3f57c3be970788b8bf5713cd29a2cb91a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "e5b685ee-7757-453e-bbf4-aab8b82d633b", "node_type": "1", "metadata": {}, "hash": "dcf68a54555a7ce5d1644aed2ea5d2e3900b0ed2b6583410fcc8dfff9112ea56", "class_name": "RelatedNodeInfo"}}, "text": "However, the combination of factors described above has led to published process maps often being outof-date by the time of publication, tending to make it difficult to establish empirical relationships between beam sizes and powder depth, and linking results to existing knowledge of larger beam sizes, [28] and outcomes from computational models. However, single track experimental work which results in process maps leads to a better understanding of not just the porosity formation mechanisms, but also the inter-layer penetration and the resulting microstructures which are formed and have a direct effect on\\\\\nthe as-built mechanical properties of the material. Yadroitsev and Smurov, [29], [30], provide examples of the early attempts at generalising rules for melt-pool instabilities, but these were typically done with low laser powers and energy densities. These have been based upon an often-used method of direct melting powder onto base-plates or substrates made through machining traditionally fabricated metal plates. Although these base-plates or substrates may be compositionally similar to the material powder used, they may have a very different microstructure. This puts into question whether the penetration of the melt pool into the plate or substrate is equivalent to what occurs at the powder-bed level of the process.\n\nIt has only been relatively recently that the formation of keyhole melt formations has been demonstrated, [26], [31], [32]. These defects are usually avoided by using a suitable selection of machine parameters within pre-selected bands. With a two- to three-fold increase in the available laser powers, it is becoming apparent that there is no simple linear relationship between power and speed which would allow an equivalent increase in build rates, and it may be that at higher laser powers the transition to keyholing may be more difficult to control.\n\n\\subsection*{1.4 Objectives of this work}\nThe aim of this work is to extend knowledge of the LPBF melt pool development by the creation of a new standard for measuring single-track process maps and structures. Key aspects which need to be met by these experimental techniques should include:\n\n\\begin{itemize}\n  \\item Capture instabilities and melt-pool profiles as a function of laser power and speed, validated to empirical expectations and previous experimental work.\n\n  \\item Be representative of tracks as they would be laid at multiple layers in the process.\n\n  \\item $\\quad$ Not be constrained to any single alloy powder.\n\n  \\item Be 'high throughput' in that they allow not only a complete exploration of machine parameters within a single build, but also, they must be easy to remove from the base plate and ready for rapid metallographic preparation and microscopy.\n\n  \\item Allow for the exploration of additional parameters such as powder depth in a controlled manner.\n\n\\end{itemize}\n\n\\subsection*{1.5 Publications}\nThe following two publications feature some the research performed during this study. The first has been published and can be read in Appendix 1. The second publication will be published later this year.\n\n\\begin{itemize}\n  \\item [1] \"Verification of Numerically Calculated Cooling Rates of Powder Bed Additive Manufacturing\", HW Mindt, M Megahed, NP Lavery, A Giordimaina, SGR Brown, TMS 2016 145th Annual Meeting \\& Exhibition, 205-212\n\n  \\item [2] \"Validation and optimisation of a new high-throughput Crucible method for single-line melt-pool characterisation\", A. Philo, S. Sillars, A.Giordimaina, S. Mehraban, S.G.R. Brown, N.P. Lavery, To be published in Journal of Materials Processing Technology, 2018\n\n\\end{itemize}\n\n\\section*{Chapter 2 Overview of Additive Manufacturing Systems}\n\\subsection*{2.1 Introduction}\nThe standards organisation ASTM International (American Society of Testing Materials) has defined Additive Manufacturing, [33], as follows:\n\n\u201c... A process of joining materials to make objects from 3D model data, usually layer upon layer, as opposed to subtractive manufacturing methodologies. Synonyms: additive fabrication, additive processes, additive techniques, additive layer manufacturing, layer manufacturing, and freeform fabrication\"\n\nThe variety of manufacturing methods that fall under this definition are numerous as is the range of useable materials; including polymers, ceramics, composites and metals These materials can be delivered in multiple forms, such as liquid, microscopic powder, granular powder or wire form.\n\nIn this chapter, a detailed explanation and analysis for three different types of metal-based additive manufacturing methods are discussed, followed by a more in-depth discussion of the equipment used during this research.", "start_char_idx": 32561, "end_char_idx": 37268, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "e5b685ee-7757-453e-bbf4-aab8b82d633b": {"__data__": {"id_": "e5b685ee-7757-453e-bbf4-aab8b82d633b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "206fd717-a444-459e-9afa-3e47aca391ca", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b80f5ab029c315f3b80edd87c98815dfac9f644da28527c65d26f992d3cb84c5", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a6b1373a-bc40-4f69-ae19-5d8f5c57a692", "node_type": "1", "metadata": {}, "hash": "b087b1eee09d2bef4f6af3c798dc7035a70e55fa382f65d9b73f5bc93f18df85", "class_name": "RelatedNodeInfo"}}, "text": "Synonyms: additive fabrication, additive processes, additive techniques, additive layer manufacturing, layer manufacturing, and freeform fabrication\"\n\nThe variety of manufacturing methods that fall under this definition are numerous as is the range of useable materials; including polymers, ceramics, composites and metals These materials can be delivered in multiple forms, such as liquid, microscopic powder, granular powder or wire form.\n\nIn this chapter, a detailed explanation and analysis for three different types of metal-based additive manufacturing methods are discussed, followed by a more in-depth discussion of the equipment used during this research.\n\n\\subsection*{2.2 Electron Beam Melting}\nElectron beam melting (EBM) is a powder bed-based AM process, similar to SLM, where an electron beam is used as a heat source to melt or sinter material to create 3D objects. Unlike the previously discussed AM methods (stereolithography and fused deposition modelling), EBM can be used to process a wide range of metal materials, such as titanium alloys, aluminium alloys, cobalt-base alloys, steel and copper, [34]-[39]. However, EBM is not used with ceramic and plastic materials, as EBM requires electrically conductive material to function. The EBM process takes place under high vacuum conditions, typically between 10 ${ }^{4}$ and $10^{-2}$ Torr, [37], and as such the EBM process has the added benefit of reducing oxidation.\n\nEBM, like other AM processes, allows much more freedom for design than other conventional fabrication processes. This allows for the creation of parts with highly complex structures and geometries and reduced build weight. EBM-made parts can achieve near $100 \\%$ density and have mechanical properties comparable to or sometimes better than ascast or wrought parts without post-processing, [38], [40], [41]. The EBM process has received growing interest and has seen increasing applications in the aerospace and automotive industries, [42]-[44]. EBM has the ability to process biocompatible alloys, and has thus generated applications in the medical and dental industries, [45], [15], [46], [47]. EBM utilises one or more electron beams to melt the metal powder bed. This constant stream of electrons is created using an electron emitter, such as a heated tungsten filament, kept under high vacuum conditions $\\left(10^{-5}\\right.$ Torr). The emitter and the beam require vacuum conditions as electrons would interact with gas molecules otherwise, decreasing the efficiency of the process. Working under vacuum reduces the risk of contamination of the melt pool and oxidation, as previously stated.\n\nA high voltage is passed through the filament, causing thermal electron emission to occur. A stream of electrons is ejected from the filament, and it is directed as a beam towards the powder bed using inertia-free electromagnetic lenses. The lack of moving mechanical parts allows the beam to move almost instantaneously from point to point, reaching speeds of up to $10^{5} \\mathrm{~ms}^{-1},[48]$. The kinetic energy from the electrons in the beam is transferred and converted into thermal energy as it interacts with the metal powder bed, causing the powder particles to melt and coalesce or sinter together.\n\nThe powder bed must be initially heated by scanning the electron beam several times over the entirety of the bed. This causes the powder to sinter slightly, improving the electric conductivity and helping prevent the repulsion of charged powder particles, [49]. The powder particles are separated from each other after the build is complete by abrasive blasting, using the same powder material as the blasting agent. Pronounced necking produced by sintering is not present, and the powder can usually be almost completely recycled and reused.\n\nA variant of the EBM process is electron beam freeform fabrication, where the material can be introduced in the form of a continuous wire, which is fed into the melt pool under an electron beam. Multiple wires of different materials or composition can be used to produce functionally graded parts or parts with custom alloy compositions. This method is found to be nearly $100 \\%$ efficient in feedstock consumption as well as achieving $95 \\%$ power usage efficiency, [50].\n\n\\subsection*{2.3 Laser Metal Deposition}\nLaser metal deposition (LMD) is a type of AM method in which the powder material is fed into a high-power laser beam using a nozzle system. A number of different technologies utilise this method, such as laser engineering net shaping (LENS), [51], direct metal deposition (DMD), [52], laser net shape manufacturing (LNSM), [53], and others. The nozzle is coaxially or laterally oriented to the incoming beam, as depicted in Figure 1.", "start_char_idx": 36604, "end_char_idx": 41352, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a6b1373a-bc40-4f69-ae19-5d8f5c57a692": {"__data__": {"id_": "a6b1373a-bc40-4f69-ae19-5d8f5c57a692", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e5b685ee-7757-453e-bbf4-aab8b82d633b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f9be86d0695818e5bcb5300eda662add76ac2a75c1918045de9fedad70fb30d0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "13260667-68bc-429e-88f7-b1fa54ba2356", "node_type": "1", "metadata": {}, "hash": "aecc1cdfb35d3995d3088401b2e16187fe7d14060795a6dc3297faaa110a6563", "class_name": "RelatedNodeInfo"}}, "text": "Multiple wires of different materials or composition can be used to produce functionally graded parts or parts with custom alloy compositions. This method is found to be nearly $100 \\%$ efficient in feedstock consumption as well as achieving $95 \\%$ power usage efficiency, [50].\n\n\\subsection*{2.3 Laser Metal Deposition}\nLaser metal deposition (LMD) is a type of AM method in which the powder material is fed into a high-power laser beam using a nozzle system. A number of different technologies utilise this method, such as laser engineering net shaping (LENS), [51], direct metal deposition (DMD), [52], laser net shape manufacturing (LNSM), [53], and others. The nozzle is coaxially or laterally oriented to the incoming beam, as depicted in Figure 1. This special apparatus can be fitted unto a CNC system or robotic arm, allowing the material to be delivered freely in any orientation [54]. The nozzle delivers the powder in an inert gas, such as nitrogen or argon, to minimize oxidation. The materials used during LMD include various metal alloy powders such as Ti-6Al-4V or Inconel 718, [55], [56], A small molten pool is generated from this process and deposited unto a substrate which it becomes fused to. More powder may be drawn into the melt pool to increase the size of the deposited metal. Tracks are closely placed to one another in an overlap configuration and on top of another until the object geometry is completed.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-027}\n\\end{center}\n\nFigure 1. Laser Metal Deposition Apparatus.\n\nLMD is a highly versatile technology. Apart from being able to manufacture new objects, it can also be used to repair or rebuild worn or damaged components and add a corrosion or wear resistant coating to existing objects, [57].\n\n\\subsection*{2.4 Selective Laser Melting}\nSelective laser melting (SLM) is a manufacturing technique most similar to laser sintering or EBM, utilising a laser source to fully melt metallic powders to create functional, complex parts with $99.9 \\%$ density without the need of post-processing. Using this method, parts can be made with mechanical and material properties matching or of better quality than parts made using traditional manufacturing.\n\nHardness values and elastic modulus of magnesium parts produced by SLM have been found to be comparable to those of cast ingots, [58]. Commercially pure titanium parts manufactured by SLM, often used to make biomechanical implants, were found to possess better mechanical properties compared to parts produced by traditional processing technologies such as casting and machining, [19]. Apart from the improvement in\\\\\nmechanical properties such as microhardness, compressive and tensile strengths, SLM offers a higher degree of freedom in designing such parts with almost no geometric constraints. Similarly, Al-12Si parts manufactured by SLM were found to possess yield and tensile strengths respectively four and two times higher than corresponding values for cast material, [59].\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-028}\n\\end{center}\n\nFigure 2. Schematic drawing of SLM process.\n\nIt is important for the atmosphere within the chamber to be inert. The presence of reactive gases, such as oxygen, have detrimental effects on the build and powder quality. Certain alloying elements, such as manganese, chromium, titanium, aluminium and silicon have a high affinity for oxygen and are commonly used in many powder materials. Oxidation, decarburisation and other problems that can impact the mechanical properties of the part are reduced by using a vacuum pump to remove air from the build chamber and replace it with a non-reactive gas such as nitrogen, helium or argon. The possibility of ignition and\\\\\ncombustion of more volatile material powders such as pure titanium is also prevented in the presence of an inert atmosphere.\n\nTypically, in most SLM systems, a single high-power laser beam is used. However, there are systems that utilise two or more lasers to increase the build rate of the process, such as SLM solutions SLM500, which uses four fibre lasers. Nd:YAG, Yd:YAG and $\\mathrm{CO}^{2}$ are commonly used lasing mediums. The lasing medium used is important as they produce beams with differing wavelengths, which are more readily absorped by different materials as shown in Figure 3.", "start_char_idx": 40597, "end_char_idx": 45014, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "13260667-68bc-429e-88f7-b1fa54ba2356": {"__data__": {"id_": "13260667-68bc-429e-88f7-b1fa54ba2356", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a6b1373a-bc40-4f69-ae19-5d8f5c57a692", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6733d3e25512b419b5e6b835c6cfc9803d0b25bbe023c31d7d3aecde1d2174ca", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "afaec2d2-02ca-43bd-b950-a642b194b88a", "node_type": "1", "metadata": {}, "hash": "310bc42f92d7a6be62e7469cad8bacfd8891f6b15c2c22c0ceef1ace8f3c57be", "class_name": "RelatedNodeInfo"}}, "text": "Oxidation, decarburisation and other problems that can impact the mechanical properties of the part are reduced by using a vacuum pump to remove air from the build chamber and replace it with a non-reactive gas such as nitrogen, helium or argon. The possibility of ignition and\\\\\ncombustion of more volatile material powders such as pure titanium is also prevented in the presence of an inert atmosphere.\n\nTypically, in most SLM systems, a single high-power laser beam is used. However, there are systems that utilise two or more lasers to increase the build rate of the process, such as SLM solutions SLM500, which uses four fibre lasers. Nd:YAG, Yd:YAG and $\\mathrm{CO}^{2}$ are commonly used lasing mediums. The lasing medium used is important as they produce beams with differing wavelengths, which are more readily absorped by different materials as shown in Figure 3.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-029}\n\\end{center}\n\nFigure 3. Absorption of laser output at different wavelengths, [60].\n\nA high-speed mirror galvanometer is used to direct the laser onto the powder bed. The galvanometer controls the speed, position and size of the laser beam, which is lastly directed into an $\\mathrm{f}-\\theta$ lens. An $\\mathrm{f}-\\theta$ lens is designed with built-in barrel distortion that allows the position of the laser spot to be altered using the product of the focal length $(F)$ and the tangent of the\\\\\ndeflection angle $(\\theta)$. This greatly simplifies the positioning algorithms required to direct the laser.\n\nPowder can be fed from a hopper mounted above the build area or a powder feed container that deliver powder from below the build area. Either delivery method deposits enough powder for a thin layer, which is spread and levelled over the build area by a roller or wiper blade. After laser treatment of the layer of powder, the build platform is lowered by a single layer thickness and the depostion and spreading process is repeated. Any excess powder is pushed into a pair of crevices, one located at the end of the build and the other behind the hopper, which lead to an overflow container. This container can fill up during long build times, and must be regularly emptied to prevent overflow powder backing up into the build area.\n\nThe main processing parameters are laser power $(P)$, point distance $(\\mu \\mathrm{m})$, hatch spacing $(\\mu m)$, focal spot diameter $(\\mu m)$, exposure time $(\\mu \\mathrm{s})$, scan speed $\\left(\\mathrm{mms}^{-1}\\right)$, layer thickness $(\\mu \\mathrm{m})$ and scan strategy. Laser power is set and limited by the laser hardware. In certain systems the laser is not applied continously but is moved in a discrete manner from one point to the next. The point distance is the distance between two successive laser points, whilst the hatch spacing is the distance between two consecutive lines in a hatch pattern. The diameter of the laser spot can be altered by changing the distance from the laser focus plane and the powder bed, as shown in Figure 4. The exposure time is the amount of time the laser spends on each point. The scan speed can be determined by considering the ratio between point distance and exposure time. The laser off-time between successive points is not accounted for using this ratio. The layer thickness is the distance the build platform descends after finishing a single layer. The scan strategy is the pattern followed by the laser for every layer in the horizontal plane. The pattern used in the scan strategy is usually offset by increments in this angle between successive layers.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-031}\n\\end{center}\n\nFigure 4. Laser focus positions with respect to the powder bed.\n\nFeatures on the same layer such as the core, border and skin are given different parameters to achieve appropriate properties to the in-layer section. For example, the skin region, which is the region that makes up the surface of the part, will require different build properties from the core region which makes the bulk of the part. These properties improve the surface quality of the part. This scan strategy works well for regions of the surface facing along the zaxis, known as upskin and downskin, resulting in a reduction in overall roughness and giving a smooth surface finish.", "start_char_idx": 44141, "end_char_idx": 48519, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "afaec2d2-02ca-43bd-b950-a642b194b88a": {"__data__": {"id_": "afaec2d2-02ca-43bd-b950-a642b194b88a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "13260667-68bc-429e-88f7-b1fa54ba2356", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "75dfc9959abf7a0824ee057b8adbc09bbf898f917d9e21b04fa8d2b15f15476c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "900a4cbb-0055-4620-82bd-d8d8eb58f6ec", "node_type": "1", "metadata": {}, "hash": "f8c0e636b1d7a419dce8dac0839e27175d531bbeb514ee419b0a188c2081c521", "class_name": "RelatedNodeInfo"}}, "text": "The pattern used in the scan strategy is usually offset by increments in this angle between successive layers.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-031}\n\\end{center}\n\nFigure 4. Laser focus positions with respect to the powder bed.\n\nFeatures on the same layer such as the core, border and skin are given different parameters to achieve appropriate properties to the in-layer section. For example, the skin region, which is the region that makes up the surface of the part, will require different build properties from the core region which makes the bulk of the part. These properties improve the surface quality of the part. This scan strategy works well for regions of the surface facing along the zaxis, known as upskin and downskin, resulting in a reduction in overall roughness and giving a smooth surface finish. Other properties include an offset region, border regions and regions dedicated to overhangs.\n\nFour commonly used scanning patterns are the stripe, checkerboard, islands and meander. The stripe pattern divides the layer into bands of single tracks divided by a hatching distance. Each band can overlap with the next. The scan direction remains the same from layer to layer, but the band changes position slightly. The checkerboard and island patterns divide the layer into a patchwork of squares of a fixed side length, resembling a checkerboard. The line direction in each square is perpendicular to its neighbouring square.\n\nWhen the squares are built in a random order, this method is referred to as the islands pattern. When the equivalent of the white squares, corresponding to a checkerboard layout, is built first, followed by the black squares, this method is referred to as the checkerboard pattern. In a meander pattern, the scan direction for every line is the same. The pattern is rotated by a fixed angle for every layer.\n\n\\subsection*{2.5 Lasers}\nLight, radiant heat and other forms of radiation can be described as electromagnetic disturbances in the form of waves that propagate through the electromagnetic field. Light describes the way in which radiant energy is carried through space and time, [61]. It has a dual nature, wherein light can act both as a wave and as a particle, referred to as a photon, [62].\n\n\n\\begin{equation*}\nE=h f=\\frac{h c}{\\lambda} \\tag{1}\n\\end{equation*}\n\n\n$E=$ speed of light $\\left(\\mathrm{m} \\mathrm{s}^{-1}\\right)$\n\n$h=$ Planck's constant $\\left(6.63 \\times 10^{-34} \\mathrm{Js}\\right)$\n\n$\\mathrm{f}=$ frequency of the radiation $(\\mathrm{Hz})$\n\n$\\lambda=$ wavelength of the photon $(\\mu \\mathrm{m})$\n\nLASER is an acronym of \"light amplification by stimulated emission of radiation\". Lasers are used to emit light that is amplified and with the same wavelength, phase and direction. There are three central components that make up a laser: the lasing medium, the energy pump and an optical cavity. The basic operating mechanisms of a laser are shown in Figure 5.\n\nWhen the lasing medium gets excited by energy, light is emitted in all directions. The lasing medium can be in the form of a gas, liquid or semi-conducting material. The energy pump provides excited electrons to the lasing material. Mechanisms include electricity from a power supply, flash tubes, lamps or energy from another laser. The optical cavity reflects light from the lasing medium back into itself. It usually consists of two mirrors, one at each end of the lasing material. The light generated from the lasing material is reflected between the two mirrors, increasing the strength of the beam via amplification of the energy from the\\\\\nexcitation mechanism in the form of light. A partially transparent mirror on one end of the lasing material allows some light to leave the optical cavity to be used for the production of the laser beam.\n\nEnergy is delivered to the lasing medium from the pump, and is stored in the form of electrons within the atoms or molecules of the medium. These electrons are elevated to different quantum levels, or energy states that are usually unstable. Electrons in unstable energy states release the energy back as photons almost immediately, returning back to a ground state. The wavelength of the photons emitted is determined by the energy levels of the electrons. In some materials, such as those used as a lasing medium, the electrons achieve a metastable state, wherein the atom or molecule remains excited for a longer time.", "start_char_idx": 47651, "end_char_idx": 52103, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "900a4cbb-0055-4620-82bd-d8d8eb58f6ec": {"__data__": {"id_": "900a4cbb-0055-4620-82bd-d8d8eb58f6ec", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "afaec2d2-02ca-43bd-b950-a642b194b88a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d6817c800716ccf638900953b77239997cd03e7ec9cb032cb52ea2f559892861", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5242c577-c797-4fec-a135-81da979d83dc", "node_type": "1", "metadata": {}, "hash": "a7046e6b9db09fa3fa75df0979484143b370b6108ef6e944f7396928570df2a6", "class_name": "RelatedNodeInfo"}}, "text": "The light generated from the lasing material is reflected between the two mirrors, increasing the strength of the beam via amplification of the energy from the\\\\\nexcitation mechanism in the form of light. A partially transparent mirror on one end of the lasing material allows some light to leave the optical cavity to be used for the production of the laser beam.\n\nEnergy is delivered to the lasing medium from the pump, and is stored in the form of electrons within the atoms or molecules of the medium. These electrons are elevated to different quantum levels, or energy states that are usually unstable. Electrons in unstable energy states release the energy back as photons almost immediately, returning back to a ground state. The wavelength of the photons emitted is determined by the energy levels of the electrons. In some materials, such as those used as a lasing medium, the electrons achieve a metastable state, wherein the atom or molecule remains excited for a longer time. Before laser action can occur, energy must be pumped to the lasing medium until most of the atoms or molecules are in the metastable state rather than the grounded state. This is called population inversion.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-034}\n\\end{center}\n\nFigure 5. Basic Laser Operation, [63].\n\nThe spontaneous decay of a few metastable electrons to lower energy levels occurs. The photons emitted cause a chain reaction, reacting with the remaining metastable electrons. The photons released from this chain reaction have precisely the same wavelength, phase and direction as the previous photons. This action occurs in the optical cavity.\n\nMost of the photons are lost, but those that decay in the direction of the mirrors reach the end of the lasing medium and are reflected back into the material. This continues the chain reaction and more photons are released. A portion of the photons that arrive at the partially reflecting mirror emerge as the laser beam, whilst the rest are reflected back into the cavity. Nd: YAG (linear formula $\\mathrm{Nd}: \\mathrm{Y}_{3} \\mathrm{Al}_{5} \\mathrm{O}_{12}$ ) is used as a crystalline, semi conductive solid state lasing material. Triple ionised neodymium replaces yttrium ions within the structure of an\\\\\nyttrium aluminium garnet to alter the conductivity of the crystal, and provides the lasing capability to the material. Nd:YAG produces light at a wavelength of $1064 \\mathrm{~nm}$, which is one order of magnitude smaller than $\\mathrm{CO}_{2}$ lasers. This short wavelength is more readily absorbed by metallic components and is thus widely used in manufacturing industry for uses such as cutting and welding of steels and drilling of super alloys used for gas turbines.\n\n\\subsection*{2.6 Renishaw Systems}\nThe Renishaw AM line of systems use metal powder bed fusion technology, as classified by ASTM international. They produce metal parts from a bed of fine metal powders, the diameter of which should range between 15 microns and 45 microns. The systems can handle a wide range of metal powders, including titanium alloy Ti-6Al-4V, cobalt chromium CoCr, aluminium alloy AlSi10Mg, stainless steel 316L and nickel alloy Inconel 625. Such machines allow additional material to be loaded into the machine whilst it is still running.\n\n\\subsection*{2.7 AM250 Specifications}\nAll the work undertaken for this thesis was done on a Renishaw AM250, pictured on the lefthand image in Figure 6, installed at Swansea University in 2012. The AM250 has a 250mm by $250 \\mathrm{~mm}$ by $300 \\mathrm{~mm}$ build envelope, with a $250 \\mathrm{~mm}$ by $250 \\mathrm{~mm}$ build plate which can be heated to $140^{\\circ} \\mathrm{C}$, which is shown on the right-hand image in Figure 6. The laser used in the AM250 is a 200W Ytterbium fibre laser operating at a wavelength of $1070 \\mathrm{~nm}$ and modulated with a frequency of $100 \\mathrm{kHz}$.", "start_char_idx": 51116, "end_char_idx": 55048, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5242c577-c797-4fec-a135-81da979d83dc": {"__data__": {"id_": "5242c577-c797-4fec-a135-81da979d83dc", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "900a4cbb-0055-4620-82bd-d8d8eb58f6ec", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "bde425224a5cf41589cb0d1efded17005680fea41d3f16a72b42d23efa7fb24e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2777076d-96df-4a10-88c0-807ba3c9c974", "node_type": "1", "metadata": {}, "hash": "a68ccc388c9f44561677cead95a80902313bbefcbfcda581d7f0e47146cc67c3", "class_name": "RelatedNodeInfo"}}, "text": "Such machines allow additional material to be loaded into the machine whilst it is still running.\n\n\\subsection*{2.7 AM250 Specifications}\nAll the work undertaken for this thesis was done on a Renishaw AM250, pictured on the lefthand image in Figure 6, installed at Swansea University in 2012. The AM250 has a 250mm by $250 \\mathrm{~mm}$ by $300 \\mathrm{~mm}$ build envelope, with a $250 \\mathrm{~mm}$ by $250 \\mathrm{~mm}$ build plate which can be heated to $140^{\\circ} \\mathrm{C}$, which is shown on the right-hand image in Figure 6. The laser used in the AM250 is a 200W Ytterbium fibre laser operating at a wavelength of $1070 \\mathrm{~nm}$ and modulated with a frequency of $100 \\mathrm{kHz}$. The laser spot size is typically $70 \\mu \\mathrm{m}$, and the layer thickness controlled by the z-stage which can move with an accuracy of $\\pm 2 \\mu \\mathrm{m}$ gives layers between $20 \\mu \\mathrm{m}$ and $70 \\mu \\mathrm{m}$, but typically set at $50 \\mu \\mathrm{m}$. Quoted build speeds ranged from $5 \\mathrm{~cm}^{3}$ to $20 \\mathrm{~cm}^{3}$, depending on material, with maximum $X$ - and $Y$ - scanning speeds of up to $2000 \\mathrm{~mm} / \\mathrm{s}$.\n\nThe original machine was initially supplied with the MTT AUTOFAB software. As of recent, in 2017, Renishaw also supplied a number of working licences for QuantAM build preparation\\\\\nsoftware, a state-of-the-art software package designed specifically for use with Renishaw AM machines.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-036}\n\\end{center}\n\nFigure 6. AM250\n\nLeft) The Renishaw AM250 Right) Z-drive to which baseplate is attached.\n\nThe results of a calibration test using a beam profiler for a variable focus selection of $70 \\mu \\mathrm{m}$ are shown in Table 1 below. From this it can be seen that the beam spot size at the $0 \\mathrm{~mm}$ focal point is slightly elliptical with a minor axis ( $x$-direction) of $66.46 \\mu \\mathrm{m}$, and a major axis $(y$ direction) of $72.02 \\mu \\mathrm{m}$.", "start_char_idx": 54350, "end_char_idx": 56359, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2777076d-96df-4a10-88c0-807ba3c9c974": {"__data__": {"id_": "2777076d-96df-4a10-88c0-807ba3c9c974", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5242c577-c797-4fec-a135-81da979d83dc", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b212a4c7044d8ee417c5491ff065c8f280f64e5e2170b9af0748b6a72749aa93", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "56493c3f-ebf3-45ac-a792-a5d3d8f8ba72", "node_type": "1", "metadata": {}, "hash": "c56884eceab7eeedc63bb65524d50d15120abe8a2fdd329fea6851de0f9b86ab", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-036}\n\\end{center}\n\nFigure 6. AM250\n\nLeft) The Renishaw AM250 Right) Z-drive to which baseplate is attached.\n\nThe results of a calibration test using a beam profiler for a variable focus selection of $70 \\mu \\mathrm{m}$ are shown in Table 1 below. From this it can be seen that the beam spot size at the $0 \\mathrm{~mm}$ focal point is slightly elliptical with a minor axis ( $x$-direction) of $66.46 \\mu \\mathrm{m}$, and a major axis $(y$ direction) of $72.02 \\mu \\mathrm{m}$.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\n\\begin{tabular}{c}\nFocus, \\\\\n$(\\mathbf{m m})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nAverage X, \\\\\n$(\\boldsymbol{\\mu m})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nSpot Size \\\\\nIncrease \\\\\n\\end{tabular} & \\begin{tabular}{c}\nAverage Y, \\\\\n$(\\boldsymbol{\\mu m})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nSpot Size \\\\\nIncrease \\\\\n\\end{tabular} \\\\\n\\hline\n$\\mathbf{5}$ & 126.23 & $14.76 \\%$ & 148.3862069 & $-30.4 \\%$ \\\\\n\\hline\n$\\mathbf{4}$ & 110.00 & $18.46 \\%$ & 133.06 & $33.7 \\%$ \\\\\n\\hline\n$\\mathbf{3}$ & 92.86 & $27.23 \\%$ & 99.53 & $18.2 \\%$ \\\\\n\\hline\n$\\mathbf{2}$ & 72.98 & $5.48 \\%$ & 84.21 & $1.1 \\%$ \\\\\n\\hline\n$\\mathbf{1}$ & 69.19 & $4.10 \\%$ & 83.31 & $15.7 \\%$ \\\\\n\\hline\n$\\mathbf{0}$ & 66.46 &  & 72.02 &  \\\\\n\\hline\n$\\mathbf{- 1}$ & 67.37 & $1.36 \\%$ & 71.16 & $-1.2 \\%$ \\\\\n\\hline\n$\\mathbf{- 2}$ & 69.64 & $3.38 \\%$ & 71.31 & $0.2 \\%$ \\\\\n\\hline\n$\\mathbf{- 3}$ & 74.80 & $7.41 \\%$ & 76.32 & $7.0 \\%$ \\\\\n\\hline\n$\\mathbf{- 4}$ & 84.66 & $13.18 \\%$ & 83.14 & $8.9 \\%$ \\\\\n\\hline\n$\\mathbf{- 5}$ & 102.57 & $21.15 \\%$ & 92.55 & $11.3 \\%$ \\\\\n\\hline\n$\\mathbf{- 6}$ & 118.4965517 & $15.53 \\%$ & 99.53103448 & $7.5 \\%$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 1. Spot size calibration of the Renishaw AM250 used in this work.\n\nThe laser is controlled by $X$ - and $Y$ - galvanometers which re-direct the laser beam down through an F-theta lens which focusing the beam onto the base plate. The main parameters which are controlled in the AM250 are the point distance (d1 in Figure 7), the hatch spacing\\\\\n(d3 in Figure 7), the laser power (W) and the exposure time ( $\\mu \\mathrm{s})$. Additional parameters related to the scan pattern (or hatch pattern) are shown in Figure 7. The contour of the area being printed at a given layer is sometimes surrounded by a border (or skin) in which slightly different parameters are used to provide a smoother surface finish. This border is called the volume border (labelled d4 in Figure 7). Between the border and the main internal area (called the volume area) is a small volume offset hatch (labelled d2 in Figure 7).", "start_char_idx": 55796, "end_char_idx": 58462, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "56493c3f-ebf3-45ac-a792-a5d3d8f8ba72": {"__data__": {"id_": "56493c3f-ebf3-45ac-a792-a5d3d8f8ba72", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2777076d-96df-4a10-88c0-807ba3c9c974", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "77335627b98725c847c71e6770c847f7a550ff20811c25d9100a2f1bdc4e6587", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3e84906e-f95e-4326-bf81-d69838745030", "node_type": "1", "metadata": {}, "hash": "4786a8233477fe0036655672e765c5f4039e0a6982993ffd1cf4ec9d3ac3e762", "class_name": "RelatedNodeInfo"}}, "text": "The laser is controlled by $X$ - and $Y$ - galvanometers which re-direct the laser beam down through an F-theta lens which focusing the beam onto the base plate. The main parameters which are controlled in the AM250 are the point distance (d1 in Figure 7), the hatch spacing\\\\\n(d3 in Figure 7), the laser power (W) and the exposure time ( $\\mu \\mathrm{s})$. Additional parameters related to the scan pattern (or hatch pattern) are shown in Figure 7. The contour of the area being printed at a given layer is sometimes surrounded by a border (or skin) in which slightly different parameters are used to provide a smoother surface finish. This border is called the volume border (labelled d4 in Figure 7). Between the border and the main internal area (called the volume area) is a small volume offset hatch (labelled d2 in Figure 7). The laser will typically traverse the volume border as a single line around the entire contour, after completing the internal volume area.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-037}\n\\end{center}\n\nFigure 7. Laser parameters in the Renishaw AM250.\n\nThere are various ways in which the laser scan pattern (or hatch pattern) can be selected to fill the volume area. The most commonly used hatch pattern shown in Figure 7 is the meander hatch pattern where the laser leaves one side of the contour travels to the other side and then reverses direction. An alternative scan pattern of the laser can be achieved using stripes in the same direction, and the entire area can be divided into patches The typical ranges of these parameters are given in Table 2.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline\n & Volume area & Volume border \\\\\n\\hline\nPoint distance $(\\mu \\mathrm{m})$ & $50-150$ & $50-80$ \\\\\n\\hline\nExposure time $(\\mu \\mathrm{s})$ & $50-150$ & $60-150$ \\\\\n\\hline\nPower $(\\mathrm{W})$ & $100-200$ & $90-200$ \\\\\n\\hline\nHatch spacing $(\\mu \\mathrm{m})$ & $50-150$ & N/A \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 2. Typical laser parameters for the Renishaw AM250.\n\nTogether, the point distance and the exposure time determine the scan speed of the laser (if one ignores small transitional speeds due to galvanometer movement) by\n\n\n\\begin{equation*}\n\\text { Scan speed }=1000 \\times \\frac{\\text { point distance }}{\\text { exposure time }} \\tag{2}\n\\end{equation*}\n\n\nWhere, point distance is measure in $\\mu \\mathrm{m}$ and exposure time is measured in $\\mu \\mathrm{s}$. Using the parameters in Table 2 gives scan speeds ranging from $100 \\mathrm{mms}^{-1}$ to $3000 \\mathrm{~mm}^{-1}$.\n\n\\subsection*{2.8 Conclusions}\nThis chapter has given a brief introduction and background to Additive Manufacturing, particularly in the context of powder bed fusion systems capable of process metal powder material. In particular, the Renishaw AM250 laser powder-bed fusion system was discussed, which was used throughout the work in the coming chapters.\n\n\\section*{Chapter 3 Thermo-Mechanics of melt pool formation}\n\\subsection*{3.1 Introduction}\nIdeally, parts produced by laser-powder bed fusion should be fully dense and have comparable or improved mechanical and microstructural properties to those produced using traditional methods. Additionally, this should be accomplished without the need of lengthy or expensive post-processing. The powder material that is subjected to the laser must undergo complete melting in order to reduce the possibility of pore or defect formation, [64]. Careful control over the process parameters is required in order to obtain the best possible physical properties from parts part made using powder material.\n\nIn order to melt the metal powder and maintain a suitable build speed, the energy input provided by the laser must be high enough to melt the powder in a short amount of time, in the order of microseconds. The energy from the laser quickly dissipates from the spot of laser-powder interaction, and the powder undergoes a solid-liquid-solid transition in a very short amount of time, resulting in a very steep thermal gradient.", "start_char_idx": 57630, "end_char_idx": 61679, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3e84906e-f95e-4326-bf81-d69838745030": {"__data__": {"id_": "3e84906e-f95e-4326-bf81-d69838745030", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "56493c3f-ebf3-45ac-a792-a5d3d8f8ba72", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3efbb2333e16facd267d887a69ca5e9269f75aa0e9371fcb1762462a205d9828", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a313716c-1f91-4e60-a768-35fa88ea39eb", "node_type": "1", "metadata": {}, "hash": "6be6cad0cbcecc26f656105bf438c732997c1e227e80f7936dab3bc3c807c7f9", "class_name": "RelatedNodeInfo"}}, "text": "Additionally, this should be accomplished without the need of lengthy or expensive post-processing. The powder material that is subjected to the laser must undergo complete melting in order to reduce the possibility of pore or defect formation, [64]. Careful control over the process parameters is required in order to obtain the best possible physical properties from parts part made using powder material.\n\nIn order to melt the metal powder and maintain a suitable build speed, the energy input provided by the laser must be high enough to melt the powder in a short amount of time, in the order of microseconds. The energy from the laser quickly dissipates from the spot of laser-powder interaction, and the powder undergoes a solid-liquid-solid transition in a very short amount of time, resulting in a very steep thermal gradient. This can lead to residual stress formation, crack formation and distortion in the part, [65]-[68], [30], [22].\n\nIf the energy input is too high, it can cause vaporisation of the material, causing a distinct type of pore formation known as keyholing, [26], [32], [69], [70], [31]. Conversely, if the energy input is too low, this can cause insufficient melting and wetting of the powder, which can lead to instability of the melt and so called \"balling\" of the melt bead, [22], [31], [71]-[76]. These phenomena are linked to pore formation, surface roughness and can even cause the laser-powder bed fusion process to malfunction.\n\nIn this chapter, the laser-powder bed fusion process was reviewed in detail, investigating the varying heat transfer mechanisms that take place, the solid-liquid-solid transition cycle of the powder material, and the possible defect and instability formation that may take place during this cycle.\n\n\\subsection*{3.2 The Physical Model}\nIn this section, the formation of the melt pool using a high-power laser beam will be discussed in detail and chronologically. A simplified diagram of the physical phenomena taking place has been given in Figure 8. Generally, all the heat transfer mechanisms involved fall under three types; convection, conduction and radiation.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-040}\n\\end{center}\n\nFigure 8. Physical phenomena at play in the powder-bed fusion system.\n\n\\subsection*{3.2.1 The Powder Bed}\nBefore the melt pool can be formed, a powder bed and substrate (known as the base plate) must be present. The physical attributes and composition of powder used for laser powderbed fusion can be just as influential to the build and completed parts as the processing parameters used by the machine. Physical characteristics of the powder material, such as particle size, shape and size distribution, influence the formation and topology of the powder\\\\\nbed, which subsequently influences the production of the part. Other factors, such as the storage and recycling of the powder material, can also influence the properties of the built parts due to oxidation.\n\nSpherically shaped powder particles are preferred in powder-bed based AM methods, as they have improved flowability and help form a uniform powder bed, [77], [78]. Conversely, non-spherical particles decrease compaction in the powder bed, leading to increased porosity in parts, [52]. The gas atomization method is a commonly used process for creating spherically shaped metal powder material. This method is particularly preferred as it uses an inert gas to create the powder particles, which significantly prevents oxidation of metals, such as stainless steel. During this process, molten metal is hit by a high-speed jet of inert gas, such as argon, making the metal form into spherical droplets, [79]. The droplets cool to below their melting temperature as they pass through a cooling tower, they solidify and are screened and sorted by their size.\n\nThe powder is packaged to have a certain range of powder sizes and a set particle size distribution. Very fine particles, with sizes between $0.1 \\mu \\mathrm{m}$ and $20 \\mu \\mathrm{m}$, are avoided as they can form clusters which are detrimental to powder flowability. They are also more likely to combust or explode upon making contact with a reactive gas due to their large surface area to volume ratio, [25].\n\nThe particle size distribution defines the relative frequency of particles, by mass, of the given range of sizes. This determines the flowability of the powder and the packing density of the powder bed.", "start_char_idx": 60844, "end_char_idx": 65320, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a313716c-1f91-4e60-a768-35fa88ea39eb": {"__data__": {"id_": "a313716c-1f91-4e60-a768-35fa88ea39eb", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3e84906e-f95e-4326-bf81-d69838745030", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f4287ec9847510f7e24265fef3054de3824e80889e2860af2d2bfb7c3e2cc20f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "57a26c8e-5e0b-4806-86a3-3092281069ba", "node_type": "1", "metadata": {}, "hash": "98741a48ff4304c7342d137bc8f79d11e55f80715c3060a3b4d7079a74831d2a", "class_name": "RelatedNodeInfo"}}, "text": "During this process, molten metal is hit by a high-speed jet of inert gas, such as argon, making the metal form into spherical droplets, [79]. The droplets cool to below their melting temperature as they pass through a cooling tower, they solidify and are screened and sorted by their size.\n\nThe powder is packaged to have a certain range of powder sizes and a set particle size distribution. Very fine particles, with sizes between $0.1 \\mu \\mathrm{m}$ and $20 \\mu \\mathrm{m}$, are avoided as they can form clusters which are detrimental to powder flowability. They are also more likely to combust or explode upon making contact with a reactive gas due to their large surface area to volume ratio, [25].\n\nThe particle size distribution defines the relative frequency of particles, by mass, of the given range of sizes. This determines the flowability of the powder and the packing density of the powder bed. A balanced particle powder size distribution improves the packing density of the powder bed, allowing smaller particles to fill the gaps in the as-deposited layer, [80]. The maximum particle size in the distribution would determine the minimum layer thickness that can be used, [25].\n\n\\subsection*{3.2.2 The Laser Beam}\nThe wavelength and power of the laser is determined by the type of laser beam used, and should be adapted to the powder as discussed in 2.5 The radiation emitted is typically either\\\\\nabsorbed by the material or reflected off the surface. The degree of absorption is governed by the emissivity of the surface which the radiation interacts with. Emissivity is defined as the ratio of energy radiated from a materials surface to that radiated by a perfectly emitting material, known as a blackbody. Emissivity is a dimensionless number, ranging between 0 to 1 , where 0 is a perfectly reflecting body whilst 1 is a perfectly emitting body. The emissivity of a metal surface increases with the surface roughness of material, the level of oxidation present, and its temperature, [81]-[83]. The emissivity of the materials involved will change as laser interaction continues. A molten pool has higher levels of reflectivity than loose powder, [84], [85].\n\nDue to the porous nature of the powder bed, radiation absorption is higher than that of bulk, solid metal. Laser radiation undergoes multiple reflections on the spherical surface of the powder material inside the pores of the bed, [86]. This phenomenon is known as multiple scattering, and the degree of scattering depends on the powder bed formation. A study by Boley et al., [87], demonstrated through a ray-tracing model that absorption can be increased by a factor of 2 by using an optimised powder structure.\n\n\\subsection*{3.2.3 Melting of the Powder Bed}\nThe energy from the beam not reflected from the surface is absorbed by the powder bed, causing its temperature to rise. Thermal energy is transferred between particles by heat diffusion. Once the temperature exceeds the solidus temperature of the metal, the solid-fluid phase transformation begins. Further energy input is required, known as latent heat of fusion, to fully complete the transformation. The specific latent heat of fusion of a material is the heat energy required to change $1 \\mathrm{~kg}$ of a solid material at its melting point to $1 \\mathrm{~kg}$ of liquid, without changing its temperature.\n\n\n\\begin{equation*}\nE_{m}=m H \\tag{3}\n\\end{equation*}\n\n\nWhere $E_{m}$ is the energy required to melt to material $(\\mathrm{J}), m$ is the mass $(\\mathrm{kg})$ of the material and $H$ is the specific heat capacity of the material $\\left(\\mathrm{Jkg}^{-1}\\right)$.\n\nThe law of heat conduction, or Fourier's law, states that \"the heat flux resulting from thermal conduction is proportional to the magnitude of the temperature gradient and opposite to it in sign\", [88].\n\n\\subsection*{3.3 Effects}\nAs previously mentioned in Chapter 2, there are several processing parameters controlling the laser melting process. Each parameter has a direct influence on the formation of the molten pool, and the degree of influence the parameters have on one another is not always apparent. Apart from the parameters of the machine itself, the material properties of the powder metal itself also imposes an influence on the formation of the melt.", "start_char_idx": 64412, "end_char_idx": 68694, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "57a26c8e-5e0b-4806-86a3-3092281069ba": {"__data__": {"id_": "57a26c8e-5e0b-4806-86a3-3092281069ba", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a313716c-1f91-4e60-a768-35fa88ea39eb", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "be5658e514a690bfbba636230a8b037ebafe22e2f6036ef832c89ecee7667898", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d106f6d7-e24e-4ad4-b09c-caa75126761a", "node_type": "1", "metadata": {}, "hash": "12e3a8b15ae2d6a29bb39bd2be8f7e843eef6397b96e73a3bdd6fa8e2aad9363", "class_name": "RelatedNodeInfo"}}, "text": "Where $E_{m}$ is the energy required to melt to material $(\\mathrm{J}), m$ is the mass $(\\mathrm{kg})$ of the material and $H$ is the specific heat capacity of the material $\\left(\\mathrm{Jkg}^{-1}\\right)$.\n\nThe law of heat conduction, or Fourier's law, states that \"the heat flux resulting from thermal conduction is proportional to the magnitude of the temperature gradient and opposite to it in sign\", [88].\n\n\\subsection*{3.3 Effects}\nAs previously mentioned in Chapter 2, there are several processing parameters controlling the laser melting process. Each parameter has a direct influence on the formation of the molten pool, and the degree of influence the parameters have on one another is not always apparent. Apart from the parameters of the machine itself, the material properties of the powder metal itself also imposes an influence on the formation of the melt. Control over the flow and consistency of the melt tracks tends to be more difficult for standard alloy powders with inherent narrow melting temperature ranges, [89], than for specially developed alloys or powder mixtures with wider temperature ranges, [90].\n\n\\subsection*{3.3.1 Wetting and Balling}\nWetting is defined as the ability of a liquid to form an interface with a solid surface. The degree of wetting of a liquid can be measured by its wetting angle $(\\theta)$ with the surface it is in contact with. The smaller the wetting angle, the greater the degree of wetting, as shown in Figure 9 below. For maximum adhesion and perfect wetting, the liquid must completely cover the surface $\\left(\\theta=0^{\\circ}\\right)$. As the wetting decreases, the contact angle would increase. At large contact angles $\\left(\\theta \\geq 90^{\\circ}\\right)$, conditions for wetting on the surface are considered highly unfavourable.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-044}\n\\end{center}\n\nFigure 9. Surface Wetting\n\nYoung's equation, show in below, defines the mechanical equilibrium of a liquid drop in contact with a completely solid surface, under the action of three interfacial tensions [91].\n\n$$\n\\gamma_{S G}=\\gamma_{S G}+\\left(\\gamma_{S G} \\times \\cos \\theta\\right)\n$$\n\n$Y_{L G}, Y_{S L}$ and $Y_{S G}$ represent the liquid-gas, the solid-liquid and the solid-liquid interfacial tensions, respectively. The units for these parameters are $\\mathrm{Nm}^{-1}$.\n\nOne detrimental phenomenon that can occur during laser melting is the break-up of the track during the molten phase of the powder bed-laser interaction. This is referred to as balling, as the molten material can break up into a series of isolated spherical droplets, although it should be noted that the molten track can break up into larger shapes as well. The degree of balling is influenced the wettability of the melt, which is influenced by several parameters and conditions, such as the oxygen content in the build atmosphere, [73], [92], the size and shape of powder , [93], and the influence of laser power and scan speed , [29], [73], [94], [95].\n\nBalling occurs when the forces of surface tension are more influential than the wetting and spreading of the melt. For a volume of a liquid, each molecule in the entirety of the liquid body is pulled equally in every direction by the neighbouring liquid molecules, resulting in a zero-net force. At the surfaces of the liquid, however, the molecules at such surfaces do not have neighbouring molecules in every direction to provide the balanced net force. Instead, they are pulled into the liquid body by their neighbouring molecules, creating an internal\\\\\npressure, called surface tension. The liquid therefore contracts its surface area to maintain the lowest surface energy value, and as a result the liquid takes a sphere or spherical shape. In practice, external forces such as gravity further deform the droplet, and consequently the wetting angle is affected by a combination of surface tension, gravity, surface roughness and fluid flow, such as those caused by capillary forces.\n\n\\subsection*{3.3.2 Plateau-Rayleigh Instability}\nThis phenomenon is named after Joseph Plateau and Lord Rayleigh, a Belgian physicist and an English physicist, respectively. Joseph Plateau first observed instability of a liquid during an experiment in 1873.", "start_char_idx": 67822, "end_char_idx": 72104, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d106f6d7-e24e-4ad4-b09c-caa75126761a": {"__data__": {"id_": "d106f6d7-e24e-4ad4-b09c-caa75126761a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "57a26c8e-5e0b-4806-86a3-3092281069ba", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b4a4ed0ecbcaba506a0ab3e3bcf7d8ea4f3a34e8a50a75f5bf7445e1ce47601d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1d0a274c-5b9a-45bb-855a-bf9a5bfdb339", "node_type": "1", "metadata": {}, "hash": "e5d1d5cafdad6c9c32939ce606cdb0956cfbb9b47d4cf9d3eb0469b2cc1bab4c", "class_name": "RelatedNodeInfo"}}, "text": "At the surfaces of the liquid, however, the molecules at such surfaces do not have neighbouring molecules in every direction to provide the balanced net force. Instead, they are pulled into the liquid body by their neighbouring molecules, creating an internal\\\\\npressure, called surface tension. The liquid therefore contracts its surface area to maintain the lowest surface energy value, and as a result the liquid takes a sphere or spherical shape. In practice, external forces such as gravity further deform the droplet, and consequently the wetting angle is affected by a combination of surface tension, gravity, surface roughness and fluid flow, such as those caused by capillary forces.\n\n\\subsection*{3.3.2 Plateau-Rayleigh Instability}\nThis phenomenon is named after Joseph Plateau and Lord Rayleigh, a Belgian physicist and an English physicist, respectively. Joseph Plateau first observed instability of a liquid during an experiment in 1873. When a column of water is suspended vertically, it falls under the influence of gravity as a jet. When the length of the column exceeds the diameter by a factor of around 3.13, the water no longer assumes the shape of a column and instead breaks down into a stream of droplets, [96]. The water breaks up in this way as to reduce the total surface energy of the stream.\n\nIntramolecular forces within the liquid pull equally in all directions except at the surface, where they can only pull along the surface. There is a net inward cohesive force, which acts as a driving factor in minimising the total area of the liquid, making it take a spherical shape. The force present within the surface layer of a liquid is called surface tension. It is defined as the work required per unit area $\\left(\\mathrm{Jm}^{-2}\\right)$ to create and maintain the new surface. A column of water has a much higher surface area compared to a stream of spherical droplets of the same total volume, so a lower energy state is achieved with the formation of droplets. This value is dependent on the material properties of the liquid as well as the temperature of the surface. In general, surface tension decreases with an increase in temperature. The molecules within the liquid vibrate at a higher frequency with an increase in thermal energy, reducing the cohesive forces between liquid molecules. The net inward cohesive force thereby decreases as well, decreasing the overall surface tension.\n\nThe break-up by surface tension forces is gradual, rather than being instantaneous. In 1878, Lord Rayleigh showed theoretically that a cylinder of water would deform into varicose\\\\\nperturbations, [97].These would take the form of sinusoidal periodic displacements, as shown in Figure 10.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-046}\n\\end{center}\n\nFigure 10. Plateau-Rayleigh Instabilities, [98].\n\nThe radius of the column is no longer constant, and the column breaks up into a series of narrow and wide sections. The wide sections experience low pressure whilst the narrows sections experience high pressure, causing a pressure gradient to form that in turn causes fluid flow. The flow causes the displacement amplitude to increase. Once the wavelength of these displacements exceeds the circumference of the column, the narrow sections rupture. The wider sections assume the shape of spherical droplet, achieving the lowest energy state.\n\n\\subsection*{3.3.3 Marangoni Convection}\nMarangoni convection, also known as the Gibbs-Marangoni effect, is a form of fluid flow that takes place where there is a gradient of surface tension at an interface between two phases. A liquid-gas interface is a very common instance where it would take place. Flow is driven from regions with a low surface tension to regions of high surface tension, [99]. The gradient in surface tension can be caused by changes in the chemical composition (solutocapillary\\\\\neffect), electric potential (electrocapillary effect) or temperature (thermocapillary effect). Any mixture of the effects can also occur simultaneously.\n\nSince selective laser melting is a very high energy process, thermocapillary flow is the most influential phenomena affecting Marangoni flow within the melt. During the process, the centre of the melt pool tends to be at a higher temperature than at the edge. Thus, an additional force is exerted from the hot centre to the cooler edges, causing balling to occur (i.e. a break up of an elongated liquid region into individual balls of material).", "start_char_idx": 71153, "end_char_idx": 75671, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1d0a274c-5b9a-45bb-855a-bf9a5bfdb339": {"__data__": {"id_": "1d0a274c-5b9a-45bb-855a-bf9a5bfdb339", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d106f6d7-e24e-4ad4-b09c-caa75126761a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3656615fad61bbb0f21eb24787cd29fabe00d6ecd892e845d982d201432bda99", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "8514abcc-baf0-4f45-bce0-a15d04ffc82b", "node_type": "1", "metadata": {}, "hash": "df98a9c4d5607da569f24ee79806b0fe9b8f302a2af1f9ac34225aad14ecd876", "class_name": "RelatedNodeInfo"}}, "text": "A liquid-gas interface is a very common instance where it would take place. Flow is driven from regions with a low surface tension to regions of high surface tension, [99]. The gradient in surface tension can be caused by changes in the chemical composition (solutocapillary\\\\\neffect), electric potential (electrocapillary effect) or temperature (thermocapillary effect). Any mixture of the effects can also occur simultaneously.\n\nSince selective laser melting is a very high energy process, thermocapillary flow is the most influential phenomena affecting Marangoni flow within the melt. During the process, the centre of the melt pool tends to be at a higher temperature than at the edge. Thus, an additional force is exerted from the hot centre to the cooler edges, causing balling to occur (i.e. a break up of an elongated liquid region into individual balls of material). In selective laser melting, when metal powder is melted due to laser processing, the stream of liquid formed from laser interaction is subject to the same phenomena. A steep thermal gradient is achieved between the centre and edge at the surface of the melt pool. Some key considerations are:\n\n\\begin{itemize}\n  \\item Compressibility and viscous forces are negligible.\n  \\item Specific system geometry depends on energy minimisation.\n  \\item Liquid desires to be in minimal energy state.\n\\end{itemize}\n\nFor high energy processes like laser-powder bed fusion, a steep thermal gradient is developed between centre and edge of metal pool at surface. Surface tension is a function of temperature, and the presence of a large temperature gradient induces a Marangoni flow from regions of low surface tension to regions of high surface tension, [99], i.e. from the edge of the melt pool to its centre. This flow of fluid produces an additional force in the melt pool, which is exerted onto the molten bead and positively influences the balling phenomenon.\n\nFluid flow will produce an extra force which exerts itself on the molten track of laser-powder bed fusion samples and positively influences the balling phenomenon.\n\nThe stability of a liquid during laser-powder bed fusion depends on the laser power, scanning speed, powder layer thickness, substrate material, physical properties and granulomorphometry of the powder used. Stability zones are characterised by formation of\\\\\nstab pools and continuous tracks. Instability zones are characterised by non-continuous tracks and individual droplet formation.\n\nPlateau-Rayleigh instability causes peaks and troughs to form along a track. At troughs, the melt pool height is low and it takes less time for the substrate to cool this region as there is less material present. At peaks the melt pool height is high. More material and therefore heat is present, and the liquid phase persists for longer. Connections between peaks and front part of flow breaks at troughs and they start acting like bottlenecks. Temperature profiles on the surface melt and substrate are influenced by melt topology. Temperature in the substrate decreases more quickly under troughs and increases under peaks. With such a nonmonotonous behaviour, the surface cools unevenly. Temperature field evolution is perhaps the most important parameter in laser-powder bed fusion.\n\nCapillarity and wetting are strongly correlated and are both governed by surface and melt interface energies. This depends on experimental conditions and whether the liquid wets solid powder or re-solidified material from the melt pool.\n\n\\subsection*{3.3.4 Keyholing}\nThe conditions for keyhole mode melting have been studied in laser welding applications, which are very similar to the powder-bed fusion process, [100]. Keyhole mode melting is known to be detrimental in the laser-powder bed fusion process due to pore formation [101]. Due to the Gaussian profile of the laser beam, the highest energy density is concentrated towards the centre of the beam, whilst the edges of the beam are lower. As a result, the temperature of the resulting metal pool follows this profile, and the resulting temperature gradient drives thermocapillary flow towards the centre of the melt pool and deeper into the substrate. Additionally, the high energy density at the centre of the pool can cause temperatures to rise above boiling point, causing vaporisation of the metal.\n\nThe recoil pressure from the vapour exerts a force onto the molten pool, causing a cavity to form within the melt. The cavity can additionally cause the laser to be reflected multiple times below the melt pool surface, effectively increasing its efficiency and allowing deeper\\\\\npenetration into the substrate by the laser and melt pool. This is a similar phenomenon to multiple scattering within the powder bed, as described in Chapter 3.2.2.", "start_char_idx": 74795, "end_char_idx": 79574, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "8514abcc-baf0-4f45-bce0-a15d04ffc82b": {"__data__": {"id_": "8514abcc-baf0-4f45-bce0-a15d04ffc82b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1d0a274c-5b9a-45bb-855a-bf9a5bfdb339", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "18c5ea2968ce6b7301d69ec16d124b7dc11e50ca3f54d2f46b0c9aee2e51138c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "227d52e3-6ba1-48e9-befe-f3f65916fa16", "node_type": "1", "metadata": {}, "hash": "622107437ef886c67d2742be8d0c8ba1f9ff4ff9b03e2cb78d54b8cdd0f88176", "class_name": "RelatedNodeInfo"}}, "text": "Due to the Gaussian profile of the laser beam, the highest energy density is concentrated towards the centre of the beam, whilst the edges of the beam are lower. As a result, the temperature of the resulting metal pool follows this profile, and the resulting temperature gradient drives thermocapillary flow towards the centre of the melt pool and deeper into the substrate. Additionally, the high energy density at the centre of the pool can cause temperatures to rise above boiling point, causing vaporisation of the metal.\n\nThe recoil pressure from the vapour exerts a force onto the molten pool, causing a cavity to form within the melt. The cavity can additionally cause the laser to be reflected multiple times below the melt pool surface, effectively increasing its efficiency and allowing deeper\\\\\npenetration into the substrate by the laser and melt pool. This is a similar phenomenon to multiple scattering within the powder bed, as described in Chapter 3.2.2. Once the laser moves away from the melt pool, the molten material in the upper part of the melt pool fills the void under the force of gravity. The vapour in the void becomes trapped in the lower part as the surface of the melt pool cools quickly when exposed to the inert gas atmosphere. The voids caused through this phenomenon would be spread through the track, causing severe pore formation in the part.\n\n\\section*{Chapter 4 Experimental Methods and Materials}\n\\subsection*{4.1 Optimal Density Parameters}\n\\subsection*{4.1.1 Introduction}\nFor each different batch of material powder used during the single-layer experiments, a\n\nDesign of Experiments (DOE) method was performed to find their individual optimal build parameters. The purpose of a DOE is to apply a statistics-based experiment to determine the relationship between the input parameters and the resulting outputs. In this research, the output that determined optimal input parameters was density.\n\nThe input parameters chosen for laser-powder bed fusion were laser power (W), point distance $(\\mu \\mathrm{m})$, hatch spacing $(\\mu \\mathrm{m})$ and exposure time $(\\mu \\mathrm{s})$. The nominal laser spot diameter of $70 \\mu \\mathrm{m}$ was kept constant in each DOE method. The parameters were varied according to an orthogonal array, which would be used to create different combinations of the input parameters. In this research, one of two orthogonal arrays were used, either the L9 array or the L25 array.\n\nEnergy density was calculated for each parameter combination. Energy density is a parameter that measures the energy input from the laser to the powder bed, and it is calculated using the following equation[102], [103]:\n\n\n\\begin{equation*}\nE_{d}=\\frac{P}{v \\times h \\times t} \\tag{5}\n\\end{equation*}\n\n\nwhere $E_{d}$ is the energy density $\\left(\\mathrm{Jmm}^{-3}\\right), v$ is scan speed $\\left(\\mathrm{mms}^{-1}\\right), h$ is hatch spacing $(\\mu \\mathrm{m})$ and $t$ is layer thickness $(\\mu \\mathrm{m})$. This equation is suited for continuous lasers, and since the laser used by the Renishaw AM250 is pulsed, the equation was modified as follows:\n\n\n\\begin{equation*}\nE_{d}=\\frac{P \\times\\left(\\frac{T}{h \\times p}\\right)}{\\text { layer thickness }} \\tag{6}\n\\end{equation*}\n\n\nwhere $T$ is exposure time ( $\\mu \\mathrm{s})$ and $p$ is point distance $(\\mu \\mathrm{m})$.\n\n\\subsection*{4.1.2 General Method}\nTwo DOE methods were used for the stainless steel $316 \\mathrm{~L}$ experiments, one for experiments $A$ and $B$, and one for experiments $C$ and $D$. This was due to a change to new material after the previous material had run out on the AM250 additive manufacturing machine between the two pairs of experiments. The differences in processability between batches of the same material is an important practical consideration when using additive powder-based fusion, as there can be a change in optimal parameters between the two batches due to... For the Ti6Al4V Titanium Alloy experiment, only a single batch of powder was used, hence only a single DOE method was performed prior to the experiment.\n\nFor each parameter combination, three repetitions of density measurement cubes, all of which made with $12 \\mathrm{~mm}$ sides, were built using a Renishaw AM250 machine.", "start_char_idx": 78604, "end_char_idx": 82831, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "227d52e3-6ba1-48e9-befe-f3f65916fa16": {"__data__": {"id_": "227d52e3-6ba1-48e9-befe-f3f65916fa16", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8514abcc-baf0-4f45-bce0-a15d04ffc82b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "202daf6db6b4471d9e084a0c049221a31082ad02e5ea46dfea271af82dab27df", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "98e3581a-d77b-4b57-a863-e6ca6b234861", "node_type": "1", "metadata": {}, "hash": "fe11e5715109174f84fea20698f0e72091762260ab15127c87016df2ec9d8516", "class_name": "RelatedNodeInfo"}}, "text": "\\subsection*{4.1.2 General Method}\nTwo DOE methods were used for the stainless steel $316 \\mathrm{~L}$ experiments, one for experiments $A$ and $B$, and one for experiments $C$ and $D$. This was due to a change to new material after the previous material had run out on the AM250 additive manufacturing machine between the two pairs of experiments. The differences in processability between batches of the same material is an important practical consideration when using additive powder-based fusion, as there can be a change in optimal parameters between the two batches due to... For the Ti6Al4V Titanium Alloy experiment, only a single batch of powder was used, hence only a single DOE method was performed prior to the experiment.\n\nFor each parameter combination, three repetitions of density measurement cubes, all of which made with $12 \\mathrm{~mm}$ sides, were built using a Renishaw AM250 machine. These cubes were removed from the plate after the build was completed and the bulk density of each cube was measured using three gravimetric methods:\n\n\\begin{enumerate}\n  \\item The sides of the cubes were measured using callipers to determine the approximate dimensions on each side. The volume was calculated from these dimensions, and divided by the cube's weight.\n\n  \\item The Archimedes principle was utilised by weighing the cube in and out of distilled water with a modified weighing scale.\n\n  \\item The Archimedes principle was utilised using a Sigma 700/701 tensiometer.\n\n\\end{enumerate}\n\nThe average bulk density was recorded for each combination of parameters by performing a minimum of three repetitions using each of these three gravimetric methods. The values were then used to plot the average relative density of the cubes against the laser energy density used to fabricate them.\n\nThe following sections specify the methods used for each batch of powder material. Each one varied slightly from the other. With every subsequent DOE method performed, new variable input parameters or larger orthogonal arrays were introduced as a means of capturing a more accurate set of input values for achieving maximum bulk density.\n\n\\subsection*{4.1.3 Stainless Steel 316L Powder (Experiments A and B)}\nIn the following section, the results from a study carried out by Lavery et al., [104], were used to determine the optimal settings for the batch a the batch of 316L stainless steel powder used to during experiments A and B. Two parameters, the point distance $(\\mu \\mathrm{m})$ and exposure time ( $\\mu \\mathrm{s})$, were varied using an L9 orthogonal array as seen in Table 3.\n\nThe nominal settings for $316 \\mathrm{~L}$ stainless steel powder, as recommended by the machine manufacturers, were to use a point distance of $65 \\mu \\mathrm{m}$, a laser exposure time of $110 \\mu \\mathrm{s}$, a laser power setting of $180 \\mathrm{~W}$, a hatch spacing of $124 \\mu \\mathrm{m}$ and a layer thickness of $50 \\mu \\mathrm{m}$. These settings would give a scan speed of $590 \\mathrm{mms}^{-1}$ during the build. The nominal parameters were used in the experiment, listed as B2 in Table 3.", "start_char_idx": 81925, "end_char_idx": 85019, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "98e3581a-d77b-4b57-a863-e6ca6b234861": {"__data__": {"id_": "98e3581a-d77b-4b57-a863-e6ca6b234861", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "227d52e3-6ba1-48e9-befe-f3f65916fa16", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2d256875e6406ea6e9e00829dddbbb17804254d1ce1818303d3779230de2748c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "67ab3dbd-ad1a-4d15-a485-9c592352dd89", "node_type": "1", "metadata": {}, "hash": "69d87a0eeaff04f8e62071086ca0b4b0345266705e0d0e3cac3d6512f0172d88", "class_name": "RelatedNodeInfo"}}, "text": "The nominal settings for $316 \\mathrm{~L}$ stainless steel powder, as recommended by the machine manufacturers, were to use a point distance of $65 \\mu \\mathrm{m}$, a laser exposure time of $110 \\mu \\mathrm{s}$, a laser power setting of $180 \\mathrm{~W}$, a hatch spacing of $124 \\mu \\mathrm{m}$ and a layer thickness of $50 \\mu \\mathrm{m}$. These settings would give a scan speed of $590 \\mathrm{mms}^{-1}$ during the build. The nominal parameters were used in the experiment, listed as B2 in Table 3.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n\\multirow[b]{3}{*}{}\\begin{tabular}{l}\nExposure \\\\\ntime ( $\\mu s)$ \\\\\n\\end{tabular} & \\multicolumn{9}{|c|}{Point Distance} \\\\\n\\hline\n & \\multicolumn{3}{|c|}{A $-25 \\mu \\mathrm{m}$} & \\multicolumn{3}{|c|}{B $-65 \\mu \\mathrm{m}$} & \\multicolumn{3}{|c|}{C $-105 \\mu \\mathrm{m}$} \\\\\n\\hline\n & Sample & \\begin{tabular}{c}\nScan \\\\\nSpeed \\\\\n$\\left(\\mathrm{mms}^{-1}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nEnergy \\\\\nDensity \\\\\n$\\left(\\mathrm{Jmm}^{-3}\\right)$ \\\\\n\\end{tabular} & Sample & \\begin{tabular}{c}\nScan \\\\\nSpeed \\\\\n$\\left(\\mathrm{mms}^{-1}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nEnergy \\\\\nDensity \\\\\n$\\left(\\mathrm{Jmm}^{-3}\\right)$ \\\\\n\\end{tabular} & Sample & \\begin{tabular}{c}\nScan \\\\\nSpeed \\\\\n$\\left(\\mathrm{mms}^{-1}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nEnergy \\\\\nDensity \\\\\n$\\left(\\mathrm{Jmm}^{-3}\\right)$ \\\\\n\\end{tabular} \\\\\n\\hline\n70 & A1 & 357 & 81.29 & B1 & 928 & 32.27 & $\\mathrm{C} 1$ & 1500 & 19.35 \\\\\n\\hline\n110 & A2 & 227 & 127.74 & B2 & 590 & 49.13 & $\\mathrm{C} 2$ & 954 & 30.41 \\\\\n\\hline\n150 & A3 & 166 & 174.19 & B3 & 433 & 65.41 & $\\mathrm{C} 3$ & 700 & 40.49 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 3. Design of experiments used for Chapter 4, [104].\n\nThe material powder used for Experiments $A$ and $B$ was made via gas atomisation. The nominal particle size ranged from $15 \\mu \\mathrm{m}$ to $45 \\mu \\mathrm{m}$, and the specification and the actual chemical composition of the powder is shown in Table 4.", "start_char_idx": 84517, "end_char_idx": 86541, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "67ab3dbd-ad1a-4d15-a485-9c592352dd89": {"__data__": {"id_": "67ab3dbd-ad1a-4d15-a485-9c592352dd89", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "98e3581a-d77b-4b57-a863-e6ca6b234861", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2a4f05ddb2e1a7086352e8d3828c30e78034dd07a8200a44711a5896673af1b4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3d5d7c29-929b-47a8-9d03-528e58cedbc5", "node_type": "1", "metadata": {}, "hash": "b2b0daa7d028ce56878256a0b45a455594e4095d26e32440345ce7c14e689976", "class_name": "RelatedNodeInfo"}}, "text": "Design of experiments used for Chapter 4, [104].\n\nThe material powder used for Experiments $A$ and $B$ was made via gas atomisation. The nominal particle size ranged from $15 \\mu \\mathrm{m}$ to $45 \\mu \\mathrm{m}$, and the specification and the actual chemical composition of the powder is shown in Table 4.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\nElement & $\\mathrm{Fe}$ & C & $\\mathrm{Si}$ & $\\mathrm{Mn}$ & $P$ & $\\mathrm{~S}$ & $\\mathrm{Cr}$ & $\\mathrm{Ni}$ & Mo & $\\mathrm{N}$ & $\\mathrm{Cu}$ & $\\mathrm{O}$ \\\\\n\\hline\nMinimum & Bal & - & - & - & - & - & 17.5 & 12.5 & 2.25 & - & - & - \\\\\n\\hline\nMaximum &  & 0.03 & 0.75 & 2 & 0.025 & 0.01 & 18 & 13 & 2.5 & 0.1 & 0.5 & 0.1 \\\\\n\\hline\nActual &  & 0.019 & 0.67 & 1.45 & 0.019 & 0.006 & 17.9 & 12.7 & 2.36 & 0.06 & 0.2 & 0.022 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 4. Composition, in weight percentage, of the $316 \\mathrm{~L}$ powder used in the study, [104].\n\nThe actual powder size distributions were as follows, D10 $=18.86 \\mu \\mathrm{m}, D 50=29.21 \\mu \\mathrm{m}$, $D 90=45.10 \\mu \\mathrm{m}$. These terms are a commonly used metric for describing particle size distribution, known as D-values. They specify the diameter of spherical particles that exist\\\\\nwithin a percentage of the mass from the powder sample taken. For example, the D50 value indicates that $50 \\%$ of the sample's mass is comprised of particles with a diameter less than $29.21 \\mu \\mathrm{m}$. The density measurement cubes were arranged on the base plate as seen in\n\nFigure 11. The results from this experiment are presented and discussed in detail in Chapter 5.1.1\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-053(1)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-053}\n\\end{center}\n\n(b)\n\nFigure 11. Right) Layout of the machine parameter array on the build plate, Left) as-built sample labels, [104].\n\n\\subsection*{4.1.4 Stainless Steel 316L Powder (Experiments $C$ and $D$ )}\nIn the following section, a slightly different DOE method was used on the batch of stainless steel $316 \\mathrm{~L}$ powder used during experiments $C$ and D. An L9 orthogonal array was used again, however two additional variable input parameters was introduced, laser power(W) and hatch spacing $(\\mu \\mathrm{m})$, in order to investigate their effect on output bulk density. The other two variable parameters were point distance $(\\mu \\mathrm{m})$ and exposure time $(\\mu \\mathrm{s})$. The optimal settings recommended by the manufacturers were labelled 'Opt'. The settings used are shown in Table 5. The density cube samples were assembled as seed in Figure 12. Other experimental components can be seen in this image, but they are not relevant to this particular study.", "start_char_idx": 86234, "end_char_idx": 89053, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3d5d7c29-929b-47a8-9d03-528e58cedbc5": {"__data__": {"id_": "3d5d7c29-929b-47a8-9d03-528e58cedbc5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "67ab3dbd-ad1a-4d15-a485-9c592352dd89", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a002bec71dd7889909eef3aa0a3ed2c30a285dd96b7c503cf63e9d370329a6fe", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "089bb044-f6a8-4693-8fa9-4280806d67a1", "node_type": "1", "metadata": {}, "hash": "d2a6ee4a94118b13c953f416806500dec620e4de3e378480662b96eadb673708", "class_name": "RelatedNodeInfo"}}, "text": "\\subsection*{4.1.4 Stainless Steel 316L Powder (Experiments $C$ and $D$ )}\nIn the following section, a slightly different DOE method was used on the batch of stainless steel $316 \\mathrm{~L}$ powder used during experiments $C$ and D. An L9 orthogonal array was used again, however two additional variable input parameters was introduced, laser power(W) and hatch spacing $(\\mu \\mathrm{m})$, in order to investigate their effect on output bulk density. The other two variable parameters were point distance $(\\mu \\mathrm{m})$ and exposure time $(\\mu \\mathrm{s})$. The optimal settings recommended by the manufacturers were labelled 'Opt'. The settings used are shown in Table 5. The density cube samples were assembled as seed in Figure 12. Other experimental components can be seen in this image, but they are not relevant to this particular study. The results from this experiment are presented and discussed in detail in Chapter 5.1.2\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline\n\\begin{tabular}{c}\nSample \\\\\nLabel \\\\\n\\end{tabular} & \\begin{tabular}{c}\nLaser \\\\\nPower \\\\\n$(\\mathbf{W})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nPoint \\\\\ndistance \\\\\n$(\\boldsymbol{\\mu} \\mathbf{)}$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nHatch \\\\\nSpacing \\\\\n$(\\boldsymbol{\\mu} \\mathbf{)}$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nExposure \\\\\nTime $(\\boldsymbol{\\mu s})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nEnergy \\\\\nDensity \\\\\n$\\left(\\mathbf{J m m}^{-\\mathbf{3}}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nScan \\\\\nSpeed \\\\\n$\\left(\\mathbf{m m s}^{-\\mathbf{1}}\\right)$ \\\\\n\\end{tabular} \\\\\n\\hline\nA1 & 170 & 60 & 100 & 100 & 57 & 600 \\\\\n\\hline\nA2 & 180 & 60 & 124 & 110 & 53 & 545 \\\\\n\\hline\nA3 & 190 & 60 & 149 & 120 & 51 & 500 \\\\\n\\hline\nA4 & 190 & 65 & 100 & 110 & 64 & 591 \\\\\n\\hline\nA5 & 170 & 65 & 124 & 120 & 51 & 542 \\\\\n\\hline\nA6 & 180 & 65 & 149 & 100 & 37 & 650 \\\\\n\\hline\nA7 & 180 & 70 & 100 & 120 & 62 & 583 \\\\\n\\hline\nA8 & 190 & 70 & 124 & 100 & 44 & 700 \\\\\n\\hline\nA9 & 170 & 70 & 149 & 110 & 36 & 636 \\\\\n\\hline\nOpt & 180 & 65 & 124 & 110 & 49 & 591 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 5. Laser parameters used for DOE for Chapter 5.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-054}\n\nFigure 12. Left) Density cubes, as they appeared in the assembly diagram, Right) the as-built density cube on a base plate.\n\n\\subsection*{4.1.5 Titanium Ti6Al4V Powder (Experiment E)}\nA larger L25 orthogonal array was used in this section to obtain greater accuracy for the optimal input parameters for achieving maximum bulk density. Four parameters, the laser power $(W)$, point distance $(\\mu \\mathrm{m})$, hatch spacing $(\\mu \\mathrm{m})$ and exposure time $(\\mu \\mathrm{s})$, were used to create 25 different combinations using the L25 orthogonal array, as shown in Table 6. The optimal parameters, as suggested by the manufacturer, were represented in sample A1.", "start_char_idx": 88205, "end_char_idx": 91099, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "089bb044-f6a8-4693-8fa9-4280806d67a1": {"__data__": {"id_": "089bb044-f6a8-4693-8fa9-4280806d67a1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3d5d7c29-929b-47a8-9d03-528e58cedbc5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "eebec2708f6ca1982cf4794b110da70569f8ffeb9ddb71b1755207b265ea635d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "151077d5-9d20-4890-bcab-92d8f35a1715", "node_type": "1", "metadata": {}, "hash": "657b26ddd72def0036df4589d5452349129f2ce55a9fe2311db8639bd019afdc", "class_name": "RelatedNodeInfo"}}, "text": "Left) Density cubes, as they appeared in the assembly diagram, Right) the as-built density cube on a base plate.\n\n\\subsection*{4.1.5 Titanium Ti6Al4V Powder (Experiment E)}\nA larger L25 orthogonal array was used in this section to obtain greater accuracy for the optimal input parameters for achieving maximum bulk density. Four parameters, the laser power $(W)$, point distance $(\\mu \\mathrm{m})$, hatch spacing $(\\mu \\mathrm{m})$ and exposure time $(\\mu \\mathrm{s})$, were used to create 25 different combinations using the L25 orthogonal array, as shown in Table 6. The optimal parameters, as suggested by the manufacturer, were represented in sample A1.\n\nThe results from this experiment are presented and discussed in detail in Chapter 5.1.3\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline\n\\begin{tabular}{c}\nSample \\\\\nLabel \\\\\n\\end{tabular} & \\begin{tabular}{c}\nLaser \\\\\nPower \\\\\n$(\\mathbf{W})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nPoint \\\\\ndistance \\\\\n$(\\boldsymbol{\\mu m})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nHatch \\\\\nSpacing \\\\\n$(\\boldsymbol{\\mu} \\mathbf{)}$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nExposure \\\\\nTime $(\\boldsymbol{\\mu})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nEnergy \\\\\nDensity \\\\\n$\\left(\\mathbf{J m m}^{-3}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nScan \\\\\nSpeed \\\\\n$\\left(\\mathbf{m m s}^{-\\mathbf{1}}\\right)$ \\\\\n\\end{tabular} \\\\\n\\hline\nA1 & 185 & 50 & 100 & 100 & 74 & 500 \\\\\n\\hline\nA2 & 189 & 50 & 119 & 112 & 71 & 446 \\\\\n\\hline\nA3 & 193 & 50 & 138 & 125 & 70 & 400 \\\\\n\\hline\nA4 & 197 & 50 & 157 & 138 & 69 & 362 \\\\\n\\hline\nA5 & 200 & 50 & 175 & 150 & 69 & 333 \\\\\n\\hline\nA6 & 193 & 62 & 100 & 112 & 70 & 554 \\\\\n\\hline\nA7 & 197 & 62 & 119 & 125 & 67 & 496 \\\\\n\\hline\nA8 & 200 & 62 & 138 & 138 & 65 & 449 \\\\\n\\hline\nA9 & 185 & 62 & 157 & 150 & 57 & 413 \\\\\n\\hline\nA10 & 189 & 62 & 175 & 100 & 35 & 620 \\\\\n\\hline\nA11 & 200 & 75 & 100 & 125 & 67 & 600 \\\\\n\\hline\nA12 & 185 & 75 & 119 & 138 & 57 & 543 \\\\\n\\hline\nA13 & 189 & 75 & 138 & 150 & 55 & 500 \\\\\n\\hline\nA14 & 193 & 75 & 157 & 100 & 33 & 750 \\\\\n\\hline\nA15 & 197 & 75 & 175 & 112 & 34 & 670 \\\\\n\\hline\nA16 & 189 & 88 & 100 & 138 & 59 & 638 \\\\\n\\hline\nA17 & 193 & 88 & 119 & 150 & 55 & 587 \\\\\n\\hline\nA18 & 197 & 88 & 138 & 100 & 32 & 880 \\\\\n\\hline\nA19 & 200 & 88 & 157 & 112 & 32 & 786 \\\\\n\\hline\nA20 & 185 & 88 & 175 & 125 & 30 & 704 \\\\\n\\hline\nA21 & 197 & 100 & 100 & 150 & 59 & 667 \\\\\n\\hline\nA22 & 200 & 100 & 119 & 100 & 34 & 1000 \\\\\n\\hline\nA23 & 185 & 100 & 138 & 112 & 30 & 893 \\\\\n\\hline\nA24 & 189 & 100 & 157 & 125 & 30 & 800 \\\\\n\\hline\nA25 & 193 & 100 & 175 & 138 & 30 & 725 \\\\\n\\hline\n &  &  &  &  &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 6.", "start_char_idx": 90442, "end_char_idx": 93080, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "151077d5-9d20-4890-bcab-92d8f35a1715": {"__data__": {"id_": "151077d5-9d20-4890-bcab-92d8f35a1715", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "089bb044-f6a8-4693-8fa9-4280806d67a1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1e6efcb2021079e0f36cbc7e3d8266dd2429345755c126b182d50bc4d224fe89", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "af6c0e92-6622-4e76-80d1-74e976a8f872", "node_type": "1", "metadata": {}, "hash": "cc7bd9a598c3c94185d9553169b9b7cd56d0b3d9591f62d3cff51b2c5a6a2e7c", "class_name": "RelatedNodeInfo"}}, "text": "Laser parameters used for DOE.\n\n\\subsection*{4.2 Experiment A - Direct Base Plate Method}\n\\subsection*{4.2.1 Objectives}\nThis section outlines the method used for an experiment carried out in the beginning of the project, which served as a precursor to the research performed later with single track structures. The material used in this experiment was stainless steel 316L. The purpose of the first experiment, known as Experiment A, was to investigate the influence of laser power (W) and exposure time ( $\\mu \\mathrm{s}$ ) on the formation of square-shaped structures built on top of a separate plain carbon steel plate substrate. The track formation, size and appearance were the features of interest.\n\n\\subsection*{4.2.2 Experimental Design}\nThe structures were initially designed to include multiple layers, ranging from 2 to 48 layers. The original aim of the experiment was to investigate the change in the physical structure from layer to layer. However, the build failed after only building the first layer, and thus only single layer structures were investigated.\n\nSix sets of processing parameter settings were used, as seen in Table 7. The point distance and hatch spacing were kept constant at $65 \\mu \\mathrm{m}$ and $124 \\mu \\mathrm{m}$, respectively. The laser spot diameter was kept constant at $70 \\mu \\mathrm{m}$. The layer thickness used for this build was $50 \\mu \\mathrm{m}$ and a stripes-type hatch pattern was used. Since the build failed after only one layer, all structures were built in the horizontal direction, perpendicular to the wiper blade direction.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline\n\\begin{tabular}{c}\nSample \\\\\nID \\\\\n\\end{tabular} & \\begin{tabular}{c}\nLaser \\\\\nPower \\\\\n$(\\mathrm{W})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nExposure \\\\\nTime \\\\\n$(\\mu \\mathrm{s})$ \\\\\n\\end{tabular} \\\\\n\\hline\n1 & 100 & 75 \\\\\n\\hline\n2 & 100 & 150 \\\\\n\\hline\n3 & 150 & 75 \\\\\n\\hline\n4 & 150 & 150 \\\\\n\\hline\n5 & 200 & 75 \\\\\n\\hline\n6 & 200 & 150 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 7. Experiment A (SS316L) - Laser Parameters used.\n\nA series of 8 square-base shaped 3D objects were to be built for each setting, each with an area of $20 \\mathrm{~mm}$ by $20 \\mathrm{~mm}$. These squares were assembled into rectangular regions, each measuring $80 \\mathrm{~mm}$ by $20 \\mathrm{~mm}$. The square structures were designed to have an ascending number of layers to be built, ranging from 2 to 48 . The number of layers to be built for each square-base structure and their position is noted in Figure 13\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-057}\n\nFigure 13. Experiment A (SS316L) - Experimental Design Left) Experimental Design, Right) Photographs of sectioned samples.\n\nRather than being built directly unto the base plate, a mild steel plate was used, which was $3.8 \\mathrm{~mm}$ thick. This plate was machined to fit over the base plate of the Renishaw 250 machine, as well as to bolt onto it. The purpose of this sub-plate was to act in a sacrificial capacity. Once the build was complete, the sub-plate could be removed and divided quite easily, facilitating subsequent microscopy.\n\nAfter the build was completed, the sub-plate was removed from the base plate and each rectangle was cut into separate pieces. The rectangular pieces were observed under a Keyence VHX 6000 series light microscope, taking photographs of the formed melt pools from an overhead view.\n\nAfter taking these images, each square structure in the rectangular pieces were cut out.\n\nFrom each square structure, cuts would be taken, one cut in the horizontal direction, that is, perpendicular to the build direction, and one in the vertical direction, parallel to the build direction. The horizontal cuts were used to observe an effective cross-section of a single row\\\\\nof melt pools along the laser direction, whilst the longitudinal cuts were used to observe a cross-section across multiple rows perpendicular to the laser path.", "start_char_idx": 93081, "end_char_idx": 97060, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "af6c0e92-6622-4e76-80d1-74e976a8f872": {"__data__": {"id_": "af6c0e92-6622-4e76-80d1-74e976a8f872", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "151077d5-9d20-4890-bcab-92d8f35a1715", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "fb621f1bedfade479722bdfcb19d9e284ecc480ddecaf0a9f119f5e73e81cdac", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f449ad72-6772-4d9f-9139-9ed00a064953", "node_type": "1", "metadata": {}, "hash": "787cfd7f338c83d3672c78d17749fe9a10f690ab36166ce1a941fcc58e6e97f8", "class_name": "RelatedNodeInfo"}}, "text": "The purpose of this sub-plate was to act in a sacrificial capacity. Once the build was complete, the sub-plate could be removed and divided quite easily, facilitating subsequent microscopy.\n\nAfter the build was completed, the sub-plate was removed from the base plate and each rectangle was cut into separate pieces. The rectangular pieces were observed under a Keyence VHX 6000 series light microscope, taking photographs of the formed melt pools from an overhead view.\n\nAfter taking these images, each square structure in the rectangular pieces were cut out.\n\nFrom each square structure, cuts would be taken, one cut in the horizontal direction, that is, perpendicular to the build direction, and one in the vertical direction, parallel to the build direction. The horizontal cuts were used to observe an effective cross-section of a single row\\\\\nof melt pools along the laser direction, whilst the longitudinal cuts were used to observe a cross-section across multiple rows perpendicular to the laser path. These samples were mounted, etched and observed under a Reichert-Jung MEF3 light microscope fitted with a digital camera. Greater detail on the metallographic methods used to prepare these samples can be found in Appendix 2. The etchant used was Kalling's Reagent No. 2, which is used to show the general structure of austenitic stainless alloys. The combined cross-sectional and overhead photographs are shown in Figure 20 through Figure 25, with the location of the cut-direction shown below the cross-sectional image using a red arrow.\n\nThe resulting photographs taken from the single layer experiment from both the surface and cross-section samples were analysed using ImageJ image processing software to measure the sizes of certain features such as melt pool dimensions, layer thickness and gap sizes between visible structures in the cross-sectional samples. The results from this experiment are presented and discussed in detail in Chapter 5.2\n\n\\subsection*{4.3 Experiment B - Single-Lines on Recessed Plates Method}\n\\subsection*{4.3.1 Objectives}\nThe purpose of this experiment was to investigate the effect of two processing parameters, laser power $(\\mathrm{W})$ and scan speed $\\left(\\mathrm{mms}^{-1}\\right)$, on the formation of single line structures. Instead of creating several overlapping tracks like in Experiment A, this experiment was to focus on the formation of individual tracks, separated from neighbouring tracks by using a large hatch spacing. The same material powder, stainless steel 316L, would be used for this experiment.\n\n\\subsection*{4.3.2 Experimental Design}\nThe parameters were divided into six groups, each group with a specific power setting (75W, 100W, 125W, 150W, 175W and 200W). For each group, 10 different laser speeds were used, ranging from $100 \\mathrm{mms}^{-1}$ to $1000 \\mathrm{mms}^{-1}$, with a $100 \\mathrm{mms}^{-1}$ step size. The exposure time was altered whilst the point distance used for every sample was kept constant at $60 \\mu \\mathrm{m}$. The parameters used can be seen in Table 8.", "start_char_idx": 96051, "end_char_idx": 99106, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f449ad72-6772-4d9f-9139-9ed00a064953": {"__data__": {"id_": "f449ad72-6772-4d9f-9139-9ed00a064953", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "af6c0e92-6622-4e76-80d1-74e976a8f872", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "10cd85d8b3ebf37f53d95c029962917af23d560e8c4afbb3dc0475f0c2c0499c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "8040be2d-0c0e-4879-b62d-e79e1522afdc", "node_type": "1", "metadata": {}, "hash": "0a1adb1e8b6447fe2c65cdc829c33b7c52a1d4b0e14e32306d72e6b599e9867c", "class_name": "RelatedNodeInfo"}}, "text": "Instead of creating several overlapping tracks like in Experiment A, this experiment was to focus on the formation of individual tracks, separated from neighbouring tracks by using a large hatch spacing. The same material powder, stainless steel 316L, would be used for this experiment.\n\n\\subsection*{4.3.2 Experimental Design}\nThe parameters were divided into six groups, each group with a specific power setting (75W, 100W, 125W, 150W, 175W and 200W). For each group, 10 different laser speeds were used, ranging from $100 \\mathrm{mms}^{-1}$ to $1000 \\mathrm{mms}^{-1}$, with a $100 \\mathrm{mms}^{-1}$ step size. The exposure time was altered whilst the point distance used for every sample was kept constant at $60 \\mu \\mathrm{m}$. The parameters used can be seen in Table 8.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n & \\multicolumn{10}{|c|}{Scan Speed $\\left(\\mathrm{mms}^{-1}\\right)$} &  \\\\\n\\hline\n &  & 100 & 200 & 300 & 400 & 500 & 600 & 700 & 800 & 900 & 1000 \\\\\n\\hline\n &  & \\multicolumn{10}{|c|}{Exposure Time ( $\\mu \\mathrm{s})$} \\\\\n\\hline\n\\multirow{6}{*}{\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-059}\n} & 200 & 600 & 300 & 200 & 150 & 120 & 100 & 86 & 75 & 67 & 60 \\\\\n\\hline\n & 175 & 600 & 300 & 200 & 150 & 120 & 100 & 86 & 75 & 67 & 60 \\\\\n\\hline\n & 150 & 600 & 300 & 200 & 150 & 120 & 100 & 86 & 75 & 67 & 60 \\\\\n\\hline\n & 125 & 600 & 300 & 200 & 150 & 120 & 100 & 86 & 75 & 67 & 60 \\\\\n\\hline\n & 100 & 600 & 300 & 200 & 150 & 120 & 100 & 86 & 75 & 67 & 60 \\\\\n\\hline\n & 75 & 600 & 300 & 200 & 150 & 120 & 100 & 86 & 75 & 67 & 60 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 8. Experiment B (SS316L) - Processing parameters used.\n\nFor this experiment, the base plate was modified to be able to fit rectangular shaped mild steel inserts. The base-plate had five rectangular sections milled out from the surface, cutting a rectangular volume measuring $200 \\mathrm{~mm}$ by $25 \\mathrm{~mm}$. The insert design would have the exact dimensions of the milled sections and would be cut from stainless steel plate of the same thickness as the depth, allowing inserts to fit in easily. Additionally, both surfaces were plain, allowing the insert to be retained by gravity. The design of the milled base plate and inserts can be seen in Figure 14 below.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-060}\n\\end{center}\n\nFigure 14. Experiment B (SS316L) - Experimental design.\n\nThis design was chosen for several reasons. Firstly, it would be easier and quicker to investigate the final single tracks, unlike the design used for experiment $A$. The design used for experiment $A$ required an entire plate to be bolted onto the base plate, and subsequently that plate had to be machined several times before the structures produced could be isolated and undergo metallographic preparation. Furthermore, an entire steel plate had to be used with only a very limited area being used for the experiment. Using the insert method, the structure would be almost immediately available for metallographic preparation and only a single cut would be needed to obtain the cross-section. Several inserts could be prepared in advance, allowing repetition of the experiment to be performed very easily.", "start_char_idx": 98328, "end_char_idx": 101613, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "8040be2d-0c0e-4879-b62d-e79e1522afdc": {"__data__": {"id_": "8040be2d-0c0e-4879-b62d-e79e1522afdc", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f449ad72-6772-4d9f-9139-9ed00a064953", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "706ec001a293c9ab1ec2ce964f2c6c897b213b7ceb08092d630acfb4f0b50ad3", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9cbcf635-cabd-49e8-af2c-9a84507547ad", "node_type": "1", "metadata": {}, "hash": "3da3587b265a0d580a1a1db8d134a51adb1472b97139e35b0e99a5bba95e8a44", "class_name": "RelatedNodeInfo"}}, "text": "Experiment B (SS316L) - Experimental design.\n\nThis design was chosen for several reasons. Firstly, it would be easier and quicker to investigate the final single tracks, unlike the design used for experiment $A$. The design used for experiment $A$ required an entire plate to be bolted onto the base plate, and subsequently that plate had to be machined several times before the structures produced could be isolated and undergo metallographic preparation. Furthermore, an entire steel plate had to be used with only a very limited area being used for the experiment. Using the insert method, the structure would be almost immediately available for metallographic preparation and only a single cut would be needed to obtain the cross-section. Several inserts could be prepared in advance, allowing repetition of the experiment to be performed very easily.\n\nThe modified base plate was bolted into a Renishaw AM250 machine. A mild steel insert was placed in each of the five recesses. The machine was placed under vacuum conditions and an argon atmosphere was introduced into the build chamber, just as if a regular build was being prepared. The build plate was lowered by $50 \\mu \\mathrm{m}$, and powder was deposited from\\\\\nthe hopper. This amount of powder was spread over the inserts to achieve an estimated $50 \\mu \\mathrm{m}$ powder layer thickness.\n\nOn each insert, six sets of single lines were produced, each with ten lines, as seen in the bottom-right image in Figure 14. Each set had an assigned laser power setting, ranging from $200 \\mathrm{~W}$ to $75 \\mathrm{~W}$. Each line produced had a different exposure time, changing the scan speed used for each line, ranging from $1000 \\mathrm{mms}^{-1}$ to $100 \\mathrm{mms}^{-1}$. Effectively the experiment was repeated five times, once for each insert, at different positions on the base plate. After the lines were built, the machine was evacuated, the chamber door could be opened and the inserts were removed from the build plate. The lines were investigated under a ZEISS Smartzoom 5 Automated Digital Microscope to obtain the topographical images, whilst cross-sections were taken using similar methods used in Experiment A and Appendix\n\n\\begin{enumerate}\n  \\setcounter{enumi}{1}\n  \\item These cross-sections were observed and recorded under a Zeiss Primotech Light Microscope, and the width and depth of each track was measured from these images. The results from this experiment are presented and discussed in detail in Chapter 5.3\n\\end{enumerate}\n\n\\subsection*{4.4 Crucible Method (CM)}\n\\subsection*{4.4.1 Introduction}\nIn both experiments A and B, the substrates used in each experiment were made from mild steel. Apart from being made from a completely different material than the material powder used, these substrates were made via machining rather than additive manufacturing. The resulting structures from these experiments was indicative of track formation for the very first layers of a build, where the powder is melted unto a base plate. However, these tracks would not be representative of those formed at subsequent layers much further away from the base plate. Therefore, a novel substrate design, called the \"crucible\", was developed to tackle these issues. The crucible substrate would not only be able to emulate the in-situ surface conditions of additive manufacturing, but could also allow for adjustments in the layer depth to be used as an additional process parameter during the investigation.\n\n\\subsection*{4.4.2 Crucible Design}\nThe crucible is a rectangularly shaped substrate, roughly measuring $10 \\mathrm{~mm} \\times 15 \\mathrm{~mm} \\times$\n\n$5 \\mathrm{~mm}$, ass seen in Figure 15. At the top-most, vertical side of the crucible, that is, opposite the side of the base plate it is built on, is a rectangular recess that is only a few layers deep, or even a single layer. For the experiments performed in this research, the layer thickness for an individual layer in each build was $50 \\mu \\mathrm{m}$, whilst the recess depth ranged from 50 $200 \\mu \\mathrm{m}$. The purpose of this recess is to hold an isolated layer of powder of a depth controlled by the user, and thus can be introduced as an input parameter.", "start_char_idx": 100758, "end_char_idx": 104967, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9cbcf635-cabd-49e8-af2c-9a84507547ad": {"__data__": {"id_": "9cbcf635-cabd-49e8-af2c-9a84507547ad", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8040be2d-0c0e-4879-b62d-e79e1522afdc", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "26bca72f1e8ee9c8077e886ede510972573e76be4addc49df7997ecb7374645e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "4c1d029b-07b2-4511-90d1-67e221193ad3", "node_type": "1", "metadata": {}, "hash": "1a055c792aabce66eeaeafe9ffde8b85e1ae2157fde6d5595b97b498ea1c6caa", "class_name": "RelatedNodeInfo"}}, "text": "\\subsection*{4.4.2 Crucible Design}\nThe crucible is a rectangularly shaped substrate, roughly measuring $10 \\mathrm{~mm} \\times 15 \\mathrm{~mm} \\times$\n\n$5 \\mathrm{~mm}$, ass seen in Figure 15. At the top-most, vertical side of the crucible, that is, opposite the side of the base plate it is built on, is a rectangular recess that is only a few layers deep, or even a single layer. For the experiments performed in this research, the layer thickness for an individual layer in each build was $50 \\mu \\mathrm{m}$, whilst the recess depth ranged from 50 $200 \\mu \\mathrm{m}$. The purpose of this recess is to hold an isolated layer of powder of a depth controlled by the user, and thus can be introduced as an input parameter. The crucible allows for the investigation of single tracks to be built on the same type of material as the tracks themselves, avoiding the use of possibly dissimilar materials, or materials made using different processes.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-062}\n\nFigure 15. The Crucible Design.\n\nUpper Left: Vertical view, Lower Left: Horizontal view, Upper Right: Cross Section showing recess, Lower Right: Diagonal view.\n\nThe general crucible structure would be built using standard operating parameters for the material being used, whilst the single tracks being investigated are built using different combinations of testing parameters. Between the construction of the crucible and the construction of the tracks, which is the final layer of the build, the AM250 was paused for 15 minutes. This was done in order to allow the previous layers to undergo sufficient cooling, thus the heat generated from the construction of the crucible was minimised in order for it to not be a factor in the experiment.\n\nEach crucible holds a set of tracks, which ranged from 3 to 12, which are each separated from one another by a minimum of $500 \\mu$. An example of a 3-track crucible can be seen on the right-hand side of Figure 16. The experiment is constructed in one build, with no intermediate steps to follow during, before or after a build like in previous experimental methods proposed. The crucibles are removed from the base plate by the use of a set of pliers, or even by hand. Several crucibles can be placed on a base plate, allowing for repetitions or a very wide parameter selection range. On the AM250, around 90-120 crucibles could easily be built on the $250 \\mathrm{~mm} \\times 250 \\mathrm{~mm}$ build envelope, as seen on the lefthand side of Figure 16.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-063}\n\nFigure 16. Left) CAD drawing of crucibles used during an experiment, Right) Three single track structures placed at the top of the crucibles.\n\nThe experimental design for each crucible experiment was similar, though there were crucial differences between each one. For example, whilst Experiments $\\mathrm{C}$ and $\\mathrm{E}$ introduced the\\\\\nlayer thickness as a parameter, tracks made for Experiment D used only a single layer. These details are discussed in greater detail below.\n\n\\subsection*{4.4.3 Experiment C - Verification of Single-Track Crucible Methodology}\n\\section*{Objectives}\nThis experiment sought to utilise the standardised crucible design mentioned in the previous section to its fullest ability on a new experiment. It was the first experiment to use the methodology described in the previous section. Stainless steel $316 \\mathrm{~L}$ was used as the material powder.\n\nThe main objective of this experiments was to investigate the influence of laser power, scan speed, and surface energy density on the formation of single-track structures. Surface energy density is a value calculated from the laser power and the scan speed used to indicate the amount of energy being delivered from the laser to the area under its influence. It is calculated using the following equation.\n\n\n\\begin{equation*}\nE \\rho=\\frac{P}{v d} \\tag{7}\n\\end{equation*}", "start_char_idx": 104242, "end_char_idx": 108227, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "4c1d029b-07b2-4511-90d1-67e221193ad3": {"__data__": {"id_": "4c1d029b-07b2-4511-90d1-67e221193ad3", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9cbcf635-cabd-49e8-af2c-9a84507547ad", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9e74fe34577dd1a4e608037295e799903fdeaf6fe8540774182d43b2c9da1520", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "28ac17cc-32ed-4234-99a9-92ed27a6569a", "node_type": "1", "metadata": {}, "hash": "10cc8dcfb623050eb33db75e3ccdc07584bcb599e74e6d70baabb3d6f0cc69c5", "class_name": "RelatedNodeInfo"}}, "text": "\\subsection*{4.4.3 Experiment C - Verification of Single-Track Crucible Methodology}\n\\section*{Objectives}\nThis experiment sought to utilise the standardised crucible design mentioned in the previous section to its fullest ability on a new experiment. It was the first experiment to use the methodology described in the previous section. Stainless steel $316 \\mathrm{~L}$ was used as the material powder.\n\nThe main objective of this experiments was to investigate the influence of laser power, scan speed, and surface energy density on the formation of single-track structures. Surface energy density is a value calculated from the laser power and the scan speed used to indicate the amount of energy being delivered from the laser to the area under its influence. It is calculated using the following equation.\n\n\n\\begin{equation*}\nE \\rho=\\frac{P}{v d} \\tag{7}\n\\end{equation*}\n\n\nwhere $E \\rho$ is surface energy density $\\left(\\mathrm{Jmm}^{-2}\\right), P$ is laser power $(\\mathrm{W}), v$ is scan speed $(\\mathrm{mm} / \\mathrm{s})$ and $d$ is laser spot diameter $(\\mathrm{mm})$. The variance of laser power and scan speed for fixed surface energy density values was investigated. Additionally, due to the new crucible methodology, these different parameter combinations were investigated at varying layer powder depths by introducing crucibles with varying recess depths.\n\n\\section*{Experimental Design}\n7 surface energy density values were established, ranging from $80 \\mathrm{~J} \\mathrm{~mm}^{-2}$ to $4 \\mathrm{~J} \\mathrm{~mm}^{-2}$. For each energy density value, 4 laser power settings would be used, ranging for $200 \\mathrm{~W}$ to $100 \\mathrm{~W}$. The scan speed for each corresponding laser power setting was calculated according to the following equation, which is a slight modification of equation above.\n\n\n\\begin{equation*}\nv=\\frac{P}{E \\rho . d} \\tag{8}\n\\end{equation*}\n\n\nWhere $d$ was kept constant at $70 \\mu \\mathrm{m}$. A table of the different parameter combinations can be seen in Table 9 below.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-065}\n\\end{center}\n\nTable 9. Experiment C (SS316L) - Processing parameters.\n\nFor each parameter, each parameter combination would have 10 single tracks, each $15 \\mathrm{~mm}$ in length, built on 4 crucible substrates, each one with a different recess depth. The recess depth ranged from $50 \\mu \\mathrm{m}$ to $200 \\mu \\mathrm{m}$ with a step size of $50 \\mu \\mathrm{m}$. The crucibles were built at standard parameters for stainless steel 316L. In total, 112 crucibles with single track structures were built during this experiment. After the build was completed using the Renishaw AM250, the samples were removed and collected off the base plate and labelled accordingly. Each crucible had the topmost surface photographed using a ZEISS Smartzoom 5 Automated Digital Microscope. These images would be used to examine the overall stability of the lines formed.\n\nCrucible samples with successfully built lines were prepared for metallographic examination.\n\nThe techniques and specific methods used are listed in Appendices 3 and 4. Beraha II was used as a new etchant for the metallographic preparation of stainless steel $316 \\mathrm{~L}$ samples. At a colour etchant, it was found to clearly distinguish grains and grain boundaries much move vividly than the previous used Kalling's Reagent.\n\nThe samples were examined under a Zeiss Primotech Light Microscope. Cross-sectional images of the single melt tracks and any notable features around the melt were photographed. The image processing package Fiji, [105], was used to measure the dimensions of each track photograph.\n\nThis included:\n\na. Maximum width, the measurement of the widest section of the melt.\n\nb. Base width, the width of the track at the surface level of the substrate.\n\nc. Height, the height of the track directly above the surface level of the substrate.\n\nd. Remelting depth, the depth of the track directly below the surface level of the substrate.\n\nThe size and presence of pores and other notable features was also recorded.", "start_char_idx": 107351, "end_char_idx": 111458, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "28ac17cc-32ed-4234-99a9-92ed27a6569a": {"__data__": {"id_": "28ac17cc-32ed-4234-99a9-92ed27a6569a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "4c1d029b-07b2-4511-90d1-67e221193ad3", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "dfb53ff2bcebfe1b97c7f0c9979baec9cc9e6d6d7b7a37ecd9ddfdebd1ef9024", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2e9acd88-aa21-46bc-8adb-57b9874a5ffc", "node_type": "1", "metadata": {}, "hash": "4fad727d1394d7d975c9b171a9adf8579905dfc02eec4e59d5e3c83608d8313b", "class_name": "RelatedNodeInfo"}}, "text": "At a colour etchant, it was found to clearly distinguish grains and grain boundaries much move vividly than the previous used Kalling's Reagent.\n\nThe samples were examined under a Zeiss Primotech Light Microscope. Cross-sectional images of the single melt tracks and any notable features around the melt were photographed. The image processing package Fiji, [105], was used to measure the dimensions of each track photograph.\n\nThis included:\n\na. Maximum width, the measurement of the widest section of the melt.\n\nb. Base width, the width of the track at the surface level of the substrate.\n\nc. Height, the height of the track directly above the surface level of the substrate.\n\nd. Remelting depth, the depth of the track directly below the surface level of the substrate.\n\nThe size and presence of pores and other notable features was also recorded. The results from this experiment are presented and discussed in detail in Chapter 0\n\n\\subsection*{4.4.4 Experiment D - Single-Tracks on Crucible Substrates}\n\\section*{Objectives}\nThe purpose of this experiment was to repeat the experimental procedures used in\n\nExperiment B, where single track structures were constructed using stainless steel 316L\n\npowder onto mild steel inserts. Instead of inserts made of mild steel, the crucible design from\n\nExperiment $\\mathrm{C}$ was used as a substrate. Using the crucible design was considered to be\n\nmore representative of the laser-powder bed fusion process for layers being built away from the base plate, that is, the bulk of the build.\n\nBuilding at the level or very near to the baseplate poses major differences. The temperature gradient is much larger, due to the cooling effect of the base plate being so immediate to the track formation. The surface of the base plate is much smoother, as it is a machine polished surface. In contrast, during the bulk of the build, tracks form at greater distances to the base plate, up to around $300 \\mathrm{~mm}$ in the Renishaw AM250, relieving an amount of heat lost through conduction to the baseplate. The type of surface that most of the tracks would form on are previously built layers, made of several tracks assembled in some form of stripe formation. This gives a wavy, uneven and much rougher surface when compared to the plane build plate surface. The relative sensitivity of the two approaches deserves attention, and the investigation performed in this section serves to investigate the differences and possible similarities between the two procedures.\n\n\\section*{Experimental Design}\nThe parameters used in this experiment were the exact ones used in Experiment B, in which a series of single line tracks were built using stainless steel 316L powder atop mild carbon steel inserts. The parameters used can be seen in Table 16 below.", "start_char_idx": 110609, "end_char_idx": 113394, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2e9acd88-aa21-46bc-8adb-57b9874a5ffc": {"__data__": {"id_": "2e9acd88-aa21-46bc-8adb-57b9874a5ffc", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "28ac17cc-32ed-4234-99a9-92ed27a6569a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f8308873c24b1c0f2217e1df276ed496f51f426d1f7c47806d2d69b85d4603a8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ae1da1b8-2521-493b-907c-16908a79eabc", "node_type": "1", "metadata": {}, "hash": "bbfef5f6156dc0091de434aa6c6e500dbca705f8a4b827abd25d8ffb0dcd076e", "class_name": "RelatedNodeInfo"}}, "text": "In contrast, during the bulk of the build, tracks form at greater distances to the base plate, up to around $300 \\mathrm{~mm}$ in the Renishaw AM250, relieving an amount of heat lost through conduction to the baseplate. The type of surface that most of the tracks would form on are previously built layers, made of several tracks assembled in some form of stripe formation. This gives a wavy, uneven and much rougher surface when compared to the plane build plate surface. The relative sensitivity of the two approaches deserves attention, and the investigation performed in this section serves to investigate the differences and possible similarities between the two procedures.\n\n\\section*{Experimental Design}\nThe parameters used in this experiment were the exact ones used in Experiment B, in which a series of single line tracks were built using stainless steel 316L powder atop mild carbon steel inserts. The parameters used can be seen in Table 16 below.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n & \\multicolumn{10}{|c|}{Scan Speed $\\left(\\mathrm{mms}^{-1}\\right)$} &  \\\\\n\\hline\n &  & 100 & 200 & 300 & 400 & 500 & 600 & 700 & 800 & 900 & 1000 \\\\\n\\hline\n &  & \\multicolumn{10}{|c|}{Exposure Time ( $\\mu \\mathrm{s})$} \\\\\n\\hline\n\\multirow{6}{*}{\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-067}\n} & 200 & 600 & 300 & 200 & 150 & 120 & 100 & 86 & 75 & 67 & 60 \\\\\n\\hline\n & 175 & 600 & 300 & 200 & 150 & 120 & 100 & 86 & 75 & 67 & 60 \\\\\n\\hline\n & 150 & 600 & 300 & 200 & 150 & 120 & 100 & 86 & 75 & 67 & 60 \\\\\n\\hline\n & 125 & 600 & 300 & 200 & 150 & 120 & 100 & 86 & 75 & 67 & 60 \\\\\n\\hline\n & 100 & 600 & 300 & 200 & 150 & 120 & 100 & 86 & 75 & 67 & 60 \\\\\n\\hline\n & 75 & 600 & 300 & 200 & 150 & 120 & 100 & 86 & 75 & 67 & 60 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 10. Experiment D (SS316L) - Processing parameters used.\n\nFor each parameter listed, a set of three single track melts were produced within the recess depth of a crucible. Since the thickness of the powder layer used for Experiment B was estimated at $50 \\mu \\mathrm{m}$, the crucible pit depth was set at $50 \\mu \\mathrm{m}$.\n\nAfter being built on the Renishaw AM250, the exact metallographic preparation procedures used for Experiment $\\mathrm{C}$ were performed on the samples collected in this experiment. The results from this experiment are presented and discussed in detail in Chapter 0\n\n\\subsection*{4.4.5 Experiment $E$ - Crucible Single-Track experiments using Ti-6Al-4V}\n\\section*{Objectives}\nIn this section, the crucible substrate design was used to create single-line tracks using the titanium alloy Ti-6Al-4V metal powder. Apart from investigating the effect of laser power and scan speed on the formation of Ti-6AL-4V single-tracks, the effect of the powder depth was also investigated by varying the recess depth of the crucible substrate, similar to experiment\n\nC. Additionally, this experiment was performed to test the applicability of the crucible methodology using a different powder material to stainless steel 316L.\n\n\\section*{Experimental Design}\nTo accomplish the experimental objective, three groups of parameters were formed, each with a specific laser power used (100W, 150W and 200W). For each group, six different scan speeds were to be used, which would be varied by altering the point distance and exposure times. The array of parameter combinations used for this experiment are shown in Table 11 below.", "start_char_idx": 112434, "end_char_idx": 115892, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ae1da1b8-2521-493b-907c-16908a79eabc": {"__data__": {"id_": "ae1da1b8-2521-493b-907c-16908a79eabc", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2e9acd88-aa21-46bc-8adb-57b9874a5ffc", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "778708773f9f17df7528a365a3d160d625681752670ed43dedfb92b43f7c299a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "43f535fc-81c5-4431-9911-43ae08228386", "node_type": "1", "metadata": {}, "hash": "0e63437e65bae37196afe17d106454267c715c43a632aee4d9547ab484463a6e", "class_name": "RelatedNodeInfo"}}, "text": "Apart from investigating the effect of laser power and scan speed on the formation of Ti-6AL-4V single-tracks, the effect of the powder depth was also investigated by varying the recess depth of the crucible substrate, similar to experiment\n\nC. Additionally, this experiment was performed to test the applicability of the crucible methodology using a different powder material to stainless steel 316L.\n\n\\section*{Experimental Design}\nTo accomplish the experimental objective, three groups of parameters were formed, each with a specific laser power used (100W, 150W and 200W). For each group, six different scan speeds were to be used, which would be varied by altering the point distance and exposure times. The array of parameter combinations used for this experiment are shown in Table 11 below.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\n\\begin{tabular}{c}\nSample \\\\\nID \\\\\n\\end{tabular} & \\begin{tabular}{c}\nPower \\\\\n$(\\mathrm{W})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nPoint \\\\\nDistance \\\\\n$(\\mu \\mathrm{m})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nExposure \\\\\nTime \\\\\n$(\\mu \\mathrm{s})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nScan \\\\\nSpeed \\\\\n$\\left(\\mathrm{mms}^{-1}\\right)$ \\\\\n\\end{tabular} \\\\\n\\hline\nA1 & 100 & 50 & 100 & 500 \\\\\n\\hline\nA2 & 100 & 60 & 80 & 750 \\\\\n\\hline\nA3 & 100 & 75 & 75 & 1000 \\\\\n\\hline\nA4 & 100 & 120 & 80 & 1500 \\\\\n\\hline\nA5 & 100 & 150 & 75 & 2000 \\\\\n\\hline\nA6 & 100 & 180 & 60 & 3000 \\\\\n\\hline\nB1 & 150 & 50 & 100 & 500 \\\\\n\\hline\nB2 & 150 & 60 & 80 & 750 \\\\\n\\hline\nB3 & 150 & 75 & 75 & 1000 \\\\\n\\hline\nB4 & 150 & 120 & 80 & 1500 \\\\\n\\hline\nB5 & 150 & 150 & 75 & 2000 \\\\\n\\hline\nB6 & 150 & 180 & 60 & 3000 \\\\\n\\hline\nC1 & 200 & 50 & 100 & 500 \\\\\n\\hline\nC2 & 200 & 60 & 80 & 750 \\\\\n\\hline\nC3 & 200 & 75 & 75 & 1000 \\\\\n\\hline\nC4 & 200 & 120 & 80 & 1500 \\\\\n\\hline\nC5 & 200 & 150 & 75 & 2000 \\\\\n\\hline\nC6 & 200 & 180 & 60 & 3000 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 11. Experiment E (Ti-6Al-4V) - Processing parameters used.\n\nFor each parameter combination, single tracks would be built at increasing layer depths as performed in experiment $\\mathrm{C}$. The recess depth of the crucible would increase from $50 \\mu \\mathrm{m}$ to $200 \\mu \\mathrm{m}$ with a step size of $50 \\mu \\mathrm{m}$. For each parameter, a series of 15 single tracks of lengths of $13 \\mathrm{~mm}$ would be built atop each of the four crucibles. The crucibles were built using the\\\\\nprocessing parameters recommended by the manufacturers, which were a laser power of $185 \\mathrm{~W}$, a point distance of $62 \\mu \\mathrm{m}$, a hatch spacing of $157 \\mu \\mathrm{m}$ and an exposure time of $150 \\mu \\mathrm{s}$. After the build was completed, the samples were removed and collected off the base plate. The tracks were investigated using an Alicona Infinite Focus microscope, which could take both a 2D high resolution image and a 3D surface map of the single track structures From the 3D image, the average height of the tracks, the roughness of the tracks and the roughness of the surfaces surrounding the tracks was measured.", "start_char_idx": 115094, "end_char_idx": 118135, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "43f535fc-81c5-4431-9911-43ae08228386": {"__data__": {"id_": "43f535fc-81c5-4431-9911-43ae08228386", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ae1da1b8-2521-493b-907c-16908a79eabc", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8fae35dd2663681331689efe4339d7c92f850a7396b7d9a06b9e4013c0598e05", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fb0748de-5014-4cc7-821c-c7fb65044763", "node_type": "1", "metadata": {}, "hash": "b69ea4c0ea54d2860aca209ae5752f70f2d02b37bbf6500b4b05bc426c927045", "class_name": "RelatedNodeInfo"}}, "text": "For each parameter, a series of 15 single tracks of lengths of $13 \\mathrm{~mm}$ would be built atop each of the four crucibles. The crucibles were built using the\\\\\nprocessing parameters recommended by the manufacturers, which were a laser power of $185 \\mathrm{~W}$, a point distance of $62 \\mu \\mathrm{m}$, a hatch spacing of $157 \\mu \\mathrm{m}$ and an exposure time of $150 \\mu \\mathrm{s}$. After the build was completed, the samples were removed and collected off the base plate. The tracks were investigated using an Alicona Infinite Focus microscope, which could take both a 2D high resolution image and a 3D surface map of the single track structures From the 3D image, the average height of the tracks, the roughness of the tracks and the roughness of the surfaces surrounding the tracks was measured. These measurements were obtained by taking a profile measurement of the track through its centre, in a direction parallel to the build direction. The average height and line build percentage of each track was calculated from the numerical data from obtained from the profile measurement. Crucible samples with successfully built lines were prepared for metallographic examination. The techniques and specific methods used are listed in Appendix 5. Kroll's reagent was used as an etchant. The etched samples were examined under a Keyence VHX 6000 series light microscope and cross-sectional images were obtained. The results from this experiment are presented and discussed in detail in Chapter 5.6\n\n\\section*{Chapter 5 Results}\n\\subsection*{5.1 Optimal Density Parameters}\nThe following section shows the results from Chapter 4.1 The optimal parameters, which give the highest bulk density values, were identified and used as a comparative value to the results found in experiments $A$ to $E$.\n\n\\subsection*{5.1.1 Stainless Steel 316L Powder (Experiments $A$ and B)}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-070}\n\\end{center}\n\nFigure 17. Relative density with laser input energy as measured using gravimetric based methods in Lavery et al. , [104].\n\nThe bulk density values for each density measurement value were plot in a graph against the laser energy density values, as seen in Figure 17. The peak density from this experiment was achieved at the sample labelled B3-1. The combination of parameters used at B3-1 was taken as a reference point for which builds using this batch of stainless steel 316 powder could be optimised, in this case in terms of relative density. These parameters combinations\\\\\nused to create these samples were a laser power of $180 \\mathrm{~W}$, a scan speed of $433 \\mathrm{mms}^{-1}$ and an energy density value of $65 \\mathrm{Jmm}^{-2}$. These parameter settings were compared to the results obtained at similar parameter settings used in experiments A and B.\n\nSamples A1-2, A2-3 and A3-2 were found to have increased porosity as the laser energy density values increased. Decreasing the point distance caused scan speeds to become slower, thereby allowing the laser to deliver more energy into the powder bed per unit of time. This additional energy input caused defects and pores to form, thereby lowering the relative density of the cubes.\n\n\\subsection*{5.1.2 Stainless Steel 316L Powder (Experiments $C$ and D)}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-071}\n\\end{center}\n\nFigure 18. Relative density with input energy measured in DOE experiment for Chapter 5, (SS316L).\n\nThe measured density values were used to plot the average relative density of the cubes against the laser energy density used to fabricate them, as seen in Figure 18. It can be seen that the nominal settings, labelled \"Opt\", did not give the highest relative density for lowest energy density. The optimal parameters for relative density were found at $A 3$, where the laser power was $190 \\mathrm{~W}$ and scan speed of $500 \\mathrm{mms}^{-1}$, with an energy density value of $64 \\mathrm{Jmm}^{-3}$.", "start_char_idx": 117324, "end_char_idx": 121337, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fb0748de-5014-4cc7-821c-c7fb65044763": {"__data__": {"id_": "fb0748de-5014-4cc7-821c-c7fb65044763", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "43f535fc-81c5-4431-9911-43ae08228386", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0c13812aa21c74b79264320419bd38a9626193ef4fd86543d98307414d7ec605", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "309b09f9-9e24-4d43-a425-4eb807b2b5d5", "node_type": "1", "metadata": {}, "hash": "deec029b1b400a33b0e7d7845f58afdc60ff6a489b9aaaaef211dd960ab5af3a", "class_name": "RelatedNodeInfo"}}, "text": "Relative density with input energy measured in DOE experiment for Chapter 5, (SS316L).\n\nThe measured density values were used to plot the average relative density of the cubes against the laser energy density used to fabricate them, as seen in Figure 18. It can be seen that the nominal settings, labelled \"Opt\", did not give the highest relative density for lowest energy density. The optimal parameters for relative density were found at $A 3$, where the laser power was $190 \\mathrm{~W}$ and scan speed of $500 \\mathrm{mms}^{-1}$, with an energy density value of $64 \\mathrm{Jmm}^{-3}$. These values were found to be not at all dissimilar to those obtained for the previous batch, where the optimal energy density value was $65 \\mathrm{Jmm}^{-3}$. This indicated that\\\\\nthere was very little to no changes in the processability of the two batches of material powder.\n\nThe combination of parameters used at A3 were taken as a reference point for which builds could be optimised, at least in the case of relative density. These parameters would be compared to the results obtained at similar parameter settings used in experiments C and D.\n\n\\subsection*{5.1.3 Titanium Ti6Al4V Powder (Experiment E)}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-072}\n\\end{center}\n\nFigure 19. Relative density with input energy measured in DOE experiment for Chapter 6, (Ti-6Al-4V).\n\nThe average densities of each sample were plot as a function of laser energy density, as seen in Figure 19. The optimal combination of parameters which gave the highest relative density (97.3\\%) for the lowest possible energy density $\\left(57 \\mathrm{Jmm}^{-3}\\right)$ was found at sample A9. The sample used a laser power of $185 \\mathrm{~W}$, a scan speed of $413 \\mathrm{mms}^{-1}$, and an energy density value of $57 \\mathrm{Jm}^{-3}$ The nominal parameters, as used for sample A1, was found with an inferior average relative density of $96.2 \\%$ at a higher energy density of $74 \\mathrm{Jmm}^{-3}$. The scan speed for the nominal parameters was slightly higher, at $500 \\mathrm{mms}^{-1}$.\n\nThe combination of parameters used at A9 were taken as a reference point for which builds using the current batch of Ti-6Al-4V powder could be optimised, at least in the case of\\\\\nrelative density. These parameters would be compared to the results obtained at similar parameter settings used in experiment $\\mathrm{E}$.\n\n\\subsection*{5.2 Experiment A-Direct Base Plate Method}\n\\subsection*{5.2.1 Results}\nTable 12 shows the average length, measured in the horizontal direction, and width, measured in the vertical direction, and the average height, measured in both directions, of each stainless steel 316L structure. These results were gathered from the overhead images taken using the Keyence VHX 6000 series light microscope, displayed in Figure 20 to Figure 25. The red arrows in the bottom two topographical images of each figure show the direction in which the above cross-sectional image was taken. If applicable, the gap size between successive melt tracks was recorded In samples 45 and 6 the deqree of melt nool overlap was high enough to eliminate any gap formation.", "start_char_idx": 120748, "end_char_idx": 123932, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "309b09f9-9e24-4d43-a425-4eb807b2b5d5": {"__data__": {"id_": "309b09f9-9e24-4d43-a425-4eb807b2b5d5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fb0748de-5014-4cc7-821c-c7fb65044763", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "bbfe467f283b114213a4678475140507d2acfe9dcceee120b4b8959fe1f566d8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "64b1ac77-cda6-4e4a-b978-c33241a9a78a", "node_type": "1", "metadata": {}, "hash": "b1b1548aa6e7b5a8def9989e74596633bb71c6a949c07cec8195a1a7b030a536", "class_name": "RelatedNodeInfo"}}, "text": "These parameters would be compared to the results obtained at similar parameter settings used in experiment $\\mathrm{E}$.\n\n\\subsection*{5.2 Experiment A-Direct Base Plate Method}\n\\subsection*{5.2.1 Results}\nTable 12 shows the average length, measured in the horizontal direction, and width, measured in the vertical direction, and the average height, measured in both directions, of each stainless steel 316L structure. These results were gathered from the overhead images taken using the Keyence VHX 6000 series light microscope, displayed in Figure 20 to Figure 25. The red arrows in the bottom two topographical images of each figure show the direction in which the above cross-sectional image was taken. If applicable, the gap size between successive melt tracks was recorded In samples 45 and 6 the deqree of melt nool overlap was high enough to eliminate any gap formation.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline\n\\begin{tabular}{c}\nSample \\\\\nID \\\\\n\\end{tabular} & \\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-073}\n & \\begin{tabular}{l}\nLaser \\\\\nPower \\\\\nOutput \\\\\n(W) \\\\\n\\end{tabular} & \\begin{tabular}{c}\nAverage \\\\\nHeight $(\\mu \\mathrm{m})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nAverage \\\\\nLength \\\\\n$(\\mu \\mathrm{m})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nAverage \\\\\nWidth \\\\\n$(\\mu \\mathrm{m})$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nAverage \\\\\nMaximum \\\\\nGap size \\\\\n$(\\mu \\mathrm{m})$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nAverage \\\\\nMinimum \\\\\nGap size \\\\\n$(\\mu \\mathrm{m})$ \\\\\n\\end{tabular} \\\\\n\\hline\n1 & \\multirow{3}{*}{$75 \\mu s$} & 100W & 16.9 & 70.1 & 83.9 & 65.1 & 28.7 \\\\\n\\hline\n3 &  & 150W & 24 & 94.2 & 105.5 & 38.4 & 20.8 \\\\\n\\hline\n5 &  & $200 W$ & 78.15 & 122.6 & 132.5 & n/a & $\\mathrm{n} / \\mathrm{a}$ \\\\\n\\hline\n2 & \\multirow{3}{*}{$150 \\mu \\mathrm{s}$} & 100W & 18.95 & 91.7 & 101.7 & 39.4 & 23 \\\\\n\\hline\n4 &  & 150W & 34.3 & 108.2 & 123.6 & n/a & $\\mathrm{n} / \\mathrm{a}$ \\\\\n\\hline\n6 &  & $200 W$ & 50.65 & $\\mathrm{n} / \\mathrm{a}$ & 133.6 & n/a & $\\mathrm{n} / \\mathrm{a}$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 12. Experiment A (SS316L) - Average Length, Width, Height and Gap Size taken from surface images.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-074(1)}\n\\end{center}\n\nFigure 20. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 1.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-074}\n\\end{center}\n\nFigure 21. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 2.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-075}\n\\end{center}\n\nFigure 22. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 3.", "start_char_idx": 123053, "end_char_idx": 125830, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "64b1ac77-cda6-4e4a-b978-c33241a9a78a": {"__data__": {"id_": "64b1ac77-cda6-4e4a-b978-c33241a9a78a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "309b09f9-9e24-4d43-a425-4eb807b2b5d5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "72cce61beaeb85219cb5b78ceecb678d62a7fc6bf608b452e81f454e9ca5c97c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bc956fe2-7630-4a60-a3c7-b3d7b30930aa", "node_type": "1", "metadata": {}, "hash": "62507e3cc262515241e7b2cd3702159c113f29948006d9a65784ad73f695cd8d", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-074(1)}\n\\end{center}\n\nFigure 20. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 1.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-074}\n\\end{center}\n\nFigure 21. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 2.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-075}\n\\end{center}\n\nFigure 22. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 3.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-075(1)}\n\\end{center}\n\nFigure 23. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 4.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-076}\n\\end{center}\n\nFigure 24. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 5.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-076(1)}\n\\end{center}\n\nFigure 25. Experiment A (SS316L) - Cross-sectional and topographical results, Sample 6.\n\nThe average length, width and height of the tracks formed during the experiment were plot against the laser power and scan speed used to fabricate them, as seen in Figure 26. Track length, width and height would clearly increase with laser power. It should be noted that the track length value at $200 \\mathrm{~W}$ and $150 \\mu$ s could not be included as the distinction between separate tracks could not be found due to overlapping of melt pools. Increasing exposure time would also increase these attributes. Since the range in exposure times was limited to two, fairly low values, this increase was not as pronounced as the changes seen between tracks built at different laser powers.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-077}\n\\end{center}\n\nFigure 26. Experiment A (SS316L) - Changes in the track dimensions and gap sizes.\n\nIn tracks made using low laser power and low exposure time (samples 1 to 3), individual melt beads are easily discernible from one another. A sizeable gap between each successive row of tracks could be observed, as seen in Figure 20, Figure 21 and Figure 22. As laser power was increased, this gap grew smaller until the presence of overlapping tracks prevented gap formation. At high laser power and exposure time (samples 4 to 6), it became\\\\\nincreasingly difficult to isolate individual melt beads, as track overlap had drastically increased, as seen in Figure 23, Figure 24 and Figure 25.\n\n\\subsection*{5.2.2 Discussion}\nA sharp demarcation can be seen between the stainless-steel powder structures. The stainless-steel structure is plainly white and without visible grain boundaries, whilst the substrate is clearly stained and has marked grain boundaries. It is possible that the etchant used was not strong enough to affect the grain boundaries in the stainless-steel structure, as it has a higher resistance to chemical attacks.\n\nThe height and length values would increase with both laser power and exposure times. The largest structure sizes would be found at $200 \\mathrm{~W}$. It was shown that increasing the input energy from the laser, whether it is done by increasing the laser power itself or increasing the amount of time the laser spot spent at each point, would cause the volume of melted powder material to increase. The molten material would solidify after the laser had passed to the next point, where heat would be lost through the mechanisms described in Chapter 3. Increasing the volume of molten material would result in increasing the volume of the solidified tracks.\n\nAt lower exposure times, particularly for samples 1,3 and 5 , made using $75 \\mu \\mathrm{s}$, the resulting structures solidified with limited wetting and spreading on the substrate.", "start_char_idx": 125244, "end_char_idx": 129181, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bc956fe2-7630-4a60-a3c7-b3d7b30930aa": {"__data__": {"id_": "bc956fe2-7630-4a60-a3c7-b3d7b30930aa", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "64b1ac77-cda6-4e4a-b978-c33241a9a78a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4ade404593a49ce9ac29df10d339c12924276fc61f4ce1a8c1bc0ae77280f3d9", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0bb4d2d3-7519-420f-b2ed-380f9d902de7", "node_type": "1", "metadata": {}, "hash": "deec59a3522b23d86438d3e41526c0acfa30da757c56e68421ba7a8d6c48987b", "class_name": "RelatedNodeInfo"}}, "text": "The height and length values would increase with both laser power and exposure times. The largest structure sizes would be found at $200 \\mathrm{~W}$. It was shown that increasing the input energy from the laser, whether it is done by increasing the laser power itself or increasing the amount of time the laser spot spent at each point, would cause the volume of melted powder material to increase. The molten material would solidify after the laser had passed to the next point, where heat would be lost through the mechanisms described in Chapter 3. Increasing the volume of molten material would result in increasing the volume of the solidified tracks.\n\nAt lower exposure times, particularly for samples 1,3 and 5 , made using $75 \\mu \\mathrm{s}$, the resulting structures solidified with limited wetting and spreading on the substrate. This can be seen in figures 22, 24 and 26, where there was little to no penetration into the substrate. Compared to the other structures formed at the higher exposure time of $150 \\mu \\mathrm{s}$, as seen in in figure 23 , 25 and 27 , the former structures are more spherical, and have a steeper angle coming off of the substrate. Structures made in samples 2, 4 and 6, on the other hand, are flattened and are in complete contact with the substrate. Overall, wetting and spreading of the molten powder is seen to increase with energy input.\n\n\\subsection*{5.2.3 Conclusions}\nFrom the results, it can be concluded that there is systematic variation in track morphology when the process parameters are altered, namely that increasing the input energy tends to\\\\\nincrease the size of the resultant structures. With suboptimal processing parameters, features such as gaps can form in between tracks, which could cause porosity to form in parts produced with multiple layers. The experimental method used in this chapter made it difficult to quantify certain measurements, as tracks would overlap over each other, making it difficult to isolate individual melt pools and quantify their dimensions. To address this issue, a new technique was developed as described in the next section, allowing a better isolation of single tracks and their formation.\n\n\\subsection*{5.3 Experiment B - Single-Lines on Recessed Plates Method}\n\\subsection*{5.3.1 Results}\nTopographical images of the single tracks from experiment B were compiled into a process map as a function of scan speed on the horizontal axis, and laser power on the vertical axis, as seen in Figure 27. Each image is comprised of three track formations, made using the same laser power and scan speed process parameters. The regions of the process map without an image signify that track formation was not successful at those corresponding parameters. Using the same axes as Figure 27, a process map was constructed using cross-sectional images obtained using the same parameters, as seen in Figure 28. On both figures, the optimal parameter combination used from the DOE method in chapter 5.1.1 was included as a figure in these process maps as a reference to the parameters used to obtain optimal bulk density for this specific batch of powder material.\n\nAn additional process map was created using measurements of the percentage of the length of continuously laid track observed against the total length of the track specified in the design of the experiment. Essentially, this process map documented the percentage of successfully fabricated track, and was called the line-build percentage. This process map can be seen in Table 13. In this table, the cells are identified in five different colours, used to identify the type of track formation that took place at the specified laser power and scan speed combination.\n\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_91a5199dc912785ed628g-080.jpg?height=1387&width=1939&top_left_y=1037&top_left_x=138}\n\nFigure 27. Experiment B (SS316L) - Topographical process map at 504m layer depth. The red dot show Renishaw recommended operating conditions.\n\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_91a5199dc912785ed628g-081.jpg?height=1511&width=1693&top_left_y=1032&top_left_x=387}\n\nFigure 28.", "start_char_idx": 128340, "end_char_idx": 132481, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0bb4d2d3-7519-420f-b2ed-380f9d902de7": {"__data__": {"id_": "0bb4d2d3-7519-420f-b2ed-380f9d902de7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bc956fe2-7630-4a60-a3c7-b3d7b30930aa", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8b47bec6c825bdf4a5797dfd1d99137435d7bf0415406829abde4294d5ef8153", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "e8533e97-0a0d-4814-bb04-02a94a393173", "node_type": "1", "metadata": {}, "hash": "3f7be322aa388cf90df967f0d2cb7dc9252a62eb333eb00dab4ec3b9f92a1087", "class_name": "RelatedNodeInfo"}}, "text": "In this table, the cells are identified in five different colours, used to identify the type of track formation that took place at the specified laser power and scan speed combination.\n\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_91a5199dc912785ed628g-080.jpg?height=1387&width=1939&top_left_y=1037&top_left_x=138}\n\nFigure 27. Experiment B (SS316L) - Topographical process map at 504m layer depth. The red dot show Renishaw recommended operating conditions.\n\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_91a5199dc912785ed628g-081.jpg?height=1511&width=1693&top_left_y=1032&top_left_x=387}\n\nFigure 28. Experiment B (SS316L) - Cross-sectional process map at $50 \\mu \\mathrm{m}$ I The red dot shows the shows the parameters used at the Renishaw recommended 0\n\n\\subsection*{5.3.2 Discussion}\nFocusing on single track formations allowed for greater clarity in identifying the way in which tracks would form in relation to the energy input. At the high energy input ranges, where laser power was between $200 \\mathrm{~W}$ to $150 \\mathrm{~W}$, and very slow scan speeds, $100 \\mathrm{mms}^{-1}$, tracks formed as continuous, smooth tracks with negligible variation in the pattern of the tracks formed, as observed in Figure 29i. These track-types have been annotated in Table 13 as the blue section.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-082(1)}\n\nFigure 29. Experiment B (SS316L) -The five types of topographical tracks which formed during experiment. From left to right: i) continuous/regular tracks (200W, $\\left.100 \\mathrm{mms}^{-1}\\right)$, ii) continuous/irregular tracks (150W, $\\left.400 \\mathrm{mms}^{-1}\\right)$, iii) discontinuous/irregular tracks (150W, $\\left.400 \\mathrm{mms}^{-1}\\right)$, iv) balling $\\left.\\left(175 \\mathrm{~W}, 700 \\mathrm{mms}^{-1}\\right), v\\right)$ build failure (100W. $1000 \\mathrm{mms}^{-1}$ ).", "start_char_idx": 131868, "end_char_idx": 133753, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "e8533e97-0a0d-4814-bb04-02a94a393173": {"__data__": {"id_": "e8533e97-0a0d-4814-bb04-02a94a393173", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0bb4d2d3-7519-420f-b2ed-380f9d902de7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ac503b7c6a72a7c81801b056022cad8f4417b9a1a71316c84b34bba4d77f6204", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c3b40a1a-b6f3-48f1-b1f5-107dd636c712", "node_type": "1", "metadata": {}, "hash": "2f66b0f89a224918234ab4da6c736a21e3f4aaf3d35dcc1aea1ec6a28be1cc35", "class_name": "RelatedNodeInfo"}}, "text": "Experiment B (SS316L) -The five types of topographical tracks which formed during experiment. From left to right: i) continuous/regular tracks (200W, $\\left.100 \\mathrm{mms}^{-1}\\right)$, ii) continuous/irregular tracks (150W, $\\left.400 \\mathrm{mms}^{-1}\\right)$, iii) discontinuous/irregular tracks (150W, $\\left.400 \\mathrm{mms}^{-1}\\right)$, iv) balling $\\left.\\left(175 \\mathrm{~W}, 700 \\mathrm{mms}^{-1}\\right), v\\right)$ build failure (100W. $1000 \\mathrm{mms}^{-1}$ ).\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n\\multirow{6}{*}{\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-082}\n} & 200 & 100 & 100 & 100 & 97.4 & 97.7 & 82.2 & 73.1 & 58.5 & 55.5 & 54.7 \\\\\n\\hline\n & 175 & 100 & 100 & 98.6 & 91.9 & 91.5 & 77.3 & 57.9 & 45.6 & 39 & 29.8 \\\\\n\\hline\n & 150 & 100 & 100 & 98.5 & 89.7 & 82.1 & 53.3 & 12.8 & 0 & 0 & 0 \\\\\n\\hline\n & 125 & 100 & 98.3 & 95.9 & 79.7 & 58.2 & 45.2 & 0 & 0 & 0 & 0 \\\\\n\\hline\n & 100 & 100 & 97.1 & 73.9 & 35.7 & 16.4 & 0 & 0 & 0 & 0 & 0 \\\\\n\\hline\n & 75 & 100 & 68.9 & 13.7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n\\hline\n &  & 100 & 200 & 300 & 400 & 500 & 600 & 700 & 800 & 900 & 1000 \\\\\n\\hline\n &  &  &  &  &  & 10 & (im) &  &  &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 13. Experiment B (SS316L) - Process Map with line build percentages,\n\ndivided into sections, i) blue - continuous/regular tracks, ii) green -\n\ncontinuous/irregular tracks, iii) yellow - discontinuous/irregular tracks, iv) orange balling, v) red - build failure.\n\n\\section*{Continuous Regular Tracks and Keyhole Mode Melting}\nThe tracks would build with a consistent width, and had a rounded-front pattern similar to the tracks formed at the high power and high exposure time samples in Experiment A, namely\\\\\nsamples 4 (Figure 23) and 6 (Figure 25). This seems to suggest that the high energy input suitably melts the powder layer underneath the laser area and the melts wets to the substrate. Additionally, the melt also spreads out and flattens, creating the smooth surfaces observed in Figure 29i. The line-build percentage for each repetition of these build conditions was $100 \\%$, indicating that there was complete melting of the material that came in contact with the lasers' path.\n\nThese would be regarded as ideal formations for laser-additive manufacturing from the topographical results. However, the cross-sectional results reveal that these tracks have Vshaped penetrations into the substrate, with pores that form near the bottom of such penetrations. Examples of both phenomena can be seen in the same cross-section on the right-hand side of Figure 30. It is assumed that vaporisation of the melt would occur due to the excessively high temperatures, and that keyhole mode melting had occurred in these tracks, as discussed in chapter 3.3.4 Parts made using these parameters could exhibit porosity, although remelting of previous layers may eliminate the effect of porosity caused by keyholing.", "start_char_idx": 133277, "end_char_idx": 136235, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c3b40a1a-b6f3-48f1-b1f5-107dd636c712": {"__data__": {"id_": "c3b40a1a-b6f3-48f1-b1f5-107dd636c712", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e8533e97-0a0d-4814-bb04-02a94a393173", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4c84ee18490b90a60583f69534276b08126425db4d3785f3ba97f7f3e505be5c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "879e1ebf-5d8e-4b71-b51c-7195975cb374", "node_type": "1", "metadata": {}, "hash": "c6780b088f8713c689dfba27a9115084c91511f3e1978a9d845dff7c22bb0f5d", "class_name": "RelatedNodeInfo"}}, "text": "The line-build percentage for each repetition of these build conditions was $100 \\%$, indicating that there was complete melting of the material that came in contact with the lasers' path.\n\nThese would be regarded as ideal formations for laser-additive manufacturing from the topographical results. However, the cross-sectional results reveal that these tracks have Vshaped penetrations into the substrate, with pores that form near the bottom of such penetrations. Examples of both phenomena can be seen in the same cross-section on the right-hand side of Figure 30. It is assumed that vaporisation of the melt would occur due to the excessively high temperatures, and that keyhole mode melting had occurred in these tracks, as discussed in chapter 3.3.4 Parts made using these parameters could exhibit porosity, although remelting of previous layers may eliminate the effect of porosity caused by keyholing. Spreading of the melt due to good wetting conditions is further evidenced here, as these tracks were found to have the widest cross-sections.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-083}\n\nFigure 30. Experiment B (SS316L) - The three types of cross-sectional tracks formed during experiment. Left) 125W, $600 \\mathrm{mms}^{-1}$, Middle) 200W, $300 \\mathrm{mms}^{-1}$, Right) $150 \\mathrm{~W}, 500 \\mathrm{mms}^{-1}$\n\n\\section*{Continuous Irregular Tracks}\nTracks would remain continuous under conditions of high laser power, between 200W to $75 \\mathrm{~W}$, and relatively low scan speeds, between $500 \\mathrm{mms}^{-1}$ and $100 \\mathrm{mms}^{-1}$, with the line build\\\\\npercentages ranging between $100 \\%$ and $97 \\%$. However, track formation in this range of the process map would not exhibit the homogenous, smooth patterns seen in the previous track formations, as observed in Figure 29ii. Kinks and slight distortions in the track were observed, unlike the smooth and consistent tracks seen in Figure 29i.\n\nThe occurrence of these kinds of distortions were generally observed to increase with scan speed, as seen in Figure 31. These distortions could be attributed to the melt not having enough time to wet to the substrate due to fast scan speeds, or the melt not achieving a sufficient temperature to wet to the substrate, or a combination of both factors.\n\nThe cross-sectional results show that tracks made at these conditions have a large degree of penetration into the substrate, often with half or more of the melt bead underneath the substrate. The wetting angle is small, though not as minute as those observed for continuous, regular tracks, which were almost completely flat. This suggests that the melt achieved a considerable degree of wetting and spreading over the substrate. Since the tracks retained a $100 \\%$ to near-100\\% line-build percentage, these tracks are referred to as continuous and irregular tracks.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-084}\n\\end{center}\n\nFigure 31. Experiment B (SS316L) - Variation of the melt pool stability with scan speed.\n\nThese conditions are considered the ideal types of track formations conducive to creating ideal, near-fully dense parts. The results from the DOE method correlate with this statement, as is evidenced in Figure 28, where tracks made with similar processing parameters to the DOE method, indicated by the red dot, were found to produce ellipsoidal, bead-shaped cross-sections. They have been annotated in Table 13 as the green section.\n\n\\section*{Balling}\nAt higher scan speeds, tracks would begin to fragment into a mixture of cylindrical bead structures and large spherical droplets or bulges, as observed in Figure 29iii. The line-build percentage would range between $95.9 \\%$ and $73.1 \\%$, leaving the track full of gaps. The wettability of the melt pool would decrease, resulting in the formation of bulges along the track, as can be seen in the $400 \\mathrm{mms}^{-1}$ track in Figure 31.\n\nThe wettability of the melt would decrease with less power or increased scan speed. This formation is referred as being discontinuous and irregular. The range of parameters would form as a narrow band in the process map, and have been annotated in Table 13 as the yellow section.", "start_char_idx": 135326, "end_char_idx": 139588, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "879e1ebf-5d8e-4b71-b51c-7195975cb374": {"__data__": {"id_": "879e1ebf-5d8e-4b71-b51c-7195975cb374", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c3b40a1a-b6f3-48f1-b1f5-107dd636c712", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "81219e239d4aeb9c3c8d1abcb573b18d07f58b4c905bbd7273120d3036d2c75a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c306a05e-6ef0-417f-9e54-0bd540615fee", "node_type": "1", "metadata": {}, "hash": "a901865d4fca969a7622fadf0d7d26da5df8bcf9a46186bc612b22a6904981a6", "class_name": "RelatedNodeInfo"}}, "text": "They have been annotated in Table 13 as the green section.\n\n\\section*{Balling}\nAt higher scan speeds, tracks would begin to fragment into a mixture of cylindrical bead structures and large spherical droplets or bulges, as observed in Figure 29iii. The line-build percentage would range between $95.9 \\%$ and $73.1 \\%$, leaving the track full of gaps. The wettability of the melt pool would decrease, resulting in the formation of bulges along the track, as can be seen in the $400 \\mathrm{mms}^{-1}$ track in Figure 31.\n\nThe wettability of the melt would decrease with less power or increased scan speed. This formation is referred as being discontinuous and irregular. The range of parameters would form as a narrow band in the process map, and have been annotated in Table 13 as the yellow section.\n\nAt even higher scan speeds, the tracks would only form as a series of solidified droplets, with very low line-build percentages, ranging between $68.9 \\%$ and $13.7 \\%$. These track formations can be seen in Figure 29iv, and have been annotated in Table 13 in the orange section.\n\nThe balling phenomenon was repeatedly observed both in the topographical and crosssectional results. With this parameter combinations, powder was still able to melt, although the volume of the melt would be comparatively low when compared to tracks with higher input energy. The lower volume of liquid that forms has reduced contact area with the solid substrate, which leads to poor wetting, flow and spreading conditions. Additionally, since the energy input is decreased, the temperature of the melt is also comparatively low. Surface tension of most liquids generally increases with decreasing temperature. This is due to cohesive forces of liquid metals increasing with reduced molecular thermal activity, leading\\\\\nto worsened wettability. [106]. The viscosity of the melt becomes considerably high, severely limiting liquid flow, and this in turn decreases the rheological performance of the melt with solid surfaces [107]. Surface tension at such conditions becomes the dominant force controlling the shape of the melt, and the tracks solidify as a series of spheroidal, broken-up structures. This is further evidenced in the cross-sectional results, where a spherical melt bead barely penetrates into the previous substrate layer, resulting in a large contact angle. At the highest scan speeds and lowest laser power range, tracks would either fail to build at all or very sparingly. This range of processing parameters has been annotated in Table 13 in the red section. At these parameters, only a small volume of molten material would form, with limited contact to the substrate.\n\n\\section*{Verification of Results}\nAs part of the verification for the method used in this experiment, the results from the width and depth measurements of the tracks formed were compared to the results from a similar experiment carried out by Bertoli et al, [31]. In the Bertoli et al. experiment, single track formations were fabricated using a custom SLM system with a 1070nm Yb-fiber laser. These tracks were made using stainless steel $316 \\mathrm{~L}$ powder, and the laser power and scan speed used to create these tracks were varied to investigate their effect on the formation of the melt pool. The single tracks were constructed Onto a stainless steel $316 \\mathrm{~L}$ substrate.\n\nThe average track width and track depth were plot against laser power and scan speed. The track width plots can be seen in Figure 32 and Figure 33, whilst the plots for track depth can be seen in Figure 34 and Figure 35.\n\nA linear or exponential line of best fit was drawn using these results to investigate the relationship between scan speed and the width or depth of the track. The results from the Bertoli el al. experiment were taken from tracks constructed using laser power settings of $100 \\mathrm{~W}$ and $200 \\mathrm{~W}$, with scan speed ranging between $600 \\mathrm{mms}^{-1}$ and $100 \\mathrm{mms}^{-1}$. These results were marked on each plot using a dark grey circle and also had a line of best fit drawn, distinguished from the other trendlines as a dashed, grey line.\n\nIt was generally observed that track width and depth would increase as scan speed decreased at all laser power settings. This observation was also true for the Bertoli et al. results. Track width and depth would also increase with laser power, obtaining large width and depth values for the same scan speed at higher power settings.", "start_char_idx": 138788, "end_char_idx": 143274, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c306a05e-6ef0-417f-9e54-0bd540615fee": {"__data__": {"id_": "c306a05e-6ef0-417f-9e54-0bd540615fee", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "879e1ebf-5d8e-4b71-b51c-7195975cb374", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ad9b096d44a80a0112b87c0897f2e294a194f2ea0dafe266efcefc60cf03c651", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d11d5541-ac08-43c3-b9f6-b071d15462e9", "node_type": "1", "metadata": {}, "hash": "a53ce8a08daad03f450d6f7ddca8d7f1e566e4cf08592687a03d2e414853a969", "class_name": "RelatedNodeInfo"}}, "text": "A linear or exponential line of best fit was drawn using these results to investigate the relationship between scan speed and the width or depth of the track. The results from the Bertoli el al. experiment were taken from tracks constructed using laser power settings of $100 \\mathrm{~W}$ and $200 \\mathrm{~W}$, with scan speed ranging between $600 \\mathrm{mms}^{-1}$ and $100 \\mathrm{mms}^{-1}$. These results were marked on each plot using a dark grey circle and also had a line of best fit drawn, distinguished from the other trendlines as a dashed, grey line.\n\nIt was generally observed that track width and depth would increase as scan speed decreased at all laser power settings. This observation was also true for the Bertoli et al. results. Track width and depth would also increase with laser power, obtaining large width and depth values for the same scan speed at higher power settings.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-087}\n\\end{center}\n\nFigure 32. Experiment B (SS316L) - Track width at the 75-125W range compared to results from Bertoli et al, [31].\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-087(1)}\n\\end{center}\n\nFigure 33. Experiment B (SS316L) - Track width at the 150-200W range compared to results from Bertoli et al, [31].\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-088}\n\\end{center}\n\nFigure 34. Experiment B (SS316L) - Track depth at the 75-125W range compared to results from Bertoli et al, [31].\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-088(1)}\n\\end{center}\n\nFigure 35. Experiment B (SS316L) - Track depth at the 150-200W range compared to results from Bertoli et al, [31].\n\nAt $100 \\mathrm{~W}$ and $200 \\mathrm{~W}$, the width values from the Bertoli et al. experiment were comparable to the results obtained in experiment $B$, as seen in the middle section of Figure 32 and the right most section in Figure 33. At 100W, the depth measurements obtained from Bertoli et al.\\\\\nwere considerably larger than those obtained for Experiment B, as seen in the middle section of Figure 34. At 200W, the depth results were slightly larger but were more comparable to the depths observed in Experiment $B$, as seen in the right most section of Figure 35.\n\nThe depth values achieved in this experiment were also compared to those generated by a deep penetration melting empirical model, developed by Gladush and Smurov, [108], used for predicting keyhole formation during laser welding. This model was later referenced and slightly modified by King et al, [26], to be used to predict keyhole formation during SLM. The equation included the material property of absorptivity as a modification which more accurately represents the amount of powder absorbed by the powder material. The model is based on a relatively simplistic analytical solution (the Rosenthal welding solution) can give a relationship between depth of penetration to the laser power and scanning speed:\n\n\n\\begin{equation*}\nd=\\frac{A P}{2 \\pi k T_{b}} \\ln \\left(\\frac{\\sigma+\\frac{D}{v}}{\\sigma}\\right) \\tag{9}\n\\end{equation*}\n\n\nWhere $d$ was depth (m), $A$ was absorptivity (dimensionless), $P$ was laser power (W), $k$ was thermal conductivity $\\left(\\mathrm{Wm}^{-1} \\mathrm{~K}^{-1}\\right), T_{B}$ was the boiling point of the material $(\\mathrm{K}), \\sigma$ was the spot size of the laser beam and $v$ was the scanning speed of the laser $\\left(\\mathrm{ms}^{-1}\\right)$.\n\nThe material properties of stainless steel 316L were taken from Gladush and Smurov, [108], and are listed below in Table 14.", "start_char_idx": 142377, "end_char_idx": 146051, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d11d5541-ac08-43c3-b9f6-b071d15462e9": {"__data__": {"id_": "d11d5541-ac08-43c3-b9f6-b071d15462e9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c306a05e-6ef0-417f-9e54-0bd540615fee", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "07a783ccbb253078a5a5fdd8f607639592130538e8fc76ed8717017937ee4f1b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "eb1e5a7f-5560-47ed-ae87-bc7f9ffe47b7", "node_type": "1", "metadata": {}, "hash": "fc94cf907f0acfb94c8781ad197b3f5c9d70627fbd84ee4e36edcf552a1f50ba", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{equation*}\nd=\\frac{A P}{2 \\pi k T_{b}} \\ln \\left(\\frac{\\sigma+\\frac{D}{v}}{\\sigma}\\right) \\tag{9}\n\\end{equation*}\n\n\nWhere $d$ was depth (m), $A$ was absorptivity (dimensionless), $P$ was laser power (W), $k$ was thermal conductivity $\\left(\\mathrm{Wm}^{-1} \\mathrm{~K}^{-1}\\right), T_{B}$ was the boiling point of the material $(\\mathrm{K}), \\sigma$ was the spot size of the laser beam and $v$ was the scanning speed of the laser $\\left(\\mathrm{ms}^{-1}\\right)$.\n\nThe material properties of stainless steel 316L were taken from Gladush and Smurov, [108], and are listed below in Table 14.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline\nSymbol & Property & Value & Units \\\\\n\\hline\n$\\rho$ & Density & 7980 & $\\mathrm{kgm}^{-3}$ \\\\\n\\hline\n$h_{s}$ & Enthalpy at melting & 1200000 & $\\mathrm{Jkg}^{-1}$ \\\\\n\\hline\n$A$ & Absorptivity & 0.4 &  \\\\\n\\hline\n$D$ & Diffusivity & 0.000006 & $\\mathrm{~m}^{2} \\mathrm{~s}^{-1}$ \\\\\n\\hline\n$T_{m}$ & Temperature at melt & 1650 & ${ }^{\\circ} \\mathrm{K}$ \\\\\n\\hline\n$C$ & Specific heat capacity & 700 & $\\mathrm{Jkg}^{-1} \\mathrm{~K}^{-1}$ \\\\\n\\hline\n$K$ & Thermal conductivity & 31 & $\\mathrm{WmK}^{2}$ \\\\\n\\hline\n$P$ & Power & $100-400$ & $\\mathrm{~W}$ \\\\\n\\hline\n$u$ & Speed & $50-4000$ & $\\mathrm{~ms}^{-1}$ \\\\\n\\hline\n$\\sigma$ & Laser spot size & 0.000035 & $\\mathrm{M}$ \\\\\n\\hline\n$T_{b}$ & Temperature at boil & 3500 & ${ }^{\\circ} \\mathrm{K}$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 14. Values used to calculate values for penetration depth equation from Gladush and Smurov , [108].\n\nThe values of the measured experimental and predicted melt pool depths were compared in Figure 36 and Figure 37 below. A fairly good correlation can be seen between the predicted and measured depths, except at the higher laser powers of $200 \\mathrm{~W}$ and $150 \\mathrm{~W}$, as seen in the two right-most plots in Figure 37. At these power settings, the data obtained from the experiments follows the equation data quite well for the scan speeds between $600 \\mathrm{mms}^{-1}$ and $300 \\mathrm{mms}^{-1}$. At the slower speeds of $200 \\mathrm{mms}^{-1}$ and $100 \\mathrm{mms}^{-1}$, the measured track depth increased drastically for both these power settings. This was due to the very deep keyhole formations were observed in most of the samples, due to the vaporisation effect discussed in the previous section.\n\nIt should be noted that since a mild carbon steel substrate was used, any degree of penetration into the substrate would cause the stainless steel $316 \\mathrm{~L}$ powder melt to combine with the mild steel. As keyholing would cause the melt to penetrate further into the substrate, the material properties of the melt would change drastically, and would no longer resemble the input variables used in the empirical equation. However, the trends displayed by the measured and the analytical solution are in relatively good agreement.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-091}\n\\end{center}\n\nFigure 36. Experiment B (SS316L) - Comparison of measured and predicted melt pool depths at the 75-125W range according to equation from Gladush and Smurov, [108].", "start_char_idx": 145456, "end_char_idx": 148611, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "eb1e5a7f-5560-47ed-ae87-bc7f9ffe47b7": {"__data__": {"id_": "eb1e5a7f-5560-47ed-ae87-bc7f9ffe47b7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d11d5541-ac08-43c3-b9f6-b071d15462e9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4e505bb46b718c852479ee8aace286ca429a3ae3d5f9737294f9436b8e1121db", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "22216350-7264-49b4-8dcf-d961b333508b", "node_type": "1", "metadata": {}, "hash": "61dd801ed097ae24bd4f886d22439f6ff4e2c494465d0300a1cbccb156057bbc", "class_name": "RelatedNodeInfo"}}, "text": "It should be noted that since a mild carbon steel substrate was used, any degree of penetration into the substrate would cause the stainless steel $316 \\mathrm{~L}$ powder melt to combine with the mild steel. As keyholing would cause the melt to penetrate further into the substrate, the material properties of the melt would change drastically, and would no longer resemble the input variables used in the empirical equation. However, the trends displayed by the measured and the analytical solution are in relatively good agreement.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-091}\n\\end{center}\n\nFigure 36. Experiment B (SS316L) - Comparison of measured and predicted melt pool depths at the 75-125W range according to equation from Gladush and Smurov, [108].\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-091(1)}\n\\end{center}\n\nFigure 37. Experiment B (SS316L) - Comparison of measured and predicted track depths at the 150-200W range according to equation from Gladush and Smurov, [108].\n\nThe line build percentage values and depth-to-width ratios were used to build two contour maps, as seen in Figure 39 and Figure 40, respectively. The depth-to-width ratio, also known as the aspect ratio, is commonly used to distinguish between conduction mode and keyhole mode melting during laser interaction with metals, [109], where keyhole mode melting is expected to be observed at high values. The exact value for the depth-to-width ratio transition point can vary according to the material and equipment used. A generic assumption used for welding and melting of metals is that any track formed with a depth-toweld ratio less than 0.5 has undergone conduction mode melting, [110]. A marker was used in both these contour maps to indicate the laser power and scan speed used to create the optimal density from the DOE performed at the beginning of the chapter.\n\nIn Figure 39, optimal line build percentages are seen at the left-most portion of the contour map, where the line-build percentage for the tracks was 100\\%. At high laser power settings, ranging between $150 \\mathrm{~W}$ and $200 \\mathrm{~W}$, scan speed can range between $100 \\mathrm{mms}^{-1}$ and $300 \\mathrm{mms}^{-1}$ to obtain $100 \\%$ on line build percentage values. This range is limited to the $100 \\mathrm{mms}^{-1} \\mathrm{scan}$ speed at lower power settings of $125 \\mathrm{~W}$ and $100 \\mathrm{~W}$. The parameters used for the optimal DOE fell between a $95 \\%$ and $90 \\%$ in the same contour plot. Tracks built in this region were continuous but distortions, gaps and bulges were observed to form throughout the track, which could be attributed to incomplete wetting of the track, as seen below in Figure 38. In Figure 40, the depth to width ratios at the left most corner of the contour map are exceptionally high, in the regions where keyhole formation was commonly observed. The parameters used for the optimal DOE fell into a region where the depth-to-width ratio indicated that conduction mode melting would take place.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-093(1)}\n\nFigure 38. Experiment B (SS316L) - Topographical images of tracks built using parameters similar to the DOE optimal parameters $\\left(180 \\mathrm{~W}, 433 \\mathrm{mms}^{-1}\\right)$. left) $200 \\mathrm{~W}, 400 \\mathrm{mms}^{-1}$, right) $175 \\mathrm{~W}, 500 \\mathrm{mms}^{-1}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-093}\n\\end{center}\n\nFigure 39. Experiment B (SS316L) - Contours of build ratios of single tracks.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-094}\n\\end{center}\n\nFigure 40. Experiment B (SS316L) - Contours of depth to width ratio of single tracks.", "start_char_idx": 147806, "end_char_idx": 151645, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "22216350-7264-49b4-8dcf-d961b333508b": {"__data__": {"id_": "22216350-7264-49b4-8dcf-d961b333508b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "eb1e5a7f-5560-47ed-ae87-bc7f9ffe47b7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9a9948e58e1420033b803b17cd681b7834ca14596c8ee607a1e1a7ef8f4ab5c9", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "664abf92-ca43-4a5e-a2e4-68b744d84e74", "node_type": "1", "metadata": {}, "hash": "6cdeedb794758ac50dc1f91ecd3800c3581e19834487e1e7d3f0cfaf0e89dec6", "class_name": "RelatedNodeInfo"}}, "text": "left) $200 \\mathrm{~W}, 400 \\mathrm{mms}^{-1}$, right) $175 \\mathrm{~W}, 500 \\mathrm{mms}^{-1}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-093}\n\\end{center}\n\nFigure 39. Experiment B (SS316L) - Contours of build ratios of single tracks.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-094}\n\\end{center}\n\nFigure 40. Experiment B (SS316L) - Contours of depth to width ratio of single tracks.\n\n\\subsection*{5.3.3 Conclusions}\nAs similarly observed in Experiment A, a systematic variation in track morphology was observed when the laser power and scan speed process parameters were altered. Tracks built using exceptionally high scanning speeds or low laser power resulted in fragmentation and balling due to insufficient melting or wetting to the previous layer. High laser power and low scanning speed resulted in vaporisation of the material, causing keyhole formation. This can cause porosity to form below the surface of the track. Although keyholing was observed at these regions, it should be noted that the depth-to-width ratios at these regions were slightly above 1, indicating that the level of keyholing is relatively low.\n\nThe results obtained from Experiment B compared well to those from Bertoli et al, [31], as well as following the trends given by empirical/analytical solutions. Similarly, they also compliment the DOE optimal parameters, in that keyholing was avoided at the laser power and scan speed range where the DOE parameters lie. Track fragmentation and balling were also avoided in this range, factors which are detrimental to part density.\n\nFrom the results in this experiment, within the range of the processing parameters used, the optimal combination of laser power and scan speed would have to be $200 \\mathrm{~W}$ and $300 \\mathrm{mms}^{-1}$\\\\\nrespectively. Although the track produced at these settings had irregularities, keyhole mode melting was avoided using these settings, which would reduce the chance for porosities to form. At faster speeds, track instability would increase, whilst at lower power, line build percentage would decrease.\n\n\\subsection*{5.4 Experiment C - Verification of Single-Track Crucible Methodology}\n\\subsection*{5.4.1 Results}\nThe topographical images taken of the melt tracks for Experiment $C$ were compiled into a four process maps, one for each layer thickness used $(50 \\mu \\mathrm{m}, 100 \\mu \\mathrm{m}, 150 \\mu \\mathrm{m}$ and $200 \\mu \\mathrm{m})$, and can be seen in Figure 41, Figure 43, Figure 45 and Figure 47. Since the scan speeds used for each sample varied so greatly, the process maps were plotted as a function of laser power in the vertical axis, and surface energy density in the horizontal axis. It should be noted that the scan speed used for the tracks increases from left to right in the process maps. Each image comprises of four lines which are a repetition of the same power and scan speed. A red dot was included in Figure 41, referencing the optimal processing parameters used for obtaining bulk density in chapter 5.1.2 Cross-sections of the melt tracks are shown in Figure 42, Figure 44, Figure 46 and Figure 48, and are presented in an identical manner to the topographical results. The line build percentages for each set of parameters can be found in Table 12.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-097}\n\\end{center}\n\nIncreasing Scan Speed $\\left(\\mathrm{mm} \\mathrm{s}^{-1}\\right)$\n\nFigure 41. Experiment C (SS316L) - Topographical process map at 50 $\\mathrm{mm} \\mathrm{la}$\n\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_91a5199dc912785ed628g-098.jpg?height=1368&width=1988&top_left_y=944&top_left_x=91}\n\nFigure 42.", "start_char_idx": 151171, "end_char_idx": 154925, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "664abf92-ca43-4a5e-a2e4-68b744d84e74": {"__data__": {"id_": "664abf92-ca43-4a5e-a2e4-68b744d84e74", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "22216350-7264-49b4-8dcf-d961b333508b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "dff045faaad7a6ecd37cce9a538e9f8a45a8bfe79b14ccf3f6dc4402f51476be", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "31cb2e40-f851-458e-8bd1-96f1aeef6a13", "node_type": "1", "metadata": {}, "hash": "a4e36c4b0886fda2ffb7126803669f1082d1f6fd1562cb609970d089ae4dd0c2", "class_name": "RelatedNodeInfo"}}, "text": "The line build percentages for each set of parameters can be found in Table 12.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-097}\n\\end{center}\n\nIncreasing Scan Speed $\\left(\\mathrm{mm} \\mathrm{s}^{-1}\\right)$\n\nFigure 41. Experiment C (SS316L) - Topographical process map at 50 $\\mathrm{mm} \\mathrm{la}$\n\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_91a5199dc912785ed628g-098.jpg?height=1368&width=1988&top_left_y=944&top_left_x=91}\n\nFigure 42. Experiment C (SS316L) - Cross-sectional process map at $50 \\mu \\mathrm{m}$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-099}\n\\end{center}\n\nIncreasing Scan Speed $\\left(\\mathrm{mm} \\mathrm{s}^{-1}\\right)$\n\nFigure 43. Experiment C (SS316L) - Topographical process map at $100 \\mu \\mathrm{m}$\n\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_91a5199dc912785ed628g-100.jpg?height=1442&width=1988&top_left_y=952&top_left_x=91}\n\nFigure 44. Experiment C (SS316L) - Cross-sectional process map at $100 \\mu \\mathrm{m}$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-101}\n\\end{center}\n\nIncreasing Scan Speed $\\left(\\mathrm{mm} \\mathrm{s}^{-1}\\right)$\n\nFigure 45. Experiment C (SS316L) - Topographical process map at $150 \\mu \\mathrm{m}$\n\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_91a5199dc912785ed628g-102.jpg?height=1477&width=1942&top_left_y=949&top_left_x=154}\n\nFigure 46. Experiment C (SS316L) - Cross-sectional process map at $150 \\mu \\mathrm{m}$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-103}\n\\end{center}\n\nIncreasing Scan Speed $\\left(\\mathrm{mm} \\mathrm{s}^{-1}\\right)$\n\nFigure 47. Experiment C (SS316L) - Topographical process map at $200 \\mu \\mathrm{m}$\n\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_91a5199dc912785ed628g-104.jpg?height=1445&width=1990&top_left_y=948&top_left_x=90}\n\nFigure 48. Experiment C (SS316L) - Cross-sectional process map at $200 \\mu \\mathrm{m}$\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\n\\hline\n & \\multicolumn{8}{|c|}{$50 \\mu \\mathrm{m}$} \\\\\n\\hline\n\\multirow{4}{*}{\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-105(1)}\n} & $200 W$ & 100 & 100 & 100 & 93.6 & 82.5 & 59.2 & 31.8 \\\\\n\\hline\n & $160 \\mathrm{~W}$ & 100 & 100 & 100 & 100 & 87.8 & 74.9 & 20 \\\\\n\\hline\n & $130 \\mathrm{~W}$ & 100 & 100 & 100 & 100 & 99 & 89 & 34 \\\\\n\\hline\n & $100 \\mathrm{~W}$ & 100 & 99.1 & 96.2 & 96.9 & 92.5 & 67.6 & 51.", "start_char_idx": 154433, "end_char_idx": 156935, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "31cb2e40-f851-458e-8bd1-96f1aeef6a13": {"__data__": {"id_": "31cb2e40-f851-458e-8bd1-96f1aeef6a13", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "664abf92-ca43-4a5e-a2e4-68b744d84e74", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "bfcd83244d8b29e213745499973b9e78bc146983dc32ae7afebd8189a68a3ee0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0d1e450a-d842-4174-bd2c-32511f8037ae", "node_type": "1", "metadata": {}, "hash": "e61bfb365ec9bdee09648b4e578eb43cb57ae43e0ef94bd1232054f5b62ae41d", "class_name": "RelatedNodeInfo"}}, "text": "6 & 82.5 & 59.2 & 31.8 \\\\\n\\hline\n & $160 \\mathrm{~W}$ & 100 & 100 & 100 & 100 & 87.8 & 74.9 & 20 \\\\\n\\hline\n & $130 \\mathrm{~W}$ & 100 & 100 & 100 & 100 & 99 & 89 & 34 \\\\\n\\hline\n & $100 \\mathrm{~W}$ & 100 & 99.1 & 96.2 & 96.9 & 92.5 & 67.6 & 51.9 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\n\\hline\n & \\multicolumn{8}{|c|}{$100 \\mu \\mathrm{m}$} \\\\\n\\hline\n\\multirow{4}{*}{\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-105(3)}\n} & $200 W$ & 100 & 100 & 99 & 70.1 & 79.9 & 47.3 & 12.8 \\\\\n\\hline\n & $160 \\mathrm{~W}$ & 100 & 100 & 100 & 98 & 66.6 & 48.3 & 0 \\\\\n\\hline\n & 130W & 100 & 100 & 100 & 95 & 68.6 & 67 & 0 \\\\\n\\hline\n & $100 \\mathrm{~W}$ & 100 & 98.1 & 94.7 & 94 & 72.9 & 50.3 & 15.5 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\n\\hline\n & \\multicolumn{8}{|c|}{$150 \\mu \\mathrm{m}$} \\\\\n\\hline\n\\multirow{4}{*}{\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-105(2)}\n} & $200 \\mathrm{~W}$ & 100 & 100 & 93.2 & 68.4 & 55.9 & 15.4 & 0 \\\\\n\\hline\n & $160 \\mathrm{~W}$ & 100 & 100 & 100 & 89.2 & 58.8 & 23.2 & 0 \\\\\n\\hline\n & $130 \\mathrm{~W}$ & 100 & 100 & 100 & 82.8 & 59.4 & 50.1 & 0 \\\\\n\\hline\n & $100 \\mathrm{~W}$ & 98 & 98.5 & 87.6 & 89.3 & 69.3 & 41.7 & 0 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\n\\hline\n & \\multicolumn{8}{|c|}{$200 \\mu \\mathrm{m}$} \\\\\n\\hline\n\\multirow{4}{*}{\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-105}\n} & $200 W$ & 100 & 89.7 & 92 & 61.2 & 42.9 & 0 & 0 \\\\\n\\hline\n & $160 \\mathrm{~W}$ & 100 & 100 & 97 & 76.3 & 42.1 & 2.4 & 0 \\\\\n\\hline\n & $130 \\mathrm{~W}$ & 100 & 100 & 96 & 72.6 & 51.1 & 23.2 & 0 \\\\\n\\hline\n & $100 \\mathrm{~W}$ & 98 & 98.4 & 87 & 65.2 & 55.9 & 17.", "start_char_idx": 156691, "end_char_idx": 158497, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0d1e450a-d842-4174-bd2c-32511f8037ae": {"__data__": {"id_": "0d1e450a-d842-4174-bd2c-32511f8037ae", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "31cb2e40-f851-458e-8bd1-96f1aeef6a13", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "558f59e242558ba8d3e101ed45b2215634b13d1a1b8d4c857ce10dc403058b01", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "900efd78-707b-41f0-9dd7-aabc289c6fd1", "node_type": "1", "metadata": {}, "hash": "d4ad9a52190988c9e79706b415fd10bb2c444c522d1394d5403c5b35e235fb0e", "class_name": "RelatedNodeInfo"}}, "text": "7 & 92 & 61.2 & 42.9 & 0 & 0 \\\\\n\\hline\n & $160 \\mathrm{~W}$ & 100 & 100 & 97 & 76.3 & 42.1 & 2.4 & 0 \\\\\n\\hline\n & $130 \\mathrm{~W}$ & 100 & 100 & 96 & 72.6 & 51.1 & 23.2 & 0 \\\\\n\\hline\n & $100 \\mathrm{~W}$ & 98 & 98.4 & 87 & 65.2 & 55.9 & 17.8 & 0 \\\\\n\\hline\n &  & 80 & 40 & 30 & 20 & 12 & 8 & 4 \\\\\n\\hline\n &  & \\multicolumn{7}{|c|}{Surface Energy Density $\\left(\\mathrm{Jmm}^{-2}\\right)$} \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 15. Experiment C (SS316L) - Process maps with line build percentages for each layer depth, given in bold over each table.\n\n\\subsection*{5.4.2 Discussion}\nUsing the DOE parameters mentioned in Chapter 5.1.2 at a layer depth of $50 \\mu \\mathrm{m}$ resulted in low line build percentages, between $82.5 \\%$ and $59.2 \\%$. Line fragmentation and balling was prominent, which is usually associated with causing detrimental properties within parts.\n\nTracks formed with similar processing parameters in Experiment B formed irregularly, but as continuous, unfragmented tracks with a line build percentage above $90 \\%$. This difference could be due to the difference in substrates used, and will be further discussed in detail in the results and discussion for Experiment E.\n\nFor each layer depth, three distinct types of track formations were identified. Their typical cross-sectional appearance can be seen in Figure 49.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-106(1)}\n\nFigure 49. Experiment C (SS316L) - The three types of tracks formed.\n\nLeft) Balling at $130 \\mathrm{~W}, 4 \\mathrm{Jmm}^{-2}, 844 \\mathrm{mms}^{-1}$ Middle) Rounded top at $160 \\mathrm{~W}, 20 \\mathrm{Jmm}^{-2}$, $169 \\mathrm{mms}^{-1}$ Right) Large track with V-shaped penetration $100 \\mathrm{~W}, 30 \\mathrm{Jmm}^{-2}, 130 \\mathrm{mms}^{-1}$. Each formed at $50 \\mu \\mathrm{m}$ layer thickness.\n\n\\section*{Flattened Tracks and Keyhole Mode Melting}\nThe most distinctive and unique form of track formation were the flattened, continuous\n\ntracks, as observed in Figure 50. The uppermost surface of the melt bead was observed to\n\nbe level with the surface of the substrate, and the bead was seen to be completely\n\nsubmerged within the substrate. The resolidified bead had an ellipsoidal shape, and a\n\ndistinct ridge at the bottom of the bead, as seen on the right-hand image of Figure 50. In\n\naddition, some of these structures would have a clearly visible pore at the bottom of the melt pool, as seen in the right-hand image of Figure 49.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-106}\n\nFigure 50. Experiment C (SS316L) - Left) Tracks build on the crucible substrate, with distinctive, flattened tracks appearing on the left-hand side. Right) Crosssectional image taken using the same parameters.\n\nBuilt at $200 \\mathrm{~W}, 80 \\mathrm{Jm}^{-2}, 65 \\mathrm{mms}^{-1}$ and at layer depth of $50 \\mu \\mathrm{m}$.\n\nThis distinctive track formation was observed to occur at the regions of highest surface\n\nenergy density, at $80 \\mathrm{Jmm}^{-2}$, at relatively low layer depths of $50 \\mu \\mathrm{m}$ and $100 \\mu \\mathrm{m}$. Continuous\\\\\nun-flattened tracks would form alongside these flattened tracks, even though the same processing parameters were used to create them, as seen on the left-hand image of Figure 50.", "start_char_idx": 158256, "end_char_idx": 161551, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "900efd78-707b-41f0-9dd7-aabc289c6fd1": {"__data__": {"id_": "900efd78-707b-41f0-9dd7-aabc289c6fd1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0d1e450a-d842-4174-bd2c-32511f8037ae", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "183d5c7b03bb29c5500e94d405766ce253f337afbbf2d4ca356f9f600b58c166", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "8e570054-2d50-4d13-81fb-17f3b4d30299", "node_type": "1", "metadata": {}, "hash": "9a210b473b787194fc79da3c2234e8cf814d1ba67844e0e81f37e0545b218aca", "class_name": "RelatedNodeInfo"}}, "text": "Experiment C (SS316L) - Left) Tracks build on the crucible substrate, with distinctive, flattened tracks appearing on the left-hand side. Right) Crosssectional image taken using the same parameters.\n\nBuilt at $200 \\mathrm{~W}, 80 \\mathrm{Jm}^{-2}, 65 \\mathrm{mms}^{-1}$ and at layer depth of $50 \\mu \\mathrm{m}$.\n\nThis distinctive track formation was observed to occur at the regions of highest surface\n\nenergy density, at $80 \\mathrm{Jmm}^{-2}$, at relatively low layer depths of $50 \\mu \\mathrm{m}$ and $100 \\mu \\mathrm{m}$. Continuous\\\\\nun-flattened tracks would form alongside these flattened tracks, even though the same processing parameters were used to create them, as seen on the left-hand image of Figure 50. The only exception was at one particular combination of processing parameters, at $100 \\mathrm{~W}, 32 \\mathrm{mms}^{-1}, 80 \\mathrm{Jmm}^{-2}$ and a layer depth of $50 \\mu \\mathrm{m}$, where nearly all the formed tracks exhibited these features.\n\nFrom the cross-sectional analysis, it was observed that the characteristics of these melt pools resembled those formed by keyhole welding processes, [111], [112]. The scan speeds used during laser welding are considerably low, whilst the laser power is relatively high. A common rule of thumb for welding structural steels is that $1 \\mathrm{~kW}$ of power requires a rate of around $17 \\mathrm{mms}^{-1}$ to penetrate $1.5 \\mathrm{~mm}$ of material, [113]. Whilst the laser power only ranged between $200 \\mathrm{~W}$ and $100 \\mathrm{~W}$ in these experiments, the thickness of the affected material was comparatively small, at around $50 \\mu \\mathrm{m}$ to $100 \\mu \\mathrm{m}$. The speeds at which flattened formations would form ranged from $32 \\mathrm{mms}^{-1}$ to $65 \\mathrm{mms}^{-1}$. The slow speed of the laser meant that the exposure time was quite high, ranging between $1.5 \\mathrm{~s}$ and $3 \\mathrm{~s}$. At such conditions, it was assumed that keyhole mode melting takes effect. This was further evidenced by the presence of voids at the bottom edge of the $\\mathrm{V}$-shaped penetrations, as explained in Experiment B.\n\nKeyhole mode melting occurs due to the material reaching boiling temperatures rapidly due to the extremely high temperatures. Plasma, ionised vapour, and plume, vapourised material, form within the melt, causing a narrow, deeply penetrating void to form, called a keyhole. The keyhole is maintained through equilibrium of the forces arising from the combined effect of material vapourisation and plasma formation, and hydrostatic pressure and surface tension, the forces of the melt that act to close the void. During keyhole formation, solid material either at the edges of the melt pool or from the remelted layers of the substrate flows around the keyhole cavity and is driven towards the edges of the melt pool by Marangoni flow. Figure 51 displays the mechanisms in affect during keyhole mode melting. As the fluid is spread to the edges, it causes the nearby solid material, whether powder material or previous layers from the substrate, to reach their melting point, and the\\\\\nvolume of the melt pool increases. This widens the melt pool considerably, and at these processing parameters the width of the melt pools at these parameters exceeded the beam diameter by around 7 to 8 times.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-108}\n\\end{center}\n\nFigure 51. Keyhole formation and fluid flow in the melt pool, taken from Stanciu et al. [113]\n\nWhen the laser beam moves to the next point, several processes occur. The plasma inside the keyhole is extinguished, the vaporization pressure decays, and the keyhole collapses through the effects of surface tension and gravity. The void forms at the bottom of the melt pool, as described in Chapter 3.", "start_char_idx": 160833, "end_char_idx": 164639, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "8e570054-2d50-4d13-81fb-17f3b4d30299": {"__data__": {"id_": "8e570054-2d50-4d13-81fb-17f3b4d30299", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "900efd78-707b-41f0-9dd7-aabc289c6fd1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e57149162a2271452984d9413c0f09bbe407d063db6936a096b9554d7551f437", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "757504ec-31d1-4178-9626-7a94cc1725e0", "node_type": "1", "metadata": {}, "hash": "b307e7ba1493196c3ed753a774169cefa64e07a0f38eb58d9cdb4c060987a742", "class_name": "RelatedNodeInfo"}}, "text": "This widens the melt pool considerably, and at these processing parameters the width of the melt pools at these parameters exceeded the beam diameter by around 7 to 8 times.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-108}\n\\end{center}\n\nFigure 51. Keyhole formation and fluid flow in the melt pool, taken from Stanciu et al. [113]\n\nWhen the laser beam moves to the next point, several processes occur. The plasma inside the keyhole is extinguished, the vaporization pressure decays, and the keyhole collapses through the effects of surface tension and gravity. The void forms at the bottom of the melt pool, as described in Chapter 3.\n\n\\section*{Continuous Regular Tracks}\nThe second type of track formation were continuous tracks, similar to those seen in Experiment B. The melt profile would have an ellipsoidal shape, with half or more of the bead volume penetrated into the substrate as seen in the middle image of Figure 49. At $50 \\mu \\mathrm{m}$ layer depth, tracks would build in such a manner between the ranges of $80 \\mathrm{Jmm}^{-2}$ and $20 \\mathrm{Jmm}^{-2}$. The range of surface energy densities at which such tracks would be built would narrow slightly with increasing powder depth, ranging between $80 \\mathrm{Jmm}^{-2}$ and $30 \\mathrm{Jmm}^{-2}$ for layer depths of $100 \\mu \\mathrm{m}$ and above. Whilst these tracks were continuous, with line build rates\\\\\nof around $98 \\%$ or higher, as seen in Table 15, many would exhibit irregularities and distortions. A general observation was that as layer thickness was increased, the height and width of the tracks formed would increase due to the increase in powder volume. For some of these tracks, whilst the topographical images would show relatively smooth, continuous tracks, keyhole pore formation was observed at every layer thickness used, and would usually occur at higher surface energy density ranges, between $80 \\mathrm{Jmm}^{-2}$ and $30 \\mathrm{Jmm}^{-}$ 2. Whilst these pores formed in the same manner as described in the previous section, an amount of the melt bead would still be visible over the substrate surface, and tracks would be visibly unflattened. The scan speeds used in these instances was slow enough to cause vapourisation of the melt, but fast enough as not to cause excessive melting of the substrate.\n\n\\section*{Balling}\nDiscontinuous, balled tracks would form at regions of low surface energy density. At 504m layer depth, the tracks that formed between the energy densities of $12 \\mathrm{Jmm}^{-2}$ and $4 \\mathrm{Jmm}^{-2}$ would break up into a series of spheroidal shapes, as seen in Figure 41. The range of surface energy densities at which balling would occur would increase with layer depth; with $20 \\mathrm{Jmm}^{-2}$ and $4 \\mathrm{Jmm}^{-2}$ at $100 \\mu \\mathrm{m}, 20 \\mathrm{Jmm}^{-2}$ and $8 \\mathrm{Jmm}^{-2}$ at $150 \\mu \\mathrm{m}$, and $30 \\mathrm{Jmm}^{-2}$ and $20 \\mathrm{Jmm}^{-2}$ for $200 \\mu \\mathrm{m}$. Tracks would fail to form at energy densities of $4 \\mathrm{Jmm}^{-2}$ for layer depths above $150 \\mu \\mathrm{m}$, and at $8 \\mathrm{Jmm}^{-2}$ or above for $200 \\mu \\mathrm{m}$. These tracks would form with low line build percentages, as seen in Table 15, at rates of $82.5 \\%$ or lower.\n\nIncreasing the layer thickness was seen to increase the balling effect, and lessen the wettability of the melt on the substrate surface. Additionally, the width of the structures was found to increase with layer thickness, due to the increase in powder volume. Increasing the volume of material requires the energy input to increase to compensate for the energy required to melt more material. At these parameter combinations, the energy absorbed by the powder was insufficient, resulting in a relatively low temperature of the melt pool.", "start_char_idx": 163961, "end_char_idx": 167767, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "757504ec-31d1-4178-9626-7a94cc1725e0": {"__data__": {"id_": "757504ec-31d1-4178-9626-7a94cc1725e0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8e570054-2d50-4d13-81fb-17f3b4d30299", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4897b5bca0f007239d2ca4aff0359a005d79c42f4f64400dbf7116220beb935a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "51558a81-72db-4a89-afdf-f2d2ebf032a5", "node_type": "1", "metadata": {}, "hash": "cc1fa557cd40e03937426077e221e0afae8cbd2033abdceb36343ac3da5e68db", "class_name": "RelatedNodeInfo"}}, "text": "Tracks would fail to form at energy densities of $4 \\mathrm{Jmm}^{-2}$ for layer depths above $150 \\mu \\mathrm{m}$, and at $8 \\mathrm{Jmm}^{-2}$ or above for $200 \\mu \\mathrm{m}$. These tracks would form with low line build percentages, as seen in Table 15, at rates of $82.5 \\%$ or lower.\n\nIncreasing the layer thickness was seen to increase the balling effect, and lessen the wettability of the melt on the substrate surface. Additionally, the width of the structures was found to increase with layer thickness, due to the increase in powder volume. Increasing the volume of material requires the energy input to increase to compensate for the energy required to melt more material. At these parameter combinations, the energy absorbed by the powder was insufficient, resulting in a relatively low temperature of the melt pool. Due to the low temperature of the melt, the surface tension forces of the melt would be the dominant forming factor in determining its shape, resulting in balling of the melt, poor\\\\\nwettability and reduced fluid flow. Additionally, the distance between the melt and the substrate would have increased, leading to reduced contact between them. These two factors result in the formation of isolated droplets instead of continuous tracks, as the reduced wetting area would not be able to support large molten tracks. As volume of the melt would increase with layer depth, balling would become more prominent.\n\n\\section*{Depth-to-Width Contour Map}\nThe average width and depth values measured from the tracks created in this experiment were used to make four contour plots of the depth-to-width ratios, as seen in Figure 52 below. It was generally observed that the depth-to-width ratio would increase with surface energy density. The red and orange regions, where depth-to-width ratios were near 0.6 or above, are regions where keyhole mode melting was observed. This was due to either laser power being too high, scan speed being too low, or a combination of both, resulting in vapourisation of the melt. At the green and yellow regions, where depth-to-width ratios ranged between 0.5 and 0.2 , tracks would form as continuous tracks with suitable penetration into the substrate. At light blue or white regions, where depth-to-width ratios ranged between near 0.2 or lower, prominent balling was observed. Penetration depth would be minimal or not even measurable in many cases.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-111}\n\nFigure 52. Experiment C (SS316L) - Contours of depth-to-width ratios at the different layer depths.\n\n\\subsection*{5.4.3 Conclusions}\nIt was found that surface energy density was not a suitable variable for predicting track formation, as tracks built using the same surface energy values with different parameters gave wildly different results to one another.\n\nA distinct form of track formation was observed, which was not observed in any other experiment mentioned in this research. Using large exposure times, ranging between $1.5 \\mathrm{~s}$ and 3s, resulted in excessive heating of the powder and substrate material. This resulted in keyhole mode melting and the elimination of the track height above the substrate as the melt bead would sink below the surface.\n\nIncreasing the layer depth was found to increase the prominence of balling, as increasing the powder volume was found to reduce the wettability between the substrate and the melt. The general trends seen in previous experiments regarding the changes in scan speed and laser power were observed in this experiment as well. The degradation of track stability as scan speed increased was plainly observed in the results.\n\nTracks were found to build with desirable properties, that is to say, as continuous, regular tracks with no visible pore formation, at many different input parameter combinations for varying layer depth. For each layer depth investigated, the following process parameters were selected for their optimal track formation properties. These parameters were selected as they had formed continuous, smooths tracks with $100 \\%$ build rates and low depth-towidth ratios at their specified layer depth:\\\\\nI. $50 \\mu \\mathrm{m}$ depth: Laser power of $100 \\mathrm{~W}$ and scan speed of $87 \\mathrm{mms}^{-1}\\left(30 \\mathrm{Jmm}^{-2}\\right)$.\n\nII.", "start_char_idx": 166938, "end_char_idx": 171261, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "51558a81-72db-4a89-afdf-f2d2ebf032a5": {"__data__": {"id_": "51558a81-72db-4a89-afdf-f2d2ebf032a5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "757504ec-31d1-4178-9626-7a94cc1725e0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a4b48251690f64c0be0361ffca39006189a7c358ccb1e1323bdfebab900d7a3d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a6061be5-b13d-42f6-a7e2-b1383aa4c064", "node_type": "1", "metadata": {}, "hash": "ed023ea0ccdac6e380dff64121aa30c256d9765dc58878b618693fa657666cf7", "class_name": "RelatedNodeInfo"}}, "text": "The general trends seen in previous experiments regarding the changes in scan speed and laser power were observed in this experiment as well. The degradation of track stability as scan speed increased was plainly observed in the results.\n\nTracks were found to build with desirable properties, that is to say, as continuous, regular tracks with no visible pore formation, at many different input parameter combinations for varying layer depth. For each layer depth investigated, the following process parameters were selected for their optimal track formation properties. These parameters were selected as they had formed continuous, smooths tracks with $100 \\%$ build rates and low depth-towidth ratios at their specified layer depth:\\\\\nI. $50 \\mu \\mathrm{m}$ depth: Laser power of $100 \\mathrm{~W}$ and scan speed of $87 \\mathrm{mms}^{-1}\\left(30 \\mathrm{Jmm}^{-2}\\right)$.\n\nII. $\\quad 100 \\mu \\mathrm{m}$ depth: Laser power of $100 \\mathrm{~W}$ and scan speed of $87 \\mathrm{mms}^{-1}\\left(30 \\mathrm{Jmm}^{-2}\\right)$.\n\nIII. $150 \\mu \\mathrm{m}$ depth: Laser power of $130 \\mathrm{~W}$ and scan speed of $113 \\mathrm{mms}^{-1}\\left(30 \\mathrm{Jmm}^{-2}\\right)$\n\nIV. $200 \\mu \\mathrm{m}$ depth: Laser power of $130 \\mathrm{~W}$ and scan speed of $84 \\mathrm{mms}^{-1}\\left(40 \\mathrm{Jmm}^{-2}\\right)$.\n\n\\subsection*{5.5 Experiment D - Single-Tracks on Crucible Substrates}\n\\subsection*{5.5.1 Results}\nTopographical images of the tracks successfully constructed from experiment $D$ were compiled into a process map as a function of scan speed on the horizontal axis, and laser power on the vertical axis, as seen in Figure 53. Using the same axes as Figure 53, a process map was made using cross-sectional images using the same parameters, as seen in Figure 54. On both figures, the optimal parameter combination used for the DOE in Chapter 5.1.2 was included as a figure in these process maps as a reference to the parameters used to obtain optimal bulk as-built density for this specific batch of powder material.\n\nAn additional process map was created using the line build percentages measured from the successfully built tracks, using the same technique mentioned in the experimental design section for experiment B. This process map can be seen in Table 16. Each image comprises three lines, which are a repetition of the tracks using the same power and scan speed. Areas with missing images are regions where the combination of laser power and scan speed caused little or no track formation.", "start_char_idx": 170382, "end_char_idx": 172881, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a6061be5-b13d-42f6-a7e2-b1383aa4c064": {"__data__": {"id_": "a6061be5-b13d-42f6-a7e2-b1383aa4c064", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "51558a81-72db-4a89-afdf-f2d2ebf032a5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "34cb455c0846383ebb255a244085d0f50a8f1bb7ecf174dfa32332f8047e1d56", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "4297f5f0-aa39-4bb6-a07c-b35f1892428d", "node_type": "1", "metadata": {}, "hash": "f012f28e47d74e08f360744246041d0329cd2e65bbe7bd9c84cf33317e4560c1", "class_name": "RelatedNodeInfo"}}, "text": "Using the same axes as Figure 53, a process map was made using cross-sectional images using the same parameters, as seen in Figure 54. On both figures, the optimal parameter combination used for the DOE in Chapter 5.1.2 was included as a figure in these process maps as a reference to the parameters used to obtain optimal bulk as-built density for this specific batch of powder material.\n\nAn additional process map was created using the line build percentages measured from the successfully built tracks, using the same technique mentioned in the experimental design section for experiment B. This process map can be seen in Table 16. Each image comprises three lines, which are a repetition of the tracks using the same power and scan speed. Areas with missing images are regions where the combination of laser power and scan speed caused little or no track formation.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n\\multirow{6}{*}{\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-113}\n} & 200 & 100.0 & 100.0 & 100.0 & 99.0 & 98.5 & 95.0 & 82.3 & 78.7 & 59.2 & 57.2 \\\\\n\\hline\n & 175 & 100.0 & 100.0 & 100.0 & 98.3 & 92.5 & 77.6 & 68.9 & 61.7 & 41.3 & 40.8 \\\\\n\\hline\n & 150 & 100.0 & 100.0 & 99.0 & 97.9 & 82.9 & 69.9 & 48.7 & 30.7 & 16.5 & 10.7 \\\\\n\\hline\n & 125 & 100.0 & 100.0 & 99.7 & 97.1 & 81.9 & 56.1 & 20.0 & 0.0 & 0.0 & 0.0 \\\\\n\\hline\n & 100 & 100.0 & 99.5 & 98.0 & 73.7 & 54.5 & 25.4 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n\\hline\n & 75 & 100.0 & 93.5 & 72.8 & 38.7 & 11.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n\\hline\n &  & 100 & 200 & 300 & 400 & 500 & 600 & 700 & 800 & 900 & 1000 \\\\\n\\hline\n &  &  &  &  &  & n Spe & $\\mathrm{mms}$ &  &  &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 16. Experiment $D$ (SS316L) - Process map with line build percentages.\n\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_91a5199dc912785ed628g-114.jpg?height=1448&width=1990&top_left_y=955&top_left_x=84}\n\nFigure 53. Experiment D (SS316L) - Topographical process map\n\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_91a5199dc912785ed628g-115.jpg?height=1677&width=1851&top_left_y=989&top_left_x=228}\n\nFigure 54. Experiment D (SS316L) - Cross-sectional process mar\n\n\\subsection*{5.5.2 Discussion}\n\\section*{Track Formation and Width Comparison}\nIn direct comparison to the results from Experiment B, the range in which continuous and regular tracks was reduced by one parameter combination, at the lower laser power setting at $150 \\mathrm{~W}$ and $100 \\mathrm{mms}^{-1}$. Tracks built within this region had a $100 \\%$-line build rate, and are annotated as the blue sections in Table 16. Conversely, the range at which continuous, irregular tracks could form had increased.", "start_char_idx": 172011, "end_char_idx": 174713, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "4297f5f0-aa39-4bb6-a07c-b35f1892428d": {"__data__": {"id_": "4297f5f0-aa39-4bb6-a07c-b35f1892428d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a6061be5-b13d-42f6-a7e2-b1383aa4c064", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "53530458f0dbb8e230b9334a57076c623a5c2e76ac56be4de2a40b0cc9c6138f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "82b72d1b-dab8-4a25-aedb-d9e780f9d2ec", "node_type": "1", "metadata": {}, "hash": "419fe2695632ba4ca9c895e615fb71140245b5fb35eb9e84e564e391b0a255dc", "class_name": "RelatedNodeInfo"}}, "text": "Experiment D (SS316L) - Cross-sectional process mar\n\n\\subsection*{5.5.2 Discussion}\n\\section*{Track Formation and Width Comparison}\nIn direct comparison to the results from Experiment B, the range in which continuous and regular tracks was reduced by one parameter combination, at the lower laser power setting at $150 \\mathrm{~W}$ and $100 \\mathrm{mms}^{-1}$. Tracks built within this region had a $100 \\%$-line build rate, and are annotated as the blue sections in Table 16. Conversely, the range at which continuous, irregular tracks could form had increased. At laser power values between 175W and 100W, the range by which tracks with near-100\\% could be fabricated had increased by $100 \\mathrm{~mm}^{-1}$. Additionally, the range in which track could be built with 100\\%-line build rate within this region had also increased. This region is highlighted in green in Table 16. This trend was observed for the other two types of track formations, including the irregular/discontinuous tracks and balled tracks, highlighted in yellow and orange in Table 16.\n\nThe range of process parameters at which track formation could occur had also increased, though the formations were only weakly dispersed balled droplets. In the regions where track failed to build entirely on the insert substrates in Experiment B, such as at 150W and $1000 \\mathrm{mms}^{-1}$, track formation had occurred, although it was minimal (10.7\\%).\n\nThe results from the width measurements from experiment B were compared to the results from the following experiment. The comparison between the width values can be seen in Figure 55 and Figure 56 below.\n\nThe average track widths measured from samples built using crucible substrates in experiment $D$ were found to be much larger than those measured from their counterparts in\n\nexperiment $B$, which were constructed using mild steel inserts. Most of the tracks built using the exact same processing parameters were found to be substantially larger when built on crucibles, except for the values at $175 \\mathrm{~W}$, where both sets of measurements gave results similar to one another.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-117}\n\\end{center}\n\nFigure 55. Experiment D (SS316L) - Track widths compared with Experiment B (SS316L) at the 75-125W range.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-117(1)}\n\\end{center}\n\nFigure 56. Experiment D (SS316L) - Track widths compared with Experiment B (SS316L) at the 150-200W range.\n\nThe comparison between the results of Experiment B and Experiment D show that track formation was more favoured in Experiment D. Additionally, the width of the structures observed was seen to increase. The only real difference between the two experiments is the type of substrate used. Experiment B used a mild steel plate with a planar surface i.e. flat, smooth surface. Experiment D used the crucible substrate of stainless steel 316L, made using the laser-fusion additive manufacturing method, using the recommended parameters by the manufacturer.\n\nOne of the factors that can influence balling is the presence of oxide contamination. As the steel inserts were prepared in an oxygen environment, a certain degree of oxidation was expected to occur. As a consequence, wetting between the melt and oxide layer on the surface is reduced, [114]. As the crucible substrate was constructed in an environment relatively free of oxygen, the surface could have had a reduced oxide presence, resulting in better wetting properties between the melt and surface and decreased track build failure. The final layer to be printed for the crucible, that is to say, the surface of the substrate that the tracks would build upon, had perpendicular scanning pattern in relation to the track formation. This layer, and the other layers that built the bulk of the crucible, were built parallel to the build plate, with a sloping angle of $0^{\\circ}$. A horizontal surface made via laserpowder bed fusion usually has the least surface roughness at this sloping angle, [115]. However, as seen in Experiment A, laser-powder bed fusion still tends to create surfaces with rippled, wave-like patterns, and as a result these surfaces would have a higher surface roughness than machined and polished surfaces.", "start_char_idx": 174151, "end_char_idx": 178475, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "82b72d1b-dab8-4a25-aedb-d9e780f9d2ec": {"__data__": {"id_": "82b72d1b-dab8-4a25-aedb-d9e780f9d2ec", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "4297f5f0-aa39-4bb6-a07c-b35f1892428d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "5d3172d8b94cbc6fcc77cb626882cd16f8548c5346a3ec50fd023d298026bc3c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b56939f0-e28b-4350-ae55-d81a07b8d69f", "node_type": "1", "metadata": {}, "hash": "b57eaf5836ebdb33527f7f428520fe51b74f1e6eb249b874c25b7790fbbb6578", "class_name": "RelatedNodeInfo"}}, "text": "As the crucible substrate was constructed in an environment relatively free of oxygen, the surface could have had a reduced oxide presence, resulting in better wetting properties between the melt and surface and decreased track build failure. The final layer to be printed for the crucible, that is to say, the surface of the substrate that the tracks would build upon, had perpendicular scanning pattern in relation to the track formation. This layer, and the other layers that built the bulk of the crucible, were built parallel to the build plate, with a sloping angle of $0^{\\circ}$. A horizontal surface made via laserpowder bed fusion usually has the least surface roughness at this sloping angle, [115]. However, as seen in Experiment A, laser-powder bed fusion still tends to create surfaces with rippled, wave-like patterns, and as a result these surfaces would have a higher surface roughness than machined and polished surfaces. Increasing surface roughness affects the wettability of liquids in contact with the surface. The relationship between roughness and wettability was defined by Wenzel, [116], who stated that adding surface roughness will enhance the wettability of the melt, defined by the following equation:\n\n\n\\begin{equation*}\n\\cos \\theta_{m}=r \\cos \\theta_{Y} \\tag{10}\n\\end{equation*}\n\n\nWhere $\\theta_{m}$ is the measured contact angle, $\\theta_{Y}$ is the Young contact angle, that is, the contact angle at a $0^{\\circ}$ horizontal surface and $r$ is the roughness ratio, the ratio between the actual and projected solid surface area, with $r=1$ for a completely smooth surface, and $>1$ for a rough\\\\\none. This equation is based on the assumption that liquid penetrates into surface roughness grooves.\n\nImproving the wettability between the liquid and solid interface improves the ability of the tracks to form, as previously discussed. This is evidenced at particularly low settings, where tracks would fail to form on a smooth substrate but managed to form on the rougher crucible substrate. Improving the wettability across the entire range of process parameter combinations would result in an increase in average width for all the structures observed. This is due to the melt being able to spread more easily on its surface, thus coming into contact with more surrounding material and causing it to reach melting temperatures, increasing the volume of the melt. It has been shown in literature that for laser-powder bed fusion the wettability, and by consequence, the width of formed tracks, can increase as the surface roughness of the substrate increases due to these mechanisms, [117], [118].\n\n\\section*{Cross-Sectional Comparison}\nFrom examination of the cross-sectional images, three forms of solidified track were observed, as seen in Figure 57. In regions of low laser power, $75 \\mathrm{~W}$ to $100 \\mathrm{~W}$, or high scan speeds, $400 \\mathrm{mms}^{-1}$ to $800 \\mathrm{mms}^{-1}$, the track solidified into a spherical structure which was loosely attached to the base plate, such as at laser power 200W, scan speed $700 \\mathrm{mms}^{-1}$. This formation corresponded with the balling defect, as discussed previously in Experiments $B$ and $C$. The combination of these processing parameters would not achieve the time of temperature required in the melt pool to cause sufficient wetting with the substrate surface. In regions of middle to high laser power, between $125 \\mathrm{~W}$ and $200 \\mathrm{~W}$, and at low to moderate scan speeds, between $100 \\mathrm{mms}^{-1}$ and $400 \\mathrm{mms}^{-1}$, tracks would form with a rounded top, with a small or medium elliptical formed penetration depth. The temperature achieved at these setting was suitable for wetting and spreading of the melt, resulting in continuous track formation. At very high laser powers, between 175W and 200W, with low scan speeds, between $100 \\mathrm{mms}^{-1}$ and $200 \\mathrm{mms}^{-1}$, the track would form with a deeper V-shaped penetration\\\\\nbelow the substrate, as seen in the right-most image in Figure 57.", "start_char_idx": 177536, "end_char_idx": 181576, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b56939f0-e28b-4350-ae55-d81a07b8d69f": {"__data__": {"id_": "b56939f0-e28b-4350-ae55-d81a07b8d69f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "82b72d1b-dab8-4a25-aedb-d9e780f9d2ec", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8854391236aaa75627f1133aee8ac44b73398a4aa3b82f5d124d6f9545ad10c3", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fed33f18-4147-4b67-9809-4feda6447997", "node_type": "1", "metadata": {}, "hash": "2e6f8f2c70371375b9bc95cf2b0511ae06b8243ee2a7a5fd79a373d9de00acef", "class_name": "RelatedNodeInfo"}}, "text": "In regions of middle to high laser power, between $125 \\mathrm{~W}$ and $200 \\mathrm{~W}$, and at low to moderate scan speeds, between $100 \\mathrm{mms}^{-1}$ and $400 \\mathrm{mms}^{-1}$, tracks would form with a rounded top, with a small or medium elliptical formed penetration depth. The temperature achieved at these setting was suitable for wetting and spreading of the melt, resulting in continuous track formation. At very high laser powers, between 175W and 200W, with low scan speeds, between $100 \\mathrm{mms}^{-1}$ and $200 \\mathrm{mms}^{-1}$, the track would form with a deeper V-shaped penetration\\\\\nbelow the substrate, as seen in the right-most image in Figure 57. At this range of settings, the energy input was high enough to cause keyhole mode melting.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-120}\n\nFigure 57. Experiment D (SS316L) - The three types of tracks formed. Left) 200W, $700 \\mathrm{mms}^{-1}$, Middle) $150 \\mathrm{~W}, 300 \\mathrm{mms}^{-1}$, Right) $175 \\mathrm{~W}, 200 \\mathrm{mms}^{-1}$.\n\nKeyhole porosity was observed in three instances, and are displayed in Figure \\href{http://58.In}{58.In} the leftmost and bottom images in Figure 58, the melt pool that formed during the experiment in each instance formed a track with a deep penetration, nearly twice as deep as the track was wide, and a large pore formed at the very tip of the penetration. Conversely, the image on the right of Figure 58 had a track form with a large, cylindrical cross-section, with the track width being larger than the track depth. A small pore was present at the very tip of the penetration. Columnar grain growth within the penetration of the track, i.e. below the substrate surface, can be observed plainly in each cross-section. Smaller, equiaxed grain growth can be observed at the top of the track bead.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-121}\n\nFigure 58. Experiment D (SS316L) - Keyhole porosity observed during experiment. Top left) 200W, $300 \\mathrm{mms}^{-1}$, top right) $175 \\mathrm{~W}, 100 \\mathrm{mms}^{-1}$, bottom) $150 \\mathrm{~W}, 100 \\mathrm{mms}^{-1}$\n\n\\section*{Depth Comparison and Verification}\nA comparison between the average penetration depths of Experiment $B$ and $D$ can be seen below in Figure 59 and Figure 60. Measured depths from the crucible samples were usually deeper, although the difference was not as drastic as observed in the changes in average width. This could be attributed to the increase in wetting due to the increase in surface roughness allowing the melt to reach the substrate in a shorter amount of time, and thereby allowing increased melting of the substrate. The depths measured from the tracks made using the insert samples were slightly higher than their crucible counterparts at $175 \\mathrm{~W}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-122(1)}\n\\end{center}\n\nFigure 59. Experiment D (SS316L) - Track depths compared with Experiment B (SS316L) at the 75-125W range.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-122}\n\\end{center}\n\nFigure 60. Experiment D (SS316L) - Track depths compared with Experiment B (SS316L) at the $150-200 \\mathrm{~W}$ range.\n\nThe depth measurements were also plot against values calculated by the deep penetration melting model used in Experiment B, developed by Gladush and Smurov, [108]. These plots are shown in Figure 61 and Figure 62.\n\nA good correlation between the predicted values and measured values was observed for most laser power and scan speed combinations, particularly at the lower energy densities.", "start_char_idx": 180898, "end_char_idx": 184588, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fed33f18-4147-4b67-9809-4feda6447997": {"__data__": {"id_": "fed33f18-4147-4b67-9809-4feda6447997", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b56939f0-e28b-4350-ae55-d81a07b8d69f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2dc73f02ca6503accbf67b50b7c60768958f544831ab58ae31d8a290966c935e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1ea4e442-6f5a-4141-81c4-354a39b49a8b", "node_type": "1", "metadata": {}, "hash": "cd87facf3a0ee8be1799cac56a6cb14a8f7d10d8500bd9da36c03cea35b56f18", "class_name": "RelatedNodeInfo"}}, "text": "Experiment D (SS316L) - Track depths compared with Experiment B (SS316L) at the 75-125W range.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-122}\n\\end{center}\n\nFigure 60. Experiment D (SS316L) - Track depths compared with Experiment B (SS316L) at the $150-200 \\mathrm{~W}$ range.\n\nThe depth measurements were also plot against values calculated by the deep penetration melting model used in Experiment B, developed by Gladush and Smurov, [108]. These plots are shown in Figure 61 and Figure 62.\n\nA good correlation between the predicted values and measured values was observed for most laser power and scan speed combinations, particularly at the lower energy densities. However, at the highest range of laser power settings used, measured values at the lowest scan speeds were found to be exceptionally higher than predicted. At these parameter combinations, keyhole mode melting was observed in many samples.\n\nThis is in line with the findings of King et al [119], , who pointed out the limitations of this empirical model at high energy density melting using 400W lasers and small beam diameters, in which there was a higher propensity for keyhole mode melting to occur.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-123}\n\\end{center}\n\nFigure 61. Experiment D (SS316L) - Comparison of measured and predicted penetration depths according to equation from Gladush and Smurov, [108].\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-124}\n\\end{center}\n\nFigure 62. Experiment D (SS316L) - Comparison of measured and predicted penetration depths according to equation from Gladush and Smurov, [108].\n\n\\section*{Depth-to-Width Contour Map}\nSimilar to the discussion section for experiment $B$, the line build percentage values and depth-to-width ratios for this experiment were used to build two contour maps, shown below in Figure 64 and Figure 65, respectively. A marker was used to indicate the laser power and scan speed used to create the optimal density from the DOE performed at the beginning of the chapter.\n\nAs can be expected, the line build percentages in Figure 64 are at their highest in regions of low scan speed and at high laser power. At most laser power settings, ranging between $100 \\mathrm{~W}$ and $200 \\mathrm{~W}$, scan speed can range between $100 \\mathrm{mms}^{-1}$ and $300 \\mathrm{mms}^{-1}$ to obtain $100 \\%$ on line build percentage values. This range is limited to $100 \\mathrm{mms}^{-}$at the lowest power settings of $75 \\mathrm{~W}$, however a line build percentage of $90 \\%$ could still be achieved at $200 \\mathrm{mms}^{-1}$.\n\nWhen compared to the same contour map made for experiment B, as seen in Figure 39, the threshold for achieving $100 \\%$ track completion at moderate scan speeds of $200 \\mathrm{mms}^{-1}$ or $300 \\mathrm{mms}^{-1}$ was achieved using lower values of laser power, a range of $125 \\mathrm{~W}$ to $200 \\mathrm{~W}$, as\\\\\ncompared to a range of $150 \\mathrm{~W}$ to $200 \\mathrm{~W}$, during the crucible experiments. This is a similar observation to what was observed from the topographical maps, indicating that the threshold for achieving fully built tracks is lowered when building on substrates made using the laserpowder bed fusion process.\n\nThe parameters used for the optimal DOE would fall on the $98 \\%$ line in the crucible contour plot. Tracks built in this region were continuous but displayed certain irregularities, as seen below in the left-most image of Figure 63. On the right of this image is a cross-section taken from the same track, displaying a track bead with a spherical shape with minimal penetration into the substrate. This cross-section may have been taken at a portion of the track where \"beading up\" of the melt may have occurred, as observed in the centre of the topographical image on the left.", "start_char_idx": 183876, "end_char_idx": 187784, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1ea4e442-6f5a-4141-81c4-354a39b49a8b": {"__data__": {"id_": "1ea4e442-6f5a-4141-81c4-354a39b49a8b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fed33f18-4147-4b67-9809-4feda6447997", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "847ecf0c7dd118178148718d0b1b3ef315aa8c0c36269133c9f3c835137c6b49", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "19fffe54-75ee-44f4-8a85-d614e83ab1e3", "node_type": "1", "metadata": {}, "hash": "84a9eefbd85c28057da12247f1ac47e6875f4afbe4c2a3b14a81a860bf2f705e", "class_name": "RelatedNodeInfo"}}, "text": "This is a similar observation to what was observed from the topographical maps, indicating that the threshold for achieving fully built tracks is lowered when building on substrates made using the laserpowder bed fusion process.\n\nThe parameters used for the optimal DOE would fall on the $98 \\%$ line in the crucible contour plot. Tracks built in this region were continuous but displayed certain irregularities, as seen below in the left-most image of Figure 63. On the right of this image is a cross-section taken from the same track, displaying a track bead with a spherical shape with minimal penetration into the substrate. This cross-section may have been taken at a portion of the track where \"beading up\" of the melt may have occurred, as observed in the centre of the topographical image on the left.\n\nIn Figure 65, the depth-to-width ratios throughout the contour map remain relatively low, with the peak ratio of around 0.6 being achieved at the highest laser power and lowest scan speed combination in the top-right corner. From the cross-sectional analysis, tracks were observed with fairly deep penetrations into the track, however the depths achieved would not exceed the widths of the track bead.\n\nIn comparison to the depth-to-width contour map for Experiment B, seen in Figure 40, tracks built using the same parameters on the crucible substrates had much lower depth-to-width ratios for every parameter combination used for Experiment B.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-126(1)}\n\nFigure 63. Experiment D (SS316L) - Left) Topographical image of track built using parameters similar to DOE optimal parameters, Right) cross-section taken at the same track.\n\n(Track is $200 \\mathrm{~W}, 500 \\mathrm{mms}^{-1}$, DOE is $190 \\mathrm{~W}, 500 \\mathrm{mms}^{-1}$ )\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-126}\n\\end{center}\n\nFigure 64. Experiment D (SS316L) - Contours of line build percentage of single tracks.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-127}\n\\end{center}\n\nFigure 65. Experiment D (SS316L) - Contours of depth-to-width ratio.\n\n\\section*{Microstructure of the Single Track}\nBeraha Il proved to be more effective at revealing the microstructure of stainless steel $316 \\mathrm{~L}$ than the previously used Kalling's reagent. The substrate showed a semi-elliptical morphology, which overlap one another, representing the several multi-layered tracks that were used to make the bulk structure. For most of the single tracks, two distinct types of morphologies were observed. Columnar growth was observed at the lower ends of the bead, that is to say, towards the crucible and below the surface. At the edges of the bead which were not in contact with the substrate, smaller, cellular grains were observed. This observation is demonstrated in Figure 66, which is a cross section of a track built at $175 \\mathrm{~W}$ at $100 \\mathrm{mms}^{-1}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-128}\n\\end{center}\n\nFigure 66. Experiment D (SS316L) - Cross section of a track, highlighting the type of grain formation.\n\nThe high energy input of the laser during laser-powder bed fusion occurs over a short period of time, leading to the superfast heating and melting the melt. The heating and cooling rate can be very high $\\left(10^{3}-10^{8} \\mathrm{~K} \\mathrm{~s}^{-1}\\right),[120],[121]$, at the boundaries of the small melt pool. This causes rapid solidification at the solid/liquid and gas/liquid interfaces, leading to the nucleation and formation of very fine, cellular grains. These can be seen at the very edges of the substrate/track boundary, and prominently on the upper exposed surface of the track. The thermal gradient decreases at the inner regions of the track, particularly at the lower end, resulting in columnar growth towards the direction of the last place to cool, [122], [123].", "start_char_idx": 186975, "end_char_idx": 190979, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "19fffe54-75ee-44f4-8a85-d614e83ab1e3": {"__data__": {"id_": "19fffe54-75ee-44f4-8a85-d614e83ab1e3", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1ea4e442-6f5a-4141-81c4-354a39b49a8b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f7adb5e359cf4fea08a57cb0958ee77c90d0676fa7a204d7752cd3a7eeef6f01", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7b7b9480-bf58-4a6a-a2c1-50f9cf613bc9", "node_type": "1", "metadata": {}, "hash": "2c554773b826e06b2fd8d672c19235b678105d715a7f721e0a4979c0513766ff", "class_name": "RelatedNodeInfo"}}, "text": "The high energy input of the laser during laser-powder bed fusion occurs over a short period of time, leading to the superfast heating and melting the melt. The heating and cooling rate can be very high $\\left(10^{3}-10^{8} \\mathrm{~K} \\mathrm{~s}^{-1}\\right),[120],[121]$, at the boundaries of the small melt pool. This causes rapid solidification at the solid/liquid and gas/liquid interfaces, leading to the nucleation and formation of very fine, cellular grains. These can be seen at the very edges of the substrate/track boundary, and prominently on the upper exposed surface of the track. The thermal gradient decreases at the inner regions of the track, particularly at the lower end, resulting in columnar growth towards the direction of the last place to cool, [122], [123]. This region would be the centre of the melt pool, which has the highest temperature due to the previously discuss Gaussian distribution of the laser interaction. This is further evidenced by the observation that columnar growth was usually orientated towards the centre of the melt bead.\n\n\\subsection*{5.5.3 Conclusions}\nThe single tracks manufactured from Experiment B from Chapter 4 were repeated in Experiment D. The main difference was the use of a substrate made using the same material powder and within the same build process, referred to as the crucible substrate. In comparison, a mild steel insert was used for Experiment B. Otherwise, the same parameters\\\\\nto make the single-track formations were used, with approximately the same powder thickness.\n\nIt was found that track formation was significantly affected. Whilst the range at which smooth, continuous track could form had decreased, track build rate had increased throughout the process map. The former is attributed to the improved wettability of the melt on the rougher crucible surface. Tracks with significant fragmentation were found to build more successfully on the crucible, and would transition from highly fragmented tracks to mostly intact ones, such as at $100 \\mathrm{~W}$ and $300 \\mathrm{mms}^{-1}$, where the line build percentage increased from $73.9 \\%$ to $98 \\%$ between the two experiments. Regions within the process map where track failed to build on inserts were found to have increased track formation on crucibles, though this improvement would be limited to droplet formation. Keyhole mode melting was still observed at regions of high laser power and low scan speed, and the peak depth-to-width ratio was found to be 0.6 . However, the effect was less pronounced when compared to Experiment B, where the peak depth-to-width ratio was over 1.0. Keyhole pore formation was also reduced, with two only instances observed in Experiment D compared to the several instances in Experiment B.\n\nThe DOE optimal parameters used for Chapter 5 complimented the results obtained from this experiment. Single-tracks fabricated using near-similar process parameters produced continuous tracks with no sign of keyhole porosity, which is beneficial to optimising bulk density.\n\nFrom the results in this experiment, within the range of the processing parameters used, the optimal combination of laser power and scan speed would be $200 \\mathrm{~W}$ and $400 \\mathrm{mms}^{-1}$ respectively. Tracks formed at these settings had been fabricated without evidence of keyhole mode melting and had a reasonably high line build percentage (99\\%).\n\n\\subsection*{5.6 Experiment $E$ - Crucible Single-Track experiments using Ti-}\n\\section*{$6 \\mathrm{Al}-4 \\mathrm{~V}$}\n\\subsection*{5.6.1 Results}\nFor each layer thickness, two sets of process maps were produced. The first was assembled from the topographical images taken using the Alicona Infinite Focus microscope. The second was assembled from the images captured from the mounted cross sections taken from the crucible samples.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-130}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-130(1)}\n\\end{center}\n\nFigure 67. Experiment E (Ti-6Al-4V) - Topographical process map at $50 \\mu \\mathrm{m}$ layer depth. The red dot shows the shows the parameters used at the Renishaw recommended operating conditions.", "start_char_idx": 190196, "end_char_idx": 194446, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7b7b9480-bf58-4a6a-a2c1-50f9cf613bc9": {"__data__": {"id_": "7b7b9480-bf58-4a6a-a2c1-50f9cf613bc9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "19fffe54-75ee-44f4-8a85-d614e83ab1e3", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7b3e01077f5f8bf201d20893f61591ef6b00af357111a37dff1572b9bb4e0afd", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c37eb627-ca93-4a5e-b4a6-c34f289b20df", "node_type": "1", "metadata": {}, "hash": "dca97a198e0e461275f94749750e08a8b7af1411481ce92ef651209841695c3f", "class_name": "RelatedNodeInfo"}}, "text": "The first was assembled from the topographical images taken using the Alicona Infinite Focus microscope. The second was assembled from the images captured from the mounted cross sections taken from the crucible samples.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-130}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-130(1)}\n\\end{center}\n\nFigure 67. Experiment E (Ti-6Al-4V) - Topographical process map at $50 \\mu \\mathrm{m}$ layer depth. The red dot shows the shows the parameters used at the Renishaw recommended operating conditions.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-131}\n\\end{center}\n\nFigure 68. Experiment E (Ti-6Al-4V) - Cross-sectional process map at $50 \\mu \\mathrm{m}$ layer depth. The red dot shows the shows the parameters used at the Renishaw recommended operating conditions.\n\nTracks failed to form at speeds of $2000 \\mathrm{mms}^{-1}$ and $3000 \\mathrm{mms}^{-1}$, even at the highest laser power of $200 \\mathrm{~W}$. Stable and continuous tracks formed at laser powers of $200 \\mathrm{~W}$ and $150 \\mathrm{~W}$ and scan speeds of $500 \\mathrm{mms}^{-1}$. These parameters managed to build tracks successfully, at $99.9 \\%$ and $86.3 \\%$ line build percentages for 200W and 150W, respectively. However, the tracks built had minor irregularities and did not take the smooth, even shapes of the tracks seen in Experiment A (Figure 25), which used 316L stainless steel powder. A direct comparison can be seen in Figure 69 below. The parameters obtained from the DOE at the beginning of the experiment, $185 \\mathrm{~W}$ and $433 \\mathrm{mms}^{-1}$ for a layer thickness of $50 \\mu \\mathrm{m}$, matched closely to the results obtained in this range, suggesting that single tracks of the DOE parameters would be fabricated in a similar manner.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-132}\\\\\nFigure 69. Left) Experiment E (Ti-6Al-4V) -Single Tracks, produced at 200W,\\\\\n$500 \\mathrm{mms}^{-1}$.\n\nRight) Experiment A (SS316L) - Single Tracks, produced at 200W, 433mms ${ }^{-1}$.\n\nCross sections taken at these settings showed spherical melt beads with good penetration into the crucible surface. At a laser power of $200 \\mathrm{~W}$ and scan speed of $750 \\mathrm{mms}^{-1}$, the tracks started to become more irregularly shaped and large droplets began to form. Kinks would appear in the track and variations in height would become more apparent. Gaps would form in some sections of the tracks. Large droplets would also begin to form, with peak heights of $200 \\mu \\mathrm{m}$ that were much larger than the average track height of $132 \\mu \\mathrm{m}$. The differences between the two types of lines formed at higher speeds are highlighted in Figure 70 below, with the dark blue/purple coloured regions signifying large droplet formations.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-133}\n\nFigure 70. Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at 200W, $500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $200 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $50 \\mu \\mathrm{m}$.\n\nTracks formed at $150 \\mathrm{~W}$ laser power and with higher scan speeds of $750 \\mathrm{mms}^{-1}$ and $1000 \\mathrm{mms}^{-1}$ began to break up into droplets.", "start_char_idx": 193813, "end_char_idx": 197254, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c37eb627-ca93-4a5e-b4a6-c34f289b20df": {"__data__": {"id_": "c37eb627-ca93-4a5e-b4a6-c34f289b20df", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7b7b9480-bf58-4a6a-a2c1-50f9cf613bc9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0d8e7299e2682a2e37c54cbfa7c6a714a978ec46f91913af5100d6883675d2bb", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b36ee82b-40e3-4e2c-94f0-9815b57b9198", "node_type": "1", "metadata": {}, "hash": "8a5685266a781925253efb8b3aee704066ba07bb668138fd51f63c62717845b6", "class_name": "RelatedNodeInfo"}}, "text": "Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at 200W, $500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $200 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $50 \\mu \\mathrm{m}$.\n\nTracks formed at $150 \\mathrm{~W}$ laser power and with higher scan speeds of $750 \\mathrm{mms}^{-1}$ and $1000 \\mathrm{mms}^{-1}$ began to break up into droplets. These droplets would also reach peak heights much larger than that of continuous tracks, ranging between $200 \\mu \\mathrm{m}$ and $220 \\mu \\mathrm{m}$. Droplet formation would increase with the increase of scan speed.\n\nIn the cross sections taken from these tracks, the depth of laser penetration would be limited or not present at all. In such cases, the bead formed would appear to be completely detached and unsupported from the surface of the crucible. Most likely the bead is supported at a point out of the plane from where that particular track was sectioned. The presence of necking at the base of the bead would also be observed. It is described as a narrowing of the beads profile just above the surface of the substrate, and is clearly distinguished in Figure 71 below.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-134}\n\\end{center}\n\nFigure 71.Experiment E (Ti-6Al-4V) - Track cross-section, taken at 150W, $1000 \\mathrm{mms}^{-1}$. Necking occurs between the melt bead and substrate.\n\nTracks with similar geometries were observed at 200W and higher scan speeds of $1000 \\mathrm{mms}^{-1}$ and $1500 \\mathrm{mms}^{-1}$. Track fragmentation would increase with scan speed, and the build percentage would decrease to $77.3 \\%$ and $58.7 \\%$ respectively.\n\nAt a laser power of $100 \\mathrm{~W}$ and a scan speed of $500 \\mathrm{mms}^{-1}$, tracks formed into a mix of small portions of continuous, irregular tracks and small droplets. Large sections of track would go unbuilt. Spherical melt beads would form with limited or no penetration into the underlying powder layer. At higher scan speeds of $500 \\mathrm{mms}^{-1}$ and $750 \\mathrm{mms}^{-1}$, droplet formation would increase. Cross sections taken at $750 \\mathrm{mms}^{-1}$ showed irregularly shaped, non-rounded melt beads.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-135(1)}\n\\end{center}\n\nFigure 72. Experiment $\\mathrm{E}$ (Ti-6Al-4V) - Topographical process map at $100 \\mu \\mathrm{m}$ layer depth.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-135}\n\\end{center}\n\nFigure 73. Experiment E (Ti-6AI-4V) - Cross-sectional process map at $100 \\mu \\mathrm{m}$ layer depth.\n\nTracks failed to form at speeds ranging between $1500 \\mathrm{mms}^{-1}$ and $3000 \\mathrm{mms}^{-1}$ at this layer thickness. At a laser power of $200 \\mathrm{~W}$ and a scan speed of $500 \\mathrm{mms}^{-1}$, the tracks formed were mostly continuous, with $93.6 \\%$ of the lines successfully being built. Cross sections of these tracks showed large circular melt beads with good penetration into the crucible substrate. However, colour mapping of the 3D data showed that the tracks built were highly irregular and uneven. Whilst the tracks remained largely unbroken, the tracks would solidify into large beads along the track, with height peaking at around $220 \\mu \\mathrm{m}$, well above the average of $129 \\mu \\mathrm{m}$. This can be observed in Figure 74.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-136}\n\nFigure 74.", "start_char_idx": 196861, "end_char_idx": 200385, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b36ee82b-40e3-4e2c-94f0-9815b57b9198": {"__data__": {"id_": "b36ee82b-40e3-4e2c-94f0-9815b57b9198", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c37eb627-ca93-4a5e-b4a6-c34f289b20df", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e7915d8437af9e5573bedafaa6cdafc1787fae608b07af721de76a301c415973", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a711eecc-0b10-494e-92af-b52848b8cc97", "node_type": "1", "metadata": {}, "hash": "3b789c2670bbdba0017c3354899fc25caa19ede9f069735388a20166bc737321", "class_name": "RelatedNodeInfo"}}, "text": "At a laser power of $200 \\mathrm{~W}$ and a scan speed of $500 \\mathrm{mms}^{-1}$, the tracks formed were mostly continuous, with $93.6 \\%$ of the lines successfully being built. Cross sections of these tracks showed large circular melt beads with good penetration into the crucible substrate. However, colour mapping of the 3D data showed that the tracks built were highly irregular and uneven. Whilst the tracks remained largely unbroken, the tracks would solidify into large beads along the track, with height peaking at around $220 \\mu \\mathrm{m}$, well above the average of $129 \\mu \\mathrm{m}$. This can be observed in Figure 74.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-136}\n\nFigure 74. Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at 200W, $500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $200 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $100 \\mu \\mathrm{m}$.\n\nAt higher scan speeds, the tracks would mostly form as large droplets, and the few sections of continuous tracks that did form were visibly distorted. Track build percentage would drop to $74.5 \\%$ and $64.7 \\%$ for $750 \\mathrm{mms}^{-1}$ and $1000 \\mathrm{mms}^{-1}$ respectively. The tracks formed at this speed would reach peak heights of around $260-280 \\mu \\mathrm{m}$, with the average heights of tracks formed being $170.0 \\mu \\mathrm{m}$ and $147.3 \\mu \\mathrm{m}$ respectively. The cross-sectional images showed that\\\\\npenetration into the substrate was limited, and that necking at the base of the bead was widespread.\n\nAt a laser power of $150 \\mathrm{~W}$ and scan speed of $500 \\mathrm{mms}^{-1}$, the tracks would mostly form as a series of large droplets. As scan speed increased, penetration into the crucible would decrease, with many cases of detachment from the previous layers being seen.\n\nAt a laser power of $100 \\mathrm{~W}$, continuous track formation would very rarely be observed. Tracks would form into small droplets. The shape of the melt beads formed at $100 \\mathrm{~W}$ laser power were all irregularly shaped, with the degree of this irregularity increasing with scan speed.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-137}\n\nFigure 75. Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at 100W $500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $100 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $100 \\mu \\mathrm{m}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-138(1)}\n\\end{center}\n\nFigure 76. Experiment $\\mathrm{E}$ (Ti-6Al-4V) - Topographical process map at $150 \\mu \\mathrm{m}$ layer depth.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-138}\n\\end{center}\n\nFigure 77. Experiment E (Ti-6Al-4V) - Cross-sectional process map at $150 \\mu \\mathrm{m}$ layer depth.\n\nTracks had failed to form at scan speeds higher than $1000 \\mathrm{mms}^{-1}$ at this layer thickness.\n\nTracks would fail to form with 100W laser power.\n\nAt a laser power of $200 \\mathrm{~W}$ and a scan speed of $500 \\mathrm{mms}^{-1}$, tracks would build as continuous, irregular tracks and large droplets with peak height of around 220-280um. Cross-sectional images of these tracks showed that penetration would range greatly. At higher scan speeds, large sections of the track would go unbuilt.", "start_char_idx": 199651, "end_char_idx": 203084, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a711eecc-0b10-494e-92af-b52848b8cc97": {"__data__": {"id_": "a711eecc-0b10-494e-92af-b52848b8cc97", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b36ee82b-40e3-4e2c-94f0-9815b57b9198", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "21bb10ad3e370782a91bf638999c869c532fd7d1f83b5fa4a6b80f82d05da4c7", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "75cdb60e-9b41-476c-afa0-9be4b5aa0399", "node_type": "1", "metadata": {}, "hash": "7f6eb25340df9eab3af6ab95830aea81e99493053b407ade03256f8f50def9bf", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-138}\n\\end{center}\n\nFigure 77. Experiment E (Ti-6Al-4V) - Cross-sectional process map at $150 \\mu \\mathrm{m}$ layer depth.\n\nTracks had failed to form at scan speeds higher than $1000 \\mathrm{mms}^{-1}$ at this layer thickness.\n\nTracks would fail to form with 100W laser power.\n\nAt a laser power of $200 \\mathrm{~W}$ and a scan speed of $500 \\mathrm{mms}^{-1}$, tracks would build as continuous, irregular tracks and large droplets with peak height of around 220-280um. Cross-sectional images of these tracks showed that penetration would range greatly. At higher scan speeds, large sections of the track would go unbuilt. Track build percentage would drop from $79.4 \\%$ at $500 \\mathrm{mms}^{-1}$ to $57.0 \\%$ and $55.2 \\%$ for $750 \\mathrm{mms}^{-1}$ and $1000 \\mathrm{mms}^{-1}$, respectively. Crosssectional images taken at higher scan speeds showed melt beads that remained mostly regular and spherically shaped. Necking and detachment from the crucible surface would become more prevalent at the highest scan speed of $1000 \\mathrm{mms}^{-1}$.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-139}\n\nFigure 78. Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at 200W $500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $200 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $150 \\mu \\mathrm{m}$.\n\nAt a laser power of $150 \\mathrm{~W}$, tracks would mostly form as a series of large droplets, with peak heights of around $260-280 \\mu \\mathrm{m}$. Large sections of the track would go unbuilt, with the average track build percentages being $62.3 \\%$ and $59.0 \\%$ for $500 \\mathrm{mms}^{-1}$ and $750 \\mathrm{mms}^{-1}$, respectively. A mix of large and small droplets would form at the higher scan speed of $750 \\mathrm{mms}^{-1}$. Cross-\\\\\nsectional images revealed spherical track bead geometries with limited penetration and\n\nnecking forming at $500 \\mathrm{mms}^{-1}$. More irregularly shaped beads would form at $750 \\mathrm{mms}^{-1}$, most\n\noften detached from the crucible.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-140}\n\nHeight\\\\\nSubrange\\\\\n300\\\\\n$250-$\\\\\n$200-$\\\\\n$150-$\\\\\n$100-$\\\\\n$50-$\\\\\n$0-$\\\\\n$-50-$\n\nFigure 79. Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at 150W, $500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $150 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $150 \\mu \\mathrm{m}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-141(1)}\n\\end{center}\n\nFigure 80. Experiment E (Ti-6Al-4V) - Topographical process map at $200 \\mu \\mathrm{m}$ layer depth.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-141}\n\\end{center}\n\nFigure 81. Experiment E (Ti-6AI-4V) - Cross-sectional process map at $200 \\mu \\mathrm{m}$ layer depth.", "start_char_idx": 202377, "end_char_idx": 205361, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "75cdb60e-9b41-476c-afa0-9be4b5aa0399": {"__data__": {"id_": "75cdb60e-9b41-476c-afa0-9be4b5aa0399", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a711eecc-0b10-494e-92af-b52848b8cc97", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "59073d824b674bf30cab834c287c4ceb312cec98c6d5ca0846fa3f2bcdc1c5a7", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "475d595c-6a52-4d7d-adba-ba93027c38c5", "node_type": "1", "metadata": {}, "hash": "bc9f541891b9a21aacc0e2f227f972e8263a734b2d9635e3d46510b2c625b62b", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-141(1)}\n\\end{center}\n\nFigure 80. Experiment E (Ti-6Al-4V) - Topographical process map at $200 \\mu \\mathrm{m}$ layer depth.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-141}\n\\end{center}\n\nFigure 81. Experiment E (Ti-6AI-4V) - Cross-sectional process map at $200 \\mu \\mathrm{m}$ layer depth.\n\nTracks would only form at a laser power of $200 \\mathrm{~W}$ at this layer thickness, at scan speeds of $500 \\mathrm{mms}^{-1}$ and $750 \\mathrm{mms}^{-1}$. The presence of satellite powder particles sintered to the melt bead was most frequently observed at this layer thickness.\n\nAt $500 \\mathrm{mms}^{-1}$, large sections of track would fail to form, with only $57.3 \\%$ of tracks being built. Tracks would form as large droplets, with peak heights of around $450 \\mu \\mathrm{m}$. Cross sections of the tracks showed melt beads with minimal or no penetration to the crucible. As scan speed increased, larger sections of the track would fail to build, decreasing to $33.9 \\%$ for $750 \\mathrm{mms}^{-1}$. However, droplet formation would decrease, and short segments of irregular, continuous tracks would appear. The peak height of droplets would also lower, reaching only 300$400 \\mu \\mathrm{m}$. There was also a noted drop in the average height, from $317.6 \\mu \\mathrm{m}$ at $500 \\mathrm{mms}^{-1}$, to $218.7 \\mu \\mathrm{m}$ in $750 \\mathrm{mms}^{-1}$. The melt bead would become more irregularly shaped with increasing scan speed, with instances of extremely long necking, reaching half of the height of the bead, becoming more prevalent.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-142}\n\nFigure 82. Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at 200W, $500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $200 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $200 \\mu \\mathrm{m}$.", "start_char_idx": 204942, "end_char_idx": 206938, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "475d595c-6a52-4d7d-adba-ba93027c38c5": {"__data__": {"id_": "475d595c-6a52-4d7d-adba-ba93027c38c5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "75cdb60e-9b41-476c-afa0-9be4b5aa0399", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "03ca8a6d51eafe51595425eb7fc0247dd393c08d92d467b7f8a84b9a1fa7d3dc", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f641d336-759d-42f4-ad54-55cce00ae6d5", "node_type": "1", "metadata": {}, "hash": "45bf8da4297455d7bbc2621b41884d334b1db5d373c8f9217aa10a5146311a39", "class_name": "RelatedNodeInfo"}}, "text": "The melt bead would become more irregularly shaped with increasing scan speed, with instances of extremely long necking, reaching half of the height of the bead, becoming more prevalent.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-142}\n\nFigure 82. Experiment E (Ti-6Al-4V) - Left) Continuous tracks built at 200W, $500 \\mathrm{mms}^{-1}$, Right) continuous tracks and droplet formation, built at $200 \\mathrm{~W}, 750 \\mathrm{mms}^{-1}$, crucible depth of $200 \\mu \\mathrm{m}$.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline\n & \\multicolumn{7}{|c|}{$50 \\mu \\mathrm{m}$} \\\\\n\\hline\n\\multirow{3}{*}{\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-143(1)}\n} & 200 & 99.9 & 77.2 & 63.3 & 58.7 & 0 & 0 \\\\\n\\hline\n & 175 & 86.3 & 75.7 & 74.7 & 50 & 0 & 0 \\\\\n\\hline\n & 150 & 64.7 & 66.4 & 49.3 & 0 & 0 & 0 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline\n & \\multicolumn{7}{|c|}{$100 \\mu \\mathrm{m}$} \\\\\n\\hline\n\\multirow{3}{*}{\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-143}\n} & 200 & 93.6 & 74.5 & 64.7 & 0 & 0 & 0 \\\\\n\\hline\n & 175 & 74.8 & 65.3 & 61.1 & 0 & 0 & 0 \\\\\n\\hline\n & 150 & 64.7 & 38.1 & 0 & 0 & 0 & 0 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline\n & \\multicolumn{7}{|c|}{$150 \\mu \\mathrm{m}$} \\\\\n\\hline\n\\multirow{3}{*}{\u0630\u0c46} & 200 & 79.4 & 57 & 55.2 & 0 & 0 & 0 \\\\\n\\hline\n & 175 & 62.3 & 59 & 0 & 0 & 0 & 0 \\\\\n\\hline\n & 150 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline\n & \\multicolumn{7}{|c|}{$200 \\mu \\mathrm{m}$} \\\\\n\\hline\n\\multirow{3}{*}{\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-143(2)}\n} & 200 & 57.3 & 33.9 & 0 & 0 & 0 & 0 \\\\\n\\hline\n & 175 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n\\hline\n & 150 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n\\hline\n &  & 500 & 750 & 1000 & 1500 & 2000 & 3000 \\\\\n\\hline\n &  &  &  & Scan S & $\\mathrm{d}(\\mathrm{mm}$ &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 17.", "start_char_idx": 206423, "end_char_idx": 208499, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f641d336-759d-42f4-ad54-55cce00ae6d5": {"__data__": {"id_": "f641d336-759d-42f4-ad54-55cce00ae6d5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "475d595c-6a52-4d7d-adba-ba93027c38c5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "049c34da37a3398b4c4ddbdd85e19ec7251cf773a72e0f31e9317bccc912493a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3852aeb0-b60f-4231-afc3-054fbfd0b71d", "node_type": "1", "metadata": {}, "hash": "00ac9e2d6084375272dcba4a7aebbf4019ca53e9a8e06092e63cae8f3e834435", "class_name": "RelatedNodeInfo"}}, "text": "Experiment E (Ti-6Al-4V) - Process map with line build percentages for each layer depth, given in bold over each table.\n\n\\subsection*{5.6.2 Discussion}\nThe causes of track instability due to low laser power and high scan speed have been discussed in the previous chapters extensively. In this section, track instability, melt wettability and heat transfer into the substrate are discussed as a factor of layer thickness will be discussed.\n\nAt the top-most row of in Figure 68, at a laser power of 200W, and with scan speed ranging between $500 \\mathrm{mms}^{-1}$ and $1000 \\mathrm{mms}^{-1}$, the track beads formed clearly show penetration into the previous substrate layer. This implies that the energy supplied by the laser was sufficient enough to heat the melt enough to cause wetting and spreading over the previous layer, causing melting of both the powder bed and the previous layer. With a larger layer thickness, a larger volume of powder would need to be melted in order for the resulting melt pool to\\\\\ncome into contact with the substrate. Additionally, the melt bead that does form has much greater contact with surrounding powder material due to increased distance from the substrate and reduced wettability and fluid flow, as discussed in Experiment $\\mathrm{C}$. If these particles bind to the molten metal but fail to reach melting temperatures, they remain as solids and the resulting mixture increases the viscosity of the melt pool due to the solids' effect on impeding fluid flow [71], [124].\n\nThese factors impede the ability for the melt pool to achieve a suitable wetting angle to the previous layer, and the bulk of the melt bead forms above the substrate. Using a high laser power, low scan speed, low layer thickness or any suitable combination of these process parameters may result in increased penetration into the substrate, as partly observed the second image in Figure 83. This could increase the temperature of the melt, thereby increasing the melt volume and improve the contact between the melt and the substrate, preventing instability in the track and allow for the formation of continuous tracks, made with a layer thickness larger than $50 \\mu \\mathrm{m}$. However, for all the parameter combinations used in this experiment, all failed to form continuous tracks, that is to say, $100 \\%$ or near- $100 \\%$ line build percentage, at layer thicknesses larger than $50 \\mu \\mathrm{m}$. Increasing the layer thickness resulted in a decrease in track stability and an increase in the balling phenomenon, as seen in Figure 83 below.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-144}\n\nFigure 83. Experiment E (Ti-6Al-4V) - Tracks formed at $200 \\mathrm{~W}, 500 \\mathrm{mms}^{-1}$, at increasing layer thicknesses.\n\nFrom left to right, layer thickness was $50 \\mu \\mathrm{m}, \\mathbf{1 0 0} \\mu \\mathrm{m}, \\mathbf{1 5 0} \\mu \\mathrm{m}$ and $200 \\mu \\mathrm{m}$.\n\nAdditionally, powder particles sintered to the track were more commonly observed in crosssections taken at high layer thickness, such as the right-most cross-section in Figure 83, which was taken from a track made from a $200 \\mu \\mathrm{m}$ layer thickness.\n\nThe average widths were recorded by measuring the widest possible diameter from the cross section of the track. The results were plot against scan speed for each laser power setting used, as seen in Figure 84, Figure 85 and Figure 86. The different lines on each plot show the average width values at each layer thickness.\n\nAt the 200W plot in Figure 84, the lowest track widths were observed at the 504m layer thickness, and did not tend to vary greatly with increasing scan speed. As layer thickness increased, the width of the observed structures increased slightly as well. This trend was also noted at lower laser power settings, as seen in Figure 85 and Figure 86. The increase in average track width at increasing layer thicknesses could be attributed to the increased balling formations.\n\n\\section*{Average Track Widths - 200W}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-145}\n\\end{center}\n\nFigure 84. Experiment E (Ti-6Al-4V) - Average Track Width at 200W.", "start_char_idx": 208500, "end_char_idx": 212705, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3852aeb0-b60f-4231-afc3-054fbfd0b71d": {"__data__": {"id_": "3852aeb0-b60f-4231-afc3-054fbfd0b71d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f641d336-759d-42f4-ad54-55cce00ae6d5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d9927ca0dc7085dd6b37ac42f1fa17fbed8c0596ad1777f5d9918ae4cdbe6cd6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fe870961-29d4-4850-8410-d7f7ce1eb4ce", "node_type": "1", "metadata": {}, "hash": "7578b4a2e0e3546ef5970b4b27d6ee45da8734944f21e812b139ec8b1afa7017", "class_name": "RelatedNodeInfo"}}, "text": "The different lines on each plot show the average width values at each layer thickness.\n\nAt the 200W plot in Figure 84, the lowest track widths were observed at the 504m layer thickness, and did not tend to vary greatly with increasing scan speed. As layer thickness increased, the width of the observed structures increased slightly as well. This trend was also noted at lower laser power settings, as seen in Figure 85 and Figure 86. The increase in average track width at increasing layer thicknesses could be attributed to the increased balling formations.\n\n\\section*{Average Track Widths - 200W}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-145}\n\\end{center}\n\nFigure 84. Experiment E (Ti-6Al-4V) - Average Track Width at 200W.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-146(1)}\n\\end{center}\n\nFigure 85. Experiment E (Ti-6Al-4V) - Average Track Width at $150 \\mathrm{~W}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-146}\n\\end{center}\n\nFigure 86. Experiment E (Ti-6Al-4V) - Average Track Width at $100 \\mathrm{~W}$.\n\n\\subsection*{5.6.3 Conclusions}\nIn this chapter, the crucible method was used to successfully create single track process maps for a new material, Ti-6Al-4V titanium alloy powder. Three process parameters were investigated, the laser power, scan speed and layer thickness. The changes in the crosssectional track geometry and line stability in relation to these parameters was investigated. It was found that track stability and geometry was greatly affected by the layer thickness used during the experiment. Increasing layer thickness would increase track instability, and was seen as generally detrimental to track formation. At the highest laser power, 200W, and lowest scan speed, $100 \\mathrm{mms}^{-1}$, the line build percentage at $100 \\mu \\mathrm{m}$ layer depth reached 93.6\\%. The track was irregularly shaped but continuous, suggesting that with further optimisation of the process parameters, track stability in this region could be achieved. The DOE optimal parameters obtained from the DOE at the beginning of the chapter complimented the results obtained from this experiment. Single-tracks fabricated using nearsimilar process parameters produced continuous tracks with no sign of keyhole porosity, which is beneficial to optimising bulk density.\n\n\\section*{Chapter 6 Discussion}\nSeveral experiments have been performed in which the process parameters were varied in order to investigate the response in the formation of either single track or single layer builds. Three principle parameters were investigated, which were laser power (W), scan speed\n\n$\\left(\\mathrm{mms}^{-1}\\right)$ and layer thickness $(\\mu \\mathrm{m})$. Two different material powders were used, stainless steel $316 \\mathrm{~L}$ and titanium alloy Ti-6Al-4V, which reacted differently during their respective experiments, however the behavioural trends observed between experiments and materials remained consistent.\n\n\\section*{Process Maps}\nThe cross-sectional analysis of the single tracks built in the experiments would fall under three different and distinct geometries, as seen in Figure 87, Figure 89 and Figure 90 below. During topographical examination of the tracks, the transition between stable to unstable track formation was divided into five regions, as seen in Figure 88.\n\nThe left-most image in each cross-sectional figure shows the geometry of a typical balled track. This geometry would be observed at regions of low laser power, high scan speed, or high layer depth, where the track would break down into a series of isolated droplets. This was attributed to the low temperatures achieved in the melt causing insufficient melting of the surrounding material and insufficient wetting, which causes the melt to take the shape of a sphere to reduce surface energy. Plateau-Rayleigh forces and balling would force the molten pool to from spherical droplets as a way to reduce overall surface energy. The topographical representation of such geometries can be seen in Figure 88iii-iv. The middle image in each cross-sectional figure show what is considered the ideal geometry for fabricating structures in the laser-powder bed fusion process, often associated with conduction-mode melting.", "start_char_idx": 211932, "end_char_idx": 216276, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fe870961-29d4-4850-8410-d7f7ce1eb4ce": {"__data__": {"id_": "fe870961-29d4-4850-8410-d7f7ce1eb4ce", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3852aeb0-b60f-4231-afc3-054fbfd0b71d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c58768ec2166e143f9fbbc346ce4ff6f975f9097a10ee196e946a46e3a8adc3c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "662eff4a-4ae8-4962-b43f-c59ece23f995", "node_type": "1", "metadata": {}, "hash": "9b3c60edc9b41872c50664274cf1243aa712c5bd571db8baf118063d290d030f", "class_name": "RelatedNodeInfo"}}, "text": "The left-most image in each cross-sectional figure shows the geometry of a typical balled track. This geometry would be observed at regions of low laser power, high scan speed, or high layer depth, where the track would break down into a series of isolated droplets. This was attributed to the low temperatures achieved in the melt causing insufficient melting of the surrounding material and insufficient wetting, which causes the melt to take the shape of a sphere to reduce surface energy. Plateau-Rayleigh forces and balling would force the molten pool to from spherical droplets as a way to reduce overall surface energy. The topographical representation of such geometries can be seen in Figure 88iii-iv. The middle image in each cross-sectional figure show what is considered the ideal geometry for fabricating structures in the laser-powder bed fusion process, often associated with conduction-mode melting. The track forms with a rounded top, with a small or medium sized penetration into the previous layers. Tracks found with this geometry would form as continuous single lines with no gaps in between solidified material, as seen in Figure 88i-ii.\n\nThe temperatures achieved at the melt in these tracks would have been sufficient to cause melting of the powder and remelting of the previous layers, and the melt itself would have suitable wetting and spreading properties. The sufficient wetting of the melt plays a crucial role in forming an adhesive bond between the liquid and solids, as well as cohesive bonds between successive melt pools which form the track. This type of geometry and track formation is ideal for fabricating parts with optimal physical properties and reduced porosity. The right-most image in each cross-sectional figure shows a track that forms from keyholemode melting. This geometry was observed at regions of exceptionally high laser powder or low scan speed. These tracks would form as continuous single lines, similar to Figure 88i-ii. High energy density would cause the material to reach boiling point, causing vaporisation. The recoil pressure from the vapour exerts a force onto the molten pool, causing a cavity to form within the melt. The laser achieves deeper penetration, causing the melt pool to penetrate into previous layer and form a deep, V-shaped penetration. Keyhole-mode melting can be detrimental to the laser-powder bed fusion process, as gas can become trapped within during the melt, which can cause pores to form throughout the track, [119], [125]. Two clear examples of such void formation can be seen on the right-hand images of Figure 87 and Figure 90.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-149}\n\nFigure 87. Transition of the track geometry in Experiment B (SS316L). Left) $125 \\mathrm{~W}, 600 \\mathrm{mms}^{-1}$, Middle) $200 \\mathrm{~W}, 300 \\mathrm{mms}^{-1}$, Right) $150 \\mathrm{~W}, 500 \\mathrm{mms}^{-1}$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-150}\n\nFigure 88. The five types of tracks that formed during Experiment B (SS316L). From left to right: i) continuous/regular tracks $\\left(200 \\mathrm{~W}, 100 \\mathrm{mms}^{-1}\\right)$, ii) continuous/irregular tracks $\\left(150 \\mathrm{~W}, 400 \\mathrm{mms}^{-1}\\right)$, iii) discontinuous/irregular tracks $\\left(150 \\mathrm{~W}, 400 \\mathrm{mms}^{-1}\\right)$, iv) balling $\\left(175 \\mathrm{~W}, 700 \\mathrm{mms}^{-1}\\right)$, v) build failure $\\left(100 \\mathrm{~W}, 1000 \\mathrm{~ms}^{-1}\\right)$.\n\nThe images from both the topographical and cross-sectional analysis from each single-track experiment have been compiled into several process maps, as a means of visually describing the forms of transitions that take place during melt pool formation and solidification. Additionally, the physical measurements taken from both sets of analyses have been used to show the relationships between the processing parameters and track geometry.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-150(1)}\n\nFigure 89. Transition of the track geometry in Experiment D (SS316L).", "start_char_idx": 215361, "end_char_idx": 219473, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "662eff4a-4ae8-4962-b43f-c59ece23f995": {"__data__": {"id_": "662eff4a-4ae8-4962-b43f-c59ece23f995", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fe870961-29d4-4850-8410-d7f7ce1eb4ce", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "80b2ada436480e18172fcabab8bac257d47042e4cda3aad5f43c028894db4735", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "17915070-e460-4304-bf70-05376fccc34e", "node_type": "1", "metadata": {}, "hash": "7a6403a91cdbc5a815c5fcfec08010ac8b668968ad55148017f6191b6edb27d6", "class_name": "RelatedNodeInfo"}}, "text": "The images from both the topographical and cross-sectional analysis from each single-track experiment have been compiled into several process maps, as a means of visually describing the forms of transitions that take place during melt pool formation and solidification. Additionally, the physical measurements taken from both sets of analyses have been used to show the relationships between the processing parameters and track geometry.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-150(1)}\n\nFigure 89. Transition of the track geometry in Experiment D (SS316L). Left) $200 \\mathrm{~W}, 700 \\mathrm{mms}^{-1}$, Middle) $150 \\mathrm{~W}, 300 \\mathrm{mms}^{-1}$, Right) $175 \\mathrm{~W}, 200 \\mathrm{mms}^{-1}$.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_91a5199dc912785ed628g-151}\n\nFigure 90. Transition of the track geometry in Experiment C (SS316L). Left) $200 \\mathrm{~W}, 700 \\mathrm{mms}^{-1}$, Middle) $150 \\mathrm{~W}, 300 \\mathrm{mms}^{-1}$, Right) $175 \\mathrm{~W}, 200 \\mathrm{mms}^{-1}$.\n\n\\section*{Microstructures of the Single Track}\nDuring track formation, a distinct pattern of solidification of the grains was routinely observed. Cellular, fine grains were observed at regions of fast cooling, that is to say, the outer edges or boundaries of the melt pool. The grain growth around these finer structures was usually columnar, growing towards the direction of the last place to cool in the melt, that is to say, the centre of the bead. These mechanisms can be observed in most of the melt beads presented in Figure 89 and Figure 90.\n\n\\section*{Keyholing}\nThe degree of keyholing observed during each experiment was relatively minimal, due to the limitations in equipment, as laser power was restricted to 200W. Even with exceptionally low scan speeds, such as the parameters used in Experiment C, the amount of keyhole porosity observed was relatively low and uncommon. Many contemporary laser-powder bed fusion machines are utilising laser systems that exceed the power used in this experiment, ranging from $400 \\mathrm{~W}$ to several $\\mathrm{kW}$. If the transition into keyhole-mode melting is achieved faster at high laser powers it can become more difficult to control. The vapourisation of the melt pool not only has detrimental effects on the physical properties of the part, but the resulting plasma/metal vapour plume can cause a number of issues. It can interact directly with the laser, causing damping and scattering of the beam, [126]-[128]. The nanoscale condensate that forms after the plume cools down is mostly removed from the powder bed by high velocity shielding gas. However, there are still chances that it can contaminate the powder\\\\\nbed, which promotes metallurgical defects to form in the part, [129], [130], and due to its extremely small size, typically less than $1 \\mu \\mathrm{m}$ in size, it can coat crucial components such as the lens and makes the cleaning of the build chamber and filtration systems more frequently necessary.\n\n\\section*{The Crucible Design}\nAs an attempt to emulate the true conditions of melt pool formation and solidification during the laser-powder bed fusion process, experiments C, D and E utilised a new substrate design which could be constructed during the same build cycle as the single-track experiment. Most research involving single track formations use a plane surface, such as commercially available, hot rolled metal plates, as a substrate for generating single tracks, [161]-[163].\n\nAt in-situ conditions during the laser-powder bed fusion process, single track lines were constructed onto substrates made during the same build cycle, which were called crucibles. The crucible design was small and very easy to manufacture, resembling a $10 \\mathrm{~mm} \\times 15 \\mathrm{~mm} x$ $5 \\mathrm{~mm}$ rectangular shape. They could be built very quickly, and could be used to populate an entire build plate, allowing for dozens of different combinations to be used during a single build. The crucibles could easily be removed from the plate. Additionally, the crucible design included a cavity which could have the layer depth effectively varied.", "start_char_idx": 218875, "end_char_idx": 223056, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "17915070-e460-4304-bf70-05376fccc34e": {"__data__": {"id_": "17915070-e460-4304-bf70-05376fccc34e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "662eff4a-4ae8-4962-b43f-c59ece23f995", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ff9f63e8ce91542ffcfdfe4acef17a064e7ace8e65cb74b0f9b47ad48f1a0a33", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ff7481c5-bf73-4170-a624-bf24d76ec601", "node_type": "1", "metadata": {}, "hash": "edddc74afc9c4aaf4e05318a7babc8cba59380da6fbae8486872da66aee94478", "class_name": "RelatedNodeInfo"}}, "text": "Most research involving single track formations use a plane surface, such as commercially available, hot rolled metal plates, as a substrate for generating single tracks, [161]-[163].\n\nAt in-situ conditions during the laser-powder bed fusion process, single track lines were constructed onto substrates made during the same build cycle, which were called crucibles. The crucible design was small and very easy to manufacture, resembling a $10 \\mathrm{~mm} \\times 15 \\mathrm{~mm} x$ $5 \\mathrm{~mm}$ rectangular shape. They could be built very quickly, and could be used to populate an entire build plate, allowing for dozens of different combinations to be used during a single build. The crucibles could easily be removed from the plate. Additionally, the crucible design included a cavity which could have the layer depth effectively varied. This meant that the layer depth used to fabricate tracks could be included as a process parameter very easily. Two experiments were performed to determine the differences incurred by using the crucible design, Experiment B and D. In experiment D, single tracks were constructed onto mild steel inserts and were subject to topographical and metallographic investigation. The same exact parameters from Experiment B were used to create single tracks on crucible substrates in Experiment D.\n\nIt was found that tracks constructed on crucible substrates would form with less track fragmentation and balling than tracks constructed on the mild steel inserts. Regions within the process map where track failed to build on inserts were found to have increased track\\\\\nformation on crucibles, though this improvement could be very limited. This has been attributed to the presence of oxides on the mild steel substrates reducing wettability of the melt, and the increase in surface roughness by comparison to the insert surfaces. Additive manufacturing tends to produce uneven, wave-like surfaces, which can improve the wetting ability of melts that form on such surfaces, [117], [118].\n\nKeyhole mode melting was observed less frequently, and the depth-to-width ratios for tracks made using crucibles were far lower than for those made using the inserts. However, smooth track formation was discouraged when using the crucible substrate instead of the insert substrate.\n\nTwo other experiments, experiment $\\mathrm{C}$ and $\\mathrm{E}$, were performed to investigate the addition of layer depth as a process parameter. It was found that increasing layer depth encouraged instability and break-up of the track. Whilst most of the experiments in this research were performed using stainless steel $316 \\mathrm{~L}$ powder, Experiment E used Ti-6Al-4V titanium alloy powder, showing that the crucible design could be successfully used with different materials.\n\n\\section*{Chapter 7 Conclusions and Further Work}\nThe effects of three processing parameters on the formation of single tracks during the laserpowder bed fusion process were investigated in this work. The parameters were laser power $(W)$, scan speed $\\left(\\mathrm{mms}^{-1}\\right)$ and layer depth $(\\mu \\mathrm{m})$. The single tracks were analysed through topographical imaging and metallographic examination.\n\n\\subsection*{7.1 Specific Conclusions}\n\\begin{enumerate}\n  \\item A traditional single-track experiment (Experiment B), in which single-tracks are deposited directly onto a base-plate, was carried out with laser power ranging between $75 \\mathrm{~W}$ and $200 \\mathrm{~W}$, and with scan speed ranging between $100 \\mathrm{mms}^{-1}$ and $1000 \\mathrm{mms}^{-1}$, based on a point distance of $60 \\mu \\mathrm{m}$ and the layer depth approximately measuring $50 \\mu \\mathrm{m}$. Stainless steel $316 \\mathrm{~L}$ metal powder was used as the building material, whilst mild steel plate was used as a substrate. It was found that:\n\\end{enumerate}\n\nI. Optimal track production was achieved at a laser power and scan speed of 200W and $300 \\mathrm{mms}^{-1}$, respectively, which should be compared to optimal settings chosen through a design of experiments based on measurements of density which gave a power of $180 \\mathrm{~W}$ and a scan speed of $433 \\mathrm{mms}^{-1}$. Tracks formed at this combination were continuous, remaining unbroken throughout their length, but had formed irregularities within the track.\n\nII. Slower scan speeds yielded smoother, regular tracks, however keyhole mode melting was observed, with additional induced porosity.\n\nIII. Faster scan speeds would induce instability in the melt pool, causing track fragmentation.", "start_char_idx": 222213, "end_char_idx": 226765, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ff7481c5-bf73-4170-a624-bf24d76ec601": {"__data__": {"id_": "ff7481c5-bf73-4170-a624-bf24d76ec601", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "17915070-e460-4304-bf70-05376fccc34e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "fb774ffee807cbb67b732a16b82ce8a6f79e5f83023e517b1064ca0d4017ac09", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ced4ae64-b0dd-432c-a007-ca3e1166d839", "node_type": "1", "metadata": {}, "hash": "baf6881417a3c1d899fd6e5a44246830c5940a35b69877e53da5f8136179ec98", "class_name": "RelatedNodeInfo"}}, "text": "Stainless steel $316 \\mathrm{~L}$ metal powder was used as the building material, whilst mild steel plate was used as a substrate. It was found that:\n\\end{enumerate}\n\nI. Optimal track production was achieved at a laser power and scan speed of 200W and $300 \\mathrm{mms}^{-1}$, respectively, which should be compared to optimal settings chosen through a design of experiments based on measurements of density which gave a power of $180 \\mathrm{~W}$ and a scan speed of $433 \\mathrm{mms}^{-1}$. Tracks formed at this combination were continuous, remaining unbroken throughout their length, but had formed irregularities within the track.\n\nII. Slower scan speeds yielded smoother, regular tracks, however keyhole mode melting was observed, with additional induced porosity.\n\nIII. Faster scan speeds would induce instability in the melt pool, causing track fragmentation.\n\n\\begin{enumerate}\n  \\setcounter{enumi}{1}\n  \\item A new experiment nominated the crucible experiment (Experiment $C$ ) was carried out with stainless steel $316 \\mathrm{~L}$ metal powder and laser powers ranging between $100 \\mathrm{~W}$ and 200W. Crucible substrate layer depths were varied between $50 \\mu \\mathrm{m}$ and $200 \\mu \\mathrm{m}$. The\\\\\noptimal parameters for smooth, continuous tracks at each layer thickness were found:\\\\\nI. $50 \\mu \\mathrm{m}$ depth: Laser power of $100 \\mathrm{~W}$ and scan speed of $87 \\mathrm{mms}^{-1}$.\n\\end{enumerate}\n\nII. $100 \\mu \\mathrm{m}$ depth: Laser power of $100 \\mathrm{~W}$ and scan speed of $87 \\mathrm{mms}^{-1}$.\n\nIII. $150 \\mu \\mathrm{m}$ depth: Laser power of $130 \\mathrm{~W}$ and scan speed of $113 \\mathrm{mms}^{-1}$.\n\nIV. $200 \\mu \\mathrm{m}$ depth: Laser power of $130 \\mathrm{~W}$ and scan speed of $84 \\mathrm{mms}^{-1}$.\n\n\\begin{enumerate}\n  \\setcounter{enumi}{2}\n  \\item A crucible experiment (Experiment D) was carried out with stainless steel $316 \\mathrm{~L}$ metal powder using the same machine parameters as used in the traditional single-track experiment B. For this experiment, it was observed that\n\\end{enumerate}\n\nI. Optimal track production was achieved using a laser power and scan speed of $200 \\mathrm{~W}$ and $400 \\mathrm{mms}^{-1}$, respectively, which should be compared to optimal settings chosen through a design of experiments based on measurements of density which gave a power of $190 \\mathrm{~W}$ and a scan speed of $500 \\mathrm{mms}^{-1}$.\n\nII. Keyhole mode melting was observed at regions of high laser power and low scan speed, with a maximum peak depth-to-width ratio of 0.6\n\n\\begin{enumerate}\n  \\setcounter{enumi}{3}\n  \\item A crucible experiment (Experiment E) was carried out with titanium alloy Ti-6Al-4V as the building material with laser powers ranging between $150 \\mathrm{~W}$ and $200 \\mathrm{~W}$, and with scan speed ranging between $500 \\mathrm{mms}^{-1}$ and $3000 \\mathrm{mms}^{-1}$. Crucible substrates layer depths were varied between $50 \\mu \\mathrm{m}$ and $200 \\mu \\mathrm{m}$. Using a laser power and scan speed of $200 \\mathrm{~W}$ and $500 \\mathrm{mms}^{-1}$, respectively, produced fairly stable, but irregular tracks at the $50 \\mu \\mathrm{m}$ and $100 \\mu \\mathrm{m}$ layer depths. At higher layer depths, tracks would fail to build or form as droplets, even at high power and low scan speeds. A larger range of processing parameters would provide more conclusive results.\n\n  \\item The crucible substrate design was used successfully for three experiments. A direct comparison between single track structures made on metal-plate based substrates and the crucible substrates was carried out, and in the findings, differences were seen between the traditional single-track experiments possibly due to the surface roughness difference between the two types of substrates.", "start_char_idx": 225898, "end_char_idx": 229655, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ced4ae64-b0dd-432c-a007-ca3e1166d839": {"__data__": {"id_": "ced4ae64-b0dd-432c-a007-ca3e1166d839", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ff7481c5-bf73-4170-a624-bf24d76ec601", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f3a2effb0c3991d8dd31dfba06db0c024a25c1aa5e3f5b7195ee44bacfa24ad1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "82b0c154-88bc-42a7-8992-6eaa2f39a82c", "node_type": "1", "metadata": {}, "hash": "0936ba6840fb211bb8c3b80967394b3c1196db05ad95c44687cda52aefbd4799", "class_name": "RelatedNodeInfo"}}, "text": "Using a laser power and scan speed of $200 \\mathrm{~W}$ and $500 \\mathrm{mms}^{-1}$, respectively, produced fairly stable, but irregular tracks at the $50 \\mu \\mathrm{m}$ and $100 \\mu \\mathrm{m}$ layer depths. At higher layer depths, tracks would fail to build or form as droplets, even at high power and low scan speeds. A larger range of processing parameters would provide more conclusive results.\n\n  \\item The crucible substrate design was used successfully for three experiments. A direct comparison between single track structures made on metal-plate based substrates and the crucible substrates was carried out, and in the findings, differences were seen between the traditional single-track experiments possibly due to the surface roughness difference between the two types of substrates.\n\n\\end{enumerate}\n\n\\subsection*{7.2 General Conclusions}\n\\begin{enumerate}\n  \\item A new experiment methodology has been developed nominated the crucible experiment, in which a custom in-situ substrate is built during the same build cycle out of the same material powder. The crucible design includes an internal cavity which replicates a miniature powder bed with a variable powder layer depth. In the crucible experiment, single-tracks are fabricated within this cavity.\n\n  \\item The crucible methodology has been tested on two materials (stainless steel $316 \\mathrm{~L}$ and titanium alloy Ti-6Al-4V) and validated against a more traditional experiment in which single-tracks are deposited directly onto a baseplate.\n\n  \\item Generally, when comparing the crucible experiments to the traditional single-track experiments, tracks were formed more readily on the crucible substrate than the traditional substrate when using the same laser processing parameters. The range in which track formation would occur would increase to include more low power and/or high scan speed combinations. The recorded line build percentage would also increase across the process map.\n\n  \\item Keyhole-mode melting and pore formation was less frequently observed in the crucible method during the comparison.\n\n  \\item Optimal track production was achieved using a laser power $200 \\mathrm{~W}$ and higher scan speeds of $400 \\mathrm{mms}^{-1}$, and were closer to the machine parameters used in practise and determined from density-based design of experiments. Tracks formed at these settings were fabricated without evidence of keyhole mode melting (less induced porosity) and had a reasonably high line build percentage (99\\%).\n\n  \\item The development of the crucible method has met the main objective of this work, which was to develop and standardise a single-track experimental method which would capture in a high throughput manner the instabilities and weld-profiles as a function of machine parameters.\n\n  \\item Additionally, the crucible method is more representative of the tracks laid during the process and can work for different powder alloys.\n\n  \\item The capability of precisely varying the powder layer thickness onto which the single lines are build is an example of the usefulness of the method, but other parameters such as hatch spacing could also be explored.\n\n\\end{enumerate}\n\n\\subsection*{7.3 Further Work}\n\\begin{enumerate}\n  \\item The baseline traditional experimentation needs to be repeated with stainless steel 316L and titanium alloy Ti-6Al-4V baseplates.\n\n  \\item Crucible Experiment $D$ needs to be repeated in with a variety of layer thicknesses and with the higher power lasers now available on the REN400 and RENAM500\n\n  \\item To this extent, the use of the crucible experiment on the Reduced Build Volume available on the REN400 will allow a greater exploration and optimisation of alloy composition and powder morphologies from the perspective of single tracks.\n\n  \\item Crucible Experiment $\\mathrm{E}$ could also be repeated with a wider range of processing parameters (e.g. include hatch spacing and higher laser powers) to provide more conclusive results.\n\n  \\item The entire set of data is now ready for comparison to computational thermal models.\n\n  \\item Further analysis of transition to keyholing, particularly as a function of beam width, powder depth and using powder alloys with different powder size distributions.\n\n\\end{enumerate}\n\n\\section*{References}\n[1] K. Jensen, 'State-of-the-art of different available and coming RP-systems', in Proceedings of the 2nd Scandinavian Rapid Prototyping Conference, Exhibition and Course, Danish Technological Institute, Aarhus, 1993.\n\n[2] J. P. Kruth, 'Material Incress Manufacturing by Rapid Protyping Techniques', CIRP Ann. - Manuf. Technol., vol. 40, pp. 603-614, Dec. 1991.", "start_char_idx": 228859, "end_char_idx": 233504, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "82b0c154-88bc-42a7-8992-6eaa2f39a82c": {"__data__": {"id_": "82b0c154-88bc-42a7-8992-6eaa2f39a82c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ced4ae64-b0dd-432c-a007-ca3e1166d839", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d73ff095b3ca0f7ec91e57f55c33981e10365fd81edb5c9c04134d89462431ce", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b7c596a0-5b99-476b-9c46-44613ceec6b5", "node_type": "1", "metadata": {}, "hash": "4b233597951abf4ff7f382d6d92c9ca2ce9d9a7b65249ce120090c4a0b4706bf", "class_name": "RelatedNodeInfo"}}, "text": "include hatch spacing and higher laser powers) to provide more conclusive results.\n\n  \\item The entire set of data is now ready for comparison to computational thermal models.\n\n  \\item Further analysis of transition to keyholing, particularly as a function of beam width, powder depth and using powder alloys with different powder size distributions.\n\n\\end{enumerate}\n\n\\section*{References}\n[1] K. 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Aeronaut., Sep. 2017.\n\n\\section*{Appendix 1 - TMS Paper 3026}\n\\section*{Verification of Numerically Calculated Cooling Rates of Powder Bed Additive Manufacturing}\nH.-W. Mindt ${ }^{1}$, M. Megahed ${ }^{1}$, N.P. Lavery ${ }^{2}$, A. Giordimaina ${ }^{2}$, S.G.R. Brown ${ }^{2}$\n\n'ESI Group, Kruppstr. 90, 45145 Essen, Germany\n\n${ }^{2}$ Swansea University, Bay Campus, College of Engineering, Fabian Way, Crymlyn Burrows, Swansea, SA1 8EN United Kingdom\n\nKeywords: Additive Manufacturing, Powder Bed, Direct Metal Laser Melting, Modelling, Verification\n\npreliminary validation effort was performed by comparing the measured track widths with those predicted numerically [5] and by comparing the level of porosity obtained for different\\\\\nprocessing conditions [9]. In an attempt to approach code further verification the authors purse the specification of a reference benchmark for DMLM/SLM.\n\n\\section*{Modelling Algorithms}\nMicro-models are pursued to resolve the melt pool physics including laser radiative interaction with the powder, heat transfer, phase change and surface tension forces and Marangoni forces. They are based on computational fluid dynamics algorithms to solve the Navier-Stokes equations $[10,11,12,13]$. The momentum equations are extended using source terms to account for gravitational forces, recoil pressure and surface tension. The energy equation is complemented with source terms accounting for latent heat of fusion and evaporation as well as radiation. The laser is modelled as a Gaussian heat source. Two codes are used to solve the conservation equations, one based on the Finite Volume $[14,15,16]$ and the other on Lattice Boltzmann [17, 181. The Finite Volume code utilized is CFD-ACE+ FSLGroun [201 which has heen recently\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-166}\n\\end{center}\n\nFigure 1: (a) LPW $316 \\mathrm{~L}$ and Ti-6Al-4V powder size distributions and (b) the meandre laser track build strategy\n\nExperiment 1 (Single layer 316L)\n\nIn experiment (El) a single layer of 316L was melted onto the base plate in a meander pattern using the point distance ( $\\mathrm{PD}=65 \\mu \\mathrm{m}$ ) and hatch spacing ( $\\mathrm{HS}=124 \\mu \\mathrm{m}$ ). Various exposure times and laser powers were used, and micrographs were taken from the top and at cross-sections through the laser tracks (Figure 2) for a laser power of $200 \\mathrm{~W}$ and an exposure time of $150 \\mu \\mathrm{s}$.", "start_char_idx": 257958, "end_char_idx": 261342, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "471cb1be-3025-40e8-a04b-e279cadfee7f": {"__data__": {"id_": "471cb1be-3025-40e8-a04b-e279cadfee7f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a44309d2-6149-408f-acc0-1fcaf8c50dbe", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "74573318b1728fcfbbc1215126f8dce60e195f845d6e9a44738b9c00c17b3ccd", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b2ec9c95-77a5-418f-928f-b81d1e4e86cd", "node_type": "1", "metadata": {}, "hash": "3376da4fc6d2ee1ec36a579c9b6457ac87f3db111d48ceb76e3da5cada753825", "class_name": "RelatedNodeInfo"}}, "text": "Various exposure times and laser powers were used, and micrographs were taken from the top and at cross-sections through the laser tracks (Figure 2) for a laser power of $200 \\mathrm{~W}$ and an exposure time of $150 \\mu \\mathrm{s}$. The measurements of the 316L melt bead onto the base plate give typical widths of about $100 \\mu \\mathrm{m}$ ( $30 \\mu \\mathrm{m}$ wider than the laser beam) and heights of about $40-50 \\mu \\mathrm{m}$. There is typically a shallow (elliptical shaped) heat affected zone below the bead into the base plate (Figure 2 (b)). The bead cross section is etched and there is a clear difference between the larger grain structures in the underlying base plate, also made from 316L steel and there is evidence of pitting in the heat\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-167}\n\\end{center}\n\nRayleigh-Plateau instabilities. Measurements would indicate a laser track width of about $82 \\mu \\mathrm{m}$ which is only marginally higher than the laser diameter, however, it should be pointed out that this was done directly onto the powder, with less heat transmitted vertically it would be expected that the bead would have a higher dome than if melted onto the base plate, where it would run off closing the gaps between tracks slightly more. In normal builds using the same laser settings,\\\\\nrelative densities have been measured in the $97-99 \\%$ range with low porosity identified by micrographs. This would suggest that the re-melting during a multi-layer deposition works in much the same way as seen in experiment 2 , and any holes in the underlying layer are filled by subsequent melt liquid and smoothed by re-melting.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-168}\n\\end{center}\n\n\\section*{Results \\& Discussion}\nResults presented here are those obtained for Ti-Al6-V4. Figure l(b) shows the reference powder bed utilized for all calculations and the corresponding laser track. The particles representation is shown as resolved by the computational model. This particular specimen of the powder bed was chosen because it offers an interesting combination of smaller particles packed densely close to one another as well as some large particles that were pushed ahead of the coater causing some areas to be free of powder. Figure 5 shows a comparison of the melt pool shape as predicted by\n\ncomparing two codes that were developed separately at ESI Group and University of Swansea. The qualitative results are comparable showing similar melt pools sizes and capturing solidified surface irregularities. The cooling rate is in the order of $1 \\mathrm{e} 6{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-170}\n\\end{center}\n\nFigure 5: Top view comparison of melt pooi evolution: Left finite volume results with full range temperature scale. Right LBM results with limited legend range showing more details of the particle melting\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-171}\n\\end{center}\n\n1651-1662.\n\n\\begin{enumerate}\n  \\setcounter{enumi}{2}\n  \\item Thermal and Mechanical Finite Element Modeling of Laser Forming from Metal and Ceramic Powders. K. Dai, L. Shaw. [ed.] Elsevier Ltd. 2004, Acta Materialia, Vols. 52: 69-80.\n\n  \\item A Three Dimensional Finite Element Analysis of the Temperature Field During Laser Melting of Metal Powders in Additive Layer Manufacturing. I.A. Robert, C.J. Wang, R. Esterlein, M. Stanford D.J. Mynors, s.1. : Elsevier Ltd., 2009, International Journal f Machine Tools \\& Manufacture, Vols. 49: pp. $916-923$\n\n\\end{enumerate}\n\n\\section*{Appendix 2 - Metallographic Preparation for Experiment A}\nEach horizontal and vertical sample was mounted in a conductive thermosetting mounting resin Konductomet, supplied by Buehler.", "start_char_idx": 261109, "end_char_idx": 265009, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b2ec9c95-77a5-418f-928f-b81d1e4e86cd": {"__data__": {"id_": "b2ec9c95-77a5-418f-928f-b81d1e4e86cd", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "471cb1be-3025-40e8-a04b-e279cadfee7f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "86efaaa07ce843a6a373061cedfe2c94859063fb3181eb92095a0612e3e9d6b5", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2eae0b22-9369-40aa-923a-17ba98c28a22", "node_type": "1", "metadata": {}, "hash": "ac9d549ca13b58714eacb355f5e5aad3e39ae61dcb993aa049ef77a1c86b6ff8", "class_name": "RelatedNodeInfo"}}, "text": "K. Dai, L. Shaw. [ed.] Elsevier Ltd. 2004, Acta Materialia, Vols. 52: 69-80.\n\n  \\item A Three Dimensional Finite Element Analysis of the Temperature Field During Laser Melting of Metal Powders in Additive Layer Manufacturing. I.A. Robert, C.J. Wang, R. Esterlein, M. Stanford D.J. Mynors, s.1. : Elsevier Ltd., 2009, International Journal f Machine Tools \\& Manufacture, Vols. 49: pp. $916-923$\n\n\\end{enumerate}\n\n\\section*{Appendix 2 - Metallographic Preparation for Experiment A}\nEach horizontal and vertical sample was mounted in a conductive thermosetting mounting resin Konductomet, supplied by Buehler. Each sample mount was mounted using the Buehler SimpliMet XPS1 compression mounting machine.\n\nThe grinding and polishing of the samples were performed using an AutoMet 300 Buehler grinder-polisher. The parameters used in the table below were used to obtain the optimum polishing results with the least amount of scratches, and were used to prepare each sample:\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline\n\\begin{tabular}{l}\nAbrasive Disk/ \\\\\nPolishing cloth \\\\\nused \\\\\n\\end{tabular} & \\begin{tabular}{l}\nLubricant/ Polishing \\\\\nSuspension used \\\\\n\\end{tabular} & \\begin{tabular}{l}\nApplied \\\\\nForce (N) \\\\\n\\end{tabular} & \\begin{tabular}{l}\nDisk \\\\\nSpeed \\\\\n(RPM) \\\\\n\\end{tabular} & \\begin{tabular}{l}\nHead \\\\\nSpeed \\\\\n(RPM) \\\\\n\\end{tabular} & \\begin{tabular}{c}\nTime \\\\\n(minutes) \\\\\n\\end{tabular} \\\\\n\\hline\n\\begin{tabular}{l}\nSilicon Carbide \\\\\nGrinding Paper, \\\\\n600 Grit \\\\\n\\end{tabular} & Water & 27 & 150 & 30 & 4 \\\\\n\\hline\n\\begin{tabular}{c}\nBuehler Hercules \\\\\nH Grinding Disk \\\\\n\\end{tabular} & \\begin{tabular}{c}\nBuehler MetaDi \\\\\nSupreme $9 \\mu \\mathrm{m}$ \\\\\nDiamond Suspension \\\\\n\\end{tabular} & 27 & 150 & 30 & 2 \\\\\n\\hline\nBuehler Ultrapad & \\begin{tabular}{c}\nBuehler MetaDi \\\\\nSupreme $9 \\mu \\mathrm{m}$ \\\\\nDiamond Suspension \\\\\n\\end{tabular} & 27 & $` 150$ & 30 & 6 \\\\\n\\hline\n\\begin{tabular}{l}\nBuehler TriDent \\\\\n3um Polishing \\\\\nCloth \\\\\n\\end{tabular} & \\begin{tabular}{c}\nBuehler MetaDi \\\\\nSupreme $3 \\mu \\mathrm{m}$ \\\\\nDiamond Suspension \\\\\n\\end{tabular} & 13 & 150 & 30 & 6 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nBetween each grinding and polishing phase, the samples were washed first with water followed by ethanol. The samples were quickly dried under hot air after being washed with ethanol.\n\nEach sample was etched with a solution of $100 \\mathrm{~mL}$ ethanol, $100 \\mathrm{~mL}$ hydrochloric acid at $48 \\%$ concentration and $5 \\mathrm{~g}$ of Copper(II) Chloride, commonly referred to as Kalling's Reagent No.2. The samples were immersed in the etchant for 20-90 seconds, washed clean with water and ethanol and dried under hot air.\n\n\\section*{Appendix 3 - Metallographic Preparation for Experiment C}\nEach horizontal and vertical sample was mounted in a conductive thermosetting mounting resin Konductomet, supplied by Buehler. Each sample mount was mounted using the Buehler SimpliMet XPS1 compression mounting machine.\n\nThe grinding and polishing of the samples were performed using an AutoMet 300 Buehler grinder-polisher.", "start_char_idx": 264402, "end_char_idx": 267475, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2eae0b22-9369-40aa-923a-17ba98c28a22": {"__data__": {"id_": "2eae0b22-9369-40aa-923a-17ba98c28a22", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b2ec9c95-77a5-418f-928f-b81d1e4e86cd", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0a11e09543cc8ad8f036aee36e1d536a7807c4a6630ac5856e8d990e5591499f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1dc585c5-1a4a-4dd7-b019-a39543e79a4c", "node_type": "1", "metadata": {}, "hash": "40be07f671e203e70557d64d1021e55dddc4a5594eb53c907a2fa803f1b624b4", "class_name": "RelatedNodeInfo"}}, "text": "Each sample was etched with a solution of $100 \\mathrm{~mL}$ ethanol, $100 \\mathrm{~mL}$ hydrochloric acid at $48 \\%$ concentration and $5 \\mathrm{~g}$ of Copper(II) Chloride, commonly referred to as Kalling's Reagent No.2. The samples were immersed in the etchant for 20-90 seconds, washed clean with water and ethanol and dried under hot air.\n\n\\section*{Appendix 3 - Metallographic Preparation for Experiment C}\nEach horizontal and vertical sample was mounted in a conductive thermosetting mounting resin Konductomet, supplied by Buehler. Each sample mount was mounted using the Buehler SimpliMet XPS1 compression mounting machine.\n\nThe grinding and polishing of the samples were performed using an AutoMet 300 Buehler grinder-polisher. The parameters used in the table below were used to obtain the optimum polishing results with the least amount of scratches, and were used to prepare each sample:\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline\n\\begin{tabular}{l}\nAbrasive Disk/ \\\\\nPolishing cloth \\\\\nused \\\\\n\\end{tabular} & \\begin{tabular}{l}\nLubricant/ Polishing \\\\\nSuspension used \\\\\n\\end{tabular} & \\begin{tabular}{l}\nApplied \\\\\nForce (N) \\\\\n\\end{tabular} & \\begin{tabular}{l}\nDisk Speed \\\\\n(RPM) \\\\\n\\end{tabular} & \\begin{tabular}{l}\nHead \\\\\nSpeed \\\\\n(RPM) \\\\\n\\end{tabular} & Time (minutes) \\\\\n\\hline\n\\begin{tabular}{c}\nBuehler Hercules \\\\\nH Grinding Disk \\\\\n\\end{tabular} & \\begin{tabular}{c}\nBuehler MetaDi Supreme \\\\\n$6 \\mu \\mathrm{m}$ Diamond \\\\\nSuspension \\\\\n\\end{tabular} & 13 & 300 & 40 & \\begin{tabular}{l}\nUntil plane (usually \\\\\n$20-30$ seconds) \\\\\n\\end{tabular} \\\\\n\\hline\nBuehler Ultrapad & \\begin{tabular}{c}\nBuehler MetaDi Supreme \\\\\n$9 \\mu \\mathrm{m}$ Diamond \\\\\nSuspension \\\\\n\\end{tabular} & 13 & 200 & 40 & 5 \\\\\n\\hline\nBuehler Ultrapad & \\begin{tabular}{c}\nBuehler MetaDi Supreme \\\\\n$6 \\mu \\mathrm{m}$ Diamond \\\\\nSuspension \\\\\n\\end{tabular} & 13 & 200 & 40 & 5 \\\\\n\\hline\nBuehler TriDent & \\begin{tabular}{c}\nBuehler MetaDi Supreme \\\\\n3 $\\mu$ m Diamond \\\\\nSuspension \\\\\n\\end{tabular} & 13 & 200 & 40 & 10 \\\\\n\\hline\nBuehler TriDent & \\begin{tabular}{c}\nBuehler MetaDi Supreme \\\\\n$1 \\mu$ Diamond \\\\\nSuspension \\\\\n\\end{tabular} & 13 & 250 & 40 & 15 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nBetween each grinding and polishing phase, the samples were washed first with water followed by ethanol. The samples were quickly dried under hot air after being washed with ethanol.\n\nEach mounted was etched using Beraha II colour etchant. The preparation and appropriate precautions for using Beraha II is listed in Appendix 4. The samples were immersed in the etchant for 60-90 seconds, washed clean with water and propanol and dried under hot air.\n\n\\section*{Appendix 4 - Beraha II Etchant Preperation }\nBeraha II stock solution:\n\n\\begin{itemize}\n  \\item $800 \\mathrm{~mL}$ distilled water\n  \\item $400 \\mathrm{~mL}$ hydrochloric acid $32 \\%$\n  \\item $48 \\mathrm{~g}$ ammonium hydrogen fluoride\n\\end{itemize}\n\nFinal etchant:\n\n\\begin{itemize}\n  \\item $100 \\mathrm{~mL}$ Beraha II stock solution\n  \\item $1 \\mathrm{~g}$ potassium disulfite\n\\end{itemize}\n\nPrecautions: Wear goggles, gloves, vapour and dust respirator and synthetic apron on top of lab coat before handling materials.", "start_char_idx": 266737, "end_char_idx": 269935, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1dc585c5-1a4a-4dd7-b019-a39543e79a4c": {"__data__": {"id_": "1dc585c5-1a4a-4dd7-b019-a39543e79a4c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2eae0b22-9369-40aa-923a-17ba98c28a22", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2dcd4801692736de5f2107870ee4bf19296ed160f004cd6eed0fa94ad313a7e6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "58777ebc-4d5a-4e9b-97b6-ba0759d1db9b", "node_type": "1", "metadata": {}, "hash": "b56a49cb55f728b418ab4b8373a9a60250d69dade315e5dfdc1a1efad8be5c4b", "class_name": "RelatedNodeInfo"}}, "text": "The samples were immersed in the etchant for 60-90 seconds, washed clean with water and propanol and dried under hot air.\n\n\\section*{Appendix 4 - Beraha II Etchant Preperation }\nBeraha II stock solution:\n\n\\begin{itemize}\n  \\item $800 \\mathrm{~mL}$ distilled water\n  \\item $400 \\mathrm{~mL}$ hydrochloric acid $32 \\%$\n  \\item $48 \\mathrm{~g}$ ammonium hydrogen fluoride\n\\end{itemize}\n\nFinal etchant:\n\n\\begin{itemize}\n  \\item $100 \\mathrm{~mL}$ Beraha II stock solution\n  \\item $1 \\mathrm{~g}$ potassium disulfite\n\\end{itemize}\n\nPrecautions: Wear goggles, gloves, vapour and dust respirator and synthetic apron on top of lab coat before handling materials. Prepare all solutions in plastic containers, such as polypropylene, as ammonium bifluoride can attack glass and metals. The apparatus used for mixing the solution should also be made of plastic. Handle all materials under an active fume hood.\n\nStorage of stock solution: Store only in original receptacle, keep container tightly sealed. Storage class 8B, non-combustible corrosive liquid.\n\nDisposal of stock solution: Must not be disposed together with regular waste. Do not allow product to reach sewage system.\n\nStorage of final prepared etchant: Store only in original receptacle, keep container tightly sealed. Storage class 8B, non-combustible corrosive liquid. Keep in a cool, well-ventilated area.\n\nDisposal of final prepared etchant: Exactly the same as that of the stock solution. Method\n\nTo prepare the stock solution:\n\n\\begin{enumerate}\n  \\item Add $400 \\mathrm{~mL}$ of $32 \\%$ hydrochloric acid to $800 \\mathrm{~mL}$ of distilled water, slowly inside a fume cupboard.\n\n  \\item Add $48 \\mathrm{~g}$ of ammonium hydrogen fluoride. Allow to dissolve before moving on.\n\n\\end{enumerate}\n\nTo prepare final etchant:\n\n\\begin{enumerate}\n  \\item Add $1 \\mathrm{~g}$ of potassium disulfite to $100 \\mathrm{~mL}$ of the stock solution, allowing it to dissolve before starting the etch. Solution can be stored and used within 1 to 2 hours.\n\\end{enumerate}\n\n\\section*{Appendix 5 - Metallographic Preparation for Experiment E}\nAny sample with successfully built lines was sawed in half using a Buehler IsoMet 4000\n\nPrecision Cutter and subsequently mounted in Metprep Conducto-Mount conductive mounting compound. This was done using a Buehler SimpliMet XP51 mounting system. The crucibles of the same set of parameters were mounted together for convenience. The mounted samples were then ground and polished according to the procedures listed in the table below.", "start_char_idx": 269281, "end_char_idx": 271796, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "58777ebc-4d5a-4e9b-97b6-ba0759d1db9b": {"__data__": {"id_": "58777ebc-4d5a-4e9b-97b6-ba0759d1db9b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1dc585c5-1a4a-4dd7-b019-a39543e79a4c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "88dcaf7f6d25f3e90946526cb21e49276fb1ae77d5033b7ca77c00037358127c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9095c6cb-6848-4f07-9f00-9b6f81d16ea8", "node_type": "1", "metadata": {}, "hash": "279e5bd62a071284cc9493d3fda04a7c91c3ba32266770428e9198108c71a2aa", "class_name": "RelatedNodeInfo"}}, "text": "Allow to dissolve before moving on.\n\n\\end{enumerate}\n\nTo prepare final etchant:\n\n\\begin{enumerate}\n  \\item Add $1 \\mathrm{~g}$ of potassium disulfite to $100 \\mathrm{~mL}$ of the stock solution, allowing it to dissolve before starting the etch. Solution can be stored and used within 1 to 2 hours.\n\\end{enumerate}\n\n\\section*{Appendix 5 - Metallographic Preparation for Experiment E}\nAny sample with successfully built lines was sawed in half using a Buehler IsoMet 4000\n\nPrecision Cutter and subsequently mounted in Metprep Conducto-Mount conductive mounting compound. This was done using a Buehler SimpliMet XP51 mounting system. The crucibles of the same set of parameters were mounted together for convenience. The mounted samples were then ground and polished according to the procedures listed in the table below.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline\n\\begin{tabular}{l}\nAbrasive Disk/ \\\\\nPolishing cloth \\\\\nused \\\\\n\\end{tabular} & \\begin{tabular}{l}\nLubricant/ Polishing \\\\\nSuspension used \\\\\n\\end{tabular} & \\begin{tabular}{l}\nApplied \\\\\nForce $(\\mathrm{N})$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nDisk \\\\\nSpeed \\\\\n(RPM) \\\\\n\\end{tabular} & \\begin{tabular}{l}\nHead \\\\\nSpeed \\\\\n(RPM) \\\\\n\\end{tabular} & \\begin{tabular}{c}\nTime \\\\\n(minutes) \\\\\n\\end{tabular} \\\\\n\\hline\n\\begin{tabular}{c}\nSilicon Carbide \\\\\nGrinding Paper, \\\\\n600 Grit \\\\\n\\end{tabular} & Water & 27 & 300 & 40 & 5 \\\\\n\\hline\n\\begin{tabular}{c}\nSilicon Carbide \\\\\nGrinding Paper, \\\\\n1200 Grit \\\\\n\\end{tabular} & Water & 27 & 150 & 40 & 5 \\\\\n\\hline\nBuehler Ultrapad & \\begin{tabular}{c}\nBuehler MetaDi \\\\\nSupreme $9 \\mu m$ \\\\\nDiamond Suspension \\\\\n\\end{tabular} & 27 & 150 & 30 & 10 \\\\\n\\hline\n\\begin{tabular}{l}\nBuehler \\\\\nChemoMet \\\\\n\\end{tabular} & \\includegraphics[max width=\\textwidth]{2024_03_10_91a5199dc912785ed628g-176}\n & 22 & 150 & 30 & 10 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nThe polished samples were etched inside a fume cupboard using a batch of Kroll's reagent. The batch was made from the following $5 \\mathrm{ml} \\mathrm{HNO}^{3}, 10 \\mathrm{ml} \\mathrm{HF}$ at $48 \\%$ concentration, and $85 \\mathrm{ml}$ distilled water. Gloves and protective eyewear were worn whilst etching. Each specimen was swabbed with the reagent for $15-20$ seconds.\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\\usepackage{multirow}\n\n\\title{Data mining and statistical inference in selective laser melting }\n\n\n\\author{Chandrika Kamath $^{1}$}\n\\date{}", "start_char_idx": 270978, "end_char_idx": 273777, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9095c6cb-6848-4f07-9f00-9b6f81d16ea8": {"__data__": {"id_": "9095c6cb-6848-4f07-9f00-9b6f81d16ea8", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "58777ebc-4d5a-4e9b-97b6-ba0759d1db9b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b96554a2466d4a66da16eccc6ee5ac445fac746f6e5b8f5f23982124e215eb81", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c6185809-6b78-49f5-9e25-9046ee802ec0", "node_type": "1", "metadata": {}, "hash": "165d0446a4f10b31b1e2a2bcb4b8de870f4144ba3e03e9725a62f4131f5e8b52", "class_name": "RelatedNodeInfo"}}, "text": "Each specimen was swabbed with the reagent for $15-20$ seconds.\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\\usepackage{multirow}\n\n\\title{Data mining and statistical inference in selective laser melting }\n\n\n\\author{Chandrika Kamath $^{1}$}\n\\date{}\n\n\n%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?]{%\n  \\if\\relax#1\\relax%\n    \\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n  \\else%\n    \\if?#1\\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n    \\else\\svfootnotetext[#1]{#2}\\fi%\n  \\fi\n}\n\n\\begin{document}\n\\maketitle\nReceived: 13 October 2015 / Accepted: 18 December 2015 / Published online: 11 January 2016\n\n(C) Springer-Verlag London (outside the USA) 2016\n\n\\begin{abstract}\nSelective laser melting (SLM) is an additive manufacturing process that builds a complex three-dimensional part, layer-by-layer, using a laser beam to fuse fine metal powder together. The design freedom afforded by SLM comes associated with complexity. As the physical phenomena occur over a broad range of length and time scales, the computational cost of modeling the process is high. At the same time, the large number of parameters that control the quality of a part make experiments expensive. In this paper, we describe ways in which we can use data mining and statistical inference techniques to intelligently combine simulations and experiments to build parts with desired properties. We start with a brief summary of prior work in finding process parameters for high-density parts. We then expand on this work to show how we can improve the approach by using feature selection techniques to identify important variables, data-driven surrogate models to reduce computational costs, improved sampling techniques to cover the design space adequately, and uncertainty analysis for statistical inference. Our results indicate that techniques from data mining and statistics can complement those from physical modeling to provide greater insight into complex processes such as selective laser melting.\n\\end{abstract}\n\nKeywords Additive manufacturing $\\cdot$ Selective laser melting $\\cdot$ Design of experiments $\\cdot$ Sampling $\\cdot$ Feature selection $\\cdot$ Code surrogates $\\cdot$ Uncertainty analysis\n\\footnotetext{$\\boxtimes$ Chandrika Kamath\n\n\\href{mailto:kamath2@1lnl.gov}{kamath2@1lnl.gov}\n\n1 Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94551, USA\n}\n\n\\section*{1 Introduction}\nAdditive manufacturing (AM) is a process for fabricating parts, layer-by-layer, directly from a three-dimensional digital model. It presents an opportunity for producing complex parts not possible with traditional manufacturing processes, such as medical implants that are customized to each individual and lattices that reduce weight while maintaining the strength of structures. AM can also reduce both the time to market and material waste.", "start_char_idx": 273156, "end_char_idx": 276748, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c6185809-6b78-49f5-9e25-9046ee802ec0": {"__data__": {"id_": "c6185809-6b78-49f5-9e25-9046ee802ec0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9095c6cb-6848-4f07-9f00-9b6f81d16ea8", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7f98c5a3b1c610217ea457d428881032521f4a7e1874c639f3486dd369e1c689", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "77109e6a-3165-4ecd-a192-1cc2c4bc8058", "node_type": "1", "metadata": {}, "hash": "9c09bc10f8a7245ebcfc810b555d6a527bfc44a6e31b35ba38288059d1220410", "class_name": "RelatedNodeInfo"}}, "text": "\\end{abstract}\n\nKeywords Additive manufacturing $\\cdot$ Selective laser melting $\\cdot$ Design of experiments $\\cdot$ Sampling $\\cdot$ Feature selection $\\cdot$ Code surrogates $\\cdot$ Uncertainty analysis\n\\footnotetext{$\\boxtimes$ Chandrika Kamath\n\n\\href{mailto:kamath2@1lnl.gov}{kamath2@1lnl.gov}\n\n1 Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94551, USA\n}\n\n\\section*{1 Introduction}\nAdditive manufacturing (AM) is a process for fabricating parts, layer-by-layer, directly from a three-dimensional digital model. It presents an opportunity for producing complex parts not possible with traditional manufacturing processes, such as medical implants that are customized to each individual and lattices that reduce weight while maintaining the strength of structures. AM can also reduce both the time to market and material waste. However, a number of technical issues must still be addressed before widespread use of AM technology becomes a reality, including dimensional accuracy of AM parts, process optimization to quickly build complex parts with desired properties, and increased confidence in properties of parts fabricated using this process [1, $2,24]$.\n\nIn this paper, we consider selective laser melting (SLM), which is an additive manufacturing process that uses a laser beam to create three-dimensional metal parts by fusing fine metal powders together. The process, also referred to as laser powder-bed fusion, starts by first slicing a threedimensional model of the part into two-dimensional layers, each of a specified thickness, usually in the range of 30 to $100 \\mu \\mathrm{m}$. A thin layer of metal powder is then spread on a base plate and the first layer is created by selectively melting the powder in the locations indicated in the first slice of the part. The process is repeated for the second slice, and the part is built, layer by layer, with the power and speed of the laser selected so that the energy density is sufficient to melt the powder and the layer below it, thus integrating the new layer into the rest of the part.\n\nThe design freedom afforded by AM comes with associated complexity. The modeling of the process is complicated as the physical phenomena occur over a broad range of length and time scales. Three-dimensional computer\\\\\nsimulations to understand the relationship between processing parameters and the thermal behavior of the material as it is melted by the laser, for example, see $[9,11,17,19,22]$, can be quite expensive to run, even on high-performance computer systems, especially if they include various aspects of the physics underlying SLM. Exploring the design space using experiments can also be challenging as there are a large number of parameters, more than 130 by some estimates [31], that influence the process and thus the final quality of the part. Figure 1 shows some of the parameters related to the laser and the powder bed. These include:\n\n\\begin{itemize}\n  \\item The laser parameters such as (i) the laser power, ranging from 50 to $400 \\mathrm{~W}$, though higher-powered lasers are also available; (ii) the laser beam profile, usually Gaussian, though flat-top is also used; (iii) the laser scan speed, ranging from $100 \\mathrm{~mm} / \\mathrm{s}$ to over $5000 \\mathrm{~mm} / \\mathrm{s}$; (iv) the scan-line overlap, which is the distance between adjacent scan lines and must be chosen to ensure no unmelted powder remains between scan lines; and (v) the scan strategy, which is the path taken by the laser to melt the powder in appropriate places in a slice.\n\n  \\item The powder bed parameters, which include the layer thickness, the particle size distribution in the powder, and the porosity of the powder bed. The layer thickness is the amount by which the build platform is lowered for each slice. To build a part, this is set to a fixed value, typically in the range of $30-50 \\mu \\mathrm{m}$, with a larger layer thickness resulting in a reduced build time but requiring a larger energy density for melting. The layer thickness is determined by considering the particle size distribution of the powder; a layer thickness much smaller than the mean particle size would result in poor utilization of the powder as most of the particles would be swept away by the coater used to spread the layer of powder. The powder size distribution tends to change when the powder is recycled; to maintain the size distribution over time, the powder may need to be mixed with fresh powder or sieved to remove large clusters of particles sintered together.", "start_char_idx": 275891, "end_char_idx": 280442, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "77109e6a-3165-4ecd-a192-1cc2c4bc8058": {"__data__": {"id_": "77109e6a-3165-4ecd-a192-1cc2c4bc8058", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c6185809-6b78-49f5-9e25-9046ee802ec0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4f0578695350d406cb68b6f75ca98595282b2072ccf2098c588e86e6f554ecdb", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f0765d8a-248e-4774-ace0-71c52385b968", "node_type": "1", "metadata": {}, "hash": "c93e7c453201055e75ff06a962786abeccb9bb1473643e10e86504e2be3119f6", "class_name": "RelatedNodeInfo"}}, "text": "The layer thickness is the amount by which the build platform is lowered for each slice. To build a part, this is set to a fixed value, typically in the range of $30-50 \\mu \\mathrm{m}$, with a larger layer thickness resulting in a reduced build time but requiring a larger energy density for melting. The layer thickness is determined by considering the particle size distribution of the powder; a layer thickness much smaller than the mean particle size would result in poor utilization of the powder as most of the particles would be swept away by the coater used to spread the layer of powder. The powder size distribution tends to change when the powder is recycled; to maintain the size distribution over time, the powder may need to be mixed with fresh powder or sieved to remove large clusters of particles sintered together. The porosity of the powder bed introduces an added complication. When a layer of powder of a given thickness is melted, its height reduces due to the elimination of the voids in between the powder particles. The next layer of powder therefore is deeper than the amount by which the build platform drops at each layer. This thickness of the powder increases until it reaches a steady state of $l t /(1-v f)$,where $l t$ is the layer thickness and $v f$ is the void fraction. For a typical void fraction of $0.4-0.5$, the actual thickness of the powder, at steady state, is $1.667-2.0$ times the set layer thickness. Therefore, the laser parameters, such as the speed and the power, must be selected to melt through the steady-state powder thickness into the substrate below.\n\n  \\item The material properties, such as density, thermal conductivity, heat capacity, and latent heat of the material being processed also determine the amount of energy required to melt the powder and the substrate. In addition, these properties determine the width and height of the melt bead, which, in turn, influence the parameters in the scanning strategy, such as the scan-line overlap.\n\n\\end{itemize}\n\nUsing additive manufacturing technology to build a part with certain desired properties such as part density, dimensional accuracy, weight, or surface smoothness can be challenging for several reasons. First, as we have just discussed, the number of parameters that have to be set in an AM system is large. Second, the parameters can vary during the build of a part. For example, the laser beam size may change as the optics used to focus the laser get heated during use. Or the porosity of the powder bed may change depending on the distribution of the powder size particles in a layer of powder. Third, the parameters could vary across builds, for example, when the laser beam becomes uncalibrated over time and no longer remains Gaussian, or when the measured value of the laser power drifts from the set value over time, or when the powder size distribution changes as it is re-used many times. Finally, some of the material properties, such\\\\\nFig. 1 Schematic illustrating the SLM process and some of the parameters that influence the properties of a part\n\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_ac9eb55e466d65629094g-02}\\\\\nas the absorptivity, may not be known precisely, may take values within a range, or may depend on whether the material in the path of the laser beam is liquid, powder, or solid, as the absorptivity of these forms is different. All these factors introduce uncertainties that influence the repeatability of the process and create uncertainties in the properties of the additively manufactured part.\n\nIn this paper, we describe the use of techniques from data mining and statistical inference to build high-density ( $>99 \\%$ ) parts using selective laser melting. We use an iterative approach, described in Section 2, that allows us to explore the design space efficiently. We then summarize our prior work in Section 3 where we demonstrate the use of simple simulations and experiments to determine the process parameters for high-density 316L stainless steel (SS) parts. The main contribution of this paper is to build on this prior work to gain additional insight into the SLM process and improve our approach. Specifically, we consider feature selection techniques to identify the important parameters (Section 4), data-driven surrogate models to reduce computational costs (Section 5), improved sampling techniques to reduce the number of sample points in design space (Section 6), complex models to improve predictions (Section 7), and uncertainty analysis for statistical inference (Section 8). We conclude with a summary of our observations and plans for future work in Section 9.", "start_char_idx": 279610, "end_char_idx": 284263, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f0765d8a-248e-4774-ace0-71c52385b968": {"__data__": {"id_": "f0765d8a-248e-4774-ace0-71c52385b968", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "77109e6a-3165-4ecd-a192-1cc2c4bc8058", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4244ecd85f87b54b1fc0ac7c8f7d1c6d3004e7f2ad80077384115d7d25c43112", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bc4b8e39-bd4c-4302-973a-debc610fc8f4", "node_type": "1", "metadata": {}, "hash": "ec2007ca8115cdd62718c24822623c8b410ac14c9f0a6548352e806d074ff834", "class_name": "RelatedNodeInfo"}}, "text": "We use an iterative approach, described in Section 2, that allows us to explore the design space efficiently. We then summarize our prior work in Section 3 where we demonstrate the use of simple simulations and experiments to determine the process parameters for high-density 316L stainless steel (SS) parts. The main contribution of this paper is to build on this prior work to gain additional insight into the SLM process and improve our approach. Specifically, we consider feature selection techniques to identify the important parameters (Section 4), data-driven surrogate models to reduce computational costs (Section 5), improved sampling techniques to reduce the number of sample points in design space (Section 6), complex models to improve predictions (Section 7), and uncertainty analysis for statistical inference (Section 8). We conclude with a summary of our observations and plans for future work in Section 9.\n\nA brief note on the terminology used in this paper-we use the term \"model\" to mean both physical models as well as data-driven models. As the main focus of this paper is the use of data mining and statistical techniques, to make the paper accessible to a multi-disciplinary audience, we will also describe the terms used in these fields when we first introduce them.\n\n\\section*{2 Approach for process optimization}\nThere are a number of approaches to find the optimal parameters for creating additively manufactured parts with desired properties (see, for example, the summary in [15] for the work done in 316L stainless steel for $>99 \\%$ density parts). Typically, carefully designed experiments are used to study how various process parameters, such as powder quality, layer thickness, laser power, laser speed, and scanning strategies, would influence the properties, such as density and surface roughness, of a part. In some cases, small cubes are built and their properties evaluated [20,29, 34], while in others [16,21,32], a process window is first identified by using single track experiments. In these experiments, single tracks are made on a layer of powder using a range of laser power and speed values. As these experiments are simpler than building small pillars, they can be more costeffective in narrowing the range of design space for optimal parameters. Principled techniques from the field of design and analysis of experiments $[8,25]$ are also gaining acceptance. For example, Delgado et al. [5] used a full factorial experimental design with three factors (layer thickness, scan speed, and build direction), and two levels per factor, in their study on part quality for a fixed laser power. The outputs of interest were dimensional accuracy, mechanical properties, and surface roughness and an analysis of variance (ANOVA) approach was used to understand the effects of various factors on the outputs.\n\nMuch of this early work was done using systems with relatively low laser powers of 50-100 W. As a result, the design space spanned by laser power and speed was not very large and optimization through experimentation was a practical option. However, as machines with higher laser powers (of $400 \\mathrm{~W}$ or greater) have become common, using just experiments to identify optimal parameters can be prohibitively expensive. In addition, as the types of SLM machines have proliferated, the use of different beam sizes, scanning parameters, and powder size distributions has enlarged the design space so that determining the optimal parameters for each machine for different materials has become more challenging.\n\nTo address these issues in the context of identifying parameters for high-density AM parts, we devised an iterative approach that combines experiments and computer simulations. Our work was motivated by the fact that our AM machine, a Concept Laser (CL) M2 system, had a relatively narrow beam, with $\\mathrm{D} 4 \\sigma=52 \\mu \\mathrm{m}$, and maximum power of $400 \\mathrm{~W}$. (D4 $\\sigma$ is the beam diameter and, for a perfect Gaussian beam, is four times the standard deviation of the Gaussian.) This meant that we could not use the parameters for optimal density available in the literature as these were for machines with lower powers of $<225 \\mathrm{~W}$ and larger beam sizes of $\\mathrm{D} 4 \\sigma \\approx 120 \\mu \\mathrm{m}$. Given the large range of power (100-400 W) for our machine, exploring the design space using just experiments was prohibitively expensive, especially as we processed different materials, and a more efficient approach was required.\n\nFigure 2 illustrates our iterative approach that combines computer simulations and experiments using techniques from data mining and statistical inference; a practical application of this approach is illustrated in the rest of the paper.", "start_char_idx": 283339, "end_char_idx": 288116, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bc4b8e39-bd4c-4302-973a-debc610fc8f4": {"__data__": {"id_": "bc4b8e39-bd4c-4302-973a-debc610fc8f4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f0765d8a-248e-4774-ace0-71c52385b968", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b97e8b2771d3f746bbf2b36c8cf2cfa5c234bc3ee4fbbd06e649fcab150105d4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "517badab-c8b4-47ce-9b03-62246950e41a", "node_type": "1", "metadata": {}, "hash": "abbaf039c7b24d2e7324bde9d67c7da66c2264b17941f84b6a53886afade2c59", "class_name": "RelatedNodeInfo"}}, "text": "(D4 $\\sigma$ is the beam diameter and, for a perfect Gaussian beam, is four times the standard deviation of the Gaussian.) This meant that we could not use the parameters for optimal density available in the literature as these were for machines with lower powers of $<225 \\mathrm{~W}$ and larger beam sizes of $\\mathrm{D} 4 \\sigma \\approx 120 \\mu \\mathrm{m}$. Given the large range of power (100-400 W) for our machine, exploring the design space using just experiments was prohibitively expensive, especially as we processed different materials, and a more efficient approach was required.\n\nFigure 2 illustrates our iterative approach that combines computer simulations and experiments using techniques from data mining and statistical inference; a practical application of this approach is illustrated in the rest of the paper. Starting with a densely sampled design space of parameters, we run simple, and relatively inexpensive, simulations and experiments to progressively narrow the space of parameters as we move toward more expensive and accurate simulations and experiments. In each cycle, we have a set of samples that span the space of input SLM parameters. We run the experiments and/or simulations at the sample points, extract the characteristics of interest (such as the melt-pool dimensions or the part density), and analyze the data that relate the sample points to the characteristics of interest.\n\nFig. 2 Schematic illustrating the iterative process that uses data mining and statistical inference to combine simulations and experiments to reduce the time and costs to determine optimal process parameters\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-04}\n\\end{center}\n\nThis analysis could include visualization using scatter plots or parallel-coordinate plots (Section 3.1), feature selection to identify important parameters (Section 4), building surrogate models for prediction (Sections 5 and 7.2), and uncertainty analyses (Section 8) to find regions that are less sensitive to minor changes in the parameters. From this analysis, we identify a subset of samples that meets our requirements. We then perform more complex simulations and experiments at these sample points, and iterate until we have obtained the desired results.\n\nThis iterative approach has several benefits. First, by starting with simple simulations and experiments, we can quickly and efficiently identify which regions of the design space are viable as they yield melt pools that are deep enough so that a part can be built. This is particularly relevant when we are working with materials that may not have been additively manufactured before, or with machines with different process parameters, or with powders with different particle size distributions. Second, the large number of SLM process parameters implies that we need to identify sample points in a high-dimensional space, where the dimension of the space is the number of parameters. To span a space adequately, the number of samples required is exponential in the dimension. This makes it prohibitively expensive to start exploring the entire space by building many parts. Using simpler experiments and simulations lowers the cost of exploring the space of parameters more fully, thus increasing the chance of finding all sets of parameters that yield desired properties. Third, the iterative approach enables us to progressively make bigger samples and perform more complex simulations, while building on what we have learned from simpler experiments and simulations. This reduces costs as the complex simulations are computationally more expensive and it takes longer to build the bigger samples and evaluate their properties. Finally, by using data mining techniques to analyze the data from the simulations and experiments at each step, we can fully exploit the data we do collect and better guide the next set of experiments and simulations. We next describe how we used this approach to identify process parameters for highdensity 316L SS parts. We have also successfully used this approach to create parts with $>99 \\%$ density for other materials, and the ideas can also be extended to other properties of a part.\n\n\\section*{3 Creating high-density 316L SS parts}\nThis section summarizes our prior work as described in Kamath et al. [15] and provides the background for the contributions of this paper. Our primary goal was to determine the process parameters that would result in 316L stainless steel parts with > $99 \\%$ density on our Concept Laser M2 machine. A secondary goal was to understand how the density varied as we varied the laser power and speed.\n\n\\subsection*{3.1 Using simple simulations}\nTo identify the viable range of process parameters, we started with the very simple Eagar-Tsai (E-T) model [6] to determine under what conditions we would obtain melt pools that were deep enough to melt a layer of powder and the substrate below.", "start_char_idx": 287286, "end_char_idx": 292246, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "517badab-c8b4-47ce-9b03-62246950e41a": {"__data__": {"id_": "517badab-c8b4-47ce-9b03-62246950e41a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bc4b8e39-bd4c-4302-973a-debc610fc8f4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c4109dc8f853f98a6a41d3c81782d722782a3aec594feb4db8b4e869caa169c7", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "518e795f-148c-43ad-8ab2-eed3044b1aa8", "node_type": "1", "metadata": {}, "hash": "8576a269c83ba5ae18f9ce43a0513f59eab96fc95edb4e8c9e09227c4e30e433", "class_name": "RelatedNodeInfo"}}, "text": "We have also successfully used this approach to create parts with $>99 \\%$ density for other materials, and the ideas can also be extended to other properties of a part.\n\n\\section*{3 Creating high-density 316L SS parts}\nThis section summarizes our prior work as described in Kamath et al. [15] and provides the background for the contributions of this paper. Our primary goal was to determine the process parameters that would result in 316L stainless steel parts with > $99 \\%$ density on our Concept Laser M2 machine. A secondary goal was to understand how the density varied as we varied the laser power and speed.\n\n\\subsection*{3.1 Using simple simulations}\nTo identify the viable range of process parameters, we started with the very simple Eagar-Tsai (E-T) model [6] to determine under what conditions we would obtain melt pools that were deep enough to melt a layer of powder and the substrate below. Eagar-Tsai is a thermal conduction model that considers a Gaussian beam on a flat plate to describe conduction-mode laser melting. The resulting temperature distribution is used to compute the melt-pool width, depth, and length as a function of four parameters-laser power, laser speed, beam size, and laser absorptivity of the powder.\n\nThe Eagar-Tsai model does not directly relate the process parameters to the density of a part, which is the property of interest. It also does not consider powder other than the effect of powder on the laser absorptivity, so its results provide only an estimate of the melt-pool characteristics. However, this estimate was sufficient to guide the next steps in our work. In addition, the simplicity of the model makes it computationally inexpensive, taking $\\approx 1 \\mathrm{~min}$ to run on a laptop. This allows us to sample the input parameter space\n\nTable 1 Ranges and levels for the full factorial sampling of the EagarTsai model input parameter space\n\n\\begin{center}\n\\begin{tabular}{lllc}\n\\hline\nParameter & Minimum & Maximum & Levels \\\\\n\\hline\nPower $(\\mathrm{W})$ & 50 & 400 & 7 \\\\\nSpeed $(\\mathrm{mm} / \\mathrm{s})$ & 50 & 2250 & 11 \\\\\nBeam size D4 $\\sigma(\\mu \\mathrm{m})$ & 50 & 68 & 3 \\\\\nAbsorptivity $\\eta$ & 0.3 & 0.5 & 2 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nrather densely, ensuring that we consider all possible viable cases.\n\nWe sampled the four-parameter input space using a full factorial design of computer experiments ([25] and [8]). This method divides the range of each parameter into several levels, and then randomly selects a point in each cell. Table 1 lists the minimum and maximum values for each of the four input parameters, as well as the number of levels, which result in 462 simulations. The upper bound on the laser power was set to the maximum of the CL M2 machine. The lower limit on the speed was set to ensure sufficient melting at the low-power values such that the melt-pool depth would be at least $30 \\mu \\mathrm{m}$, which was the layer thickness selected for our experiments based on the prior work of Yasa [34]. The upper limit on the speed was estimated at a value that would likely result in a relatively shallow melt pool at the high-power value. The lower and upper limits on the beam size were obtained from measurements of the beam size at focus offsets of 0 and $1 \\mathrm{~mm}$. The absorptivity was assumed to be around 0.4 . By varying the beam size and the absorptivity, we accounted for possible variations in these parameters over time or build conditions as we built each part.\n\nThe output from the Eagar-Tsai model was processed to extract the melt-pool depth, width, and length. Of these three dimensions, the depth was of greatest interest as it indicates if the energy is sufficient to melt through the powder to the substrate for the given values of power and speed, under the assumption that the beam size and absorptivity might vary by a small amount. To understand how the depth was related to the four input parameters, we used parallel coordinate plots [12]. These plots are a way of displaying high-dimensional, multi-variate data. First, the values of each variable for all simulations are scaled so they lie in the same range and can be displayed in a single plot.", "start_char_idx": 291339, "end_char_idx": 295523, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "518e795f-148c-43ad-8ab2-eed3044b1aa8": {"__data__": {"id_": "518e795f-148c-43ad-8ab2-eed3044b1aa8", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "517badab-c8b4-47ce-9b03-62246950e41a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c444a77046d09237396474faa692eebd62698d10dbab1a5e98cfb2675487cc50", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f7dde400-4cca-4d9e-9bef-addbe4b362d0", "node_type": "1", "metadata": {}, "hash": "1a78f0db0b1b0b4e3ef54db6b6b4daafd1cd5a8cd76c21dab65f613c14161847", "class_name": "RelatedNodeInfo"}}, "text": "The absorptivity was assumed to be around 0.4 . By varying the beam size and the absorptivity, we accounted for possible variations in these parameters over time or build conditions as we built each part.\n\nThe output from the Eagar-Tsai model was processed to extract the melt-pool depth, width, and length. Of these three dimensions, the depth was of greatest interest as it indicates if the energy is sufficient to melt through the powder to the substrate for the given values of power and speed, under the assumption that the beam size and absorptivity might vary by a small amount. To understand how the depth was related to the four input parameters, we used parallel coordinate plots [12]. These plots are a way of displaying high-dimensional, multi-variate data. First, the values of each variable for all simulations are scaled so they lie in the same range and can be displayed in a single plot. For our data, we chose this range to be 0.0 through 4.0. Next, the five dimensions, $\\left(f_{1}, f_{2}, f_{3}, f_{4}, f_{5}\\right)$, are indicated along the $\\mathrm{x}$-axis, and their scaled values along the $\\mathrm{y}$-axis. Each simulation is represented as a poly-line connecting the values of the scaled variables, $\\left(x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\\right)$, for that simulation.\n\nFigure 3 shows the parallel coordinate plot for our 462 simulations. The values of the depth were divided into three groups for small $(<60 \\mu \\mathrm{m}$ ), moderate (between 60 and $120 \\mu \\mathrm{m}$ ), and large $(>120 \\mu \\mathrm{m}$ ), and the polylines in each group were assigned a different color. The simulations with small depth were discarded as they were likely to leave unmelted particles. The simulations with large depth were also discarded as they are the result of the energy density being too high, possibly resulting in keyhole-mode melting [18], where the laser drills into the material, leaving voids as the material vaporizes. The thresholds for identifying moderate depth were obtained as follows: For a powder layer thickness of $30 \\mu \\mathrm{m}$ and a void fraction of 0.4 , the steadystate powder thickness would be $1.667 * 30=50 \\mu \\mathrm{m}$ and, for a void fraction of 0.5 , it would be $60 \\mu \\mathrm{m}$ (see Section 1). So, the energy density must be sufficient to melt through a powder layer of 50-60 $\\mu \\mathrm{m}$ into the substrate. We ensure this by selecting the minimum depth of a viable simulation in the Eagar-Tsai model to be $60 \\mu \\mathrm{m}$. The upper threshold was set to twice the lower threshold to ensure that we had sufficient number of viable cases, though we did recognize that some of these cases could result in keyhole-mode melting.\n\nThe parallel plot also sheds some light on the relative importance of the four input parameters. Based on the clustering of the colors in the speed and power columns, we observe that simulations with low speed and high power have deep melt pools, while simulations with high speed and low power have shallow melt pools, which is what one would expect. However, there is no such clear clustering of colors in the beam size and absorptivity, indicating\\\\\nFig. 3 Parallel coordinate plot of the melt-pool depth as a function of the input parameters-laser speed, power, beam size, and absorptivity. Each simulation, represented by the scaled values\n\n$\\left(x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\\right)$ of the inputs and output, is shown on the left as a poly-line connecting these values. The polylines are colored based on the depth\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-05}\n\\end{center}\n\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_ac9eb55e466d65629094g-05(1)}\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_ac9eb55e466d65629094g-06}\n\nFig. 4 Single track experiments: Left-the 14 track tilted plate.", "start_char_idx": 294619, "end_char_idx": 298492, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f7dde400-4cca-4d9e-9bef-addbe4b362d0": {"__data__": {"id_": "f7dde400-4cca-4d9e-9bef-addbe4b362d0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "518e795f-148c-43ad-8ab2-eed3044b1aa8", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "85bc2d3e76e2edf30374287921df249dd8d1b3924e2fcdd7f0491c7786e1602d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d891f1cb-f6a3-442b-9045-e37bfa3a16f0", "node_type": "1", "metadata": {}, "hash": "6816ac8c4597df547dfbe469b4549285c6b7dab0e569ae31c65a9e799ba79a3a", "class_name": "RelatedNodeInfo"}}, "text": "Each simulation, represented by the scaled values\n\n$\\left(x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\\right)$ of the inputs and output, is shown on the left as a poly-line connecting these values. The polylines are colored based on the depth\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-05}\n\\end{center}\n\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_ac9eb55e466d65629094g-05(1)}\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_ac9eb55e466d65629094g-06}\n\nFig. 4 Single track experiments: Left-the 14 track tilted plate. Right-cross-sections of two tracks at $30 \\mu \\mathrm{m}$ layer thickness: (top) track 4 at $300 \\mathrm{~W}$ and $1800 \\mathrm{~mm} / \\mathrm{s}$, (bottom) track 5 at $300 \\mathrm{~W}$ and $1500 \\mathrm{~mm} / \\mathrm{s}$\n\nthat these inputs are less relevant to the determination of the depth, allowing us to focus on the power and speed parameters in our experiments. In Section 4, we will arrive at a similar result using quantitative techniques from data mining.\n\n\\subsection*{3.2 Using simple experiments}\nThe full sampling of the design space of the Eagar-Tsai model gives us a viable set of power and speed values as indicated by the model. However, the depth of the melt pool obtained from this simplified model is only an approximation to the actual depth of the melt pool in an experiment. Since we do not know how far the Eagar-Tsai approximation is from reality, we next performed a set of single-track experiments to obtain the melt pool dimensions for a set of power-speed combinations chosen from the viable range of parameters.\n\nSingle-track experiments [32] are a simple way to evaluate the melt pool dimensions for a material for specific values of laser power, laser speed, layer thickness, and powder size distribution. A single layer of powder at a specific layer thickness is spread on the plate, and multiple tracks made at different laser power and speed values. The plate is then cut so the cross-section of a track can be measured to obtain the melt-pool depth, height, and width. Figure 4 shows the plate with the 14 single tracks used in our experiments. The plate is $40 \\mathrm{~mm}$ by $40 \\mathrm{~mm}$ and is bolted to the build platform at the center. It is tilted so that the powder thickness is 0 at the left and increases linearly to $200 \\mu \\mathrm{m}$ at the right. This allows us to evaluate the melt-pool dimensions at several different values of layer thickness [33]. For example, a vertical cut $6 \\mathrm{~mm}$ from the left edge gives the cross-sections of the 14 tracks at a powder layer thickness of $30 \\mu \\mathrm{m}$, as shown for the two tracks in the figure, where the laser direction is perpendicular to the plane of the paper.\n\nTable 2 shows the depth of the melt pool obtained using the Eagar-Tsai model, as well as the experiments at powder layer thickness of 30 and $50 \\mu \\mathrm{m}$, for the 14 tracks. The results for the Eagar-Tsai model were generated using a fixed value for the beam size of $\\mathrm{D} 4 \\sigma=54 \\mu \\mathrm{m}$ and absorptivity of 0.3 . Our results indicate that the Eagar-Tsai model typically under-predicts the depth, though given that the model has no powder, it is difficult to compare the results with experiments that do include powder. Note that the Eagar-Tsai results use values of D $4 \\sigma$ and absorptivity that are nearer to the lower end of the ranges used in our sampling of the design space as indicated in Table 1.\\\\\nTable 2 The depth for each track from the Eagar-Tsai model and the single track experiments at layer thickness of 30 and $50 \\mu \\mathrm{m}$. The Eagar-Tsai results were obtained assuming D $4 \\sigma$ of $54 \\mu \\mathrm{m}$ and absorptivity of 0.3 .", "start_char_idx": 297916, "end_char_idx": 301663, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d891f1cb-f6a3-442b-9045-e37bfa3a16f0": {"__data__": {"id_": "d891f1cb-f6a3-442b-9045-e37bfa3a16f0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f7dde400-4cca-4d9e-9bef-addbe4b362d0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4bd8ec2995b3e62ab891efe7845a8832b3fcfa80ebf83fb5ba745d2dd17bc8a2", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "66210764-af00-4ea7-a8f5-70d691d32b12", "node_type": "1", "metadata": {}, "hash": "ef1beb7998ec1b42946a73ed342378ae4e7f6a3ef74f2365cd10affe676f95cb", "class_name": "RelatedNodeInfo"}}, "text": "Our results indicate that the Eagar-Tsai model typically under-predicts the depth, though given that the model has no powder, it is difficult to compare the results with experiments that do include powder. Note that the Eagar-Tsai results use values of D $4 \\sigma$ and absorptivity that are nearer to the lower end of the ranges used in our sampling of the design space as indicated in Table 1.\\\\\nTable 2 The depth for each track from the Eagar-Tsai model and the single track experiments at layer thickness of 30 and $50 \\mu \\mathrm{m}$. The Eagar-Tsai results were obtained assuming D $4 \\sigma$ of $54 \\mu \\mathrm{m}$ and absorptivity of 0.3 . Note the inconsistency in experiment at $50 \\mu \\mathrm{m}$ between track 5 and 6 , where a lower speed results in lower depth\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline\n\\multirow[t]{2}{*}{Track\\#} & \\multirow{2}{*}{}\\begin{tabular}{l}\nPower \\\\\n(W) \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{l}\nSpeed \\\\\n$(\\mathrm{mm} / \\mathrm{s})$ \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{l}\nE-T depth \\\\\n$(\\mu \\mathrm{m})$ \\\\\n\\end{tabular} & \\multicolumn{2}{|c|}{Depth $(\\mu \\mathrm{m})$ from experiment} \\\\\n\\hline\n &  &  &  & Layer thickness $30 \\mu \\mathrm{m}$ & Layer thickness $50 \\mu \\mathrm{m}$ \\\\\n\\hline\n1 & 400 & 1800 & 50.4 & 105 & 90 \\\\\n\\hline\n2 & 400 & 1500 & 57.6 & 119 & 137 \\\\\n\\hline\n3 & 400 & 1200 & 62.4 & 182 & 183 \\\\\n\\hline\n4 & 300 & 1800 & 43.2 & 65 & 58 \\\\\n\\hline\n5 & 300 & 1500 & 48.0 & 94 & 86 \\\\\n\\hline\n6 & 300 & 1200 & 55.2 & 114 & 76 \\\\\n\\hline\n7 & 300 & 800 & 67.2 & 175 & 207 \\\\\n\\hline\n8 & 200 & 1500 & 38.4 & 57 & 43 \\\\\n\\hline\n9 & 200 & 1200 & 43.2 & 68 & 62 \\\\\n\\hline\n10 & 200 & 800 & 52.8 & 116 & 106 \\\\\n\\hline\n11 & 200 & 500 & 67.2 & 195 & 179 \\\\\n\\hline\n12 & 150 & 1200 & 36.0 & 30 & 37 \\\\\n\\hline\n13 & 150 & 800 & 43.2 & 67 & 63 \\\\\n\\hline\n14 & 150 & 500 & 55.2 & 120 & 104 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 2 also shows that the experimental data for $30 \\mu \\mathrm{m}$ layer thickness is consistent, with higher powers and lower speeds resulting in deeper melt pools. In contrast, there are some inconsistencies in the $50 \\mu \\mathrm{m}$ results; for example, track 6 at $300 \\mathrm{~W}, 1200 \\mathrm{~mm} / \\mathrm{s}$ has a smaller depth than track 5 at $1500 \\mathrm{~mm} / \\mathrm{s}$. In some cases, the depth of a track at $50 \\mu \\mathrm{m}$ layer thickness is greater than at $30 \\mu \\mathrm{m}$. These inconsistencies are to be expected in experiments. Since we are spreading a thin layer of powder, with a particle size distribution, over a tilted plate, it is difficult to ensure that the layer thickness at the location of the cut is exactly what we expect it to be. This variation is usually small when we are in the stable regime of conduction-mode melting, as our experiments using a flat plate have shown [18].", "start_char_idx": 301016, "end_char_idx": 303851, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "66210764-af00-4ea7-a8f5-70d691d32b12": {"__data__": {"id_": "66210764-af00-4ea7-a8f5-70d691d32b12", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d891f1cb-f6a3-442b-9045-e37bfa3a16f0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8eb1a047f231a46dd4aa231900fe958e3e989b9f45ccafb3e262dd149d15a44e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1035c199-1c9a-454f-8998-3eadcab5a576", "node_type": "1", "metadata": {}, "hash": "0197e5706c21a8e5fd096e5f711c2f15055dfd31609070ed3373059d00399816", "class_name": "RelatedNodeInfo"}}, "text": "In contrast, there are some inconsistencies in the $50 \\mu \\mathrm{m}$ results; for example, track 6 at $300 \\mathrm{~W}, 1200 \\mathrm{~mm} / \\mathrm{s}$ has a smaller depth than track 5 at $1500 \\mathrm{~mm} / \\mathrm{s}$. In some cases, the depth of a track at $50 \\mu \\mathrm{m}$ layer thickness is greater than at $30 \\mu \\mathrm{m}$. These inconsistencies are to be expected in experiments. Since we are spreading a thin layer of powder, with a particle size distribution, over a tilted plate, it is difficult to ensure that the layer thickness at the location of the cut is exactly what we expect it to be. This variation is usually small when we are in the stable regime of conduction-mode melting, as our experiments using a flat plate have shown [18]. However, it introduces a source of uncertainty in our analysis.\n\n\\subsection*{3.3 Building 316L SS density pillars}\nNext, we used the results from the single-track experiments to guide the selection of parameters for building small pillars for density measurements. We built $10 \\mathrm{~mm} \\times 10 \\mathrm{~mm} \\times 8 \\mathrm{~mm}$ high pillars using a layer thickness of $30 \\mu \\mathrm{m}$ and a variety of power and speed combinations that were chosen to ensure sufficiently deep melt-pools at steady-state powder layer thickness. We used default values for all remaining process parameters [15].\n\nThe density of the pillars, measured using the Archimedes method, is shown in Fig. 5 for the first two sets of pillars, each set consisting of 24 pillars on a build plate. The first set was used to determine if we could obtain $>99 \\%$ dense pillars and the second set was used to fill the gaps in the curves. The results show that it is possible to use our approach to create high-density pillars for power values ranging from 150 to $400 \\mathrm{~W}$. For a given power value, increasing the speed leads to insufficient melting and\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-07}\n\\end{center}\n\nFig. 5 The density of 316L pillars built using Concept Laser (CL) powder for several power and speed values lower density, which is expected. The density also reduces at low speed due to voids resulting from keyhole mode laser melting; this reduction is, however, not as large as the reduction due to insufficient melting. We also observe that at higher powers, the density is high over a wider range of scan speeds, unlike at lower powers. This indicates that higher powers could provide greater flexibility in choosing process parameters that optimize various properties of a manufactured part. However, it remains to be seen if operating at higher powers will have other negative effects on the microstructure or properties of a part.\n\n\\subsection*{3.4 Improving the process}\nWe have successfully used the approach outlined in Section 3.1 through Section 3.3 on other materials and powders of different sizes. We improved the process by using a flat plate instead of a tilted plate as we found that we often used just one value for the layer thickness. This allowed us to double the number of tracks on a plate, resulting in a more extensive exploration of the design space. We have also explored ways in which we can use data mining and statistical techniques to gain insight and improve the process. We next describe how we have built on our prior work by using feature selection techniques to identify the important parameters, surrogate models for prediction, improved sampling, more complex simulations, and uncertainty analysis.\n\n\\section*{4 Identifying important variables}\nIn Section 3.1, we used parallel coordinate plots to gain a qualitative understanding of the relative importance of the four input parameters to the Eagar-Tsai model. In data mining, dimension reduction techniques [13] are often used to identify important variables and reduce the dimension of a problem, which is the number of variables or features that describe the objects in a data set. In our problem, the objects are the simulations or experiments and the features are the input or process parameters. Reducing the dimension of a problem provides several benefits. By focusing on just the important variables, it becomes easier to understand how the outputs might be related to the inputs. Furthermore, as the number of sample points required to adequately sample the design space is exponential in the number of dimensions, reducing the dimension lowers the cost of expensive simulations and experiments.", "start_char_idx": 303091, "end_char_idx": 307594, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1035c199-1c9a-454f-8998-3eadcab5a576": {"__data__": {"id_": "1035c199-1c9a-454f-8998-3eadcab5a576", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "66210764-af00-4ea7-a8f5-70d691d32b12", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "acc22391dd5dc1e4350f050508d816c9e5224658df4baeb41b761434fd85ff62", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7c3fe068-a8c7-4abb-9240-48d94465b20e", "node_type": "1", "metadata": {}, "hash": "3cad0c7e0e50d9d1636fc7898264a9e7662508036e19b9fdf110a4a1e9779529", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{4 Identifying important variables}\nIn Section 3.1, we used parallel coordinate plots to gain a qualitative understanding of the relative importance of the four input parameters to the Eagar-Tsai model. In data mining, dimension reduction techniques [13] are often used to identify important variables and reduce the dimension of a problem, which is the number of variables or features that describe the objects in a data set. In our problem, the objects are the simulations or experiments and the features are the input or process parameters. Reducing the dimension of a problem provides several benefits. By focusing on just the important variables, it becomes easier to understand how the outputs might be related to the inputs. Furthermore, as the number of sample points required to adequately sample the design space is exponential in the number of dimensions, reducing the dimension lowers the cost of expensive simulations and experiments. We can also build more accurate surrogate models (Sections 5 and 7.2) if irrelevant variables are removed from the data set.\n\nThere are a variety of dimension reduction techniques, including linear and non-linear methods that transform the data into a lower-dimensional space, as well as feature subset selection methods that rank the features in order\\\\\nof importance. We prefer feature subset methods as they directly inform us which features are important, unlike transform methods, where the interpretation of the variables in the transformed space may not be straightforward. We consider two methods that operate directly on continuous inputs and outputs, as methods that first discretize the variables could be sensitive to the discretization used.\n\nThe correlation-based feature selection (CFS) method [10] is a simple approach that calculates a figure of merit for a feature subset of $k$ features as\n\nMerit $=\\frac{k \\overline{r_{c f}}}{\\sqrt{k+k(k-1) \\overline{r_{f f}}}}$\n\nwhere $\\overline{r_{c f}}$ is the average feature-output correlation and $\\overline{r_{f f}}$ is the average feature-feature correlation. We use the Pearson correlation coefficient between two vectors, $X$ and $Y$, defined as\n\n$\\frac{\\operatorname{Cov}(X, Y)}{\\sigma_{X} \\sigma_{Y}}$\n\nwhere $\\operatorname{Cov}(X, Y)$ is the covariance between the two vectors and $\\sigma_{X}$ is the standard deviation of $X$. A higher value of Merit results when a subset of features has a high correlation $\\left(\\overline{r_{c f}}\\right)$ with the output and a low correlation $\\left(\\overline{r_{f f}}\\right)$ among themselves.\n\nIn the second feature selection method, the features are ranked using the mean squared error (MSE) as a measure of the quality of a feature [3]. This metric is used in regression trees (see Section 5) to determine which feature to use to split the samples at a node of the tree. Given a numeric feature $x$, the feature values are first sorted $\\left(x_{1}<x_{2}<\\right.$ $\\left.\\ldots<x_{n}\\right)$. Then, each intermediate value, $\\left(x_{i}+x_{i+1}\\right) / 2$, is proposed as a split point, and the samples split into two depending on whether the feature value of a sample is less than the split point or not. The MSE for a split $A$ is defined as\n\n$\\operatorname{MSE}(A)=p_{L} \\cdot s\\left(t_{L}\\right)+p_{R} \\cdot s\\left(t_{R}\\right)$\n\nwhere $t_{L}$ and $t_{R}$ are the subset of samples that go to the left and right, respectively, by the split based on $A, p_{L}$, and $p_{R}$ are the proportion of samples that go to the left and right, and $s(t)$ is the standard deviation of the $N(t)$ output values, $c_{i}$, of samples in the subset $t$ :\n\n$s(t)=\\sqrt{\\frac{1}{N(t)} \\sum_{i=1}^{N(t)}\\left(c_{i}-\\overline{c(t)}^{2}\\right)}$\n\nand $\\overline{c(t)}$ is the mean of the values in subset $t$. For each feature, the minimum MSE across the values of the feature is obtained and the features are rank ordered by increasing values of their minimum.", "start_char_idx": 306638, "end_char_idx": 310550, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7c3fe068-a8c7-4abb-9240-48d94465b20e": {"__data__": {"id_": "7c3fe068-a8c7-4abb-9240-48d94465b20e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1035c199-1c9a-454f-8998-3eadcab5a576", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a9e50b5530ceacb066fcd0c4434f47a7e6d628323ddf74144fc45c6090e2a4f7", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "566f1c0f-b468-4ee2-85af-fd95a9a57424", "node_type": "1", "metadata": {}, "hash": "e39da631789d85c848754cf802c8638b421a696c2b35e2d429cc297fe3fc4f90", "class_name": "RelatedNodeInfo"}}, "text": "For each feature, the minimum MSE across the values of the feature is obtained and the features are rank ordered by increasing values of their minimum. This method considers a feature to be important if it can split the data set into two, such that the standard deviation of the samples on either side of the split is minimized, that is, the output values are relatively similar on\\\\\nTable 3 Rank order of subsets of input parameters to the Eagar-Tsai model using the CFS method. The best subset of $k$ features is the one with the $k$ highest ranks\n\n\\begin{center}\n\\begin{tabular}{llllll}\n\\hline\n\\begin{tabular}{l}\nMelt \\\\\npool \\\\\n\\end{tabular} & Speed & Power & \\begin{tabular}{l}\nBeam \\\\\nsize \\\\\n\\end{tabular} & Absorptivity & Noise \\\\\n\\hline\nWidth & 5 & 4 & 2 & 3 & 1 \\\\\nLength & 3 & 5 & 2 & 4 & 1 \\\\\nDepth & 5 & 4 & 2 & 3 & 1 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\neach side. Note that while CFS considers subsets of features, the MSE method considers each feature individually.\n\nTable 3 presents the ordering of subsets of input features by importance, obtained using the CFS method, for the melt-pool width, length, and depth. A noise feature was added as another input; this is consistently ranked as the least important variable, as might be expected. The table indicates that for the melt-pool depth and width, the single most important input is the speed, while the two most important inputs are the speed and power. In contrast, for the length of the melt pool, the most important single input is the power, while the two most important inputs are power and absorptivity. The results for the MSE method in Table 4 are very similar, with the exception that the beam size is ranked lower than the noise variable for the depth of the melt pool. For all three melt-pool characteristics, the three lowest ranked variables have similar MSE values, so they have roughly the same order of importance.\n\nIn our problem, the depth and the width are the most important melt-pool characteristics; the depth indicates when the energy density is sufficient enough to melt through the powder into the substrate below, while the width is used to determine the distance between adjacent scan lines so that no unmelted powder particles remain between them. As the laser power and speed are the most relevant inputs to determining the melt-pool depth and width, it makes sense to focus on them first in our experiments.\n\nIn the Eagar-Tsai simulations, we chose to vary just four inputs. However, as we move to more complex simulations, feature selection and other dimension reduction techniques will become more useful in helping us to identify the important variables, potentially limiting the number of expensive\n\nTable 4 Rank order of the input parameters to the Eagar-Tsai model using the MSE method. A higher rank indicates a more relevant input\n\n\\begin{center}\n\\begin{tabular}{llllll}\n\\hline\n\\begin{tabular}{l}\nMelt \\\\\npool \\\\\n\\end{tabular} & Speed & Power & \\begin{tabular}{l}\nBeam \\\\\nsize \\\\\n\\end{tabular} & Absorptivity & Noise \\\\\n\\hline\nWidth & 5 & 4 & 2 & 3 & 1 \\\\\nLength & 3 & 5 & 2 & 4 & 1 \\\\\nDepth & 5 & 4 & 1 & 3 & 2 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nexperiments or simulations required to create parts with desired properties.\n\n\\section*{5 Building data-driven surrogate models}\nThe Eagar-Tsai model (Section 3.1) is a physical model that provides an approximation to the melt-pool dimensions given the laser power, laser speed, beam size, and absorptivity. When we run the model with various values of the input parameters to explore the design space, we create a data set that relates the specific values of the inputs to the corresponding outputs. If the design space is sampled adequately, we can use the data set to build a data-driven model which, given a set of values for the continuous inputs, will predict the continuous outputs.", "start_char_idx": 310399, "end_char_idx": 314249, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "566f1c0f-b468-4ee2-85af-fd95a9a57424": {"__data__": {"id_": "566f1c0f-b468-4ee2-85af-fd95a9a57424", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7c3fe068-a8c7-4abb-9240-48d94465b20e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "436f945cd9b7a80fe2d94d1b9f8a001db0d1ac86c7bd3c7e12140f0039c54d0f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2a138515-e07e-4eaf-a4c2-5986598f4353", "node_type": "1", "metadata": {}, "hash": "1ed86d349883a5c670b0de1d8ee5ead8b6f6e629435b4196223d1678860daf0b", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{5 Building data-driven surrogate models}\nThe Eagar-Tsai model (Section 3.1) is a physical model that provides an approximation to the melt-pool dimensions given the laser power, laser speed, beam size, and absorptivity. When we run the model with various values of the input parameters to explore the design space, we create a data set that relates the specific values of the inputs to the corresponding outputs. If the design space is sampled adequately, we can use the data set to build a data-driven model which, given a set of values for the continuous inputs, will predict the continuous outputs. There are many algorithms we can use to build such a regression model, ranging from parametric techniques that fit multi-variate functions, such as polynomials, to the data, to machine learning methods such as neural networks, regression trees, locally weighted learning, and support vector machines [13].\n\nWe consider two data-driven predictive models in this paper. This section focuses on regression trees, while the more complex Gaussian process models are discussed in Section 7.2. A regression tree [3] is a structure that is either a leaf, indicating a continuous value, or a decision node that specifies some test to be carried out on a feature, with a branch and sub-tree for each possible outcome of the test. If the feature is continuous, there are two branches, depending on whether the condition being tested is satisfied or not. The decision at each node of the tree is made to reveal the structure in the data. Regression trees tend to be relatively simple to implement, yield results that can be interpreted, and have built-in dimension reduction.\n\nA regression tree is built in two phases. In the training phase, the algorithm is \"trained\" by presenting it with a set of examples with known output values, such as the data obtained using the Eagar-Tsai model. In the test phase, the data-driven model created in the training phase is tested to determine how accurately it performs in predicting the output for known examples that were not used in building the model. If the results meet expected accuracy, the model can be put into operation to predict the output for a new sample point whose inputs are used to traverse the tree, following the decision at each node, until a leaf node is reached. The predicted value assigned to the sample is the mean of the output values of the training data that end up at that leaf node.\n\nIn building the regression tree, the test at each node is determined by examining each feature and finding the split that optimizes an impurity measure. We use the meansquared error, MSE, as defined in Section 4, as the impurity measure. The split at each node of the tree is the one that minimizes MSE across all features for the samples at that node. To avoid over fitting, we stop the splitting if the number of samples at a node is less than 5 or the standard deviation of the values of the output variable at a node has dropped below $5 \\%$ of the standard deviation of the output variable of the original data set. Note that each split creates a decision surface perpendicular to one of the axes (the feature selected for the split), dividing the data at that node into two, corresponding to sample points on the right and left side of the split location (the value of the feature used in the split). Depending on the data and the options used to build the tree, this splitting of the data can lead to a \"block\" structure in the regression model.\n\nA common approach to improving the accuracy of regression algorithms is to use an ensemble, where many models, built from the same training data using randomization, are created $[13,27,28]$. The final prediction is the mean of the prediction from each of the models. In our work, we consider ten trees in the ensemble, with randomization introduced through sampling. Instead of using all the sample points at a node to determine a split, we use a random subset of the samples [14], making each tree in the ensemble different from the others.\n\nWe consider two different measures to evaluate the accuracy of the predictive model. The first is $k$ runs of $m$-fold cross validation, where the data are divided randomly into $m$ parts, the model is trained on $(m-1)$ parts and evaluated on the part that is held out. This is repeated for each of the $m$ parts. The process is repeated $k$ times, each with a different random partition of the data. The final accuracy metric is the average of the accuracy for each of the $k \\times m$ parts.", "start_char_idx": 313638, "end_char_idx": 318186, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2a138515-e07e-4eaf-a4c2-5986598f4353": {"__data__": {"id_": "2a138515-e07e-4eaf-a4c2-5986598f4353", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "566f1c0f-b468-4ee2-85af-fd95a9a57424", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "714f1b0d6bcce08941d8dffabb586f05f234d45329b4256e0b5478572fd33b10", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5441d0b5-2c9d-4343-bac9-9cdebb08a2bf", "node_type": "1", "metadata": {}, "hash": "4c0b2b10a8a2617644a73557d7cbbacd83911d31a6f7b17695000e40537dd93b", "class_name": "RelatedNodeInfo"}}, "text": "The final prediction is the mean of the prediction from each of the models. In our work, we consider ten trees in the ensemble, with randomization introduced through sampling. Instead of using all the sample points at a node to determine a split, we use a random subset of the samples [14], making each tree in the ensemble different from the others.\n\nWe consider two different measures to evaluate the accuracy of the predictive model. The first is $k$ runs of $m$-fold cross validation, where the data are divided randomly into $m$ parts, the model is trained on $(m-1)$ parts and evaluated on the part that is held out. This is repeated for each of the $m$ parts. The process is repeated $k$ times, each with a different random partition of the data. The final accuracy metric is the average of the accuracy for each of the $k \\times m$ parts. We use the relative mean-squared error metric, defined as\n\n$\\sum_{i=1}^{n}\\left(p_{i}-a_{i}\\right)^{2} / \\sum_{i=1}^{n}\\left(\\bar{a}-a_{i}\\right)^{2}$\n\nwhere $p_{i}$ and $a_{i}$ are the predicted and actual values, respectively, of the $i$ th sample point in the test data consisting of $n$ points, and $\\bar{a}$ is the average of the actual values in the test data. This is essentially the ratio of the variance of the residual to the variance of the target (that is, actual) values and is equal to $\\left(1.0-R^{2}\\right)$, where $R^{2}$ is the coefficient of determination. The second metric is the leave-one-out (LOO) approach, where a model, which is built using all but one of the sample points, is used to predict the value at the point that is held out. For a data set with $N$ points, this is essentially $N$-fold cross validation.\n\nFigure 6 shows the accuracy of the regression tree model in predicting the depth using the 462 simulations of the Eagar-Tsai model. Panels (a) and (b) show the predicted vs. actual values using LOO for one tree and ten trees, respectively. We observe that most of the points are near the blue\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-10(7)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-10(6)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-10}\n\\end{center}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-10(1)}\n\\end{center}\n\n(d)\n\nFig. 6 Leave-one-out prediction using $\\mathbf{a}$ one tree and $\\mathbf{b}$ ten trees. $\\mathbf{c}$ Depth prediction in $\\mu \\mathrm{m}$ over a uniform grid in the power-speed space, with the beam size and absorptivity fixed. d Sample points in the viable region of (c)\n\nline at $45^{\\circ}$ (indicating perfect prediction), though the scatter is greater at larger melt-pool depths. The scatter reduces with the use of ensembles as would be expected. Using five runs of fivefold cross validation as the error metric, we obtain a relative mean-squared error of $8 \\%$ with a single tree and $3.6 \\%$ with an ensemble of ten trees.\n\nThe regression tree can be considered as a surrogate for the data from the Eagar-Tsai simulations and can be used to predict the width, depth, and length of the melt pool for a given set of inputs. Figure $6 \\mathrm{c}$ shows the depth prediction at data points on a $40 \\times 40$ grid over the power-speed design space, using a fixed value of $\\mathrm{D} 4 \\sigma=52 \\mu \\mathrm{m}$ and absorptivity of 0.4. The prediction was obtained using the 462 EagarTsai points to build a model with 10 regression trees.", "start_char_idx": 317340, "end_char_idx": 320915, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5441d0b5-2c9d-4343-bac9-9cdebb08a2bf": {"__data__": {"id_": "5441d0b5-2c9d-4343-bac9-9cdebb08a2bf", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2a138515-e07e-4eaf-a4c2-5986598f4353", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "155a0427c45d43e1e1ff953da5964964bc4c923e66326a96cebc6859fcc8360b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "4432d4ec-7f2d-4294-a67c-338e1bb5b7f6", "node_type": "1", "metadata": {}, "hash": "dd71a476fbee2dcb4c5aa3395735826cdc3bdf1baef3125741dea4282aa9229c", "class_name": "RelatedNodeInfo"}}, "text": "The scatter reduces with the use of ensembles as would be expected. Using five runs of fivefold cross validation as the error metric, we obtain a relative mean-squared error of $8 \\%$ with a single tree and $3.6 \\%$ with an ensemble of ten trees.\n\nThe regression tree can be considered as a surrogate for the data from the Eagar-Tsai simulations and can be used to predict the width, depth, and length of the melt pool for a given set of inputs. Figure $6 \\mathrm{c}$ shows the depth prediction at data points on a $40 \\times 40$ grid over the power-speed design space, using a fixed value of $\\mathrm{D} 4 \\sigma=52 \\mu \\mathrm{m}$ and absorptivity of 0.4. The prediction was obtained using the 462 EagarTsai points to build a model with 10 regression trees. Panel (d) shows the viable space in the power-speed plot, where viability is defined as $60 \\mu \\mathrm{m} \\leq$ depth $\\leq 120 \\mu \\mathrm{m}$. While each Eagar-Tsai simulation takes $\\approx 1 \\mathrm{~min}$ on a laptop, it takes a few micro-seconds to build the surrogate from the 462 simulations and practically no time to use it to generate the melt-pool depth for a set of input variables.\n\nThe accuracy of the regression tree depends on the number and location of the sample points, as well as the complexity of the function being modeled. If there are too few sample points, or they are in the wrong location, then the prediction can be poor, especially if the function being predicted is quite complex. For our set of simulations, the accuracy obtained is reasonable, though it could be improved further by adding new sample points in appropriate locations.\n\n\\section*{6 Improving sampling of design space}\nThe locations of the sample points chosen to run simulations, such as the Eagar-Tsai model, are critical to building an accurate data-driven, surrogate model based on these points. In our work, we started with stratified random sampling (Section 3.1) as we wanted to reduce the over- and under-sampling commonly associated with random sampling (see Fig. 7a). However, stratified random sampling lacks flexibility as the number of samples is determined by the number of levels along each dimension and new samples cannot be added easily. In addition, as shown in Fig. 7b, it still results in under- and over-sampled regions, though less than the regular random sampling.\n\nIn our work, we want to generate an arbitrary number of samples that are randomly placed as far from each other as possible. Since the samples points are inputs to simulations, some of which may be computationally expensive unlike the Eagar-Tsai model, we want greater control over the\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-10(5)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-10(4)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-10(3)}\n\\end{center}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-10(2)}\n\\end{center}\n\n(d)\n\nFig. 7 Sampling in a two-dimensional space: 100 samples distributed using a random sampling, $\\mathbf{b}$ stratified random sampling, $\\mathbf{c}$ Poisson-disk sampling, and $\\mathbf{d}$ best-candidate sampling\n\nFig. 8 Distance to the nearest neighbor for a set of 100 samples distributed in a fourdimensional space using (left) stratified random sampling and (right) best-candidate sampling\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-11}\n\\end{center}\n\nnumber of samples. We want to start with a small initial set, and, if necessary, add an arbitrary number of new samples, while maintaining the randomness and the constraint on the distance between samples.", "start_char_idx": 320156, "end_char_idx": 323946, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "4432d4ec-7f2d-4294-a67c-338e1bb5b7f6": {"__data__": {"id_": "4432d4ec-7f2d-4294-a67c-338e1bb5b7f6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5441d0b5-2c9d-4343-bac9-9cdebb08a2bf", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9bc306867d9f1c42d0d9223cb604a003af992789461bbef1469c74bd445b8048", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a8f0c50f-97bb-40d4-87f6-4c31ea906929", "node_type": "1", "metadata": {}, "hash": "d45b1028c64b07a601df328f4fcea9f0474be5f7b21b342c510499ec99b84b16", "class_name": "RelatedNodeInfo"}}, "text": "7 Sampling in a two-dimensional space: 100 samples distributed using a random sampling, $\\mathbf{b}$ stratified random sampling, $\\mathbf{c}$ Poisson-disk sampling, and $\\mathbf{d}$ best-candidate sampling\n\nFig. 8 Distance to the nearest neighbor for a set of 100 samples distributed in a fourdimensional space using (left) stratified random sampling and (right) best-candidate sampling\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-11}\n\\end{center}\n\nnumber of samples. We want to start with a small initial set, and, if necessary, add an arbitrary number of new samples, while maintaining the randomness and the constraint on the distance between samples. To accomplish this, we considered low-discrepancy sampling, defined as follows: let $X$ be a $d$-dimensional measure space, such as $[0,1]^{d}$. Let $R$, the collection of subsets of $X$, denote the range space. Typically, $R$ is chosen as the set of axis-aligned rectangular subsets. Then the discrepancy for a given point set $P$ of $N$ points and range space $R$ is given by\n\n$\\operatorname{Discrepancy}(P, R)=\\sup _{r \\in R}\\left\\{\\left|\\frac{|P \\cap r|}{N}-\\frac{\\mu(r)}{\\mu(X)}\\right|\\right\\}$\n\nwhere $|P \\cap r|$ is the number of points in $P \\cap r$, and $\\mu(r)$ is a Lebesgue measure (this can be considered to be the area in two dimensions and volume in three dimensions). Each term in the supremum indicates how well the number of points in $r$ can be used to estimate the hyper-volume of $r$. In a low discrepancy sampling, if the volume of $r$ is a certain fraction of the volume of $X$, then the number of points in $r$ will be the same fraction of the total number of points $N$.\n\nWe investigated two low-discrepancy sampling approaches-the Poisson-disk sampling [4] and Mitchell's best-candidate sampling [23]. The Poisson-disk sampling distributes random samples such that no two samples are closer than a pre-specified distance (Fig. 7c), meeting our requirements. However, the method is not easily extensible to higher dimensions, requires the specification of the minimum distance between the samples instead of the number of samples, and does not lend itself to the addition of an arbitrary number of new samples. In contrast, Mitchell's best candidate algorithm (Fig. 7d) met all our constraints. Though it does not explicitly place samples at least a fixed distance away from each other, the process of generating the samples ensures that they are placed far apart from each other. The method itself is straightforward. It starts by placing the first point randomly. Then, for each new point, it generates randomly a pre-specified number of candidate points and selects as the next sample the candidate that has the largest nearest-neighbor distance to the current set of samples. It thus incrementally adds new sample points until the desired number have been generated.\n\nTo compare the stratified random sampling with the bestcandidate sampling on the four-dimensional input space of the Eagar-Tsai model, we generated a set of 100 samples using each method and calculated the distance to the nearest neighbor for each sample. Figure 8 shows the distances for each of the 100 samples in the two methods. Both plots have the same scale. It is clear that stratified random sampling, despite the use of grids to avoid under- or over-sampling, has a large range of nearest-neighbor distances ranging from 0.1 to more than 0.4. In contrast, most of the points in the best-candidate sampling have a nearest-neighbor distance of 0.3 , with none below 0.25 .\n\nWhen we use a small number of samples in our initial set, especially in higher-dimensional problems, it is obvious to ask how this affects the accuracy of the surrogate model built using these sample points. The answer is dependent on the problem (the complexity of the variable being modeled) and the surrogate used. We ran the Eagar-Tsai model at the 100 sample points generated using the stratified random and the best-candidate sampling methods, and evaluated the accuracy of the model using both the LOO and cross validation metrics.", "start_char_idx": 323248, "end_char_idx": 327363, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a8f0c50f-97bb-40d4-87f6-4c31ea906929": {"__data__": {"id_": "a8f0c50f-97bb-40d4-87f6-4c31ea906929", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "4432d4ec-7f2d-4294-a67c-338e1bb5b7f6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2d0d4fbbd84fae15c1510156cb70abaccd0888b2da979ff6c489d8c4f6abd481", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "8c44bf64-a57e-4331-aedd-cb8c46653fb1", "node_type": "1", "metadata": {}, "hash": "67abb694073ed8c3ce771bf4bb566fae80cc8ac03227d7f463e8d13dda7378b8", "class_name": "RelatedNodeInfo"}}, "text": "Both plots have the same scale. It is clear that stratified random sampling, despite the use of grids to avoid under- or over-sampling, has a large range of nearest-neighbor distances ranging from 0.1 to more than 0.4. In contrast, most of the points in the best-candidate sampling have a nearest-neighbor distance of 0.3 , with none below 0.25 .\n\nWhen we use a small number of samples in our initial set, especially in higher-dimensional problems, it is obvious to ask how this affects the accuracy of the surrogate model built using these sample points. The answer is dependent on the problem (the complexity of the variable being modeled) and the surrogate used. We ran the Eagar-Tsai model at the 100 sample points generated using the stratified random and the best-candidate sampling methods, and evaluated the accuracy of the model using both the LOO and cross validation metrics. Table 5 presents the relative mean-squared error resulting from five runs of five-fold cross-validation. As expected, the use of a smaller number of samples increases the cross-validation error, while using ensembles reduces it. For a single tree, the random stratified samples give slightly better results compared to the best candidate. One explanation might be that the points in the random stratified sampling are closer to each other (see\n\nTable 5 Relative mean-squared error using five runs of fivefold crossvalidation using the Eagar-Tsai model with samples generated using different methods\n\n\\begin{center}\n\\begin{tabular}{lrr}\n\\hline\nMethod & \\multicolumn{1}{c}{1 tree} & 10 trees \\\\\n\\hline\nRandom stratified (462 samples) & $8.0 \\%$ & $3.6 \\%$ \\\\\nRandom stratified (100 samples) & $24.0 \\%$ & $12.4 \\%$ \\\\\nBest candidate (100 samples) & $27.1 \\%$ & $12.3 \\%$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-12(6)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-12}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-12(1)}\n\\end{center}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-12(7)}\n\\end{center}\n\n(d)\n\nFig. 9 Leave-one-out prediction using for a sample of 100 points generated using stratified sampling with $\\mathbf{a} 1$ tree and $\\mathbf{b} 10$ trees and bestcandidate sampling with $\\mathbf{c} 1$ tree and $\\mathbf{d} 10$ trees\n\nFig. 8) and therefore are better predictors. For 100 samples, using an ensemble of 10 trees removes any differences between the random stratified and best candidate methods. Though the results are less accurate in comparison with the larger number of samples, they are nonetheless sufficient for our use in identifying viable regions of design space. The results for LOO metric are shown in Fig. 9; there is little difference between the two sampling methods, and, as expected, the use of ensembles reduces the scatter for both methods.\n\nAs with our larger sample set, we also created an ensemble of 10 regression trees using the 100 samples from each method and used them to generate the melt-pool depth at the sample points in the $40 \\times 40$ grid over the power-speed design space, as shown in Fig. 10. We used a fixed value of $\\mathrm{D} 4 \\sigma=52 \\mu \\mathrm{m}$ and absorptivity of 0.4 . The prediction now has a more pronounced \"block\" form, which is expected given the small number of points and the use of regression trees with the axis-parallel division of the design space. We also observe that the region with deep melt-pools at low speeds is no longer considered non-viable; this is likely because the small number of sample points is not sufficient to capture the rapidly increasing depth in this region.", "start_char_idx": 326477, "end_char_idx": 330275, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "8c44bf64-a57e-4331-aedd-cb8c46653fb1": {"__data__": {"id_": "8c44bf64-a57e-4331-aedd-cb8c46653fb1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a8f0c50f-97bb-40d4-87f6-4c31ea906929", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "94545ee7681b62a1cbb7883d0395a4763b8b2818064034cf7061dc91ab02de17", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "57c9f9db-129d-4242-ad03-a4f720ea70d9", "node_type": "1", "metadata": {}, "hash": "305b817876a982c6da659e039df003fa30bda500b95d2accea8bf4f37d34df1a", "class_name": "RelatedNodeInfo"}}, "text": "As with our larger sample set, we also created an ensemble of 10 regression trees using the 100 samples from each method and used them to generate the melt-pool depth at the sample points in the $40 \\times 40$ grid over the power-speed design space, as shown in Fig. 10. We used a fixed value of $\\mathrm{D} 4 \\sigma=52 \\mu \\mathrm{m}$ and absorptivity of 0.4 . The prediction now has a more pronounced \"block\" form, which is expected given the small number of points and the use of regression trees with the axis-parallel division of the design space. We also observe that the region with deep melt-pools at low speeds is no longer considered non-viable; this is likely because the small number of sample points is not sufficient to capture the rapidly increasing depth in this region.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-12(3)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-12(5)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-12(2)}\n\\end{center}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-12(4)}\n\\end{center}\n\n(d)\n\nFig. 10 Prediction using the 100 samples from random stratified sampling (a, b) and best-candidate sampling (c, d). a, c: prediction of depth in $\\mu \\mathrm{m}$ over a uniform grid in the power-speed space, with the beam size and absorptivity fixed. b, d: the sample points in the viable region in (a, c), respectively\\\\\nexplore the design space extensively, it lacks much of the physics involved in SLM. In particular, it does not include powder, making it challenging to compare the melt-pool dimensions with experiments. An obvious improvement is to use a more complex model, with additional physics. As these models are computationally expensive, we can only run a small number of sample points. Therefore, we need to consider more sophisticated data-driven surrogates to address the small-sample issues with regression trees. We next describe two complex models-one physical and one data-driven-to alleviate these concerns. This fits into our iterative approach outlined in Section 2, where we progressively use more complex experiments and simulations.\n\n\\subsection*{7.1 More complex physical models}\nThe Verhaeghe model [30] starts by considering the different physical phenomena that are involved in the laser melting of powder on a substrate. The laser beam interacts with the powder particles that melt into liquid. The heat transfer is different in the low-conductivity powder and the densified material. The temperature gradients in the melt pool can give rise to convection, both natural and Marangoni. Surface tension effects may lead to wetting or balling of the liquid melt pool. To incorporate all these aspects into a simple and pragmatic model, the authors use an enthalpy-based formulation of the heat transfer equation. This accounts for the various phase transitions in the material, including evaporation, where the vapor phase is assumed to be removed by the inert gas that flows over the powder bed. Unlike the Eagar-Tsai and other simplified models, the reference frame does not move with the heat source, enabling the study of the effect of changing substrate structure from a powder bed to a dense metal. A Gaussian heat source is assumed. To keep the model simple, certain important phenomena, such as surface-tension-driven shape evolution of the liquid bath, are not considered. However, the compaction of the powder bed due to melting is accounted for by using an iterative shrinking procedure.\n\nThe Verhaeghe model, given the additional physics that is included, is more computationally expensive than the Eagar-Tsai model, requiring about 1-3 $\\mathrm{h}$ of computational time (depending on the laser speed) on a small 8 processor cluster.", "start_char_idx": 329489, "end_char_idx": 333404, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "57c9f9db-129d-4242-ad03-a4f720ea70d9": {"__data__": {"id_": "57c9f9db-129d-4242-ad03-a4f720ea70d9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8c44bf64-a57e-4331-aedd-cb8c46653fb1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0dffb14881aa98c9406a78dc45558ee7388fa38058646e8c0859935aa5bcd979", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bdd58f0f-977c-4dda-9df2-bd0e1931aa92", "node_type": "1", "metadata": {}, "hash": "9bd0991946b6d12babf01ccc4373ed50ea42e3257c5fcb7bf5254ba55abd43b0", "class_name": "RelatedNodeInfo"}}, "text": "This accounts for the various phase transitions in the material, including evaporation, where the vapor phase is assumed to be removed by the inert gas that flows over the powder bed. Unlike the Eagar-Tsai and other simplified models, the reference frame does not move with the heat source, enabling the study of the effect of changing substrate structure from a powder bed to a dense metal. A Gaussian heat source is assumed. To keep the model simple, certain important phenomena, such as surface-tension-driven shape evolution of the liquid bath, are not considered. However, the compaction of the powder bed due to melting is accounted for by using an iterative shrinking procedure.\n\nThe Verhaeghe model, given the additional physics that is included, is more computationally expensive than the Eagar-Tsai model, requiring about 1-3 $\\mathrm{h}$ of computational time (depending on the laser speed) on a small 8 processor cluster. While this is a moderate requirement in terms of computational resources, the Verhaeghe model has a larger number of parameters, such as the powder layer thickness, the void fraction, and the material properties, such as the absorptivity and conductivity of the various material phases, not all of which are known precisely. While the addition of the new physics in the Verhaeghe model makes it more realistic relative to the Eagar-Tsai model, the new parameters introduce new sources of uncertainties and lead to a higherdimensional design space. Therefore, our initial work has focused mainly on exploring the effects of two parameters to understand the model - the layer thickness and the void fraction of the powder.\n\nTable 6 shows the depth predictions obtained using the Verhaeghe model for the power and speed values used in the 14 track experiment described in Section 3.2. We report results for two values of void fraction for the powder, 0.4 and 0.5 , as the void fraction is typically in this range. The grid spacing used in the Verhaeghe model is $2.5 \\mu \\mathrm{m}$.", "start_char_idx": 332471, "end_char_idx": 334485, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bdd58f0f-977c-4dda-9df2-bd0e1931aa92": {"__data__": {"id_": "bdd58f0f-977c-4dda-9df2-bd0e1931aa92", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "57c9f9db-129d-4242-ad03-a4f720ea70d9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7b07fd2d60b2da765f0c2f43f9ad768e3be2f47a6118e19c1df758c0e739ad4e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d1bbfbe7-444d-43c2-8233-3a92bb7fb721", "node_type": "1", "metadata": {}, "hash": "1937fe6bd6d485ac050966605c62697c537cb188ca014fd43f117dcd5b367bc8", "class_name": "RelatedNodeInfo"}}, "text": "While the addition of the new physics in the Verhaeghe model makes it more realistic relative to the Eagar-Tsai model, the new parameters introduce new sources of uncertainties and lead to a higherdimensional design space. Therefore, our initial work has focused mainly on exploring the effects of two parameters to understand the model - the layer thickness and the void fraction of the powder.\n\nTable 6 shows the depth predictions obtained using the Verhaeghe model for the power and speed values used in the 14 track experiment described in Section 3.2. We report results for two values of void fraction for the powder, 0.4 and 0.5 , as the void fraction is typically in this range. The grid spacing used in the Verhaeghe model is $2.5 \\mu \\mathrm{m}$. We\\\\\nTable 6 Single-track experiments with predictions using the Verhaeghe model with void fractions of 0.4 and 0.5\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\n\\hline\n\\multirow{3}{*}{}\\begin{tabular}{l}\nTrack \\\\\nnumber \\\\\n\\end{tabular} & \\multirow{3}{*}{}\\begin{tabular}{l}\nPower \\\\\n(W) \\\\\n\\end{tabular} & \\multirow{3}{*}{}\\begin{tabular}{l}\nSpeed \\\\\n$(\\mathrm{mm} / \\mathrm{s})$ \\\\\n\\end{tabular} & \\multicolumn{3}{|c|}{Depth (layer thickness $=30 \\mu \\mathrm{m})$} & \\multicolumn{3}{|c|}{Depth (layer thickness $=50 \\mu \\mathrm{m})$} \\\\\n\\hline\n &  &  & \\multirow{2}{*}{}\\begin{tabular}{l}\nExperiment \\\\\n$(\\mu \\mathrm{m})$ \\\\\n\\end{tabular} & \\multicolumn{2}{|c|}{Verhaeghe $(\\mu \\mathrm{m})$} & \\multirow{2}{*}{}\\begin{tabular}{l}\nExperiment \\\\\n$(\\mu \\mathrm{m})$ \\\\\n\\end{tabular} & \\multicolumn{2}{|c|}{Verhaeghe $(\\mu \\mathrm{m})$} \\\\\n\\hline\n &  &  &  & $\\mathrm{vf}=0.4$ & $v f=0.5$ &  & $\\mathrm{vf}=0.4$ & $\\mathrm{vf}=0.5$ \\\\\n\\hline\n1 & 400 & 1800 & 105 & 105.0 & 97.5 & 90 & 100.0 & 100.0 \\\\\n\\hline\n2 & 400 & 1500 & 119 & 127.5 & 117.5 & 137 & 122.5 & 122.5 \\\\\n\\hline\n3 & 400 & 1200 & 182 & 163.5 & 147.5 & 183 & 157.5 & 157.5 \\\\\n\\hline\n4 & 300 & 1800 & 65 & 75.0 & 67.5 & 58 & 67.5 & 70.0 \\\\\n\\hline\n5 & 300 & 1500 & 94 & 90.0 & 82.5 & 86 & 85.0 & 85.0 \\\\\n\\hline\n6 & 300 & 1200 & 114 & 115.0 & 105.0 & 76 & 110.0 & 110.0 \\\\\n\\hline\n7 & 300 & 800 & 175 & 172.5 & 155.0 & 207 & 170.0 & 170.0 \\\\\n\\hline\n8 & 200 & 1500 & 57 & 55.0 & 50.0 & 43 & 47.5 & 50.0 \\\\\n\\hline\n9 & 200 & 1200 & 68 & 70.0 & 62.5 & 62 & 62.5 & 65.0 \\\\\n\\hline\n10 & 200 & 800 & 116 & 105.0 & 95.0 & 106 & 97.5 & 100.0 \\\\\n\\hline\n11 & 200 & 500 & 195 & 165.0 & 147.5 & 179 & 162.5 & 160.0 \\\\\n\\hline\n12 & 150 & 1200 & 30 & 47.5 & 45.0 & 37 & 40.0 & 42.5 \\\\\n\\hline\n13 & 150 & 800 & 67 & 72.5 & 67.5 & 63 & 65.0 & 67.5 \\\\\n\\hline\n14 & 150 & 500 & 120 & 112.5 & 102.5 & 104 & 107.5 & 107.5 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nmake several observations on Table 6.", "start_char_idx": 333730, "end_char_idx": 336424, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d1bbfbe7-444d-43c2-8233-3a92bb7fb721": {"__data__": {"id_": "d1bbfbe7-444d-43c2-8233-3a92bb7fb721", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bdd58f0f-977c-4dda-9df2-bd0e1931aa92", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "88b8275d363c64c23d6f22c7f15f224697c413bfcaa83c7af4589c7161d96b13", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6e8dd456-ed7c-4084-8af1-d93e18b6f74c", "node_type": "1", "metadata": {}, "hash": "06b5107497e1ef1d6f0a1ca433ad9c55475f7d34ab8ea936f934d2326df41254", "class_name": "RelatedNodeInfo"}}, "text": "First, the results for both 30 and $50 \\mu \\mathrm{m}$ layer thickness using the Verhaeghe model is closer to the experiment than the Eagar-Tsai results in Table 2. Second, the change in void fraction does not have an appreciable effect on the depth when the layer thickness is $50 \\mu \\mathrm{m}$. However, for layer thickness of $30 \\mu \\mathrm{m}$, the melt-pool depth at void fraction of 0.5 is lower than at 0.4 , suggesting that a larger amount of metal in the powder layer gives deeper melt pools. Also, we might intuitively expect that with a deeper layer of powder at $50 \\mu \\mathrm{m}$, the melted region in the substrate would be shallower as more powder has to melt first before the substrate melts. However, this is true only at void fraction of 0.4 , but not at 0.5. These results indicate that the predictions from the Verhaeghe model depend in a complex way on the void fraction and the layer thickness - the two factors that determine how much metal is in the powder layer.\n\n\\subsection*{7.2 More complex data-driven surrogate models}\nThere are other more complex surrogate models that could be used as an alternative to the regression tree model discussed in Section 5, such as model trees, neural networks or support vector machines. We chose Gaussian process (GP) models [26] for our work as they provide not just a prediction but also an uncertainty on the prediction, which is useful, given the many sources of uncertainty in building additively manufactured parts.\n\nThere are several ways in which we can interpret Gaussian processes. A simple explanation in a brief tutorial by Ebden [7] considers a one-dimensional problem with a training set of $N$ samples, $\\left\\{x_{1}, \\ldots, x_{N}\\right\\}$ and the associated output values $\\mathbf{y}=\\left\\{y_{1}, \\ldots, y_{N}\\right\\}$. A Gaussian process is a collection of random variables, any finite number of which have a joint Gaussian distribution [26]. GPs can be considered to be an extension of multivariate Gaussian distributions to infinite dimensions. Since our training data with $N$ samples can be thought of as a single point sampled from an $\\mathrm{N}$-variate Gaussian distribution, they can be partnered with a Gaussian process. The mean of this GP is often taken to be zero.\n\nTwo samples $x_{i}$ and $x_{j}$ in the training data are related to each other through the covariance function $k\\left(x_{i}, x_{j}\\right)$. We chose the squared-exponential function\n\n$k\\left(x_{i}, x_{j}\\right)=\\sigma_{f}^{2} \\exp \\left(\\frac{-\\left(x_{i}-x_{j}\\right)^{2}}{2 l^{2}}\\right)$\n\nwhere the maximum allowable covariance is $\\sigma_{f}^{2}$ and $l$ is a length parameter that determines the extent of influence of each point. $\\sigma_{f}^{2}$ should be set to a large value for functions that cover a broad range of values. If points $x_{i}$ and $x_{j}$ are close to each other, the covariance is near maximum, so the values of the outputs at the two points are highly correlated.\\\\\nIf the two points are far away, then the correlation is near zero, so the value at one point does not influence the value at the other point. Therefore, the parameter $l$ controls the smoothness of the interpolation.\n\nSuppose we want to use the training data to predict the output at a new sample point $x_{*}$.", "start_char_idx": 336425, "end_char_idx": 339696, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "6e8dd456-ed7c-4084-8af1-d93e18b6f74c": {"__data__": {"id_": "6e8dd456-ed7c-4084-8af1-d93e18b6f74c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d1bbfbe7-444d-43c2-8233-3a92bb7fb721", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e00c2b2b540187ac7bcd0b8590daf1a08265ba7c3f4b661db0735381d292d36c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "e81044a3-3d52-4848-a190-f9f0446729a2", "node_type": "1", "metadata": {}, "hash": "92d0aede7a35d9dd350a705fc3134252cdc2dfcb2eb3b5bea63de698a9c9fb22", "class_name": "RelatedNodeInfo"}}, "text": "$\\sigma_{f}^{2}$ should be set to a large value for functions that cover a broad range of values. If points $x_{i}$ and $x_{j}$ are close to each other, the covariance is near maximum, so the values of the outputs at the two points are highly correlated.\\\\\nIf the two points are far away, then the correlation is near zero, so the value at one point does not influence the value at the other point. Therefore, the parameter $l$ controls the smoothness of the interpolation.\n\nSuppose we want to use the training data to predict the output at a new sample point $x_{*}$. Then, as the data can be represented as a sample from a multivariate Gaussian distribution, we have\n\n$\\left[\\begin{array}{c}\\mathbf{y} \\\\ y_{*}\\end{array}\\right]=\\mathcal{N}\\left(\\mathbf{0},\\left[\\begin{array}{ll}K_{*} & K_{*}^{T} \\\\ K_{*} & K_{* *}\\end{array}\\right]\\right)$,\n\nwhere $\\mathbf{y}$ is the output variable corresponding to the $N$ training data, $y_{*}$ is the prediction of the output at point $x_{*}$, and the submatrices are defined as follows:\n\n$K=\\left[\\begin{array}{cccc}k\\left(x_{1}, x_{1}\\right) & k\\left(x_{1}, x_{2}\\right) & \\ldots & k\\left(x_{1}, x_{N}\\right) \\\\ k\\left(x_{2}, x_{1}\\right) & k\\left(x_{2}, x_{2}\\right) & \\ldots & k\\left(x_{2}, x_{N}\\right) \\\\ \\vdots & \\vdots & . . & \\vdots \\\\ k\\left(x_{N}, x_{1}\\right) & k\\left(x_{N}, x_{2}\\right) & \\ldots & k\\left(x_{N}, x_{N}\\right)\\end{array}\\right]$,\n\n$K_{*}=\\left[k\\left(x_{*}, x_{1}\\right) k\\left(x_{*}, x_{2}\\right) \\ldots k\\left(x_{*}, x_{N}\\right)\\right]$,\n\nand\n\n$K_{* *}=k\\left(x_{*}, x_{*}\\right)$\n\nThe probability of $y_{*}$, that is, the output at the new sample point, is then given by\n\n$\\bar{y}_{*}=K_{*} K^{-1} \\mathbf{y}$\n\nand the uncertainty in the estimate is given by the variance\n\n$\\operatorname{var}\\left(y_{*}\\right)=K_{* *}-K_{*} K^{-1} K_{*}^{T}$\n\nThe parameters $l$ and $\\sigma_{f}$ of the Gaussian process can be calculated from the training data using a maximum likelihood approach. It is also possible to include a Gaussian noise component in the output variable, but in our current analysis, we have assumed the noise to be zero.\n\nSince the Gaussian process is a more complex model, it is obvious to ask if it can give accurate predictions with a small number of sample points and perform better than regression trees by avoiding the \"block\" structure in the predictions seen in Figs. 6 and 10. To evaluate this, we used the 462 Eagar-Tsai samples generated using random stratified sampling and the 100 Eagar-Tsai samples generated using the best candidate algorithm as our two training data sets, and used GP to predict the depth at data points on a $40 \\times 40$ grid over the power-speed design space, using a fixed value of $\\mathrm{D} 4 \\sigma=52 \\mu \\mathrm{m}$ and absorptivity of 0.4 . Our results are presented in Fig. 11. We also include the standard deviation in the prediction, which represents the uncertainty, and the viable region consisting of points where $60 \\mu \\mathrm{m} \\leq$ depth $\\leq 120 \\mu \\mathrm{m}$.\n\nWe make a number of observations. First, regardless of the number of points used to build the model, the predictions are more continuous and the block structure seen with\n\nFig. 11 GP prediction using the Eagar-Tsai model with the 462 random stratified samples (left) and the 100 best candidate samples (right).", "start_char_idx": 339128, "end_char_idx": 342448, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "e81044a3-3d52-4848-a190-f9f0446729a2": {"__data__": {"id_": "e81044a3-3d52-4848-a190-f9f0446729a2", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "6e8dd456-ed7c-4084-8af1-d93e18b6f74c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3fb4c20fc54bff6eafa918e495b66467c70adbbfc1853f4c44e96aca77d1088b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1efdae20-552b-45fc-8e14-5cf59199b45a", "node_type": "1", "metadata": {}, "hash": "23318d3d978cec8c494121eba8e507ecd9e35219e3eecb460d2ea046f33969ab", "class_name": "RelatedNodeInfo"}}, "text": "Our results are presented in Fig. 11. We also include the standard deviation in the prediction, which represents the uncertainty, and the viable region consisting of points where $60 \\mu \\mathrm{m} \\leq$ depth $\\leq 120 \\mu \\mathrm{m}$.\n\nWe make a number of observations. First, regardless of the number of points used to build the model, the predictions are more continuous and the block structure seen with\n\nFig. 11 GP prediction using the Eagar-Tsai model with the 462 random stratified samples (left) and the 100 best candidate samples (right). Top to bottom: depth prediction in $\\mu \\mathrm{m}$, the standard deviation in the prediction, and the sample points in the viable region\\\\\nDepth, Gaussian process, 462 training points\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-15(4)}\n\\end{center}\n\nStd-dev of depth, 462 training points\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-15(1)}\n\\end{center}\n\nViable points\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-15}\n\\end{center}\n\nDepth, Gaussian process, 100 training points\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-15(2)}\n\\end{center}\n\nStd-dev in depth, 100 training points\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_ac9eb55e466d65629094g-15(3)}\n\nregression trees is not present. The viable region using just 100 points is close to the viable region using 462 points though the predicted values are different. This indicates that, for our problem, the GP model gives an accurate viable region even with the smaller number of sample points. Second, the uncertainty in prediction using 462 samples is high at high speeds. This is due to extrapolation as the sample points had a maximum speed of $2250 \\mathrm{~mm} / \\mathrm{s}$ (Table 1), while the maximum speed on the grid of test points is $2500 \\mathrm{~mm} / \\mathrm{s}$. Third, for the same reason, there are three viable test points in the top right of the bottom left plot that have a depth greater than $60 \\mu \\mathrm{m}$ and a standard deviation of nearly 16 . This indicates that GP predictions can be poor in regions outside the training data and the high uncertainty is an indication that we should not trust these results. However, this behavior is not seen when we build the model with fewer training samples. We suspect that the larger distance between the sample points leads to greater smoothness of the interpolating function so that the depth at high power and speed remains below the cut off threshold of $60 \\mu \\mathrm{m}$. Finally, there is greater uncertainty in predictions at low speed and high powers; this is due to extrapolation in this region as well as the rapidly changing values of the depth. However, the uncertainty using 100 points is smaller than using 462 points.\n\n\\section*{8 Statistical inference}\nWe have shown that the Verhaeghe model gives results that are closer to the experimental data in comparison with the Eagar-Tsai model (Section 7.1) and that the Gaussian process model can give reasonable predictions even with few sample points (Section 7.2). We next investigate if we can combine the two types of models to build a surrogate with few sample points that will give results comparable with\n\nFig. 12 GP prediction of depth as a function of a power for different speed values and $\\mathbf{b}$ speed for different power values, using the Verhaeghe model run at the 34 viable Eagar-Tsai samples.", "start_char_idx": 341900, "end_char_idx": 345438, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1efdae20-552b-45fc-8e14-5cf59199b45a": {"__data__": {"id_": "1efdae20-552b-45fc-8e14-5cf59199b45a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e81044a3-3d52-4848-a190-f9f0446729a2", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "74fa2273f7770d8c1d835607732984738e3d728be582b2f9f747f5c530d1583b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "61315f96-0b19-4e8b-84f9-1b4071ab9392", "node_type": "1", "metadata": {}, "hash": "fbba3ab14aad42b0b2f6c4d96b4bcf77f68936ae560b37d0a9c7d949b8df5cfb", "class_name": "RelatedNodeInfo"}}, "text": "Finally, there is greater uncertainty in predictions at low speed and high powers; this is due to extrapolation in this region as well as the rapidly changing values of the depth. However, the uncertainty using 100 points is smaller than using 462 points.\n\n\\section*{8 Statistical inference}\nWe have shown that the Verhaeghe model gives results that are closer to the experimental data in comparison with the Eagar-Tsai model (Section 7.1) and that the Gaussian process model can give reasonable predictions even with few sample points (Section 7.2). We next investigate if we can combine the two types of models to build a surrogate with few sample points that will give results comparable with\n\nFig. 12 GP prediction of depth as a function of a power for different speed values and $\\mathbf{b}$ speed for different power values, using the Verhaeghe model run at the 34 viable Eagar-Tsai samples. $D 4 \\sigma=52 \\mu \\mathrm{m}$ and $\\eta=0.40$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_ac9eb55e466d65629094g-16(3)}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-16}\n\\end{center}\n\n(b) experiments, along with an associated uncertainty on the predictions. We follow the iterative approach for process optimization (Section 2), starting with simple simulations and experiments and progressively using more complex simulations and experiments to constrain the space of process parameters.\n\nWe start with the 100 simulations of the Eagar-Tsai model generated using the best-candidate sampling method (Section 6). Of these, 34 samples have depth $>60 \\mu \\mathrm{m}$ and form the viable set of points. These range in power from 150 to $400 \\mathrm{~W}$ and in speed from 500 to $1600 \\mathrm{~mm} / \\mathrm{s}$. We then run the Verhaeghe model at these points using a void fraction of 0.5 and a layer thickness of $30 \\mu \\mathrm{m}$ and build a Gaussian process surrogate with the resulting melt-pool depth values.\\\\\nFigures 12 and 13 show the prediction from the Gaussian process at various values of laser power, speed, beam size, and absorptivity, with the other variables held constant. The uncertainty range shown is at two standard deviations. We observe larger uncertainty during extrapolation, for example, Fig. 12a at values of power less than $150 \\mathrm{~W}$ and Fig. $12 \\mathrm{~b}$ at values of speed greater than $1600 \\mathrm{~mm} / \\mathrm{s}$. The behavior seen in the curves is as expected-increasing power or reducing speed increases the depth as does reducing the beam size or increasing the absorptivity. For a given power, the variation of the depth with speed is non-linear (Fig. 12b), while the variation in depth with power for a fixed speed is close to, but not quite, linear. Figure 13 indicates that the depth varies linearly with both beam size and absorptivity.\\\\\nFig. 13 GP prediction of depth as a function of $\\mathbf{a} 2 \\sigma$ for different $\\eta$ values and $\\mathbf{b} \\eta$ for different $2 \\sigma$ values using the Verhaeghe model run at the 34 viable Eagar-Tsai samples. Power $=250 \\mathrm{~W}$ and speed $=$ $1200 \\mathrm{~mm} / \\mathrm{s}$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_ac9eb55e466d65629094g-16(2)}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-16(1)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-17(4)}\n\\end{center}\n\nFig. 14 Comparing 14 track experiments with GP prediction using depth from the Verhaeghe model at the 34 viable Eagar-Tsai samples. Layer thickness $=30 \\mu \\mathrm{m}$, void fraction $=0.5$.", "start_char_idx": 344541, "end_char_idx": 348195, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "61315f96-0b19-4e8b-84f9-1b4071ab9392": {"__data__": {"id_": "61315f96-0b19-4e8b-84f9-1b4071ab9392", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1efdae20-552b-45fc-8e14-5cf59199b45a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "093c939c2a0028f8bc0bc310468d42e598c81a980653f6561fc6021c9f9f21fe", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f441da60-a990-4916-a428-260c6d21dcda", "node_type": "1", "metadata": {}, "hash": "cf46561e0cadf78567d39741cf8ca0a15d52c44c5a80c0dd9bd604ea2792eab4", "class_name": "RelatedNodeInfo"}}, "text": "14 Comparing 14 track experiments with GP prediction using depth from the Verhaeghe model at the 34 viable Eagar-Tsai samples. Layer thickness $=30 \\mu \\mathrm{m}$, void fraction $=0.5$. Error bars are at one standard deviation\n\nNext, we used the Gaussian process surrogate to predict the depth at the power and speed values for the 14 single tracks described in Section 3.2, with $D 4 \\sigma=52 \\mu \\mathrm{m}$ and $\\eta=0.40$, and compared the results with the experiments as shown in Fig. 14. We notice that when the depth is large, the surrogate under-predicts the depth. To confirm that this was not due to the resolution used in the Verhaeghe model, we repeated one of the cases using (i) double the cell size and (ii) double the number of grid points in all dimensions. There was no change in the results in either case, indicating that the Verhaeghe model might not include all the physics required for predicting deep melt pools.\n\nWe also observed that the error bars are larger at smaller values of the depth. These are all tracks at higher speeds, and in some cases, have speeds outside the range of the 34 sample points used in building the surrogate. To confirm that this large uncertainty was due to extrapolation, we included additional sample points that had an EagarTsai depth of $55 \\mu \\mathrm{m}$ or higher, instead of $60 \\mu \\mathrm{m}$ or higher. The seven new points included some with speed larger than $1600 \\mathrm{~mm} / \\mathrm{s}$, bringing the samples used for building the surrogate closer to the speed values used in the experiments. For these 41 sample points, we ran the Verhaeghe model for four cases: layer thickness of 30 and $50 \\mu \\mathrm{m}$ and void fractions of 0.4 and 0.5 . For each case, we built a Gaussian process surrogate and used it to predict the depth of the 14 track experiments as before. Our results in Fig. 15 indicate\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-17(2)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-17(3)}\n\\end{center}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-17}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ac9eb55e466d65629094g-17(1)}\n\\end{center}\n\n(d)\n\nFig. 15 Comparing 14 track experiments with GP prediction using depth from the Verhaeghe model at the 41 viable Eagar-Tsai samples. Error bars are at one standard deviation. Layer thickness and void fraction are as follows: $\\mathbf{a} 30 \\mu \\mathrm{m}, 0.4 ; \\mathbf{b} 30 \\mu \\mathrm{m}, 0.5 ; \\mathbf{c} 50 \\mu \\mathrm{m}, 0.4 ;$ and $\\mathbf{d} 50 \\mu \\mathrm{m}, 0.5$\\\\\nthat we were able to reduce the uncertainty associated with small values of melt-pool depth in Fig. 14. Comparing panels (a) and (b) in Fig. 15, we find that using a void fraction of 0.4 gives GP predictions that are closer to the experiments than a void fraction of 0.5 for a layer thickness of $30 \\mu \\mathrm{m}$. Changing the void fraction for the $50 \\mu \\mathrm{m}$ layer thickness has little effect as was observed in Table 6.\n\nThese results show that the Verhaeghe model, combined with predictions using a GP surrogate, can give reasonable results for melt-pool depths for 316L stainless steel. The uncertainty associated with the predictions is small, giving us greater confidence in the results.", "start_char_idx": 348009, "end_char_idx": 351417, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f441da60-a990-4916-a428-260c6d21dcda": {"__data__": {"id_": "f441da60-a990-4916-a428-260c6d21dcda", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "61315f96-0b19-4e8b-84f9-1b4071ab9392", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9cbed8914ceeb8e7a4466f96bd141018c006840bd4bbbfc43f18380c0a0bdac4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "28f8e057-7c4c-4ddc-8ca4-8343a7342725", "node_type": "1", "metadata": {}, "hash": "ac5650923b8381ee83946757cc993df379bb432e8506b7e00dbe93ba92e4cb66", "class_name": "RelatedNodeInfo"}}, "text": "14. Comparing panels (a) and (b) in Fig. 15, we find that using a void fraction of 0.4 gives GP predictions that are closer to the experiments than a void fraction of 0.5 for a layer thickness of $30 \\mu \\mathrm{m}$. Changing the void fraction for the $50 \\mu \\mathrm{m}$ layer thickness has little effect as was observed in Table 6.\n\nThese results show that the Verhaeghe model, combined with predictions using a GP surrogate, can give reasonable results for melt-pool depths for 316L stainless steel. The uncertainty associated with the predictions is small, giving us greater confidence in the results.\n\n\\section*{9 Conclusions}\nIn this paper, we demonstrated several different ways in which techniques from data mining and statistical inference can be used to provide scientific insight and improve process optimization in selective laser melting, enabling us to quickly build parts with desired properties, such as high density. We showed how we can combine more complex physical and data-driven models to improve accuracy of prediction and, through uncertainty analysis, gain confidence in the process parameters selected for SLM. Our future work will include using the Verhaeghe model, coupled with Gaussian processes, to understand the effects of other variables such as powder size distributions and material parameters. We will also extend our work to other materials to understand if results are broadly applicable.\n\nAcknowledgments The author acknowledges the contributions of Wayne King (implementation and execution of the Eagar-Tsai model), John W. Gibbs (implementation of the Verhaeghe model), Paul Alexander (operation of the Concept Laser M2), and Mark Pearson and Cheryl Evans (metallographic preparation and measurement). We also thank the Sheffield Machine Learning group for making the Gaussian process freely available at \\href{http://sheffieldml.github.io/GPy/}{http://sheffieldml.github.io/GPy/}. LLNLJRNL-680063: This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. This work was funded by the LDRD Program at LLNL under project tracking code 13-SI-002.\n\n\\section*{References}\n\\begin{enumerate}\n  \\item Bourell DL, Leu MC, Rosen DW (2009) Roadmap for additive manufacturing - Identifying the future of freeform processing. The University of Texas at Austin\n\n  \\item Bourell DL, Rosen DW, Leu MC (2014) The roadmap for additive manufacturing and its impact. 3D Print Addit Manuf 1:6-9\n\n  \\item Breiman L, Friedman JH, Olshen RA, Stone CJ (1984) Classification and regression trees. CRC Press, Boca Raton\n\n  \\item Bridson R (2007) Fast Poisson disk sampling in arbitrary dimensions. In: ACM SIGGRAPH 2007 sketches. ACM, New York\n\n  \\item Delgado J, Ciurana J, Rodriguez C (2012) Influence of process parameters on part quality and mechanical properties for DMLS and SLM with iron-based materials. Int J Adv Manuf Technol 60:601-610\n\n  \\item Eagar T, Tsai N (1983) Temperature-fields produced by traveling distributed heat-sources. Weld J 62:S346-S355\n\n  \\item Ebden M (2008) Gaussian process for regression and classification: a quick introduction. arXiv: 1505.02965, submitted May 2015\n\n  \\item Fang KT, Li R, Sudjianto A (2005) Design and modeling for computer experiments. Chapman and Hall/CRC Press, Boca Raton\n\n  \\item Gusarov AV, Yadoirtsev I, Bertrand P, Smurov I (2009) Model of radiation and heat transfer in laser-powder interaction zone at selective laser melting. J Heat Transf 131:072,101\n\n  \\item Hall MA (2000) Correlation-based feature selection for discrete and numeric class machine learning. In: Proceedings of 17th international conference on machine learning. Morgan Kaufmann, San Francisco, pp 359-366\n\n  \\item Hodge NE, Ferencz RM, Solberg JM (2014) Implementation of a thermomechanical model for the simulation of selective laser melting. Comput Mech 54:33-51\n\n  \\item Inselberg A (2009) Parallel coordinates: visual multidimensional geometry and its applications.", "start_char_idx": 350812, "end_char_idx": 354824, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "28f8e057-7c4c-4ddc-8ca4-8343a7342725": {"__data__": {"id_": "28f8e057-7c4c-4ddc-8ca4-8343a7342725", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f441da60-a990-4916-a428-260c6d21dcda", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1617321b11b6c68d0ac38b470bd5662bb7ce05e93a52165339599f9cf4456277", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "e1aabd19-21e6-4a54-aeac-b4b7682c04a3", "node_type": "1", "metadata": {}, "hash": "2380d4162aa2ef99af9dbdbcd9ec0a17177007da517b608a03f9c0a571f133ab", "class_name": "RelatedNodeInfo"}}, "text": "Chapman and Hall/CRC Press, Boca Raton\n\n  \\item Gusarov AV, Yadoirtsev I, Bertrand P, Smurov I (2009) Model of radiation and heat transfer in laser-powder interaction zone at selective laser melting. J Heat Transf 131:072,101\n\n  \\item Hall MA (2000) Correlation-based feature selection for discrete and numeric class machine learning. In: Proceedings of 17th international conference on machine learning. Morgan Kaufmann, San Francisco, pp 359-366\n\n  \\item Hodge NE, Ferencz RM, Solberg JM (2014) Implementation of a thermomechanical model for the simulation of selective laser melting. Comput Mech 54:33-51\n\n  \\item Inselberg A (2009) Parallel coordinates: visual multidimensional geometry and its applications. Springer, New York\n\n  \\item Kamath C (2009) Scientific data mining: a practical perspective. Society for Industrial and Applied Mathematics (SIAM), Philadelphia\n\n  \\item Kamath C, Cant\u00fa-Paz E (2001) Creating ensembles of decision trees through sampling. In: Proceedings of the 33rd symposium on the interface: computing science and statistics\n\n  \\item Kamath C, El-dasher B, Gallegos GF, King WE, Sisto A (2014) Density of additively-manufactured, 316L SS parts using laser powder-bed fusion at powers up to $400 \\mathrm{~W}$. Int J Adv Manuf Technol 74:65-78\n\n  \\item Kempen K, Thijs L, Yasa E, Badrossamay M, Verheecke W, Kruth JP (2011) Process optimization and microstructural analysis for selective laser melting of AlSi10Mg. In: Bourell D (ed) Proceedings of solid freeform fabrication symposium, vol 22. University of Texas at Austin, Austin, pp 484-495\n\n  \\item Khairallah SA, Anderson A (2014) Mesoscopic simulation model of selective laser melting of stainless steel powder. J Mater Process Technol 214:2627-2636\n\n  \\item King WE, Barth HD, Castillo VM, Gallegos GF, Gibbs JW, Hahn DE, Kamath C, Rubenchik AM (2014) Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing. J Mater Process Technol 214:2915-2925\n\n  \\item K\u00f6rner C, Attar E, Heinl P (2011) Mesoscopic simulation of selective beam melting processes. J Mater Process Technol 211:978987\n\n  \\item Kruth J, Badrossamay M, Yasa E, Deckers J, Thijs L, Van Humbeeck J (2010) Part and material properties in selective laser melting of metals. In: Proceedings of 16th international symposium on electromachining (ISEM XVI), Shanghai\n\n  \\item Laohaprapanon A, Jeamwatthanachai P, Wongcumchang M, Chantarapanich N, Chantaweroad S, Sitthiseripratip K, Wisutmethangoon S (2012) Optimal scanning condition of selective laser melting processing with stainless steel 3161 powder. Material and Manufacturing Technology Ii, Pts 1 and 2. Trans Tech Publications Ltd, Stafa-Zurich, pp 816820\n\n  \\item Li Y, Gu D (2014) Parametric analysis of thermal behavior during selective laser melting additive manufacturing of aluminum alloy powder. Mater Des 63:856-867\n\n  \\item Mitchell DP (1991) Spectrally optimal sampling for distribution ray tracing. Comput Graph 25(4):157-164\n\n  \\item National Institute of Standards and Technology (2013) Measurement Science Roadmap for Metal-Based Additive Manufacturing. Tech. rep. National Institute of Standards and Technology\n\n  \\item Oehlert GW, Freeman WH (2000) A first course in design and analysis of experiments. Available from \\href{http://users.stat.umn.edu/}{http://users.stat.umn.edu/} gary/Book.html\n\n  \\item Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. MIT Press, Cambridge\n\n  \\item Rokach L (2010) Pattern classification using ensemble methods.", "start_char_idx": 354112, "end_char_idx": 357637, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "e1aabd19-21e6-4a54-aeac-b4b7682c04a3": {"__data__": {"id_": "e1aabd19-21e6-4a54-aeac-b4b7682c04a3", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "28f8e057-7c4c-4ddc-8ca4-8343a7342725", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4d3eaac300bbd0ed0735f6b9d01d48f96efb44622b0256f94e9f1798a61f197d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "324dd781-64b3-45eb-813e-04b00dca48eb", "node_type": "1", "metadata": {}, "hash": "1c0e31c66a8c8568cd484d888128abd7b8906d64fa460116eadfd6bcfe00ff1a", "class_name": "RelatedNodeInfo"}}, "text": "Mater Des 63:856-867\n\n  \\item Mitchell DP (1991) Spectrally optimal sampling for distribution ray tracing. Comput Graph 25(4):157-164\n\n  \\item National Institute of Standards and Technology (2013) Measurement Science Roadmap for Metal-Based Additive Manufacturing. Tech. rep. National Institute of Standards and Technology\n\n  \\item Oehlert GW, Freeman WH (2000) A first course in design and analysis of experiments. Available from \\href{http://users.stat.umn.edu/}{http://users.stat.umn.edu/} gary/Book.html\n\n  \\item Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. MIT Press, Cambridge\n\n  \\item Rokach L (2010) Pattern classification using ensemble methods. World Scientific Publishing, Singapore\n\n  \\item Rokach L, Maimon O (2014) Data mining with decision trees: theory and applications. World Scientific Publishing, Singapore\n\n  \\item Spierings A, Levy G (2009) Comparison of density of stainless steel 316L parts produced with selective laser melting using different powder grades. In: Bourell D (ed) 20th annual international solid freeform fabrication symposium, an additive manufacturing conference. University of Texas at Austin, Austin, pp 342-353\n\n  \\item Verhaeghe F, Craeghs T, Heulens J, Pandalaers L (2009) A pragmatic model for selective laser melting with evaporation. Acta Mater 57:6006-6012\n\n  \\item Yadroitsev I (2009) Selective laser melting: direct manufacturing of 3D-objects by selective laser melting of metal powders. LAP Lambert Academic Publishing\n\n  \\item Yadroitsev I, Gusarov A, Yadroitsava I, Smurov I (2010) Single track formation in selective laser melting of metal powders. $\\mathrm{J}$ Mater Process Technol 210:1624-1631\n\n  \\item Yadroitsev I, Smurov I (2010) Selective laser melting technology: from the single laser melted track stability to 3D parts of complex shape. Phys Procedia 5:551-560\n\n  \\item Yasa E (2011) Manufacturing by combining selective laser melting and selective laser erosion / laser re-melting. Ph.D. thesis, Faculty of Engineering, Department of Mechanical Engineering. Katholieke Universiteit Leuven, Heverlee, Leuven. Available from Katholieke Universiteit Leuven\n\n\\end{enumerate}\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\n\\title{Analysis of laser-induced microcracking in tungsten under additive manufacturing conditions: Experiment and simulation }\n\n\n\\author{Bey Vrancken*, Rishi K. Ganeriwala, Manyalibo J. Matthews}\n\\date{}\n\n\n%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?", "start_char_idx": 356953, "end_char_idx": 360128, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "324dd781-64b3-45eb-813e-04b00dca48eb": {"__data__": {"id_": "324dd781-64b3-45eb-813e-04b00dca48eb", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e1aabd19-21e6-4a54-aeac-b4b7682c04a3", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "23bc51b274c0c890471a72b83702135ca522fb500ab3088a58950601e810f316", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0ab7db18-b16e-4df0-9f06-0dfe19bcd18e", "node_type": "1", "metadata": {}, "hash": "4d2809b2a1a5bbccf8ed69166048f49c235f198ad67f798e4900108d2fd6670b", "class_name": "RelatedNodeInfo"}}, "text": "\\author{Bey Vrancken*, Rishi K. Ganeriwala, Manyalibo J. Matthews}\n\\date{}\n\n\n%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?]{%\n  \\if\\relax#1\\relax%\n    \\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n  \\else%\n    \\if?#1\\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n    \\else\\svfootnotetext[#1]{#2}\\fi%\n  \\fi\n}\n\n\\begin{document}\n\\maketitle\nFull length article\n\nLawrence Livermore National Laboratory, 7000 East Avenue, Livermore CA 94550, USA\n\n\\section*{A R T I C L E I N F O}\n\\section*{Article History}\nReceived 24 January 2020\n\nRevised 30 April 2020\n\nAccepted 30 April 2020\n\nAvailable online 17 May 2020\n\n\\section*{Keywords:}\nTungsten\n\nMicrocracking\n\nBrittle-to-ductile transition\n\nResidual stresses\n\nAdditive manufacturing\n\n\\begin{abstract}\nA B S T R A C T Tungsten is receiving increasing interest as a plasma facing material in the ITER fusion reactor, collimators, and other structural, high temperature applications. Concurrently, there is a demand for manufacturing techniques capable of processing tungsten into the desired geometries. Additive manufacturing is a promising technique able to produce complex parts, but the structural integrity is compromised by microcracking. This work combines thermomechanical simulations with in situ high-speed video of microcracking in single laser-melted tracks, visualizing the ductile-to-brittle transition. Microcracking is shown to occur in a narrow temperature interval between $450 \\mathrm{~K}-650 \\mathrm{~K}$, and to be strain rate dependent. The size of the crack-affected area around the scan track is determined by the maximum Von Mises residual stress, whereas crack network morphology depends on the local orientation of the principal stress. The fundamental understanding provided by this work contributes to future efforts in crack free, additively manufactured tungsten.\n\\end{abstract}\n\n(C) 2020 Acta Materialia Inc. Published by Elsevier Ltd. This is an open access article under the CC BY license. (\\href{http://creativecommons.org/licenses/by/4.0/}{http://creativecommons.org/licenses/by/4.0/})\n\n\\section*{1. Introduction}\nTungsten is a preferred material for high temperature applications due to its favorable thermomechanical properties, such as a high melting point, high thermal conductivity, and moderate thermal expansion. Additionally, its high density and extremely low sputter erosion rate make it suitable for radiation or other extreme environments, with applications ranging from waveguides and collimators, to plasma facing components (PFC) in the ITER fusion reactor [1,2]. Despite these favorable properties, the widespread use of tungsten is limited by a low thermal shock resistance and brittleness at low temperatures. For extremely demanding applications such as the PFC in ITER, the recrystallization-induced loss of strength and ductility by repeated thermal loading also needs to be addressed [3-5].\n\nThe ductile-to-brittle transition temperature or DBTT determines the lower temperature limit of the practical working range. At this temperature, the screw dislocations that could move with relative ease at higher temperatures turn immobile, leading to a sudden and drastic decrease of the ductility at lower temperatures [6]. Unfortunately, the ductile-to-brittle transition (DBT) occurs above room temperature ( $473 \\mathrm{~K}-673 \\mathrm{~K}$ or higher [7-9]) and is inevitably encountered when cooling down from processing at high-temperature.", "start_char_idx": 359671, "end_char_idx": 363494, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0ab7db18-b16e-4df0-9f06-0dfe19bcd18e": {"__data__": {"id_": "0ab7db18-b16e-4df0-9f06-0dfe19bcd18e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "324dd781-64b3-45eb-813e-04b00dca48eb", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "eefe6c952d9894dabec567e6a7c8d39ef07b696fafe345dc0fc1c28183180c94", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2d0586d2-01f4-43b4-8934-570098601a06", "node_type": "1", "metadata": {}, "hash": "1ac0ae4328c001177469f84a7e2d502c77ad27c068950438cc11bcbf6a848d59", "class_name": "RelatedNodeInfo"}}, "text": "Despite these favorable properties, the widespread use of tungsten is limited by a low thermal shock resistance and brittleness at low temperatures. For extremely demanding applications such as the PFC in ITER, the recrystallization-induced loss of strength and ductility by repeated thermal loading also needs to be addressed [3-5].\n\nThe ductile-to-brittle transition temperature or DBTT determines the lower temperature limit of the practical working range. At this temperature, the screw dislocations that could move with relative ease at higher temperatures turn immobile, leading to a sudden and drastic decrease of the ductility at lower temperatures [6]. Unfortunately, the ductile-to-brittle transition (DBT) occurs above room temperature ( $473 \\mathrm{~K}-673 \\mathrm{~K}$ or higher [7-9]) and is inevitably encountered when cooling down from processing at high-temperature. At that moment, processing-induced residual stresses can lead to microcracking. The DBTT depends heavily on the interstitial\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author.\n\\end{itemize}\n\nE-mail addresses: \\href{mailto:Vrancken1@llnl.gov}{Vrancken1@llnl.gov} (B. Vrancken), \\href{mailto:Ganeriwala1@Ilnl.gov}{Ganeriwala1@Ilnl.gov} (R.K. Ganeriwala), \\href{mailto:Matthews11@llnl.gov}{Matthews11@llnl.gov} (M.J. Matthews).\n}\n\nimpurity content, with a small increase from $10 \\mathrm{ppm}$ to $50 \\mathrm{ppm}$ oxygen impurity content increasing the DBTT from $623 \\mathrm{~K}$ to $823 \\mathrm{~K}$ [10]. In additive manufacturing (AM), more specifically in laser powder bed fusion (LPBF), rapid and repetitive local heating, solidification, and cooling cycles create high residual stresses that lead to distortions [11,12], cracking [13,14], and affect mechanical properties [15]. High densities larger than $98 \\%$ have been reported in several AM studies of tungsten [13,16-18], but none were able to avoid the formation of microcracks $[19,20]$.\n\nPossible mitigation strategies have included alloying and process optimizations, with limited success in either case. For example, cracking was reduced by the addition of nanosized $\\mathrm{ZrC}$ powder to the original tungsten powder, as the $\\mathrm{ZrC}$ appeared to have survived exposure to the high temperature tungsten melt, leading to a $50 \\%$ reduction in grain size [21]. Alloying with up to $5 \\mathrm{wt} \\%$ Ta by using powder blends has seen mixed results with no improvement observed in Ref. [16], but reduced cracking by $80 \\%$ according to Ref. [22]. In the latter study, the reduction is attributed to a change in solidification mode from planar to cellular that trapped nanosized pores at the cell walls. These pores originated from boiling $\\mathrm{WO}_{\\mathrm{x}}$ oxides and are thought to provide a similar strengthening effect as the nanopores in potassium doped $\\mathrm{W}$ [23]. On the other hand, modifications of the process conditions rather than the alloy composition focused mainly on base plate preheating, with a $673 \\mathrm{~K}$ preheated substrate not leading to significant improvements [16], though a reduction in cracking was observed when using a substrate preheated to $1273 \\mathrm{~K}$ [17]. Using femtosecond laser pulses rather than a continuous mode laser limited the\\\\\nthermally affected zone in Ref. [24], which contributed to a reduction of microcracking, though the mechanism was not discussed. For Mo, in which microcracks form due to the DBT as well, laser power/scan speed ratios $P / v<1 \\mathrm{~J} / \\mathrm{mm}$ were found to reduce cracking in combination with a support structure that limited thermal conduction to the base plate [25]. Research into the thermal or mechanical properties of LPBF W is limited due to the microcracking.", "start_char_idx": 362610, "end_char_idx": 366352, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2d0586d2-01f4-43b4-8934-570098601a06": {"__data__": {"id_": "2d0586d2-01f4-43b4-8934-570098601a06", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0ab7db18-b16e-4df0-9f06-0dfe19bcd18e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "23470a071e4fa78b9b3123aa763e3ae71d8a8a9be647f904464b5dea2d7efdac", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "06043e4f-9348-4575-aaae-155a4665a644", "node_type": "1", "metadata": {}, "hash": "1f17a282c879f73f0936775f87bde24e2aaf2fac674d3a402c975519ea8b588e", "class_name": "RelatedNodeInfo"}}, "text": "Using femtosecond laser pulses rather than a continuous mode laser limited the\\\\\nthermally affected zone in Ref. [24], which contributed to a reduction of microcracking, though the mechanism was not discussed. For Mo, in which microcracks form due to the DBT as well, laser power/scan speed ratios $P / v<1 \\mathrm{~J} / \\mathrm{mm}$ were found to reduce cracking in combination with a support structure that limited thermal conduction to the base plate [25]. Research into the thermal or mechanical properties of LPBF W is limited due to the microcracking. Nevertheless, the compressive strength at room temperature was determined to be $1253 \\mathrm{MPa}$, and the thermal conductivity equal to $148 \\mathrm{~W} /\\left(\\mathrm{m}^{*} \\mathrm{~K}\\right)[18]$, compared to $1432 \\mathrm{MPa}$ (tension) and $173 \\mathrm{~W} /\\left(\\mathrm{m}^{*} \\mathrm{~K}\\right)$ for stress relieved tungsten [26].\n\nThough it is understood by now that the DBT is the cause of microcracks in LPBF of tungsten, a fundamental understanding of their formation is still lacking, since research has been restricted to the post mortem examination of crack networks. This work utilizes in situ, high-speed video of tungsten single tracks to study in more detail the influence of the process parameters and melt geometry on the cracking mechanism by providing a visualization of the DBT. Additionally, a calibrated thermomechanical model utilizing Lawrence Livermore National Laboratory's Diablo [27] finite element code allows correlation of the cracking with residual stress, strain rate, and temperature. The results provide guidance for process parameter selection, and will act as a baseline to compare the influence of process and alloy modifications on mitigating microcracking in LPBF of $\\mathrm{W}$.\n\n\\section*{2. Materials \\& methods}\n\\subsection*{2.1. High-speed video}\nThe high-speed imaging platform is described in detail in Ref. [28], and is shown schematically in Fig. 1. A Photron SA-X2 high-speed camera coupled to high numerical optics (Mitutoyo 10x/NA0.1 microscope objective, $32 \\mathrm{~mm}$ working distance) captures high resolution video at a $50 \\mathrm{kHz}$ frame rate and $768 \\times 328$ pixel resolution, which was equivalent to a $620 \\times 265 \\mu \\mathrm{m}$ field of view. The field of view was stationary, focused on the center of the track, and the laser scanned across the image (shown in red). Top-down vision is made possible by the dichroic longpass filter mounted above the $\\mathrm{W}$ substrate, transparent to wavelengths $>1000 \\mathrm{~nm}$, but reflecting the wavelengths used for imaging to the high-speed camera (shown in green in Fig. 1). A Cavilux HF $500 \\mathrm{~W}$ low coherence laser source $(\\lambda=808 \\mathrm{~nm})$ pulsed at $1 \\mu$ s provided coaxial illumination through a beamsplitter inside a Navitar Zoom 6000 system. A $1070 \\mathrm{~nm}$ wavelength JK FL600 Yb:glass fiber laser operating in continuous wave mode with a maximum power output of $600 \\mathrm{~W}$ was used to scan single, $2 \\mathrm{~mm}$ long tracks on a tungsten plate. A $50 \\mu \\mathrm{m}$ and $100 \\mu \\mathrm{m}$ Gaussian beam diameter $\\left(1 / e^{2}\\right)$ were used to investigate the effect of beam spot size. 10 and 20 repetitions were performed for each parameter set utilizing a $50 \\mu \\mathrm{m}$ beam and $100 \\mu \\mathrm{m}$ beam, respectively. Ar was flown freely over the substrate at a rate of $0.51 / \\mathrm{min}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-2}\n\\end{center}\n\nFig. 1.", "start_char_idx": 365795, "end_char_idx": 369360, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "06043e4f-9348-4575-aaae-155a4665a644": {"__data__": {"id_": "06043e4f-9348-4575-aaae-155a4665a644", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2d0586d2-01f4-43b4-8934-570098601a06", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "95bc9f292e3ae240d41a4a990f5252e3226f9c537024b136ffc46124b2337ebb", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "968732b4-552c-4dd4-a78f-af2e43e1e747", "node_type": "1", "metadata": {}, "hash": "21b9d08456a4dfb7e6182cdc2445a9b1a1efdc5cb284e997606f290afdd86601", "class_name": "RelatedNodeInfo"}}, "text": "A $50 \\mu \\mathrm{m}$ and $100 \\mu \\mathrm{m}$ Gaussian beam diameter $\\left(1 / e^{2}\\right)$ were used to investigate the effect of beam spot size. 10 and 20 repetitions were performed for each parameter set utilizing a $50 \\mu \\mathrm{m}$ beam and $100 \\mu \\mathrm{m}$ beam, respectively. Ar was flown freely over the substrate at a rate of $0.51 / \\mathrm{min}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-2}\n\\end{center}\n\nFig. 1. Schematic of the optical setup for top down high-speed video of laser scans on a tungsten plate.\\\\\nThe $2 \\mathrm{~mm}$ thick $\\mathrm{W}$ substrates were cut from a $25.4 \\mathrm{~mm}$ diameter, $>99.95 \\%$ purity W rod supplied by Eagle Alloys Corporation using wire EDM, after which the surface was partially ground using 600grit $\\mathrm{SiO}_{2}$ paper. The oxygen content of the plate as reported by the manufacturer was $30 \\mathrm{ppm}$.\n\n\\subsection*{2.2. Characterization}\nThe top surface of the scan track morphology and crack-affected zone surrounding the track were examined using a Keyence VK-X100 3D laser scanning microscope, as well as the melt pool width for calibration of the thermomechanical models. The substrates were sectioned, ground, and polished using standard metallographic sample preparation techniques. The microstructure was revealed using swab etching for 5-60 s with a modified Murakami's reagent ( $15 \\mathrm{~g} \\mathrm{~K}_{3} \\mathrm{Fe}$ $(\\mathrm{CN})_{4}+2 \\mathrm{~g} \\mathrm{KOH}$ dissolved in $100 \\mathrm{ml} \\mathrm{H}_{2} \\mathrm{O}$ ), and examined using a FEI Quanta 200 environmental SEM.\n\n\\subsection*{2.3. Thermomechanical model}\nThe implicit, Lagrangian finite element code Diablo [27], which employs distributed memory parallelism, was used to perform thermal and thermomechanical simulations of the single tracks on a tungsten substrate. Convection, radiation, and evaporation boundary conditions were included on the top surface of the model. An emissivity of 0.35 was used and a convection coefficient of $6 \\mathrm{~W} / \\mathrm{m}^{2}-\\mathrm{K}$ was calculated from the experimental Ar flow conditions of laminar flow over a flat plate [29]. For both convection and radiation, a far field temperature of $\\mathrm{T}_{\\infty}=303 \\mathrm{~K}$ was used. The evaporation boundary condition includes the effects of latent heat of evaporation and the heat loss due to mass flux from vaporization [30]. The bottom surface of the plate was fixed at $T_{0}=303 \\mathrm{~K}$. For the mechanical simulations, zero normal displacements were prescribed on all sides of the computational domain except the top surface. As Diablo is a Lagrangian code, fluid flow after melting is not explicitly modeled. As such, a Goldak [31] type volumetric heat source was used and the ellipsoidal dimensions were tuned to match the experimental melt pool width. Effective absorptivity values varied from 0.35 to 0.65 depending on the process parameters and were determined from experiments conducted in Ref [32]. Interpolation between the experimental absorptivity measurements was performed for process parameter settings not directly measured.\n\nTemperature-dependent thermophysical properties (thermal conductivity, specific heat, density, coefficient of thermal expansion, and latent heats of phase change) for pure $\\mathrm{W}$ were obtained up to melt from Refs $[33,34]$. Temperature-dependent mechanical and material properties (Young's modulus, yield stress, Poisson's ratio, hardening modulus) were obtained up to at least $1473 \\mathrm{~K}$ from Appendix A of the ITER structural design criteria for in-vessel components (SDC-IC) [26]. No mechanical properties could be found at higher temperatures. As such, the yield stress was linearly extrapolated to $0 \\mathrm{MPa}$ at the melt temperature, such that there would be 0 deviatoric stress at temperatures greater than melt.", "start_char_idx": 368881, "end_char_idx": 372781, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "968732b4-552c-4dd4-a78f-af2e43e1e747": {"__data__": {"id_": "968732b4-552c-4dd4-a78f-af2e43e1e747", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "06043e4f-9348-4575-aaae-155a4665a644", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f3705a2dabc87571a8fc235e5a53fd920e7e7bdee20c6e439fc9f65ee4946df8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9d6a5624-8d9a-4f52-ab42-7a54c2d89471", "node_type": "1", "metadata": {}, "hash": "aa87eb0b82ac2f6ae7b848b6fd76cd3dc8ea9ddbae462bca9e0bfad04f9f768f", "class_name": "RelatedNodeInfo"}}, "text": "Interpolation between the experimental absorptivity measurements was performed for process parameter settings not directly measured.\n\nTemperature-dependent thermophysical properties (thermal conductivity, specific heat, density, coefficient of thermal expansion, and latent heats of phase change) for pure $\\mathrm{W}$ were obtained up to melt from Refs $[33,34]$. Temperature-dependent mechanical and material properties (Young's modulus, yield stress, Poisson's ratio, hardening modulus) were obtained up to at least $1473 \\mathrm{~K}$ from Appendix A of the ITER structural design criteria for in-vessel components (SDC-IC) [26]. No mechanical properties could be found at higher temperatures. As such, the yield stress was linearly extrapolated to $0 \\mathrm{MPa}$ at the melt temperature, such that there would be 0 deviatoric stress at temperatures greater than melt. Similarly, the Young's modulus was decreased to $10 \\%$ of its room temperature value upon reaching melt. All other material properties were held constant above their reported temperature range. A finite deformation, strain rate independent material model with linear isotropic hardening was used, as described in [35]. All accumulated plastic strains were reset upon reaching the melt temperature. Further details concerning the numerical solution strategies employed by Diablo can be found in [36].\n\nHalf symmetry was used to reduce the size of the simulations. The symmetry plane was along the center of the scan track with normal vector transverse to the scan. A mesh size of $10 \\mu \\mathrm{m}$ was used along the longitudinal direction ( $\\mathrm{x})$ of the beam and 5-10 $\\mu \\mathrm{m}$ spacing along the transverse direction (y) within the vicinity of the melt pool. A similar mesh size was used in the $z$, or depth, direction. The mesh\\\\\nsize increased further away from the melt area. The total simulation domain was $3.5 \\times 1.25 \\times 2 \\mathrm{~mm}^{3}$, which was large enough to ensure that uncertainties in the boundary conditions at the edges of the computational domain did not affect the predicted temperatures or stresses in the regions and time scales of interest. The simulations employed approximately 1 million elements and required computation times on the order of $10^{3}$ to $10^{4} \\mathrm{cpu}$-hours each, based upon the process parameter settings and physics involved (thermal vs. thermomechanical). The mesh size was determined via a refinement study where using a more refined mesh did not significantly change the temperatures in the region of interest.\n\nThe ellipsoidal dimensions of the Goldak heat source were calibrated by matching the experimental melt pool width with the model melt pool width, as shown in Fig. 2a. The resulting predicted melt lengths compare well with the experimentally observed melt lengths in Fig. 2b.\n\n\\section*{3. Results}\nThe parameter sets used in this work are shown in Fig. 3, consisting of different scan speeds $v$, laser power $P$, and laser beam diameter $\\emptyset$. The linear energy input $P / v$ covered by the parameter sets in Fig. 3 ranges between $0.6<P / v<6 \\mathrm{~J} / \\mathrm{mm}$. Although various scaling terms have been used to normalize data presented from LPBF experiments [37,38], the results below will show that $P / v$ achieves the most physically relevant scaling for this work. For high laser powers, longitudinal cracks along the center line of the track occurred as indicated by the red markers, which will be discussed in Section 3.2.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_e3da621bda4f21053917g-3(1)}\n\nFig. 2. Comparison of the experimentally determined (a) melt pool width, and (b) melt pool length, and the predicted width and length from the thermal model. Horizontal error bars are $\\pm$ one standard deviation. The melt dimensions in the simulations were constant in the steady state regime. The red markers correspond to datasets in which longitudinal cracking was observed, which will be discussed in Section 3.1 and 3.2. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-3}\n\\end{center}\n\nFig. 3.", "start_char_idx": 371908, "end_char_idx": 376184, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9d6a5624-8d9a-4f52-ab42-7a54c2d89471": {"__data__": {"id_": "9d6a5624-8d9a-4f52-ab42-7a54c2d89471", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "968732b4-552c-4dd4-a78f-af2e43e1e747", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "696fb58f8867ac5e11496f7edb5824bbfd77da6343a95bbfac00722e492eed87", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b6c71492-cb27-484c-b691-eac91278dd21", "node_type": "1", "metadata": {}, "hash": "3d2cd9ed538ade5ed94f44d15c361170265f32ea29026d7ac64d927977c28b4d", "class_name": "RelatedNodeInfo"}}, "text": "2. Comparison of the experimentally determined (a) melt pool width, and (b) melt pool length, and the predicted width and length from the thermal model. Horizontal error bars are $\\pm$ one standard deviation. The melt dimensions in the simulations were constant in the steady state regime. The red markers correspond to datasets in which longitudinal cracking was observed, which will be discussed in Section 3.1 and 3.2. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-3}\n\\end{center}\n\nFig. 3. Laser power $\\mathrm{P}$ - Scan speed $\\mathrm{v}$ - beam diameter $\u00d8$ combinations used in this work. The red markers indicate parameter combinations that led to longitudinal cracking. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)\n\n\\subsection*{3.1. Melt pool behavior}\nTwo representative melt pool geometries encountered in this work are shown in Fig. 4. Contrary to metal alloys such as $316 \\mathrm{~L}$ or AlSi10Mg, W does not have a clearly defined melt pool boundary when processed by LPBF. Instead, epitaxial growth and a planar solidification front ensure there is a seamless transition between the substrate microstructure and the solidification structure, as in other pure metals like Ta [39], or alloys with a small solidification range such as Ti6Al4V [40]. In this work, the substrate microstructure consisted of elongated grains perpendicular to the surface on which the tracks were scanned, which is similar to the elongated grains that develop in the build direction during LPBF of W [16]. Therefore, the microstructure of the substrate and single scan track in this work are representative of the microstructure that develops during LPBF, and the crack paths into the substrate are similar to the vertical cracks previously encountered in LPBF of W [13].\n\nFor most of the parameter sets, the melt pool is stable and in the socalled 'conduction mode' (Fig. 4a), except the sets indicated by the red markers in Fig. 3 that led to deeper melt pools and longitudinal cracking (Fig. 4b). In Fig. 4a, the track surface is flat with minor formation of a chevron pattern, and the melt pool is shallow with depth $d=25 \\mu \\mathrm{m}$. The melt width $w(73 \\pm 2 \\mu \\mathrm{m})$ is smaller than the beam diameter $\\emptyset=100 \\mu \\mathrm{m}$, indicating that the tails of the Gaussian distributed laser power are not sufficiently powerful to heat the material above the melting point $T_{m}=3695 \\mathrm{~K}$. In contrast, the top surface track morphology shown in Fig. 4b is indicative of a more violent melt behavior. The power $P=450 \\mathrm{~W}$ was high enough to boil the tungsten at $T_{b}=6203 \\mathrm{~K}$, creating a vapor depression resulting in a deeper melt with depth $d=223 \\mu \\mathrm{m}$. Further on, the scan track shown in Fig. 6 has a melt width $w=116 \\pm 2 \\mu \\mathrm{m}$. Its chevron pattern is more apparent than that in Fig. 4a due to the higher laser power, yet is less unstable than in Fig. 4b. This periodic rippling of weld beads has long been observed and is attributed to different phenomena, including instability due to evaporation, thermocapillary instability, or varying solidification rates [41].\n\nIn Fig. 5, the round and square markers show an increasing melt pool width with increasing laser power. The cross-shaped markers indicate that the melt pool remains shallow (width/depth ratios $w / d$ $>2$ ) for most parameter combinations except for high laser powers $P$ $>400 \\mathrm{~W}$, as shown in red, again corresponding to the red parameter sets in Fig. 3 for which longitudinal cracking was observed. In those cases, the melt pool is nearly as deep as it is wide, which resulted in thin, vertically oriented grains in the center of the melt pool (Fig. 4b). Applying the scaling laws derived by Rubenchik et al.", "start_char_idx": 375519, "end_char_idx": 379538, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b6c71492-cb27-484c-b691-eac91278dd21": {"__data__": {"id_": "b6c71492-cb27-484c-b691-eac91278dd21", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9d6a5624-8d9a-4f52-ab42-7a54c2d89471", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "70c30df5a631d5dec7f3e2339540543ba335ec630c4e3ced2419ea4efa376f9b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3f8cd7a2-ce70-4f6b-baa1-0ab94274cc4b", "node_type": "1", "metadata": {}, "hash": "de68ed0f81c3cc6951797e1313fac034bf8567ef593a639cd6d6ca4fc591caba", "class_name": "RelatedNodeInfo"}}, "text": "4b. This periodic rippling of weld beads has long been observed and is attributed to different phenomena, including instability due to evaporation, thermocapillary instability, or varying solidification rates [41].\n\nIn Fig. 5, the round and square markers show an increasing melt pool width with increasing laser power. The cross-shaped markers indicate that the melt pool remains shallow (width/depth ratios $w / d$ $>2$ ) for most parameter combinations except for high laser powers $P$ $>400 \\mathrm{~W}$, as shown in red, again corresponding to the red parameter sets in Fig. 3 for which longitudinal cracking was observed. In those cases, the melt pool is nearly as deep as it is wide, which resulted in thin, vertically oriented grains in the center of the melt pool (Fig. 4b). Applying the scaling laws derived by Rubenchik et al. [37] leads to a scan speed independent, $380 \\mathrm{~W}$ laser power to reach the boiling temperature at $6203 \\mathrm{~K}$. However, experimental results by Matthews et al.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-4(1)}\n\\end{center}\n\nFig. 4. Melt pool top surface and cross section for (a) $P=300 \\mathrm{~W}, v=300 \\mathrm{~mm} / \\mathrm{s}, \\emptyset=100 \\mu \\mathrm{m}$, and (b) $P=450 \\mathrm{~W}, v=100 \\mathrm{~mm} / \\mathrm{s}, \\emptyset=100 \\mu \\mathrm{m}$. The crack network scales with the melt pool size, which is shallow in (a) but deep in (b), leading to a deep penetration of cracks into the substrate seen on the right. The black arrows indicate transversal cracks.\n\n[32] indicate that this threshold power increases with increasing scan speed. The threshold in this work was observed between $350 \\mathrm{~W}$ and $400 \\mathrm{~W}$ for $v=300 \\mathrm{~mm} / \\mathrm{s}$, and above $400 \\mathrm{~W}$ for $v=400 \\mathrm{~mm} / \\mathrm{s}$ and $500 \\mathrm{~mm} / \\mathrm{s}$. Boiling induces a deeper melt cavity, which in turn roughly doubles the absorptivity through multiple scattering of the laser within that cavity [32,42]. The depths of tracks created using $\\emptyset=50 \\mu \\mathrm{m}$ was not investigated, nor was it possible to distinguish the melt pool cross section from the substrate microstructure for parameter sets where $P=200 \\mathrm{~W}$.\n\n\\subsection*{3.2. Cracking behavior}\nThe crack network around the scan track shown in Fig. 6 is representative of the crack pattern for most parameter sets. The cracks are roughly transversal across the scan vector but still adhere to grain boundaries, surrounded by a branched crack network in an area roughly 3-4 times the melt width. Moreover, the vertical crack on the right in Fig. 4b shows that cracks not only occur far away from the scan track, but also penetrate deeply into the substrate, with crack propagation facilitated by the elongated grain structure of the substrate.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-4}\n\\end{center}\n\nFig. 5. Melt pool width and width-to-depth ratio as a function of laser power P. Melt pool depth data was only analyzed for $\\emptyset=100 \\mu \\mathrm{m}$ parameter sets. The red markers correspond to parameter sets for which longitudinal cracking was observed. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)\\\\\nIn Fig. 7, a video still shows the locations of two transversal cracks and the delay between passage of the melt pool and cracking. The full video is found in Supplementary Video 1, where a moderate amount of turbulence is visible on the melt pool top surface through the specular reflections, which contributes to the formation of the surface ripples on the solidified track. More importantly, it is evident that the two cracking events within the solidified material do not occur in the vicinity of the melt pool.", "start_char_idx": 378701, "end_char_idx": 382563, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3f8cd7a2-ce70-4f6b-baa1-0ab94274cc4b": {"__data__": {"id_": "3f8cd7a2-ce70-4f6b-baa1-0ab94274cc4b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b6c71492-cb27-484c-b691-eac91278dd21", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7b727ca97fa7beb13e440422800db1ec0bcf951e693c7748952adf7449a6eb57", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bd22baf9-9c54-4964-851e-34d1cb950cf6", "node_type": "1", "metadata": {}, "hash": "b2e61adf28865bbc03cc7b493097577f609d204febf62de6cb2a779f0af69620", "class_name": "RelatedNodeInfo"}}, "text": "5. Melt pool width and width-to-depth ratio as a function of laser power P. Melt pool depth data was only analyzed for $\\emptyset=100 \\mu \\mathrm{m}$ parameter sets. The red markers correspond to parameter sets for which longitudinal cracking was observed. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)\\\\\nIn Fig. 7, a video still shows the locations of two transversal cracks and the delay between passage of the melt pool and cracking. The full video is found in Supplementary Video 1, where a moderate amount of turbulence is visible on the melt pool top surface through the specular reflections, which contributes to the formation of the surface ripples on the solidified track. More importantly, it is evident that the two cracking events within the solidified material do not occur in the vicinity of the melt pool. Rather, there is a delay after the passage of the melt pool before a crack appears. While Supplementary Video 1 is a single example for $P=450 \\mathrm{~W}, v=300 \\mathrm{~mm} / \\mathrm{s}$, and $\\emptyset=50 \\mu \\mathrm{m}$, examples for other $P-v-\\emptyset$ combinations are provided in the other supplementary materials (available online). As the videos are restricted to the surface, it is not clear whether the cracks initiate near the surface or within the material. Cracks traversing the scan track, which is on the order of magnitude $100 \\mu \\mathrm{m}$ wide, appeared instantaneously between two frames at a $50 \\mathrm{kHz}$ frame rate, indicating crack growth rates of at least $5 \\mathrm{~m} / \\mathrm{s}$. Given that most cracks in the track are transversal, the crack spacing can be determined by the total crack count divided by the total track length. Fig. 8a shows that this crack spacing increases with increasing laser power, rising from $250 \\mu \\mathrm{m}$ to $600 \\mu \\mathrm{m}$ before the onset of longitudinal cracking. The longitudinal cracks partially relieve the residual stress and fewer transversal cracks are induced as a result.\n\nIn Fig. 8b, the time delay between solidification and cracking shows a linear correlation with the linear energy input $P / v$, which will be discussed in Section 4.1. Each data point is the median of cracking delays determined from 10 (for $\\emptyset=50 \\mu \\mathrm{m}$ ) or 20 videos (for $\\emptyset=100 \\mu \\mathrm{m}$ ). The median is chosen over the average to represent the asymmetry in cracking delays. Correspondingly, the error bars represent the interquartile range (IQR). The IQR is asymmetric around the median value, as there are fewer cracks at shorter delays. In the remainder of the text, the time delays and derived crack temperatures are reported as median values with error bars corresponding to the IQR. Consistent with previous plots, the red markers indicate the presence of longitudinal cracking. The red markers show that the time delays for transversal cracks to occur when longitudinal cracks are present are slightly longer than those without longitudinal cracking, though the difference is not statistically significant. While most cracks were transversal across the scan track, this longitudinal cracking occurred for higher laser powers, which coincided with a wider, but more importantly, deeper melt pool (Fig. 5). Improper width/ depth ratios $<2$ in welding are known to produce excessive amounts of transversal strain and unfavorable grain orientations that can lead to longitudinal cracking [43]. Fig. 4b shows that the deep melt pool shape leads to the formation of thin, vertically oriented grains in the\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-5(2)}\n\\end{center}\n\nFig. 6. Confocal image of a scan track $(v=300 \\mathrm{~mm} / \\mathrm{s}, P=400 \\mathrm{~W}, \\emptyset=100 \\mu \\mathrm{m})$, with indication of the zone around the track in which cracks are induced.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-5}\n\\end{center}\n\nFig. 7.", "start_char_idx": 381658, "end_char_idx": 385689, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bd22baf9-9c54-4964-851e-34d1cb950cf6": {"__data__": {"id_": "bd22baf9-9c54-4964-851e-34d1cb950cf6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3f8cd7a2-ce70-4f6b-baa1-0ab94274cc4b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f8616ed90cf75a4131ec263087032c654aaaa02acd6884bbde3d65d87af4bb98", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f02d269e-0f9c-471e-bebb-34110d81368f", "node_type": "1", "metadata": {}, "hash": "e8bf2d325af4132a9e17676821742da4028b0d2610b6a06093db26fb258c1423", "class_name": "RelatedNodeInfo"}}, "text": "Fig. 4b shows that the deep melt pool shape leads to the formation of thin, vertically oriented grains in the\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-5(2)}\n\\end{center}\n\nFig. 6. Confocal image of a scan track $(v=300 \\mathrm{~mm} / \\mathrm{s}, P=400 \\mathrm{~W}, \\emptyset=100 \\mu \\mathrm{m})$, with indication of the zone around the track in which cracks are induced.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-5}\n\\end{center}\n\nFig. 7. Still image of the top down high speed video of a laser scan $(P=450 \\mathrm{~W}$, $v=300 \\mathrm{~mm} / \\mathrm{s}, \\emptyset=50 \\mu \\mathrm{m}$ ) with two delayed cracking events.\n\nmiddle of the solidified melt pool which provide an easy growth path for longitudinal cracks to occur.\n\n\\subsection*{3.3. Crack temperature}\nBy multiplying with the scan speed, the time delay in Fig. 8b can be converted to a distance behind the trailing edge of the melt pool. In turn, this distance is used in the thermal simulations to extract the temperature at the crack location. This is illustrated in Fig. 9, showing the thermal field created by the laser traveling left to right at $v=100 \\mathrm{~mm} / \\mathrm{s}, P=450 \\mathrm{~W}$, and $\\emptyset=100 \\mu \\mathrm{m}$, with the laser positioned at $x=0.9 \\mathrm{~mm}$. The simulated melt pool is a near perfect circle in agreement with the experiment, and the length/width ratio is small even for higher speeds due to the high thermal conductivity of $\\mathrm{W}$. Thermal gradients in the longitudinal direction at the solidification front exceed $3 \\times 10^{7} \\mathrm{~K} / \\mathrm{m}$ while cooling rates approach $5 \\times 10^{6} \\mathrm{~K} / \\mathrm{s}$.\n\nThe box plot on Fig. 9 shows the median crack delay distance $\\pm$ the IQR. The lines on either side extend out to the minimum and maximum observed delays. The cracking temperature range for all parameter sets is shown in Fig. 10a as a function of $P / v$. Cracking consistently happened in the $450 \\mathrm{~K}-650 \\mathrm{~K}$ interval in which the DBT is expected to occur. The presence of longitudinal cracks is again indicated by the red markers. Some error bars are large and extend above the DBTT range. The large uncertainties are caused by a combination of several factors. First, the stochastic nature of material failure and in particular the location thereof, which is determined by local defects that are distributed randomly in the material. Second, it is possible that cracks initiate inside the material rather than on the surface, where the material is cooler These cracks then propagate along the path of least resistance, which may branch into the warmer region, showing up on the surface in areas where they would not be strictly expected. Lastly, local strain rate differences can contribute as well, and will be discussed together with Fig. 10b in Section 4.2.\n\n\\subsection*{3.4. Crack network size and morphology}\nThe top view of the Von Mises residual stresses after completion of the scan are shown in Fig. 11a for $v=300 \\mathrm{~mm} / \\mathrm{s}, P=300 \\mathrm{~W}$, and $\\emptyset=100 \\mu \\mathrm{m}$. The inner dashed white line indicates the material that underwent melting and solidification, i.e. the scan track. The outer dashed line is an indication of the crack-affected area as described in Fig. 6, and is seen to correspond to the region in which the Von Mises stress is high. In Fig. 11b-d, the longitudinal, transversal, and Von mises stresses are shown along $x=0$, scaled by the melt pool half width so that a value of 1 on the horizontal axis corresponds to the edge of the scan track (shaded in red). These stresses are shown for five distinct $P / v$ ratios which span the range of values investigated in this work.", "start_char_idx": 385160, "end_char_idx": 388959, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f02d269e-0f9c-471e-bebb-34110d81368f": {"__data__": {"id_": "f02d269e-0f9c-471e-bebb-34110d81368f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bd22baf9-9c54-4964-851e-34d1cb950cf6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "af332622039f6a66dacc29c3604b565b536b835dcbbf85b276031b0fc25e02eb", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ec7826d6-3a7a-4bb6-bc9e-cad990ab1043", "node_type": "1", "metadata": {}, "hash": "7c7db8b646c653b612b806d3eee7f6154e6c3f4ec4345303cca3979cc7565f94", "class_name": "RelatedNodeInfo"}}, "text": "11a for $v=300 \\mathrm{~mm} / \\mathrm{s}, P=300 \\mathrm{~W}$, and $\\emptyset=100 \\mu \\mathrm{m}$. The inner dashed white line indicates the material that underwent melting and solidification, i.e. the scan track. The outer dashed line is an indication of the crack-affected area as described in Fig. 6, and is seen to correspond to the region in which the Von Mises stress is high. In Fig. 11b-d, the longitudinal, transversal, and Von mises stresses are shown along $x=0$, scaled by the melt pool half width so that a value of 1 on the horizontal axis corresponds to the edge of the scan track (shaded in red). These stresses are shown for five distinct $P / v$ ratios which span the range of values investigated in this work. From the line graphs in Fig. 11b-d, the longitudinal stress is over $1300 \\mathrm{MPa}$ and the transversal stress is smaller than $600 \\mathrm{MPa}$ within the scan track, whereas the transversal stress peaks around $1000 \\mathrm{MPa}$ adjacent to the track as the longitudinal stress falls to\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_e3da621bda4f21053917g-5(1)}\n\nFig. 8. (a) The crack spacing along the scan track increases with increasing laser power. Error bars correspond to $\\pm$ one standard deviation. (b) Linear correlation between the linear energy input $\\mathrm{P} / \\mathrm{v}$ and the delay between solidification and cracking $\\left(\\mathrm{R}^{2}=0.98\\right.$, excluding the red markers and setting the intercept at zero according to Eq. (1) in Section 4.1$)$. The crack delay is shown as the median values, the error bars correspond to the IQR. The red markers indicate the presence of longitudinal cracking in addition to transversal cracking. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-6}\n\\end{center}\n\nFig. 9. Top view of Diablo thermal model of a scan track using $v=100 \\mathrm{~mm} / \\mathrm{s}, P=450 \\mathrm{~W}, \\emptyset=100 \\mu \\mathrm{m}$, with a boxplot indication of the temperature range at which cracking occurs.\n\n$0 \\mathrm{MPa}$ quickly, further away from the track. The large longitudinal stress in the scan track contributes to the transversal nature of the cracks within the track, whereas the increase in transversal stress adjacent to the track leads to the more angled, branched network of cracks in the crack-affected zone. This zone is often bounded by cracks running parallel to the scan track at roughly the location of the maximum transversal stress in Fig. 11c. There is no apparent difference in the distribution or magnitude of the transversal stress for parameters sets that displayed longitudinal cracking (see line v300P500 indicating $v=300 \\mathrm{~mm} / \\mathrm{s}$ and $P=500 \\mathrm{~W}$ ). This is because the discrepancy between the model and experiments is larger for cases in which boiling occurred, leading to a more turbulent, deeper melt pool. While the model does take boiling into account in the thermal balance, any associated melt pool phenomena are not captured by the model. As mentioned in Section 3.1, the deeper melt pool and vertically oriented grains assist in the formation of longitudinal cracks.\n\nThe Von Mises stress shown in Fig. 11d is relatively constant at $1300 \\mathrm{MPa}-1400 \\mathrm{MPa}$ in the crack-affected area but decreases quickly outside of it. The exact extent of the crack-affected zone is nondeterministic and is influenced by a combination of temperature, stress magnitude, stress orientation, local defects in the microstructure, and the occurrence of previous cracks in the vicinity that act as local stress relievers. Nevertheless, the crack-affected zone (shaded in blue in Fig.", "start_char_idx": 388232, "end_char_idx": 392038, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ec7826d6-3a7a-4bb6-bc9e-cad990ab1043": {"__data__": {"id_": "ec7826d6-3a7a-4bb6-bc9e-cad990ab1043", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f02d269e-0f9c-471e-bebb-34110d81368f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "23895a1bdb61e4d25d79cd60450350fc9503c0acb9f1868ab4a21fe9bf8a7a2b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "676df5ec-dc62-4c1d-93fc-18b5a61466ad", "node_type": "1", "metadata": {}, "hash": "7b8e0c6672732617d589cec4ffd05d7ee458a99cc925796bef66fa24664d6655", "class_name": "RelatedNodeInfo"}}, "text": "This is because the discrepancy between the model and experiments is larger for cases in which boiling occurred, leading to a more turbulent, deeper melt pool. While the model does take boiling into account in the thermal balance, any associated melt pool phenomena are not captured by the model. As mentioned in Section 3.1, the deeper melt pool and vertically oriented grains assist in the formation of longitudinal cracks.\n\nThe Von Mises stress shown in Fig. 11d is relatively constant at $1300 \\mathrm{MPa}-1400 \\mathrm{MPa}$ in the crack-affected area but decreases quickly outside of it. The exact extent of the crack-affected zone is nondeterministic and is influenced by a combination of temperature, stress magnitude, stress orientation, local defects in the microstructure, and the occurrence of previous cracks in the vicinity that act as local stress relievers. Nevertheless, the crack-affected zone (shaded in blue in Fig. 11b-d) is roughly bounded by the region in which the Von\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_e3da621bda4f21053917g-6(1)}\n\nFig. 10. (a) Temperature at the microcracking location as a function of $P / v$, extracted from the thermal Diablo model. (b) Strain rate for all $100 \\mu \\mathrm{m}$ beam P-v combinations upon reaching $650 \\mathrm{~K}$ (the maximum crack temperature), extracted from the thermomechanical Diablo model. The temperature markers are the median values, the error bars correspond to the IQR, which is asymmetric. The red markers correspond to parameter sets for which longitudinal cracking was observed. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) $1000 \\mathrm{MPa}$ to $1150 \\mathrm{MPa}$ in the DBT temperature interval observed in this work [26].\n\n\\section*{4. Discussion}\n\\subsection*{4.1. Cracking delay vs $P / v$}\nA Goldak heat source approximation was used in the thermomechanical model to accurately capture the melt pool shape. However, since cracks occur at a significant distance from the melt pool, in a region where temperatures are closer to $T_{0}$ than $T_{m}$, it is convenient to consider the linear correlation between the cracking time delay $\\Delta t$ and the linear energy input $P / v$ using the simple Rosenthal equation [44], which utilizes a point heat source and is given by:\n\n$T-T_{0}=\\left(\\frac{q / v}{2 \\pi k t}\\right) e^{-r^{2} / 4 \\alpha t}$\n\nIn Eq. (1), $T_{0}$ is the surrounding equilibrium temperature, $q$ the heat input, $v$ the scan speed, $k$ the thermal conductivity, $\\alpha$ the thermal diffusivity, and $r$ the distance from the centerline of the track. Considering the centerline $(r=0)$ and with $q=A P$, where $A$ is the absorptivity and $P$ the laser power, the time between solidification at $T_{m}$ and reaching a certain, fixed cracking temperature $T_{\\text {crack }}$ is shown to be proportional to $P / v$, as shown in Eq. (2).\n\n\n\\begin{equation*}\n-t_{m}=\\frac{P}{v}\\left(\\frac{A}{2 \\pi k}\\right)\\left(\\frac{1}{T_{\\text {crack }}-T_{0}}-\\frac{1}{T_{m}-T_{0}}\\right) \\tag{2}\n\\end{equation*}\n\n\n\\subsection*{4.2. Strain rate dependence}\nRather than a constant cracking temperature, there is a noticeable increase for lower $P / v$ shown in Fig. 10a. To supplement the thermal model, a thermomechanical model for all $100 \\mu$ m beam $P-v$ combinations was used to determine the residual stresses and strain rates. The calculated strain rates at the crack location ranged from $0.5 \\mathrm{~s}^{-1}$ to $6 \\mathrm{~s}^{-1}$, as shown in Fig. 10b. These strain rates were extracted at the location corresponding to the maximum crack temperature observed in Fig. 10a $(650 \\mathrm{~K})$.", "start_char_idx": 391103, "end_char_idx": 394807, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "676df5ec-dc62-4c1d-93fc-18b5a61466ad": {"__data__": {"id_": "676df5ec-dc62-4c1d-93fc-18b5a61466ad", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ec7826d6-3a7a-4bb6-bc9e-cad990ab1043", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0dda15854ab71f498a11d726e39080da3a0d7095f540dcf4bacaa7a7045f70ce", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "e5688456-a1af-4321-a526-b9db761df2c1", "node_type": "1", "metadata": {}, "hash": "eccda764258b0f7537b782fbfd11c1b112332cb6ee596f85c78e75f8c8181a33", "class_name": "RelatedNodeInfo"}}, "text": "\\subsection*{4.2. Strain rate dependence}\nRather than a constant cracking temperature, there is a noticeable increase for lower $P / v$ shown in Fig. 10a. To supplement the thermal model, a thermomechanical model for all $100 \\mu$ m beam $P-v$ combinations was used to determine the residual stresses and strain rates. The calculated strain rates at the crack location ranged from $0.5 \\mathrm{~s}^{-1}$ to $6 \\mathrm{~s}^{-1}$, as shown in Fig. 10b. These strain rates were extracted at the location corresponding to the maximum crack temperature observed in Fig. 10a $(650 \\mathrm{~K})$. The strain rates in other locations will differ, and will be higher closer to the melt pool. Given the dependency of the DBTT on the strain rate discussed below, this may be an additional factor in the large uncertainties in the determined cracking temperature intervals. However, possible subsurface crack initiation is likely the most significant factor.\n\nIn Refs. [45-47], the sensitivity of the DBTT to the strain rate was investigated for strain rates between $10^{-5} \\mathrm{~s}^{-1}-10^{-2} \\mathrm{~s}^{-1}$. The DBTT was found to display an Arrhenius-type correlation with the strain rate: $\\dot{\\varepsilon}=A \\exp \\left(E_{D B T} / k T_{D B T}\\right)$, where $A$ is a scaling factor, $k$ the Boltzmann constant, and $\\mathrm{E}_{\\mathrm{DBT}}$ the activation energy for the mechanism governing the DBT. The DBTT decreased by roughly $80-90 \\mathrm{~K}$ in the strain rate interval investigated in literature, with a lower DBTT for lower strain rates. Using the correlation found in literature on the strain rates in this work would correspond to a $40-45 \\mathrm{~K}$ increase of the DBTT for lower $P / v$ ratios. The observed increase, however, is around $150 \\mathrm{~K}$.\\\\\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-7(4)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-7(1)}\n\\end{center}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-7(3)}\n\\end{center}\n\n(d)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-7}\n\\end{center}\n\nFig. 11. (a) Top view of the Von Mises residual stress after the laser scan has completed, for $v=300 \\mathrm{~mm} / \\mathrm{s}, P=300 \\mathrm{~W}$ and $\\emptyset=100 \\mu \\mathrm{m}$. The inner dashed line indicates the scan track, while the outer dashed line is a rough indication of the crack affected zone around the track. (b-d) Line graphs of the residual stress in the longitudinal direction (b), transversal direction (c), and Von Mises stress (d), as a function of normalized transverse distance, at $x=0$ after cooldown. The $x$-axis in (b-d) is scaled by the melt width so that 1 corresponds to the edge of the scan track. The red shaded area designates the scan track, the blue shaded area the crack-affected zone. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)\n\nAn Arrhenius plot of the strain rate dependence of the DBTT in this work is given in Fig. 12, in comparison with literature data. According to Giannattasio et al.", "start_char_idx": 394218, "end_char_idx": 397463, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "e5688456-a1af-4321-a526-b9db761df2c1": {"__data__": {"id_": "e5688456-a1af-4321-a526-b9db761df2c1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "676df5ec-dc62-4c1d-93fc-18b5a61466ad", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "918c73446aae7206b2a85f28e25f07944cd2944d10ed7c46b2a42fc8368fa67c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "850e454e-f016-4492-9a01-7cc4f1410f8f", "node_type": "1", "metadata": {}, "hash": "cce5210457e7cb808e65968e0cf09b74be8ca735b9d12ee72dab879903052614", "class_name": "RelatedNodeInfo"}}, "text": "The inner dashed line indicates the scan track, while the outer dashed line is a rough indication of the crack affected zone around the track. (b-d) Line graphs of the residual stress in the longitudinal direction (b), transversal direction (c), and Von Mises stress (d), as a function of normalized transverse distance, at $x=0$ after cooldown. The $x$-axis in (b-d) is scaled by the melt width so that 1 corresponds to the edge of the scan track. The red shaded area designates the scan track, the blue shaded area the crack-affected zone. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)\n\nAn Arrhenius plot of the strain rate dependence of the DBTT in this work is given in Fig. 12, in comparison with literature data. According to Giannattasio et al. [47], the activation energy for high purity tungsten is equal to $1.0 \\pm 0.1 \\mathrm{eV}$, while for low-purity sintered samples $\\mathrm{E}_{\\mathrm{DBT}}$ was equal to $1.45 \\pm 0.12 \\mathrm{eV}$, indicating that impurities not only influence the DBTT itself [10], but also its dependence on the strain rate. The work by Chilton and Wronski [45] yields $\\mathrm{E}_{\\mathrm{DBT}}=1.2 \\pm 1.0 \\mathrm{eV}$. These values are consistent with dislocation glide of screw dislocations, partially assisted by shear stresses acting upon the dislocations [46]. Extracting an activation energy from the results of this work yields $\\mathrm{E}_{\\mathrm{DBT}}=0.32 \\pm 0.05 \\mathrm{eV}$, evident by the shallow slope of the data from this work in Fig. 12\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e3da621bda4f21053917g-7(2)}\n\\end{center}\n\nFig. 12. Arrhenius plot of the strain rate dependence of the DBTT. Results from this work are compared to literature data [7,45-47]. Temperatures from this work are the median values. The red markers correspond to parameter sets for which longitudinal cracking was observed. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) $\\left(R^{2}=0.79\\right)$. This is considerably lower, but corresponds to the work by Gumbsch et al. [7], who derived an $\\mathrm{E}_{\\mathrm{DBT}}=0.2 \\mathrm{eV}$ for single crystal pure tungsten, a value consistent with edge dislocation glide $(0.2-0.5 \\mathrm{eV})$. This was later attributed to the orientation of the single crystal with respect to the loading, which allowed edge dislocation motion to be the governing DBT mechanism [46].\n\nThe major difference between this work and the work performed in literature to study the strain rate dependence of the DBT is the initial state of the material before the DBT is observed. In literature, the original dislocation density in the material is low, and the material is loaded in a fracture toughness test. The necessary dislocations to develop a sizeable crack tip plastic zone still need to be created, which in turn requires associated dislocations to move away from the dislocation nucleation sites. Screw dislocations are slower than edge dislocations, making the motion of the former the governing mechanism [47]. As the dislocation densities in laser powder bed fusion are known to be very high due to the thermal residual stresses [48], the dislocation density of the material in and surrounding the scan track will be substantially higher, possibly alleviating the need for motion of the associated screw dislocations, though this requires further investigation. Other factors affecting the results in this work include (i) the higher magnitude of the strain rate, (ii) microstructural differences, (iii) the continuous cooling nature of this work compared to the isothermal tests in literature, and (iv) that the strain rate and crack temperature are not controlled variables as in literature, but rather a result of thermomechanical modeling.\n\n\\subsection*{4.3. Crack mitigation}\nThe main crack-reducing strategy employed in literature is preheating to a temperature above the DBTT.", "start_char_idx": 396627, "end_char_idx": 400673, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "850e454e-f016-4492-9a01-7cc4f1410f8f": {"__data__": {"id_": "850e454e-f016-4492-9a01-7cc4f1410f8f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e5688456-a1af-4321-a526-b9db761df2c1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1bf72b5f69980d08e800eaa47ac27431925fcbf1949cd26b2b7e560d813aea2f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "006c1617-b2ef-440a-85a2-baeff05a4fd5", "node_type": "1", "metadata": {}, "hash": "c06e9f22c7af881c11453aa11af119cef27792b94c1e44688e0e65dbbcda389b", "class_name": "RelatedNodeInfo"}}, "text": "Screw dislocations are slower than edge dislocations, making the motion of the former the governing mechanism [47]. As the dislocation densities in laser powder bed fusion are known to be very high due to the thermal residual stresses [48], the dislocation density of the material in and surrounding the scan track will be substantially higher, possibly alleviating the need for motion of the associated screw dislocations, though this requires further investigation. Other factors affecting the results in this work include (i) the higher magnitude of the strain rate, (ii) microstructural differences, (iii) the continuous cooling nature of this work compared to the isothermal tests in literature, and (iv) that the strain rate and crack temperature are not controlled variables as in literature, but rather a result of thermomechanical modeling.\n\n\\subsection*{4.3. Crack mitigation}\nThe main crack-reducing strategy employed in literature is preheating to a temperature above the DBTT. This research suggests that using a high $P / v$ ratio would be beneficial, since the lower strain rates lead to a slightly lower DBTT, though the lower strain rate does not\\\\\ntranslate to a significantly lower residual stress. However, the crackaffected area was also larger when using a high $P$. Literature on LPBF of Mo suggests that using $P / v<1 \\mathrm{~J} / \\mathrm{mm}$ in combination with support structures that limited thermal conduction to the base plate appeared to lower DBT-driven crack densities [25]. Since the DBTT of Mo is lower than that of $\\mathrm{W}$, the heat buildup due to the use of the support structure sufficiently increased the temperature to work above the DBTT, which at the very least should avoid cracking during laser scanning, and delay it until the part is cooled down to room temperature. M\u00fcller et al. [17] saw a reduction in, but not an elimination of $\\mathrm{W}$ microcracking by using preheating up to $1273 \\mathrm{~K}$, even though this temperature is above the DBTT. It is likely that, despite the high preheating temperature, substantial residual stresses were generated that led to cracking while the part was cooled down to room temperature after the build had completed.\n\nIn addition to the influence of process parameters, the alloy composition, and more specifically the concentration of impurities, has a major effect on the cracking behavior. The atmosphere control in this work was suboptimal but unavoidable to allow in situ high speed imaging. In commercial LPBF machines, the oxygen level in the process chamber can be controlled down to $10 \\mathrm{ppm}$ and lower. In that case, the impurities in the powder feedstock will become a major issue. While the bar feedstock in this work contained relatively little oxygen $(30 \\mathrm{ppm})$, spheroidization of tungsten powders leads to an increase in impurity content. According to Tekna [49], their commercially available spherical tungsten powders in the 15-45 $\\mu \\mathrm{m}$ size range contain up to $250 \\mathrm{ppm}$ oxygen. Similarly, $30 \\mu$ m diameter, spheroidized tungsten powders manufactured at Lawrence Livermore National Laboratory contained $370 \\mathrm{ppm}$. If high oxygen concentrations in the feedstock material cannot be avoided, the process may need to be adapted to actively remove impurities during processing, for example by using a hydrogen atmosphere that could act as an oxygen getter, or by small alloy additions of an element with a higher affinity for oxygen than tungsten [50].\n\nThe results in this work confirm that even though cracks occur at the microscale, mitigating the problem requires a universal strategy rather than a localized one. The time delays at which cracking occurs are too short $(\\leq 10 \\mathrm{~ms})$ for adjusted scan strategies to affect local temperature and stress distributions, and even if they were long enough, the fundamental cracking mechanism remains active. Furthermore, the crack-affected area is much larger than the scan track itself, as evidenced by Fig. 4b. Overall, this means a global rather than a local solution to the microcracking in W during LPBF is needed that affects either or both crack driving mechanisms: the residual stress and the ductile-to-brittle transition. Alloying can lower the DBTT and cause grain boundary strengthening that impedes crack growth, while base plate preheating or in situ diode annealing [51] will lower thermal gradients and raise the working temperature above the DBTT.", "start_char_idx": 399684, "end_char_idx": 404167, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "006c1617-b2ef-440a-85a2-baeff05a4fd5": {"__data__": {"id_": "006c1617-b2ef-440a-85a2-baeff05a4fd5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "850e454e-f016-4492-9a01-7cc4f1410f8f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "634a5436d099a04d9a1ec97b1674016a79e0bc4dff8cf9bf9f9507bddbfdccb3", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fff8b775-3d63-4c59-9d28-3dc0c3c44c0d", "node_type": "1", "metadata": {}, "hash": "bb139653a2fd2150a651f03d20bafb556f1b8510ccf74dd056616856d9b2a0d5", "class_name": "RelatedNodeInfo"}}, "text": "The time delays at which cracking occurs are too short $(\\leq 10 \\mathrm{~ms})$ for adjusted scan strategies to affect local temperature and stress distributions, and even if they were long enough, the fundamental cracking mechanism remains active. Furthermore, the crack-affected area is much larger than the scan track itself, as evidenced by Fig. 4b. Overall, this means a global rather than a local solution to the microcracking in W during LPBF is needed that affects either or both crack driving mechanisms: the residual stress and the ductile-to-brittle transition. Alloying can lower the DBTT and cause grain boundary strengthening that impedes crack growth, while base plate preheating or in situ diode annealing [51] will lower thermal gradients and raise the working temperature above the DBTT. The diagnostic tools developed in this study will be used in future work to study the influence of both alloying and preheating on microcracking in $\\mathrm{W}$.\n\n\\section*{5. Conclusion}\nFor the first time, the ductile-to-brittle transition (DBT) in tungsten was directly visualized through a combined approach of thermomechanical modeling and in situ high speed video of microcracking during laser melting. The linear correlation of the cracking time delay after solidification and the linear energy input $P / v$ is supported by the analytical Rosenthal equation, and translates to a cracking temperature between $450 \\mathrm{~K}-650 \\mathrm{~K}$ for all $P-v$ combinations, consistent with the expected range of the DBT temperature. Furthermore, an increase of the cracking temperature for low $P / v$ ratios was linked with an increasing strain rate, and evidence suggests edge dislocation glide to be the governing mechanism. The size of the crack-affected zone around the scan track corresponds to areas in which the maximum\\\\\nVon Mises residual stress exceeded the material yield stress, while the local orientation of cracks depends on the local longitudinal and transverse components of the residual stress. This work uncovered the fundamental cracking mechanisms of tungsten in AM processing conditions. The results can serve as a baseline for future efforts in eliminating microcracking during AM of tungsten.\n\n\\section*{Declaration of Competing Interest}\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\n\n\\section*{Acknowledgements}\nThis work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. This work was funded by the Laboratory Directed Research and Development Program at LLNL under project tracking code 18-ERD-057 and 18-SI-003.\n\n\\section*{Supplementary materials}\nSupplementary material associated with this article can be found in the online version at doi:10.1016/j.actamat.2020.04.060.\n\n\\section*{References}\n[1] T. Hirai, S. Panayotis, V. Barabash, C. Amzallag, F. Escourbiac, A. Durocher, M. Merola, J. Linke, T. Loewenhoff, G. Pintsuk, M. Wirtz, I. 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Van Humbeeck, Microstructure and mechanical properties of a novel $\\beta$ titanium metallic composite by selective laser melting Acta Mater. 68 (2014) 150-158, doi: 10.1016/j.actamat.2014.01.018.\n\n[41] P.S.", "start_char_idx": 412974, "end_char_idx": 415486, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2429da8b-8e40-4a10-98e0-945271229ba1": {"__data__": {"id_": "2429da8b-8e40-4a10-98e0-945271229ba1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "53dd7463-8269-4124-8bc1-50aca4fed71f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c4872f90d83c76bd3fd0cfb055ba221c7af5edd3a16308754f4166a260a65fd9", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fa51cc65-e764-4350-9b8e-ba03495db558", "node_type": "1", "metadata": {}, "hash": "e0c995c22d226df9c132f95e2a1417c98600cdbb442ef10e58a4d91301ebef1a", "class_name": "RelatedNodeInfo"}}, "text": "[39] L. Thijs, M.L. Montero Sistiage, R. Wauthle, Q. Xie, J.-.P. Kruth, J. Van Humbeeck, Strong morphological and crystallographic texture and resulting yield strength anisotropy in selective laser melted tantalum, Acta Mater. 61 (2013) 4657-4668, doi: 10.1016/j.actamat.2013.04.036.\n\n[40] B. Vrancken, L. Thijs, J.-.P. Kruth, J. Van Humbeeck, Microstructure and mechanical properties of a novel $\\beta$ titanium metallic composite by selective laser melting Acta Mater. 68 (2014) 150-158, doi: 10.1016/j.actamat.2014.01.018.\n\n[41] P.S. Wei, The Physics of Weld Bead Defects, in: weld, Process (2012) https:// \\href{http://www.intechopen.com/books/welding-processes/the-physics-of-weld-beaddefects}{www.intechopen.com/books/welding-processes/the-physics-of-weld-beaddefects} .\n\n[42] J. Ye, S.A. Khairallah, A.M. Rubenchik, M.F. Crumb, G. Guss, J. Belak, M.J. Matthews, Energy Coupling Mechanisms and Scaling Behavior Associated with Laser Powder Bed Fusion Additive Manufacturing, Adv. Eng. Mater. 21 (2019) 1900185, doi: 10.1002/adem. 201900185.\n\n[43] S. Kou, Weld Metal Solidification Cracking, Weld. Metall., 2002, pp. 263-300 \\href{https://onlinelibrary.wiley.com/doi/10.1002/0471434027.ch11}{https://onlinelibrary.wiley.com/doi/10.1002/0471434027.ch11} .\n\n[44] D. Rosenthal, The theory of moving sources of heat and its application to metal treatments, Trans. Am. Soc. Mech. Eng. 43 (1946) 849-866.\n\n[45] A.C. Chilton, A.S. Wronski, The effects of strain rate and pressurization on the ductile-brittle transition temperature of polycrystalline sintered tungsten, J. Common Met. 17 (1969) 447-450, doi: 10.1016/0022-5088(69)90071-X.\n\n[46] A. Giannattasio, S.G. Roberts, Strain-rate dependence of the brittle-to-ductile transition temperature in tungsten, Philos. Mag. 87 (2007) 2589-2598, doi: 10.1080/14786430701253197.\n\n[47] A. Giannattasio, Z. Yao, E. Tarleton, S.G. Roberts, Brittle-ductile transitions in polycrystalline tungsten, Philos. Mag. (2010) \\href{https://www.tandfonline.com/doi/}{https://www.tandfonline.com/doi/} abs/10.1080/14786435.2010.502145 .\n\n[48] Y.M. Wang, T. Voisin, J.T. McKeown, J. Ye, N.P. Calta, Z. Li, Z. Zeng, Y. Zhang, W. Chen, T.T. Roehling, R.T. Ott, M.K. Santala, P.J. Depond, M.J. Matthews, A.V. Hamza, T. Zhu, Additively manufactured hierarchical stainless steels with high strength and ductility, Nat. Mater. 17 (2018) 63-71, doi: 10.1038/nmat5021.\n\n[49] Tekna Advanced Materials, W -45 Spherical Tungsten Powder Brochure, (n.d.). \\href{http://www.tekna.com}{http://www.tekna.com} (Accessed 20 December 2019).", "start_char_idx": 414950, "end_char_idx": 417502, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fa51cc65-e764-4350-9b8e-ba03495db558": {"__data__": {"id_": "fa51cc65-e764-4350-9b8e-ba03495db558", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2429da8b-8e40-4a10-98e0-945271229ba1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0d4d82775878c3ea32155007e28309129d760cbe59f796aedc719cb673ac0574", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1d632f19-a39e-4897-b26f-a3d8ff84780a", "node_type": "1", "metadata": {}, "hash": "73d1db471501d1db3a05d76ff7654cbdfda97d4738397202b75048c2ee7c81ae", "class_name": "RelatedNodeInfo"}}, "text": "[48] Y.M. Wang, T. Voisin, J.T. McKeown, J. Ye, N.P. Calta, Z. Li, Z. Zeng, Y. Zhang, W. Chen, T.T. Roehling, R.T. Ott, M.K. Santala, P.J. Depond, M.J. Matthews, A.V. Hamza, T. Zhu, Additively manufactured hierarchical stainless steels with high strength and ductility, Nat. Mater. 17 (2018) 63-71, doi: 10.1038/nmat5021.\n\n[49] Tekna Advanced Materials, W -45 Spherical Tungsten Powder Brochure, (n.d.). \\href{http://www.tekna.com}{http://www.tekna.com} (Accessed 20 December 2019).\n\n[50] K. Li, G. Ma, L. Xing, Y. Wang, C. Yu, J. Chen, J. Ma, G. Wu, W. Liu, Z. Shen, X. Huang, Crack suppression via in-situ oxidation in additively manufactured W-Ta alloy, Mater. Lett. 263 (2020) 127212, doi: 10.1016/j.matlet.2019.127212.\n\n[51] J.D. Roehling, W.L. Smith, T.T. Roehling, B. Vrancken, G.M. Guss, J.T. McKeown, M.R. Hill, M.J. Matthews, Reducing residual stress by selective large-area diode surface heating during laser powder bed fusion additive manufacturing, Addit Manuf. 28 (2019) 228-235, doi: 10.1016/j.addma.2019.05.009.\n\n\\begin{itemize}\n  \\item \n\\end{itemize}\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\\usepackage{mathrsfs}\n\n\\title{Multi-Resolution SPH Simulation of a Laser Powder Bed Fusion Additive Manufacturing Process }\n\n\n\\author{Abbreviations\\\\\nAM additive manufacturing\\\\\nCFD computational fluid dynamics\\\\\nCPU central processing unit\\\\\nFEM finite element method\\\\\nFVM finite volume method\\\\\nGPU graphics processing unit\\\\\nLBM Lattice Boltzmann method\\\\\nLPBF laser powder bed fusion\\\\\nPBF powder bed fusion\\\\\nSPH smoothed particle hydrodynamics}\n\\date{}\n\n\n\\begin{document}\n\\maketitle\nCitation: Afrasiabi, M.; L\u00fcthi, C.; Bambach, M.; Wegener, K. MultiResolution SPH Simulation of a Laser Powder Bed Fusion Additive Manufacturing Process. Appl. Sci. 2021, 11, 2962. \\href{https://doi.org/}{https://doi.org/} 10.3390/app11072962\n\nAcademic Editor: Mehrshad Mehrpouya\n\nReceived: 7 March 2021\n\nAccepted: 22 March 2021\n\nPublished: 26 March 2021\n\nPublisher's Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_97637720aa0371e31845g-01}\n\\end{center}\n\nCopyright: (C) 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// \\href{http://creativecommons.org/licenses/by/}{creativecommons.org/licenses/by/} $4.0 /$ ).\n\n\\begin{abstract}\nThis paper presents an efficient mesoscale simulation of a Laser Powder Bed Fusion (LPBF) process using the Smoothed Particle Hydrodynamics (SPH) method.", "start_char_idx": 417020, "end_char_idx": 420059, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1d632f19-a39e-4897-b26f-a3d8ff84780a": {"__data__": {"id_": "1d632f19-a39e-4897-b26f-a3d8ff84780a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fa51cc65-e764-4350-9b8e-ba03495db558", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e8237229107439ad77affad2cd5690172e93e28da14e321821c4e5d0cc96ebcf", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3e84f6e6-e754-419a-8a04-e9163e92ee93", "node_type": "1", "metadata": {}, "hash": "d4b7f56f66c70cde05a7f510af0a62e3f518d24894596790ad90dd07988180ce", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_97637720aa0371e31845g-01}\n\\end{center}\n\nCopyright: (C) 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// \\href{http://creativecommons.org/licenses/by/}{creativecommons.org/licenses/by/} $4.0 /$ ).\n\n\\begin{abstract}\nThis paper presents an efficient mesoscale simulation of a Laser Powder Bed Fusion (LPBF) process using the Smoothed Particle Hydrodynamics (SPH) method. The efficiency lies in reducing the computational effort via spatial adaptivity, for which a dynamic particle refinement pattern with an optimized neighbor-search algorithm is used. The melt pool dynamics is modeled by resolving the thermal, mechanical, and material fields in a single laser track application. After validating the solver by two benchmark tests where analytical and experimental data are available, we simulate a single-track LPBF process by adopting SPH in multi resolutions. The LPBF simulation results show that the proposed adaptive refinement with and without an optimized neighbor-search approach saves almost $50 \\%$ and $35 \\%$ of the SPH calculation time, respectively. This achievement enables several opportunities for parametric studies and running high-resolution models with less computational effort.\n\\end{abstract}\n\nKeywords: additive manufacturing; LPBF; numerical simulation; SPH; particle refinement\n\n\\section*{1. Introduction}\nLaser Powder Bed Fusion (LPBF), also known as Laser Beam Melting (LBM), is an Additive Manufacturing (AM) technique used for fabricating metallic parts with complex shapes. LPBF falls into the Powder Bed Fusion (PBF) category, where a small focus spot laser is employed to melt and fuse metallic powders. Recently, LPBF-fabricated parts can feature an almost full density ( $>99.5 \\%$ ) with mechanical properties comparable to conventionally manufactured metals, according to several review papers published within the last decade, e.g., [1,2]. More indicatively, Lachmayer et al. [3] claimed in 2016 that densities greater than $99.9 \\%$ referred to the pure metal can be obtained through optimized PBF processes. The LPBF technology is being used in a wide range of industry applications, most notably in the aerospace [4,5] and medical [6,7] domains. Parallel to this rapid growth of AM in industry, understanding the interplay between process parameters and part properties is necessary to design and operate LPBF processes. Modeling and simulation of the LPBF process can help explain the experimental observations and optimize the PBF fabrication systems.\n\nAn LPBF process is inherently a multi-scale problem that involves a variety of complex phenomena such as laser-powder interactions, material phase transitions, and violent freesurface flows. Figure 1 illustrates some physical challenges of LPBF at the powder scale. In an early effort to simulate this thermally driven process, Zaeh and Branner [8] used the Finite Element Method (FEM) in a thermo-mechanically coupled analysis to study the heat impact on residual stresses and structural deformations of T-bar cantilever specimens after multiple tracks. The numerical approach they undertook, however, was based on a homogeneous powder-bed model with several simplifications such as modeling a $20 \\times$\\\\\nthicker powder layer to reduce the required simulation time. K\u00f6rner et al. [9] addressed this issue by introducing a 2D fine-scale model of the selective beam melting process using a Lattice-Boltzmann approach. They found good agreement with experimental data and predicted the melting behavior as a function of process parameters like the scan speed and powder properties. While the physical model incorporated into [9] was fairly advanced, some crucial phenomena like the Marangoni effect and recoil pressure were still lacking. Many research studies have repeatedly confirmed that these effects play a key role in the melt pool dynamics (e.g., see in $[2,10])$.\n\nIn an extension to the work of K\u00f6rner et al. [9], G\u00fcrtler and his colleagues [11] followed a similar approach and generalized the analysis of melting and re-solidification of powder to 3D space for the first time. The numerical results suffer from low resolution, and their model does not account for some governing physical phenomena such as surface heat loss and thermo-capillary effects either. In 2014, a particularly robust numerical simulation of LPBF was developed by Khairallah and Anderson [12].", "start_char_idx": 419476, "end_char_idx": 424067, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3e84f6e6-e754-419a-8a04-e9163e92ee93": {"__data__": {"id_": "3e84f6e6-e754-419a-8a04-e9163e92ee93", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1d632f19-a39e-4897-b26f-a3d8ff84780a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "97c55bc44cd0f50ece73d0bc6e7f8f04cccf0216c535dcc6499cd999e68e9085", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "dc8b2176-90c6-43c4-adea-fa0a8cf8009d", "node_type": "1", "metadata": {}, "hash": "7f28b8fc37e9f9cc7325d53f8b4961a3e1cab8d1a395a45b4ac24962e866b60c", "class_name": "RelatedNodeInfo"}}, "text": "They found good agreement with experimental data and predicted the melting behavior as a function of process parameters like the scan speed and powder properties. While the physical model incorporated into [9] was fairly advanced, some crucial phenomena like the Marangoni effect and recoil pressure were still lacking. Many research studies have repeatedly confirmed that these effects play a key role in the melt pool dynamics (e.g., see in $[2,10])$.\n\nIn an extension to the work of K\u00f6rner et al. [9], G\u00fcrtler and his colleagues [11] followed a similar approach and generalized the analysis of melting and re-solidification of powder to 3D space for the first time. The numerical results suffer from low resolution, and their model does not account for some governing physical phenomena such as surface heat loss and thermo-capillary effects either. In 2014, a particularly robust numerical simulation of LPBF was developed by Khairallah and Anderson [12]. The authors made use of a massively parallel code to simulate a single-track LPBF process in 3D using a hybrid finite element and finite volume formulation, through which they modeled a fully resolved particle bed geometry. This hybrid FEM-FVM approach, however, relies on a crude surface tension model, neglecting the effects of wetting, thermal gradients, and so on. The importance of surface tension effects in melt pool dynamics was highlighted in this paper, concluding that these effects are, in fact, the driving forces in the LPBF process. In another attempt to obtain more efficiency, Lee and Zhang [13] used the Volume of Fluid method (VOF) method with a mesh size of $3 \\mu \\mathrm{m}$ and examined the influence of process parameters on the bed geometry and formation of balling defects. No experimental validation of the LPBF simulation is performed in this work, however.\n\nA year ago, Cook and Murphy [14] published a comprehensive review paper, where they cross-compare the individual capabilities of different methods in AM modeling and simulation. It turns out that most CFD codes for AM process simulation are based on either FVM or FEM tools. A few recent publications are mentioned in the following. Lee and Zhang [15] combined a DEM powder-bed model with the melt pool CFD simulation using the package Flow-3D to model an LPBF process for IN718 - a nickel-based superalloy. Ansys Fluent ${ }^{\\circledR}$ is another commercial software employed by the AM community for PBF simulation, e.g., in [16,17]. There are also some studies on solving the melt pool CFD equations by applying the open-source CFD software OpenFOAM, e.g., by [18]. Despite the excellent insights generated by these developments into the AM process simulation, the issue with their computational effort and parallelization capability is still an open question.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_97637720aa0371e31845g-02}\n\\end{center}\n\nFigure 1. Main physical processes in melt-pool region during powder bed fusion of LPBF.\n\nIn addition to the broad class of mesh-based techniques, mesh-free particle methods have also been attempted in simulating the LPBF process. Specifically, a growing share of interest in using the Smoothed Particle Hydrodynamics (SPH) method for such applications can be noticed in the literature. In essence, SPH is a purely Lagrangian method, introduced by Lucy [19] and Gingold and Monaghan [20], that can efficiently handle large deformations, violent free surface movements, and multiphase material boundaries. For the adoption of SPH in various multi-physics and manufacturing processes, see in [21-25]. These attractive features of SPH have convinced the AM research community to apply this method to laserbased processes such as LPBF. In 2016, Hu and Eberhard [26] demonstrated promising SPH results in simulating a laser spot welding process of aluminum and suggested that SPH can offer great potential for large-scale manufacturing simulations. Trautmann et al. [27] presented a 3D SPH model of Tungsten Inert Gas (TIG) welding and validated their numerical results with experiments. The applicability of SPH to high-fidelity modeling of AM processes like LPBF is still being explored, but Russell et al. [28] have made important headway in this area. They present a robust SPH framework for modeling a 2D LPBF track, where the most important thermal-mechanical-material aspects of the process were included.", "start_char_idx": 423108, "end_char_idx": 427532, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "dc8b2176-90c6-43c4-adea-fa0a8cf8009d": {"__data__": {"id_": "dc8b2176-90c6-43c4-adea-fa0a8cf8009d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3e84f6e6-e754-419a-8a04-e9163e92ee93", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "21bc70130314a67a7b125a12227481f1d138ce76307ceb1e9abf1f6802c040f7", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "451cf889-b4ba-478b-ac34-006dcfc67dd1", "node_type": "1", "metadata": {}, "hash": "6f71023197eb2c069690bd261df475a858f048026d7f1bf5afa6587eaf8e18ad", "class_name": "RelatedNodeInfo"}}, "text": "These attractive features of SPH have convinced the AM research community to apply this method to laserbased processes such as LPBF. In 2016, Hu and Eberhard [26] demonstrated promising SPH results in simulating a laser spot welding process of aluminum and suggested that SPH can offer great potential for large-scale manufacturing simulations. Trautmann et al. [27] presented a 3D SPH model of Tungsten Inert Gas (TIG) welding and validated their numerical results with experiments. The applicability of SPH to high-fidelity modeling of AM processes like LPBF is still being explored, but Russell et al. [28] have made important headway in this area. They present a robust SPH framework for modeling a 2D LPBF track, where the most important thermal-mechanical-material aspects of the process were included. This method achieves excellent results at the powder scale but suffers from the calculation effort for simulations on a large scale or 3D. In another effort to develop SPH for AM simulations, Park and Zohdi [29] proposed coupling of SPH and FEM for thermomechanical simulation of droplet-based AM processes. Afrasiabi et al. [30] studied the material removal simulation in laser drilling and then extended this approach to 3D in [31]. However, they accounted only for the thermal aspect of the process. More recently, F\u00fcrstenau et al. [32] developed a GPU-accelerated 3D SPH model of LPBF. These authors demonstrate high-resolution SPH simulation using a discretization size of $1 \\mu \\mathrm{m}$, which is the finest particle size to date.\n\nDespite these incremental improvements of SPH AM simulations from both algorithmic and computational perspectives, all recent developments overlook the topic of adaptivity. In other words, state-of-the-art SPH models of AM use a uniform resolution for their spatial discretization. Therefore, a significant amount of SPH calculation time is wasted on unimportant regions with no (or negligible) physical contribution to the solution. In an LPBF process, for instance, the mechanism decisive for the outcome of the process occurs under the laser beam and in the vicinity of the melt pool. Consequently, the need for an efficient SPH model of LPBF within a multi-resolution framework motivates this study.\n\nTo fill the research gap identified above, an enhanced dynamic refinement algorithm via particle splitting is developed. The additional enhancement offered herein stems from the proposed optimization of the neighbor-list in multi-resolution SPH interactions. This issue was overlooked by previous multi-resolution SPH publications such as Afrasiabi et al. [33], and is addressed here. Section 2.5 gives a description of the proposed neighbor-search algorithm in more detail. The present numerical results show that the proposed adaptive approach can save almost $50 \\%$ of the computational time in $2 \\mathrm{D}$ SPH simulations of LPBF processes. Most numerical algorithms are aligned with the thermal-mechanical-material formulation of [28] for a 304 stainless steel powder bed, regarded as one the most comprehensive SPH frameworks for LPBF so far. The correctness of the code is verified through two benchmarks, where analytical and experimental data are available. Several parameter studies are performed to acknowledge the computational efficiency of the present method but to gain further insight into the capabilities of SPH in simulating an LPBF process.\n\nThe remainder of this manuscript is structured as follows. Section 2 details the computational framework of this study. First, an outline of the theoretical background implemented within the SPH code is given. The section closes by presenting the dynamic refinement scheme and describing how it applies to an LPBF process. Next, the correct working of the code is verified by two examples in Section 3. Section 4 then presents and discusses the LPBF simulation results with relevant experimental and computational comparisons. Conclusive remarks are made in Section 5.\n\n\\section*{2. Computational Framework}\nSmoothed Particle Hydrodynamics (SPH) is a Lagrangian mesh-free method used here to discretize the governing partial differential equations in space. In principle, the derivation of SPH equations starts by taking the integral form of an arbitrary function:\n\n\n\\begin{equation*}\nf(\\underline{r})=\\int_{\\Omega} f\\left(\\underline{r}^{\\prime}\\right) \\delta\\left(\\left|\\underline{r}-\\underline{r}^{\\prime}\\right|\\right) d V^{\\prime} \\tag{1}\n\\end{equation*}", "start_char_idx": 426724, "end_char_idx": 431204, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "451cf889-b4ba-478b-ac34-006dcfc67dd1": {"__data__": {"id_": "451cf889-b4ba-478b-ac34-006dcfc67dd1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "dc8b2176-90c6-43c4-adea-fa0a8cf8009d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8832cf53742903d35feda062a71d21a24eff20bb9094fb022bbffdafaf2e17f9", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a222c5e3-f6cb-40ed-9258-fba42c490f2e", "node_type": "1", "metadata": {}, "hash": "6e5ee9c52f1a2ab8799cdd349d2b44726fb46b9a884945a7ed6de1d6da026fbf", "class_name": "RelatedNodeInfo"}}, "text": "Next, the correct working of the code is verified by two examples in Section 3. Section 4 then presents and discusses the LPBF simulation results with relevant experimental and computational comparisons. Conclusive remarks are made in Section 5.\n\n\\section*{2. Computational Framework}\nSmoothed Particle Hydrodynamics (SPH) is a Lagrangian mesh-free method used here to discretize the governing partial differential equations in space. In principle, the derivation of SPH equations starts by taking the integral form of an arbitrary function:\n\n\n\\begin{equation*}\nf(\\underline{r})=\\int_{\\Omega} f\\left(\\underline{r}^{\\prime}\\right) \\delta\\left(\\left|\\underline{r}-\\underline{r}^{\\prime}\\right|\\right) d V^{\\prime} \\tag{1}\n\\end{equation*}\n\n\nand replacing the Dirac delta function with a smoothing kernel function $W\\left(\\left|\\underline{r}-\\underline{r}^{\\prime}\\right|, h\\right)$ as:\n\n\n\\begin{equation*}\nf(\\underline{r}) \\approx\\langle f(\\underline{r})\\rangle=\\int_{\\Omega_{s}} f\\left(\\underline{r}^{\\prime}\\right) W\\left(\\left|\\underline{r}-\\underline{r}^{\\prime}\\right|, h\\right) d V^{\\prime} \\tag{2}\n\\end{equation*}\n\n\nwhere $d V^{\\prime}$ is the weight of integration and $h$ the smoothing length parameter to determine the size of a finite smoothing domain $\\Omega_{s}$ (i.e., support domain). According to the first SPH publications by $[19,20]$, the approximation in Equation (2) is valid if the kernel $W$ is: (1) normalized, meaning $\\int W\\left(\\left|\\underline{r}-\\underline{r}^{\\prime}\\right|, h\\right) d V^{\\prime}=1$; (2) convergent to $\\delta$ as $h$ goes to zero; and (3) differentiable at least more than once. In addition to these three essential conditions, Monaghan [34] suggests that the kernel function should also have a compact support for efficiency reasons. The Wendland quintic [35] and quintic spline [36] functions meet all these conditions, and are chosen for the numerical simulations of this work. To discretize the kernel approximation of SPH, Equation (2) is transformed into a summation over neighboring particles. This can be achieved using, for instance, a Riemann sum over a set of $N$ neighbors within $\\Omega_{s}$ to evaluate $f$ at position $\\underline{r}$ via:\n\n\n\\begin{equation*}\n\\langle f(\\underline{r})\\rangle \\approx \\sum_{j=1}^{N} f\\left(\\underline{r}_{j}\\right) W\\left(\\left|\\underline{r}-\\underline{r}_{j}\\right|, h\\right) V_{j} \\tag{3}\n\\end{equation*}\n\n\nor rewriting Equation (3) for another particle $i$ at $\\underline{r}=\\underline{r}_{i}$ instead of an arbitrary point:\n\n\n\\begin{equation*}\n\\left\\langle f_{i}\\right\\rangle \\approx \\sum_{j=1}^{N} f_{j} W_{i j} V_{j} \\tag{4}\n\\end{equation*}\n\n\nwhere $V_{j}=m_{j} / \\rho_{j}$ is an estimate of the volume assigned to particle $j$ and the term $W\\left(\\left|\\underline{r}_{i j}\\right|, h\\right)=W\\left(r_{i j}, h\\right)$ is abbreviated to $W_{i j}$ for simplicity. Now, the spatial derivatives of $f$ can be approximated through the spatial derivatives of the smoothing kernel. A useful formulation of the SPH gradient for multi-phase flows (see in [37]) is given as:\n\n\n\\begin{equation*}\n\\left\\langle\\nabla f_{i}\\right\\rangle \\approx \\rho_{i} \\sum_{j}\\left[\\frac{f_{i}}{\\rho_{i}^{2}}+\\frac{f_{j}}{\\rho_{j}^{2}}\\right] \\nabla W_{i j} m_{j} \\tag{5}\n\\end{equation*}", "start_char_idx": 430469, "end_char_idx": 433727, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a222c5e3-f6cb-40ed-9258-fba42c490f2e": {"__data__": {"id_": "a222c5e3-f6cb-40ed-9258-fba42c490f2e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "451cf889-b4ba-478b-ac34-006dcfc67dd1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1e08094917d8e809ad6f7074e89f0eafb37fb8400c77cbbac41502e7f4a2c161", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "668ceaa5-1ceb-441e-aa3f-f9574ec357d5", "node_type": "1", "metadata": {}, "hash": "97e68a7bb034611aa8924366267e9f7ca618ab1778e52b6499085c63335bdfff", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{equation*}\n\\left\\langle\\nabla f_{i}\\right\\rangle \\approx \\rho_{i} \\sum_{j}\\left[\\frac{f_{i}}{\\rho_{i}^{2}}+\\frac{f_{j}}{\\rho_{j}^{2}}\\right] \\nabla W_{i j} m_{j} \\tag{5}\n\\end{equation*}\n\n\nFor simulating a powder bed fusion AM process, the computational model needs to account for the thermal, mechanical and material effects. In what follows, an overview of these thermal-mechanical-material equations, as well as their SPH discretizations, is outlined.\n\n\\subsection*{2.1. Thermal Model}\nIn LPBF, the energy required for melting and fusing metallic powders together is provided by a laser. The thermal effects are, therefore, addressed by solving the heat equation for incompressible flows including a laser heat source as:\n\n\n\\begin{equation*}\n\\rho c_{p} \\frac{d T}{d t}=\\underline{\\underline{\\tau}}: \\nabla \\underline{u}+\\nabla \\cdot(k \\nabla T)+Q^{\\text {laser }} \\tag{6}\n\\end{equation*}\n\n\nwhere $\\underline{\\underline{\\tau}}$ is the shear stress tensor, $\\underline{u}$ the velocity, $\\rho$ the density, $c_{p}$ the specific heat capacity, $k$ the thermal conductivity, and $Q^{\\text {laser }}$ is the laser heat source term. The viscous heating\\\\\nand conduction terms in Equation (6) are computed respectively by the SPH schemes of Marrone et al. [38], and Cleary and Monaghan [39], which are both suitable for multiphase applications. These formulations for particle $i$ are given by:\n\n\n\\begin{align*}\n\\left\\langle\\underline{\\underline{\\tau}}_{i}: \\nabla \\underline{u}_{i}\\right\\rangle & \\approx \\sum_{j}\\left(\\frac{\\mu_{i} \\mu_{j}}{\\mu_{i}+\\mu_{j}}\\right) \\frac{m_{i}}{\\rho_{j}} \\pi_{i j}\\left(\\underline{u}_{j}-\\underline{u}_{i}\\right) \\cdot \\nabla W_{i j}  \\tag{7}\\\\\n\\left\\langle\\nabla \\cdot\\left(k_{i} \\nabla T_{i}\\right)\\right\\rangle & \\approx \\sum_{j} 4\\left(\\frac{k_{i} k_{j}}{k_{i}+k_{j}}\\right) \\frac{m_{i}}{\\rho_{j}}\\left(T_{i}-T_{j}\\right) \\frac{\\left(\\underline{r}_{i}-\\underline{r}_{j}\\right)}{\\left|\\underline{r}_{i}-\\underline{r}_{j}\\right|^{2}+\\eta^{2}} \\cdot \\nabla W_{i j} \\tag{8}\n\\end{align*}\n\n\nin which:\n\n\n\\begin{equation*}\n\\pi_{i j}=2\\left(n_{D}+2\\right) \\frac{\\left(\\underline{u}_{j}-\\underline{u}_{i}\\right) \\cdot\\left(\\underline{r}_{j}-\\underline{r}_{i}\\right)}{\\left|\\underline{r}_{j}-\\underline{r}_{i}\\right|^{2}} \\tag{9}\n\\end{equation*}\n\n\nand $\\mu$ is the viscosity, $n_{D}$ the dimension factor, and $\\eta=0.1 h$ inserted here as a small parameter for ensuring non-zero denominators. For SPH Laplacian schemes more sophisticated than Equation (8) please refer to [40].\n\nThe heat source term $Q^{\\text {laser }}$ in Equation (6) still needs to be defined. In this paper, a volumetric heat source modeling approach based on the Beer-Lambert law is used for calculating the laser energy absorption. As such, increasing the penetration depth decreases the laser absorptivity exponentially. Figure 2 illustrates this scheme, in which the normalized Beer-Lambert law for the powder bed can be written as:\n\n\n\\begin{equation*}\nI(z)=\\frac{\\beta \\exp (-\\beta z)}{[1-\\exp (-\\beta L)]} \\tag{10}\n\\end{equation*}", "start_char_idx": 433535, "end_char_idx": 436573, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "668ceaa5-1ceb-441e-aa3f-f9574ec357d5": {"__data__": {"id_": "668ceaa5-1ceb-441e-aa3f-f9574ec357d5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a222c5e3-f6cb-40ed-9258-fba42c490f2e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2600ce832a7ea304c9e6bfa1cee7e3fbc8a5170c958ccbfadbe6a5389dcd2002", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7c8d6fc0-749b-4a0f-b59a-8a54f634f47a", "node_type": "1", "metadata": {}, "hash": "25802c81fb380100b117e35d360efd49340d22496dad09abdc27c2a109c27261", "class_name": "RelatedNodeInfo"}}, "text": "and $\\mu$ is the viscosity, $n_{D}$ the dimension factor, and $\\eta=0.1 h$ inserted here as a small parameter for ensuring non-zero denominators. For SPH Laplacian schemes more sophisticated than Equation (8) please refer to [40].\n\nThe heat source term $Q^{\\text {laser }}$ in Equation (6) still needs to be defined. In this paper, a volumetric heat source modeling approach based on the Beer-Lambert law is used for calculating the laser energy absorption. As such, increasing the penetration depth decreases the laser absorptivity exponentially. Figure 2 illustrates this scheme, in which the normalized Beer-Lambert law for the powder bed can be written as:\n\n\n\\begin{equation*}\nI(z)=\\frac{\\beta \\exp (-\\beta z)}{[1-\\exp (-\\beta L)]} \\tag{10}\n\\end{equation*}\n\n\nwhere $L$ is the powder bed depth and $\\beta$ the extinction coefficient, taken as a constant value according to [28,41]. The intensity distribution of the laser in the radial direction, $I(r)$, follows a normalized Gaussian distribution:\n\n\n\\begin{equation*}\nI(r)=\\frac{4 P_{L}}{\\pi R^{2}} \\exp \\left(-\\frac{4 r^{2}}{R^{2}}\\right) \\tag{11}\n\\end{equation*}\n\n\nwith $P_{L}$ indicating the laser power and $R$ the laser beam radius. Finally, the laser heat source appeared in Equation (6) can be calculated as $Q^{\\text {laser }}=a_{L} I(r, z)$ with $a_{L}$ denoting the absorption coefficient. The implementation details of a 2D Beer-Lambert laser absorption model for SPH frameworks can be found in [28]. Figure 2 gives a graphical illustration of how this absorption model is implemented in the present code.\n\nTo complete the solution of Equation (6), the set of boundary conditions, including the Dirichlet and Neumann boundary conditions, are imposed on one layer of surface particles. In this work, heat loss $q_{l}$ can occur via radiation and convection through open surfaces, calculated from:\n\n\n\\begin{equation*}\nq_{l}=-\\left[h_{c}\\left(T_{s}-T_{\\infty}\\right)+\\epsilon \\sigma\\left(T_{s}^{4}-T_{\\infty}^{4}\\right)\\right] \\tag{12}\n\\end{equation*}\n\n\nwhere $h_{c}$ is the convective heat transfer coefficient, $\\sigma=5.67 \\times 10^{-8} \\mathrm{~W} /\\left(\\mathrm{m}^{2} \\cdot \\mathrm{K}^{4}\\right)$ the StefanBoltzmann constant, $\\epsilon$ the emissivity factor, and $T_{S}$ and $T_{\\infty}$ are the surface and background temperatures.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_97637720aa0371e31845g-06}\n\nFigure 2. Illustration of the volumetric heat source modeling approach and the laser intensity distribution.\n\n\\subsection*{2.2. Mechanical Model}\nTo model the dynamics of the melt pool region in LPBF, it is usually assumed that the liquid is incompressible and the liquid pool is in a laminar flow regime. As a result of this simplification, the Navier-Stokes equations for mass and momentum conservation in a Lagrangian frame arrive at:\n\n\n\\begin{align*}\n\\frac{d \\rho}{d t} & =-\\rho \\nabla \\cdot \\underline{u}  \\tag{13}\\\\\n\\rho \\frac{d \\underline{v}}{d t} & =-\\nabla p \\underline{I}+\\mu \\nabla^{2} \\underline{u}+\\rho \\underline{g}+\\underline{b} \\tag{14}\n\\end{align*}\n\n\nwhere $p$ is the pressure, $\\underline{\\underline{I}}$ the unity tensor, $\\mu$ the dynamic (shear) viscosity, $g$ the gravitational acceleration, and $\\underline{b}$ any other volumetric body forces. To compute the spatial discretization of these equations, the $\\delta$-SPH scheme proposed by Antuono et al. [42] is employed. Consequently, Equations (13) and (14) become:", "start_char_idx": 435813, "end_char_idx": 439244, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7c8d6fc0-749b-4a0f-b59a-8a54f634f47a": {"__data__": {"id_": "7c8d6fc0-749b-4a0f-b59a-8a54f634f47a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "668ceaa5-1ceb-441e-aa3f-f9574ec357d5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "11da3ac842cde34fcbffff86edb3a59013c7ea857a19ef6e459088a6fb516ad1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d6185f0d-6868-4ab8-a2fc-ccbe1aa0d492", "node_type": "1", "metadata": {}, "hash": "642f0929a2c712e91a67af85813703c27227181716c055497d9fdb2939fac604", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{align*}\n\\frac{d \\rho}{d t} & =-\\rho \\nabla \\cdot \\underline{u}  \\tag{13}\\\\\n\\rho \\frac{d \\underline{v}}{d t} & =-\\nabla p \\underline{I}+\\mu \\nabla^{2} \\underline{u}+\\rho \\underline{g}+\\underline{b} \\tag{14}\n\\end{align*}\n\n\nwhere $p$ is the pressure, $\\underline{\\underline{I}}$ the unity tensor, $\\mu$ the dynamic (shear) viscosity, $g$ the gravitational acceleration, and $\\underline{b}$ any other volumetric body forces. To compute the spatial discretization of these equations, the $\\delta$-SPH scheme proposed by Antuono et al. [42] is employed. Consequently, Equations (13) and (14) become:\n\n\n\\begin{align*}\n\\left\\langle\\frac{d \\rho_{i}}{d t}\\right\\rangle_{i} & \\approx \\rho_{i} \\sum_{j}\\left(\\underline{v}_{i j}+\\underline{Y}_{i j}\\right) \\cdot \\nabla W_{i j} V_{j}  \\tag{15}\\\\\n\\left\\langle\\frac{d \\underline{v}_{i}}{d t}\\right\\rangle_{i} & \\approx-\\sum_{j} \\frac{1}{\\rho_{i}}\\left(\\frac{p_{j}}{\\Gamma_{i}}+\\frac{p_{i}}{\\Gamma_{j}}\\right) \\nabla W_{i j} V_{j}+\\sum_{j} \\frac{1}{\\rho_{i}}\\left(\\frac{2 \\mu_{i} \\mu_{j}}{\\mu_{i}+\\mu_{j}}\\right) \\pi_{i j} \\nabla W_{i j} V_{j}+\\underline{g}+\\frac{1}{\\rho_{i}} \\underline{b}_{i} \\tag{16}\n\\end{align*}\n\n\nwhere $\\pi_{i j}$ was defined via Equation (9), $\\Gamma_{i}=\\sum_{j} V_{j} W_{i j}$ is a renormalization factor widely used for free surface problems (e.g., in [43]), and $\\underline{Y}_{i j}$ is the $\\delta$-SPH diffusion term given by [42]:\n\n\n\\begin{equation*}\n\\underline{Y}_{i j}=-2 \\delta h c_{0}\\left[\\left(\\bar{\\rho}_{j}-\\bar{\\rho}_{i}\\right) \\frac{\\left(\\underline{r}_{i}-\\underline{r}_{j}\\right)}{\\left|\\underline{r}_{i}-\\underline{r}_{j}\\right|^{2}}\\right] \\tag{17}\n\\end{equation*}\n\n\nin which $\\delta$ denotes the $\\delta$-SPH smoothing parameter, $c_{0}$ is the sound speed, and $\\bar{\\rho}=\\rho-\\rho_{0}$. Very often in weakly compressible SPH frameworks (see in [44-47], for example), an equation of state is enforced to approximately satisfy the incompressibility condition. Russell et al. [28] proposed a modified equation of state that accounts for thermal expansion, thus well-suited to the LPBF application. This temperature-dependent equation of state computes the pressure $p$ from:\n\n\n\\begin{equation*}\np=c_{0}^{2}\\left(\\rho-\\hat{\\rho}_{0}(T)\\right) \\tag{18}\n\\end{equation*}\n\n\nwhere $\\hat{\\rho}_{0}$ is the reference density expressed by:\n\n\n\\begin{equation*}\n\\hat{\\rho}_{0}(T)=\\rho_{0, T_{r}}\\left[1+\\alpha_{T}\\left(1-\\frac{T}{T_{r}}\\right)\\right] \\tag{19}\n\\end{equation*}", "start_char_idx": 438644, "end_char_idx": 441094, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d6185f0d-6868-4ab8-a2fc-ccbe1aa0d492": {"__data__": {"id_": "d6185f0d-6868-4ab8-a2fc-ccbe1aa0d492", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7c8d6fc0-749b-4a0f-b59a-8a54f634f47a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "98e72a2ec94aadec24cb91e62c63ef2f574ea6424080baabb4284cd41ab2c13f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a4a29d7b-903c-4c96-93ad-790e12a6c052", "node_type": "1", "metadata": {}, "hash": "217cb66217e56f155ba4d9164190ddb095cfe55baac1a3cf79cdb6ec9a8bcc44", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{equation*}\np=c_{0}^{2}\\left(\\rho-\\hat{\\rho}_{0}(T)\\right) \\tag{18}\n\\end{equation*}\n\n\nwhere $\\hat{\\rho}_{0}$ is the reference density expressed by:\n\n\n\\begin{equation*}\n\\hat{\\rho}_{0}(T)=\\rho_{0, T_{r}}\\left[1+\\alpha_{T}\\left(1-\\frac{T}{T_{r}}\\right)\\right] \\tag{19}\n\\end{equation*}\n\n\nin which $T_{r}$ is refereed to as a thermal reference value for the temperature field, $\\rho_{0, T_{r}}$ a thermal reference value for the reference density field, and $\\alpha_{T}$ the volumetric thermal expansion coefficient. To complete the SPH momentum Equation (16), surface tension forces are exerted to surface particles as a traction boundary condition. In this paper, the SPH-based surface tension model employs the continuum surface force (CSF) scheme of Brackbill et al. [48] and follows the algorithm proposed by Russell et al. [28]. In a nutshell, the surface force term (without recoil pressure) can be computed from:\n\n\n\\begin{equation*}\n\\underline{F}_{s}=-\\sigma \\kappa \\underline{n}+\\underbrace{\\frac{d \\sigma}{d T}\\left[\\nabla T-\\left(\\nabla T \\cdot \\frac{\\nabla c}{|\\nabla c|}\\right) \\frac{\\nabla c}{|\\nabla c|}\\right]|\\nabla c|}_{\\text {Marangoni term (tangential) }} \\tag{20}\n\\end{equation*}", "start_char_idx": 440807, "end_char_idx": 442008, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a4a29d7b-903c-4c96-93ad-790e12a6c052": {"__data__": {"id_": "a4a29d7b-903c-4c96-93ad-790e12a6c052", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d6185f0d-6868-4ab8-a2fc-ccbe1aa0d492", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "13db217a5c91cb319ed0606db640e76ca31785412fc9ea5490385e103bce3c68", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ce192d1f-f601-4097-b72a-cdde7ff61027", "node_type": "1", "metadata": {}, "hash": "9c2c5bd708fa0aaabe3bfb437d8137bdd65ed4ce2ef94e8833fca9e815cfb7cd", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{equation*}\n\\underline{F}_{s}=-\\sigma \\kappa \\underline{n}+\\underbrace{\\frac{d \\sigma}{d T}\\left[\\nabla T-\\left(\\nabla T \\cdot \\frac{\\nabla c}{|\\nabla c|}\\right) \\frac{\\nabla c}{|\\nabla c|}\\right]|\\nabla c|}_{\\text {Marangoni term (tangential) }} \\tag{20}\n\\end{equation*}\n\n\nwhere $\\sigma$ is the surface tension coefficient, $\\kappa$ is the surface curvature, $\\underline{n}$ the surface normal vector, and $c$ the color function suggested by Adami et al. [49] to track the interface location. The term $d \\sigma / d T$ is sometimes referred to as the thermo-capillary coefficient, too. The gradient operators in Equation (20) are replaced by the same normalized SPH formulation used for the pressure term in Equation (16).\n\n\\subsection*{2.3. Material Model}\nDuring the melting/re-solidification process in LPBF, a significant amount of energy is released/absorbed as the substance undergoes a change of state. This energy is also known as the latent heat associated with the phase change. Hashemi and Sliepcevich [50] modified the heat capacity coefficient to address this important issue. In their modification, an apparent heat capacity of the form:\n\n\\[\nc_{p}(T)= \\begin{cases}c_{p}^{\\mathrm{S}} & T<T_{m}-\\delta T  \\tag{21}\\\\ \\frac{c_{p}^{\\mathrm{S}}+c_{p}^{\\mathrm{L}}}{2}+\\frac{\\mathscr{L}}{\\delta T} & T_{m}-\\frac{\\delta T}{2}<T<T_{m}+\\frac{\\delta T}{2} \\\\ c_{p}^{L} & T_{m}+\\delta T<T\\end{cases}\n\\]\n\nis defined as a function of temperature, where $c_{p}^{\\mathrm{S}}$ and $c_{p}^{\\mathrm{L}}$ are the solid and liquid heat capacities, $T_{m}$ the melting temperature, $\\mathscr{L}$ the latent heat of melting, and $\\delta T$ is the size of a phase-change temperature bandwidth. Together with this adjustment, a temperaturedependent state variable, $s(T)$, is defined to specify the phase of the material at temperature $T$. Similar to the formulation in [28], the state of a given SPH particle reads:\n\n\\[\ns(T)= \\begin{cases}0 & T<T_{m}-\\frac{\\delta T}{2}  \\tag{22}\\\\ \\frac{T-\\left(T_{m}-\\delta T / 2\\right)}{\\delta T} & T_{m}-\\frac{\\delta T}{2} \\leq T \\leq T_{m}+\\frac{\\delta T}{2} \\\\ 1 & T_{m}+\\frac{\\delta T}{2}<T\\end{cases}\n\\]\n\nwith $s=0$ representing a solid state, $s=1$ a liquid state, and $0 \\leq s \\leq 1$ a two-phase state between the solid and liquid phase.\n\n\\subsection*{2.4. Time Integration}\nThe temperature, density, and velocity of SPH particles (see in Equations (6), (15) and (16)), as well as their position, are evolved by using an explicit time integration scheme. In this work, the second-order leapfrog method is implemented on account of a good compromise between accuracy and efficiency it offers. As a necessary condition for stability issues, the maximum time step is enforced to obey a global Courant-Friedrichs-Lewy (CFL) criterion through:\n\n\n\\begin{equation*}\n\\Delta t \\leq \\mathrm{CFL} \\times \\min \\left(\\Delta t_{f}, \\Delta t_{v}, \\Delta t_{c}, \\Delta t_{b}, \\Delta t_{s}\\right) \\tag{23}\n\\end{equation*}\n\n\nconsidering each time step constraint as [39,51]:", "start_char_idx": 441731, "end_char_idx": 444731, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ce192d1f-f601-4097-b72a-cdde7ff61027": {"__data__": {"id_": "ce192d1f-f601-4097-b72a-cdde7ff61027", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a4a29d7b-903c-4c96-93ad-790e12a6c052", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2d6159fa89abb1bf54fd2c919bffc413282a95e6c75f6fd8ff2a48726918ae40", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d6a8f636-7982-4349-a11f-e638ea0f0cb9", "node_type": "1", "metadata": {}, "hash": "657991716f0dc675c7fd9b57f46b655be8bd14f861ff02881877decd21ee0024", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{equation*}\n\\Delta t \\leq \\mathrm{CFL} \\times \\min \\left(\\Delta t_{f}, \\Delta t_{v}, \\Delta t_{c}, \\Delta t_{b}, \\Delta t_{s}\\right) \\tag{23}\n\\end{equation*}\n\n\nconsidering each time step constraint as [39,51]:\n\n\n\\begin{equation*}\n\\Delta t_{f}=\\frac{h}{\\left(c_{0}+|\\underline{u}|_{\\max }\\right)}, \\quad \\Delta t_{v}=\\frac{\\rho h^{2}}{\\mu}, \\quad \\Delta t_{c}=\\frac{\\rho c_{p} h^{2}}{k}, \\quad \\Delta t_{b}=\\sqrt{\\frac{h}{|\\underline{g}|}}, \\quad \\Delta t_{s}=\\sqrt{\\frac{\\rho h^{3}}{2 \\pi \\sigma}} \\tag{24}\n\\end{equation*}\n\n\nin which the CFL coefficient is taken between 0.1 and 0.4 .\n\n\\subsection*{2.5. Dynamic Particle Refinement}\nThe novelty offered by this work lies in reducing the computational cost of the SPH LPBF simulations via spatial adaptivity. We propose a simple algorithm to refine SPH particles dynamically and increase the spatial resolution. This approach follows the procedure elaborated upon in the SPH metal cutting adoption of Afrasiabi et al. [33], which is easy to implement and well-suited to the LPBF simulation. In brief, the refinement procedure is carried out via particle splitting to decrease the discretization size (i.e., increase the spatial resolution) in some regions of the computational domain. Here, a uniform mass splitting approach is used to conserve the mass and momentum of the system. More sophisticated mass splitting approaches can be found in [52,53].\n\nInspired by the multi-resolution SPH simulation of metal cutting in [33], the spatial adaptivity here occurs inside a moving frame in the vicinity of the laser processing area, where a cubic refinement pattern is chosen for particle splitting (see Figure 3). As far as an LPBF process is concerned, such a choice seems appropriate since the melt pool region is formed under the laser beam, and this is where the most challenging physics resides. The size of this frame can be sensitive to the configuration of the LPBF process, including the laser power, the beam radius, the powder bed geometry, and so on. Choosing proper dimensions for the refinement frame ensures that important areas (e.g., melting and re-solidification zones) are always discretized with the finest resolution available.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_97637720aa0371e31845g-08}\n\nFigure 3. Schematic illustration of the particle refinement approach: (Left) demonstrating the situation before and after splitting, where particle $p$ meets the refinement criterion and is split into 4 smaller particles via a square splitting pattern; (Right) showing how the proposed refinement strategy works for an LPBF application. The initial refinement frame has a width of $4 R$, where $R$ is the laser beam radius. Particles with lower mass are depicted in blue and with smaller size.\n\nIn this work, we proposed using an initial refinement frame with a width of $4 R$ centered at the laser focal point, where $R$ is the laser beam radius. This frame moves at the same speed as the scanning laser. Only one stage of refinement is permitted here, meaning a refined particle will never be refined or coarsened again. Figure 3 displays a graphical abstract of the proposed particle refinement approach.\n\nA second improvement of the present work stems from optimizing the nearest neighbor search algorithm within a multi-resolution domain. In particle-based simulations, using an efficient way to determine and organize neighbor particles is of vital importance. Previous multi-resolution SPH studies such as [33] rely on a cell-list structure where the size of each cell is twice the \"maximum\" smoothing length in the simulation. While this strategy is straightforward and ensures the completeness of particle interaction globally, the neighbor list of a particle would involve redundant particles in refined sub-domains. This paper, however, addresses this issue by reducing the cell size throughout the refined regions according to the \"current\" smoothing length instead of the \"maximum\" smoothing length. Therefore, a significant amount of unnecessary particle interactions in the refined sub-domains are avoided, and the computational performance of the code can be further enhanced.", "start_char_idx": 444516, "end_char_idx": 448697, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d6a8f636-7982-4349-a11f-e638ea0f0cb9": {"__data__": {"id_": "d6a8f636-7982-4349-a11f-e638ea0f0cb9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ce192d1f-f601-4097-b72a-cdde7ff61027", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "85f3d5c8e2070291c47b77a5a51f5f26ed014dde21eef86eac2483d6a77527a1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "530c187c-9a72-4ef2-8e68-e59b2c669d0c", "node_type": "1", "metadata": {}, "hash": "cc62f1804cd93b052b52a72a7ba6ab4e60f7764d2ae6f8e1868b3613b79ed3bc", "class_name": "RelatedNodeInfo"}}, "text": "Figure 3 displays a graphical abstract of the proposed particle refinement approach.\n\nA second improvement of the present work stems from optimizing the nearest neighbor search algorithm within a multi-resolution domain. In particle-based simulations, using an efficient way to determine and organize neighbor particles is of vital importance. Previous multi-resolution SPH studies such as [33] rely on a cell-list structure where the size of each cell is twice the \"maximum\" smoothing length in the simulation. While this strategy is straightforward and ensures the completeness of particle interaction globally, the neighbor list of a particle would involve redundant particles in refined sub-domains. This paper, however, addresses this issue by reducing the cell size throughout the refined regions according to the \"current\" smoothing length instead of the \"maximum\" smoothing length. Therefore, a significant amount of unnecessary particle interactions in the refined sub-domains are avoided, and the computational performance of the code can be further enhanced. Figure 4 illustrates this optimization algorithm, where the choice of $h_{r}<h_{u}$ provides a more efficient neighbor search.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_97637720aa0371e31845g-09}\n\\end{center}\n\nFigure 4. Graphical illustration of the proposed cell optimization for multi-resolution SPH domains.\n\n\\section*{3. Validation}\nThe numerical results in this section are validated by comparing them to either an analytical solution or experimental data. For all cases, a quintic-spline kernel as in $[36,54]$ is used. Please note that the code used for producing the present numerical results follows the main structure of the open-source SPH codes referenced in the \"Supplementary Materials\" section of this article.\n\n\\subsection*{3.1. Liquid Droplet: Validation of Surface Tension}\nSurface tension plays a crucial role in LPBF processes. Therefore, it is necessary to investigate the method's accuracy in approximating surface tension forces before applying it to a more complex problem. For this purpose, a surface-tension driven deformation of a liquid droplet in free space (i.e., no gravity) is examined. The initial geometry of the droplet is a square of size $l=1 \\mathrm{~cm}$. Properties of the liquid material are given in Table 1.\n\nWith the surface tension forces acting as a traction boundary condition, the initial square droplet reaches an equilibrium state by transforming into a circular shape. To capture this process within the SPH framework, the first term on the right-hand side of Equation (20) is exerted to one layer of free-surface particles in the normal direction. Figure 5 shows this evolution at 5 time steps using a total of 1600 uniform particles. For better visualization, the arrows are scaled to the magnitude of curvature at surface particles.\n\nAt the last time step when $t=0.1 \\mathrm{~s}$, the SPH particles are at rest and turn into a nearly perfect circle, as expected.\n\nTable 1. Properties of water used in the SPH simulation.\n\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\n & Density & Dynamic Viscosity & Surface Tension Coefficient \\\\\n\\hline\nSymbol & $\\rho$ & $\\mu$ & $\\sigma$ \\\\\nUnit & $\\mathrm{kg} / \\mathrm{m}^{3}$ & $\\mathrm{~Pa} \\cdot \\mathrm{s}$ & $\\mathrm{N} / \\mathrm{m}$ \\\\\n\\hline\nValue & 1000 & 0.001 & 1 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_97637720aa0371e31845g-10(1)}\n\\end{center}\n\nFigure 5. Deformation of a square droplet to a circle under the effect of surface tension.\n\nThe analytical solution is considered here by calculating the radius of the circular droplet at rest. Given the incompressible condition, this computation leads to a circle with $R=0.56 \\mathrm{~cm}$, which has the same area as the initial square geometry. To show the convergence of the method, the shape of this analytical circle is compared to the convex hull of the SPH particles at the last time step in 3 different resolutions. Figure 6 demonstrates this comparison, where $\\Delta$ is the initial particle spacing for the lowest resolution case with a total of $100 \\mathrm{SPH}$ particles (i.e., $\\Delta=0.11 \\mathrm{~cm}$ ).", "start_char_idx": 447628, "end_char_idx": 451856, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "530c187c-9a72-4ef2-8e68-e59b2c669d0c": {"__data__": {"id_": "530c187c-9a72-4ef2-8e68-e59b2c669d0c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d6a8f636-7982-4349-a11f-e638ea0f0cb9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0529d98444c556ba617fcbfa3bc29b99e5f168850f441a45054808d291de7e86", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bf667d83-766c-40c4-b508-b94fd16cd5e8", "node_type": "1", "metadata": {}, "hash": "d329d6803a12360db81b2b17e00b9c7d9f1ea2cdf8752d87f66a723724492115", "class_name": "RelatedNodeInfo"}}, "text": "Deformation of a square droplet to a circle under the effect of surface tension.\n\nThe analytical solution is considered here by calculating the radius of the circular droplet at rest. Given the incompressible condition, this computation leads to a circle with $R=0.56 \\mathrm{~cm}$, which has the same area as the initial square geometry. To show the convergence of the method, the shape of this analytical circle is compared to the convex hull of the SPH particles at the last time step in 3 different resolutions. Figure 6 demonstrates this comparison, where $\\Delta$ is the initial particle spacing for the lowest resolution case with a total of $100 \\mathrm{SPH}$ particles (i.e., $\\Delta=0.11 \\mathrm{~cm}$ ). The numerical result using $d x=\\Delta / 4$ and the exact solution in this figure are nearly identical and on top of each other, indicating the accuracy and convergence of the present method.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_97637720aa0371e31845g-10}\n\\end{center}\n\nFigure 6. Convergence of the SPH results to the analytical solution in a liquid droplet test.\n\n\\subsection*{3.2. Weld Pool Experiment: Validation of Multiphysics Modeling}\nThe laser spot welding experiments of He et al. [55] are taken as reference to validate the fully coupled thermal-mechanical-material model. Specifically, the test case pertains\\\\\nto a 304 stainless steel block welded by a laser pulse of power $1967 \\mathrm{~W}$, beam radius of $0.428 \\mathrm{~mm}$, and pulse duration of $3 \\mathrm{~ms}$. The workpiece is $1.3 \\mathrm{~mm}$ by $1.3 \\mathrm{~mm}$ and $0.4 \\mathrm{~mm}$ height with material properties listed in Table 2. The convective heat transfer coefficient and emissivity factor are taken here as $h_{c}=20 \\mathrm{~W} /\\left(\\mathrm{m}^{2} \\cdot \\mathrm{K}\\right)$ and $\\epsilon=0.4$, respectively. Expressed by Russell et al. [28], the reference density is considered herein to be a function of temperature:\n\n\\[\n\\rho_{0}(T)= \\begin{cases}8020-0.50(T-298) & \\text { solid }  \\tag{25}\\\\ 7332-6.03(T-1673) & \\text { transition } \\\\ 6840-0.70(T-1773) & \\text { liquid }\\end{cases}\n\\]\n\nTo account for the thermo-capillary convection (i.e., Marangoni effect) at the melt-pool interface, the surface tension coefficient is also taken to be temperature-dependent. A common choice for $\\sigma(T)$ in this application was suggested by Sahoo et al. [56] as:\n\n\n\\begin{equation*}\n\\sigma(T)=\\sigma_{0}-A\\left(T-T_{m}\\right)-R T \\Gamma_{s} \\log \\left[1+k_{l} a_{s} \\exp \\left(-\\frac{\\Delta H_{0}}{R T}\\right)\\right] \\tag{26}\n\\end{equation*}\n\n\nin which $\\sigma_{0}=1.943 \\mathrm{~N} / \\mathrm{m}, A=0.0005 \\mathrm{~N} /(\\mathrm{m} \\cdot \\mathrm{K}), R=8.3145 \\mathrm{~J} /(\\mathrm{mol} \\cdot \\mathrm{K})$, $\\Gamma_{s}=1.3 \\times 10^{-8}(\\mathrm{~kg} \\cdot \\mathrm{mol}) / \\mathrm{m}^{2}, k_{l}=0.0032$, and $\\Delta H_{0}=-166 \\times 10^{3} \\mathrm{~J} /(\\mathrm{kg} \\cdot \\mathrm{mol})$. Together with the thermal gradient, this temperature-dependent coefficient is plugged in Equation (20) to approximate the tangential Marangoni surface tension force.\n\nA 3D SPH model of this benchmark is created by discretizing the block with approximately $25 \\mathrm{k}$ particles.", "start_char_idx": 451142, "end_char_idx": 454340, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bf667d83-766c-40c4-b508-b94fd16cd5e8": {"__data__": {"id_": "bf667d83-766c-40c4-b508-b94fd16cd5e8", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "530c187c-9a72-4ef2-8e68-e59b2c669d0c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "bec3d0c8be0d7a5e4c25aa00dc5d25a157a1c0213b6f2dddfa8b640809df4d1e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6810aeb9-5557-4dbc-9536-0c5fa8af80fc", "node_type": "1", "metadata": {}, "hash": "6fa227f105156fbf9ddb5930846c393b096cc88dfe7c9e358116d9d65716c0fc", "class_name": "RelatedNodeInfo"}}, "text": "Together with the thermal gradient, this temperature-dependent coefficient is plugged in Equation (20) to approximate the tangential Marangoni surface tension force.\n\nA 3D SPH model of this benchmark is created by discretizing the block with approximately $25 \\mathrm{k}$ particles. This setup leads to a discretization size of $d x=0.045 \\mathrm{~mm}$ and a time step in the order of $10^{-7} \\mathrm{~s}$. As for the thermal boundary conditions, a constant temperature of $T_{0}=293 \\mathrm{~K}$ is imposed on the bottom of the substrate (i.e., Dirichlet boundary condition). Furthermore, heat loss is included via radiation and convection to air through all open surfaces (i.e., Neumann boundary condition).\n\nTable 2. Material properties used for the weld pool simulation, according to [28].\n\n\\begin{center}\n\\begin{tabular}{lcccc}\n\\hline\nProperty & Symbol & Unit & Solid & Liquid \\\\\n\\hline\nDynamic viscosity & $\\mu$ & $\\mathrm{Pa} \\cdot \\mathrm{s}$ & 1.0 & 0.01 \\\\\nHeat conductivity & $k$ & $\\mathrm{~W} /(\\mathrm{m} \\cdot \\mathrm{K})$ & 20.93 & 209.3 \\\\\nSpecific heat capacity & $c_{p}$ & $\\mathrm{~J} /(\\mathrm{kg} \\cdot \\mathrm{K})$ & 711.2 & 937.4 \\\\\n\\hline\nMelting temperature & $T_{m}$ & $\\mathrm{~K}$ & \\multicolumn{2}{c}{1732} \\\\\nEvaporation temperature & $T_{e}$ & $\\mathrm{~K}$ & 3100 &  \\\\\nMelting bandwidth & $\\delta T$ & $\\mathrm{~K}$ & 100 &  \\\\\nAbsorption coefficient & $a_{L}$ & - & 0.27 &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nFigure 7 and Table 3 provide the simulation results of the weld pool geometry at $t=3 \\mathrm{~ms}$. We measured the radius and depth of the weld pool by a line distance calculator in ParaView. According to the data in Figure 7, the predicted weld pool dimensions are compared against the results from two other references, both experimental and computational, in Table 3. The comparison shows that the present values of weld pool dimension agree well with those of He et al. [55] and Russell et al. [28]. Also, the geometry of the weld pool simulated by SPH is similar to that of the physical experiment, clearly seen through the side-by-side comparison in Figure 7. Even at this fairly low resolution, the 3D SPH model predicts the depth of the weld pool by an error of $4 \\%$ and its radius by $10 \\%$.\n\nTable 3. Comparison of the weld pool dimensions: SPH vs. experiment.\n\n\\begin{center}\n\\begin{tabular}{lccc}\n\\hline\nDimension & Present SPH & Russell et al. SPH [28] & Hu et al. Experiment [55] \\\\\n\\hline\nRadius in mm (\\% error) & $0.43(-10 \\%)$ & $0.46(-4 \\%)$ & 0.48 \\\\\nDepth in mm (\\% error) & $0.27(+4 \\%)$ & $0.25(-4 \\%)$ & 0.26 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_97637720aa0371e31845g-12}\n\\end{center}\n\nFigure 7. Numerical and experimental weld pool Geometry for laser power of $1967 \\mathrm{~W}$, beam radius of $0.428 \\mathrm{~mm}$, and pulse duration of $3 \\mathrm{~ms}$ including: (Left) weld pool cross sections in a side-by-side comparison of SPH result with experiment of He et al. [55]; (Right) top view of the whole domain showing the diameter of the laser weld spot.\n\nAnother check on the model is performed by reporting the maximum temperature in the last time step. Figure 8 presents two snapshots for this purpose, showing the temperature distribution of the solidified SPH particles alongside a top view of the weld pool.", "start_char_idx": 454058, "end_char_idx": 457419, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "6810aeb9-5557-4dbc-9536-0c5fa8af80fc": {"__data__": {"id_": "6810aeb9-5557-4dbc-9536-0c5fa8af80fc", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bf667d83-766c-40c4-b508-b94fd16cd5e8", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "367c285b7d5a86aeac2d333ea5265b0413a5c44847886cb487d7976fb977aa95", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1d19aa51-2235-4f5c-bddf-e2afa1e8c667", "node_type": "1", "metadata": {}, "hash": "969be7b602d37309540dd90d5888a26b4a917d2d66a6ab698bc87940ac5cf797", "class_name": "RelatedNodeInfo"}}, "text": "Numerical and experimental weld pool Geometry for laser power of $1967 \\mathrm{~W}$, beam radius of $0.428 \\mathrm{~mm}$, and pulse duration of $3 \\mathrm{~ms}$ including: (Left) weld pool cross sections in a side-by-side comparison of SPH result with experiment of He et al. [55]; (Right) top view of the whole domain showing the diameter of the laser weld spot.\n\nAnother check on the model is performed by reporting the maximum temperature in the last time step. Figure 8 presents two snapshots for this purpose, showing the temperature distribution of the solidified SPH particles alongside a top view of the weld pool. It is observed that the maximum temperature in this simulation is $3152 \\mathrm{~K}$ found at the center of the weld spot. This value is close to $T_{\\max }=3200 \\mathrm{~K}$ from the high-resolution SPH simulation of Dao and Lou [57] and the experimental measurement of He et al. [55].\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_97637720aa0371e31845g-12(1)}\n\nFigure 8. Temperature distribution at $t=3 \\mathrm{~ms}$ for: (Left) SPH particles with temperatures higher than the melting temperature of the material; (Right) top view of the full domain including all particles.\n\n\\section*{4. Application: Laser Powder Bed Fusion}\nThe proposed multi-resolution SPH code is applied to simulate a 2D laser powder bed fusion (LPBF) process. Similar to the experimental setup of Khairallah and Anderson [12], the initial configuration is composed of a 304 stainless steel particle bed sitting on a flat substrate of the same material, with properties given in Equations (25) and (26) and Table 2. For the SPH simulation setup, one layer of circular powder particles with a diameter of $50 \\mu \\mathrm{m}$ is uniformly distributed on a $1 \\mathrm{~mm}$ long track. Figure 9 shows the dimensions and boundary conditions of this problem. We terminate the simulation at around $t=1.13 \\mathrm{~ms}$ to ensure that the powder bed is scanned and fully solidified.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_97637720aa0371e31845g-13}\n\\end{center}\n\nFigure 9. Initial configuration and boundary conditions of the LPBF simulation. A Gaussian laser beam is scanning the track from left to right, shown in orange. The size (i.e., mass) of each SPH particle inside the refinement frame is $1 / 4$ of the unrefined particles in blue.\n\n\\subsection*{4.1. Parameter Study and Some General Observations}\nThe presented spatial adaptivity algorithm helps achieve a more realistic LPBF simulation with less computational effort (see Figure 10). However, another incentive to introduce particle refinement into the current SPH LPBF models was to minimize their computational cost and allow for parameter studies in a reasonable amount of time. For instance, analyzing the sensitivity of melt pool dimensions to process parameters is a useful consideration that will assist in optimizing fabricated part quality. Therefore, the effect of the track energy on the melt geometry using the efficient SPH code is investigated in this section. According to the term used in [58], the track energy is defined here as $\\bar{E}=P_{L} / v_{S}$ with respect to the laser power and scan speed.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_97637720aa0371e31845g-13(1)}\n\\end{center}\n\nFigure 10. Effect of spatial discretization on SPH results. Particle refinement leads to a more accurate melt surface in LPBF simulation. The blue particles inside the squares represent the finest resolution in each case.\n\nSince SPH particles are incapable of representing the interface explicitly [54], a postprocessing analysis needs to be performed to accurately extract the melt geometry. The $\\alpha$-shape algorithm of Edelsbrunner et al. [59] was chosen for this purpose. Figure 11 illustrates the calculation steps of the melt geometry as an $\\alpha$-shape, depicted in green. The procedure is showcased for a laser power of $100 \\mathrm{~W}$ scanning the LPBF track at the speed of $1 \\mathrm{~m} / \\mathrm{s}$.", "start_char_idx": 456797, "end_char_idx": 460840, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1d19aa51-2235-4f5c-bddf-e2afa1e8c667": {"__data__": {"id_": "1d19aa51-2235-4f5c-bddf-e2afa1e8c667", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "6810aeb9-5557-4dbc-9536-0c5fa8af80fc", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9ae247773f56dfb4ff0983dfc1582b5a066214beac19c2c46054f606be08922f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ed3c61e4-9b73-4e9c-b9bf-24dd7dc799ce", "node_type": "1", "metadata": {}, "hash": "40686cb7d152cad7c9afb35e2946b77ae27230a2f899462318e0fa0ff65260b3", "class_name": "RelatedNodeInfo"}}, "text": "Effect of spatial discretization on SPH results. Particle refinement leads to a more accurate melt surface in LPBF simulation. The blue particles inside the squares represent the finest resolution in each case.\n\nSince SPH particles are incapable of representing the interface explicitly [54], a postprocessing analysis needs to be performed to accurately extract the melt geometry. The $\\alpha$-shape algorithm of Edelsbrunner et al. [59] was chosen for this purpose. Figure 11 illustrates the calculation steps of the melt geometry as an $\\alpha$-shape, depicted in green. The procedure is showcased for a laser power of $100 \\mathrm{~W}$ scanning the LPBF track at the speed of $1 \\mathrm{~m} / \\mathrm{s}$. Snapshots of the temperature and material phase are shown, where the state color-bar indicates the parameter $s$ defined in Equation (22). The state scale is linear, starting from the liquid state represented by red, down to the solid state shown in blue. The\n\nSPH particles with temperatures equal or greater than the melt temperature are extracted, shown in solid grey on the right top frame. The $\\alpha$-shape algorithm is then applied to these melted particles to find an explicit definition of the melt pool interface.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_97637720aa0371e31845g-14}\n\nFigure 11. Melt pool formation and calculation of the melted area for the case of $P_{L}=100 \\mathrm{~W}$ and $v_{s}=1 \\mathrm{~m} / \\mathrm{s}$ after the laser has scanned half of the powder bed.\n\nHalfway through the scanning process, the melt pool seems to reach a steady state. SPH frames are thus taken from this time instant: after the laser has scanned half of the powder bed. It is clear from the state of SPH particles in Figure 11 that the laser beam (in orange) creates a highly dynamic melt pool underneath itself, fusing the powder bed along the way. A very similar behavior and zonal distinction were also observed by previous studies in FEM [12] and (single-resolution) SPH [28].\n\nIn order to set up the parameter study, a total of 16 test cases was simulated by varying the laser power from 50 to $200 \\mathrm{~W}$ at different scan speeds of $1,1.5,2$, and $2.5 \\mathrm{~m} / \\mathrm{s}$. The finest and coarsest discretization sizes in these models were, respectively, $3 \\mu \\mathrm{m}$ and $6 \\mu \\mathrm{m}$. In Figure 12, the total melt depth $d_{m}$ is plotted in grey as a surface function of the laser power and scan speed. The blue stems in this plot indicate the 16 simulation data points. As expected, the maximum depth is found when using the maximum power $(200 \\mathrm{~W})$ at the minimum scan speed $(1 \\mathrm{~m} / \\mathrm{s})$. Moreover, a second-degree polynomial equation of $d_{m}$ expresses the best fit to the available track energies. The red curve in Figure 12 represents this graph alongside the SPH data-sets shown in black squares.\n\nFor a laser power of $200 \\mathrm{~W}$ at the scan speed of $2 \\mathrm{~m} / \\mathrm{s}$, Figure 13 shows the melt dimensions after the powder bed is scanned and fully solidified. As a verification that the present SPH results are correct, the simulated LPBF track is plotted next to the experimental monograph of [12] for a very similar case. The numerical calculations are represented at six locations sufficiently far from the two edges to average the melt shape. We found the mean approximation error in the range of $15-20 \\%$. The diameter of fine SPH particles is $\\approx 3 \\mu \\mathrm{m}$ and almost all melted sub-domains are discretized by this resolution (i.e., the red particles in Figure 13). In contrast to the LPBF simulation of Russell et al. [28], SPH particles ejected from the melt pool were not removed from the present model. A closer look at the red particles flying above the solidified track confirms this, clearly seen in Figure 13.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_97637720aa0371e31845g-15(1)}\n\nFigure 12.", "start_char_idx": 460131, "end_char_idx": 464090, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ed3c61e4-9b73-4e9c-b9bf-24dd7dc799ce": {"__data__": {"id_": "ed3c61e4-9b73-4e9c-b9bf-24dd7dc799ce", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1d19aa51-2235-4f5c-bddf-e2afa1e8c667", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "10b68ec8531d00d277ac8769f3469eb76da9946b95e6d256bcb96f288961d2e5", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "cf411c42-9876-435b-925a-1cd4d3588c43", "node_type": "1", "metadata": {}, "hash": "b834ceac13c6bba6e57e7e40b9b11ed9a4d639528ab56eebd07df369556384e1", "class_name": "RelatedNodeInfo"}}, "text": "The numerical calculations are represented at six locations sufficiently far from the two edges to average the melt shape. We found the mean approximation error in the range of $15-20 \\%$. The diameter of fine SPH particles is $\\approx 3 \\mu \\mathrm{m}$ and almost all melted sub-domains are discretized by this resolution (i.e., the red particles in Figure 13). In contrast to the LPBF simulation of Russell et al. [28], SPH particles ejected from the melt pool were not removed from the present model. A closer look at the red particles flying above the solidified track confirms this, clearly seen in Figure 13.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_97637720aa0371e31845g-15(1)}\n\nFigure 12. Prediction of the melt depth using the proposed multi-resolution SPH approach.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_97637720aa0371e31845g-15}\n\\end{center}\n\nFigure 13. Melt dimensions for $P_{L}=200 \\mathrm{~W}$ at $v_{s}=2 \\mathrm{~m} / \\mathrm{s}$ when the track is fully solidified. The melted and re-solidified SPH particles are shown in red, obtained from the present multi-resolution SPH simulation at $t=1.25 \\mathrm{~ms}$. The numerical melt depth and height are represented at 6 locations (green line segments). The experimental micrograph reprinted from Khairallah and Anderson [12] Copyright (2021), with permission from Elsevier under License Number 5013001359377.\n\nTo generate deeper insight into the LPBF process, another sensitivity analysis on the laser power effects was carried out. For this purpose, powers varying from 50 to $200 \\mathrm{~W}$ at a constant speed of $2.5 \\mathrm{~m} / \\mathrm{s}$ were considered. A full representation is depicted in Figure 14 at $t=0.13$ and $t=1 \\mathrm{~ms}$. Following from top to bottom, it becomes evident that increasing the power causes material sputtering and leads to worse surface roughness. The existence of voids between unmelted powders at $P_{L}=50 \\mathrm{~W}$ implies that this power is insufficient for fully melting the powder bed and penetrating into the substrate. On the other hand, the melt surface profile is significantly more volatile in the case of $P_{L}=200$ and necking can be observed at the solidified track. Overall, among these numerical experiments, scanning a 150-W laser at the speed of $v_{s}=2.5 \\mathrm{~m} / \\mathrm{s}$ for this LPBF setup seems to produce the best result with fewer manufacturing defects.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_97637720aa0371e31845g-16}\n\\end{center}\n\nFigure 14. Laser tracks with different powers at scan speed $2.5 \\mathrm{~m} / \\mathrm{s}$. Snapshots of the temperature distribution shown at $t=0.13 \\mathrm{~ms}$, when $1 / 3$ of the powder-bed length is melted, and at $t=1.0 \\mathrm{~ms}$, when the LPBF track is fully solidified. The color-bar limit is set to a maximum of $2173 \\mathrm{~K}$ for better visualization. The SPH particles are dynamically refined in all simulations, where the coarsest and finest discretization size used is 6 and $3 \\mu \\mathrm{m}$, respectively.\n\n\\subsection*{4.2.", "start_char_idx": 463375, "end_char_idx": 466478, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "cf411c42-9876-435b-925a-1cd4d3588c43": {"__data__": {"id_": "cf411c42-9876-435b-925a-1cd4d3588c43", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ed3c61e4-9b73-4e9c-b9bf-24dd7dc799ce", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "377743078c56389720e637af42f8e4c4a137b04d74b89c4fd85be3fddbc3a0ae", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3a175499-3392-4bb3-953f-997f22b7328a", "node_type": "1", "metadata": {}, "hash": "b292a84606a440f5ae741c48e8c9f90d6b10743f28038a0a5d7afa7669a2d77c", "class_name": "RelatedNodeInfo"}}, "text": "Laser tracks with different powers at scan speed $2.5 \\mathrm{~m} / \\mathrm{s}$. Snapshots of the temperature distribution shown at $t=0.13 \\mathrm{~ms}$, when $1 / 3$ of the powder-bed length is melted, and at $t=1.0 \\mathrm{~ms}$, when the LPBF track is fully solidified. The color-bar limit is set to a maximum of $2173 \\mathrm{~K}$ for better visualization. The SPH particles are dynamically refined in all simulations, where the coarsest and finest discretization size used is 6 and $3 \\mu \\mathrm{m}$, respectively.\n\n\\subsection*{4.2. Computational Performance}\nTo better appreciate the improvement gained by the proposed particle refinement approach, a runtime analysis was performed on 4 models:\n\n\\begin{enumerate}\n  \\item Single resolution $\\mathrm{w} / \\mathrm{o}$ dynamics particle refinement $\\mathrm{w}$ / uniform discretization size $\\Delta / 2$\n\n  \\item Multi resolution $\\mathrm{w} /$ dynamics particle refinement $\\mathrm{w} / \\mathrm{o}$ neighbor-list optimization\n\n  \\item Multi resolution $\\mathrm{w} /$ dynamics particle refinement $\\mathrm{w} /$ neighbor-list optimization\n\n  \\item Single resolution $\\mathrm{w} / \\mathrm{o}$ dynamics particle refinement $\\mathrm{w}$ / uniform discretization size $\\Delta$\n\n\\end{enumerate}\n\nThe simulation setup in all cases is the same as the reference model taken from [28], corresponding to a laser power of $100 \\mathrm{~W}$ at the scan speed of $2 \\mathrm{~m} / \\mathrm{s}$ using a discretization size of $4 \\mu \\mathrm{m}$. Elapsed simulation times are recorded for a serial C++14 implementation, run on a single CPU core of Intel\u00ae Core $^{\\mathrm{TM}}$ i5-4690 at $3.50 \\mathrm{GHz}$. Shown in Figure 15 is a comparison of the runtime associated with each model. The only difference between models 2 and 3 is using the optimized algorithm proposed for constructing the neighbor list of multi-resolution SPH particles (see in Section 2.5). This explains why the number of particles in both cases is the same (yellow graph of the left plot in Figure 15), but their runtime is different (orange vs. yellow graphs on the right plot in Figure 15). As can be seen, using the proposed optimization saves an additional $25 \\%$ of the computational cost in multi-resolution SPH schemes. Consequently, a 2D LPBF simulation of a 1-mm long track with a reasonable discretization size of $4 \\mu \\mathrm{m}$ can be finished in almost $90 \\mathrm{~min}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_97637720aa0371e31845g-17}\n\\end{center}\n\nFigure 15. Runtime performance comparison. The proposed multi-resolution model (with optimized neighbor list) outperforms the other models by reducing approximately $50 \\%$ of the computational cost of the reference model (i.e., single high resolution with $d x=4 \\mu \\mathrm{m}$ ). The total number of SPH particles used by the multi-resolution model is 3668 at the beginning and 7658 at the end of the simulation, significantly lower than a total of 11,800 particle used by the reference model 1.\n\nOn the other hand, both multi-resolution cases (models 2 and 3) could cut the final number of particles down to almost half of the reference case (model 1). The barchart comparison shows that the optimized multi-resolution simulation saves $50 \\%$ of the computational time, thus $2 \\times$ faster in providing the same result. Although not quite similar in terms of the computing platform and hardware, it is still beneficial to point out that the (single-resolution) SPH model of [28] published in 2018 was claimed to take $36 \\mathrm{~h}$ on a single CPU core.\n\n\\section*{5. Conclusions}\nThis paper developed an efficient multi-resolution SPH framework for numerical simulation of the LPBF process. Analytical and experimental validations were carried out to ensure the correct working of the code in a liquid droplet and laser spot welding test. The numerical results demonstrate the capability of the presented method in simulating the melt pool dynamics and capturing the relevant physics in an LPBF process.", "start_char_idx": 465938, "end_char_idx": 469961, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3a175499-3392-4bb3-953f-997f22b7328a": {"__data__": {"id_": "3a175499-3392-4bb3-953f-997f22b7328a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "cf411c42-9876-435b-925a-1cd4d3588c43", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "88bcf0b0ac113bf64fda7dd640648d744e173cd318609396405a8dbd3a40b3f6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "11f85a18-39d8-4a36-9d7b-44933f2ada16", "node_type": "1", "metadata": {}, "hash": "5ea83c701395ab9318a5a2c6562c4b576e78d4b62b07803cfd983720b4be0ff2", "class_name": "RelatedNodeInfo"}}, "text": "The barchart comparison shows that the optimized multi-resolution simulation saves $50 \\%$ of the computational time, thus $2 \\times$ faster in providing the same result. Although not quite similar in terms of the computing platform and hardware, it is still beneficial to point out that the (single-resolution) SPH model of [28] published in 2018 was claimed to take $36 \\mathrm{~h}$ on a single CPU core.\n\n\\section*{5. Conclusions}\nThis paper developed an efficient multi-resolution SPH framework for numerical simulation of the LPBF process. Analytical and experimental validations were carried out to ensure the correct working of the code in a liquid droplet and laser spot welding test. The numerical results demonstrate the capability of the presented method in simulating the melt pool dynamics and capturing the relevant physics in an LPBF process. By enabling dynamic particle refinement within the SPH simulation, the proposed approach reduced the calculation time remarkably and facilitated further explorations such as parameter study and fine discretization. The results from this improvement are promising: Showcased for a 2D single-track LPBF case, almost $35 \\%$ of the computational cost of SPH was saved without using the optimized neighbor-list algorithm. Using an optimized neighbor-search scheme resulted in a $15 \\%$ additional saving and led to a $2 \\times$ faster code with the same result. In brief, a 2D LPBF simulation of a 1-mm long track using SPH particles of $4 \\mu \\mathrm{m}$ diameter can now be completed in $90 \\mathrm{~min}$.\n\nThe use of SPH for AM simulation is a young but rapidly growing area of research, which opens up multiple new avenues for future developments. It is of utmost importance to strengthen the numerical model validation against physical experiments where more measurement data are available. The proposed scheme was presented for a 2D LPBF simulation but can be easily extended to 3D applications. Furthermore, the achieved saving in runtime is convincing to incorporate the dynamic refinement algorithm into the parallel SPH codes running on both CPUs and GPUs.\n\nSupplementary Materials: The following are available at https:/ /www.mdpi.com/2076-3417/11 $/ 7 / 2962 /$ s1. The software used for producing the results in this paper follows the implementation given in the following public source codes: \"MFree IWF Cut Refine\" (link: \\href{https://github.com/}{https://github.com/} iwf-inspire/mfree\\_iwf-ul-cut-refine (accessed on 24 March 2021)) and \"MFree IWF Thermal\" (link: \\href{https://github.com/iwf-inspire/thermal_iwf}{https://github.com/iwf-inspire/thermal\\_iwf} (accessed on 24 March 2021)).\n\nAuthor Contributions: M.A.: conceptualization, methodology, software, validation, formal analysis, investigation, data curation, visualization, writing, original draft preparation, and writing, review and editing. C.L.: software, data curation. M.B.: supervision, revision, project administration. K.W.: supervision, revision, project administration, and funding acquisition. All authors read and agreed to the published version of the manuscript.\n\nFunding: The authors received no specific funding for this work.\n\nInstitutional Review Board Statement: Not applicable.\n\nInformed Consent Statement: Not applicable.\n\nAcknowledgments: The authors thank Matthias R\u00f6thlin, Hagen Klippel, and Eleni Chatzi for their support and invaluable discussions during this research project.\n\nConflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; nor in the decision to publish the results.\n\n\n\n\\section*{References }\n\\begin{enumerate}\n  \\item Gu, D.D.; Meiners, W.; Wissenbach, K.; Poprawe, R. Laser additive manufacturing of metallic components: Materials, processes and mechanisms. Int. Mater. Rev. 2012, 57, 133-164. [CrossRef]\n\n  \\item King, W.E.; Anderson, A.T.; Ferencz, R.M.; Hodge, N.E.; Kamath, C.; Khairallah, S.A.; Rubenchik, A.M. Laser powder bed fusion additive manufacturing of metals; physics, computational, and materials challenges. Appl. Phys. Rev. 2015, 2, 041304.", "start_char_idx": 469104, "end_char_idx": 473289, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "11f85a18-39d8-4a36-9d7b-44933f2ada16": {"__data__": {"id_": "11f85a18-39d8-4a36-9d7b-44933f2ada16", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3a175499-3392-4bb3-953f-997f22b7328a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "5355ab4fbb043422c824b08b174a228a1181288352edb3b2e934f93b457173d7", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "78a728e8-5b93-4fc5-9c2e-ad32d7b857aa", "node_type": "1", "metadata": {}, "hash": "a15caedad6fba9ea85a2c208af03cdc73c63fb793dd1bed3c0112ef29f74fa07", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{References }\n\\begin{enumerate}\n  \\item Gu, D.D.; Meiners, W.; Wissenbach, K.; Poprawe, R. 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Methods Eng. 2007, 72, 295-324.", "start_char_idx": 479992, "end_char_idx": 482883, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "67c34963-17b6-4b20-bec1-a91580a98504": {"__data__": {"id_": "67c34963-17b6-4b20-bec1-a91580a98504", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "eab9a718-91b9-4b4d-ade3-c493cf08e356", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8f1fda2c4becd8345ca258c7764390ba79cd92994ccdfb7787de19bc92dd9314", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ec88e885-f075-4bc5-929d-04679f4ced56", "node_type": "1", "metadata": {}, "hash": "952a3d0911d031bbbba4443618885a041176d0906001d34e0e68f7705a6723ba", "class_name": "RelatedNodeInfo"}}, "text": "J. Comput. Phys. 2010, 229, 5011-5021. [CrossRef]\n\n  \\item Hashemi, H.; Sliepcevich, C. A numerical method for solving two-dimensional problems of heat conduction with change of phase. Chem. Eng. Prog. Symp. Ser. 1967, 63, 34-41.\n\n  \\item Monaghan, J.J. Smoothed particle hydrodynamics. Rep. Prog. Phys. 2005, 68, 1703. [CrossRef]\n\n  \\item Feldman, J.; Bonet, J. Dynamic refinement and boundary contact forces in SPH with applications in fluid flow problems. Int. J. Numer. Methods Eng. 2007, 72, 295-324. [CrossRef]\n\n  \\item Vacondio, R.; Rogers, B.; Stansby, P.; Mignosa, P. Variable resolution for SPH in three dimensions: Towards optimal splitting and coalescing for dynamic adaptivity. Comput. Methods Appl. Mech. Eng. 2016, 300, 442-460. [CrossRef]\n\n  \\item Afrasiabi, M. Thermomechanical Simulation of Manufacturing Processes Using GPU-Accelerated Particle Methods. Ph.D. Thesis, ETH Zurich, Zurich, Switzerland, 2020; ISBN 9783907234211. [CrossRef]\n\n  \\item He, X.; Fuerschbach, P.; DebRoy, T. Heat transfer and fluid flow during laser spot welding of 304 stainless steel. J. Phys. D Appl. Phys. 2003, 36, 1388. [CrossRef]\n\n  \\item Sahoo, P.; Debroy, T.; McNallan, M. Surface tension of binary metal-Surface active solute systems under conditions relevant to welding metallurgy. Metall. Trans. B 1988, 19, 483-491. [CrossRef]\n\n  \\item Dao, M.H.; Lou, J. Simulations of Laser Assisted Additive Manufacturing by Smoothed Particle Hydrodynamics. Comput. Methods Appl. Mech. Eng. 2021, 373, 113491. [CrossRef]\n\n  \\item Weirather, J.; Rozov, V.; Wille, M.; Schuler, P.; Seidel, C.; Adams, N.A.; Zaeh, M.F. A smoothed particle hydrodynamics model for laser beam melting of Ni-based alloy 718. Comput. Math. Appl. 2019, 78, 2377-2394. [CrossRef]\n\n  \\item Edelsbrunner, H.; Kirkpatrick, D.; Seidel, R. On the shape of a set of points in the plane. IEEE Trans. Inf. Theory 1983, 29, 551-559. [CrossRef]\n\n\\end{enumerate}\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\\usepackage{multirow}\n\n\\title{In situ and Operando X-ray Imaging of Directed Energy Deposition Additive Manufacturing }", "start_char_idx": 482378, "end_char_idx": 484715, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ec88e885-f075-4bc5-929d-04679f4ced56": {"__data__": {"id_": "ec88e885-f075-4bc5-929d-04679f4ced56", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "67c34963-17b6-4b20-bec1-a91580a98504", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "05c7062a00a57bad00ec63e87d5f19dd602df09677833a6c6ad731d24f775e41", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7b2ba363-2bba-441e-b29f-14115cb825b1", "node_type": "1", "metadata": {}, "hash": "41b92b01c3a2437bf12c48dd546e75f91efedd5dc8a1fb4f16a75f3ca79b4247", "class_name": "RelatedNodeInfo"}}, "text": "[CrossRef]\n\n  \\item Edelsbrunner, H.; Kirkpatrick, D.; Seidel, R. On the shape of a set of points in the plane. IEEE Trans. Inf. Theory 1983, 29, 551-559. [CrossRef]\n\n\\end{enumerate}\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\\usepackage{multirow}\n\n\\title{In situ and Operando X-ray Imaging of Directed Energy Deposition Additive Manufacturing }\n\n\n\\author{Y.Chen, ${ }^{1,2 *}$ S. J. Clark, ${ }^{1,2}$ L.Sinclair, ${ }^{1,2}$ C.L.A.Leung, ${ }^{1,2}$ S.Marussi, ${ }^{1,2}$\\\\\nT.Connolley, ${ }^{3}$ O.V.Magdysyuk, ${ }^{3}$ R.C. Atwood, ${ }^{3}$ G.J.Baxter, ${ }^{4}$ M.A.Jones, ${ }^{4}$\\\\\nD.G.McCartney, ${ }^{5}$ I. Todd, ${ }^{6}$ P.D.Lee, ${ }^{1,2 *}$\\\\\n${ }^{1}$ Department of Mechanical Engineering, University College London,Torrington Place, London WC1E 7JE, UK.\\\\\n${ }^{2}$ Research Complex at Harwell, Rutherford Appleton Laboratory, Oxfordshire,OX11 0FA, UK.\\\\\n${ }^{3}$ Diamond Light Source, Harwell Campus, Oxfordshire, OX11 0DE, UK.\\\\\n${ }^{4}$ Rolls-Royce plc, PO Box 31, Derby, DE24 8BJ, UK.\\\\\n${ }^{5}$ Faculty of Engineering, The University of Nottingham, Nottingham, NG7 2RD, UK.\\\\\n${ }^{6}$ Department of Materials Science and Engineering, University of Sheffield, Sir Robert Hadfield Building,\\\\\nMappin Street, Sheffield, S1 3JD, UK.\\\\\n*Corresponding authors: peter.lee@ucl.ac.uk, yunhui.chen@ucl.ac.uk.}\n\\date{}\n\n\n\\begin{document}\n\\maketitle\nThe mechanical performance of Directed Energy Deposition Additive Manufactured (DED-AM) components can be highly material dependent. Through in situ and operando synchrotron X-ray imaging we capture the underlying phenomena controlling build quality of stainless steel (SS316) and titanium alloy (Ti6242 or Ti-6Al-2Sn-4Zr-2Mo). We reveal three mechanisms influencing the build efficiency of titanium alloys compared to stainless steel: blown powder sintering; reduced melt-pool wetting due to the sinter; and pore pushing in the melt-pool. The former two directly increase lack of fusion porosity, while the later causes end of track porosity. Each phenomenon influences the melt-pool characteristics, wetting of the substrate and hence build efficacy and undesirable microstructural feature formation. We demonstrate that porosity is related to powder characteristics, pool flow, and solidification front morphology. Our results clarify DED-AM process dynamics, illustrating why each alloy builds differently, facilitating the wider application of additive manufacturing to new materials.\n\n\\section*{Introduction}\nLaser Additive Manufacturing (LAM)(1) is transforming modern manufacturing technologies and enabling direct fabrication of complex shapes(2) for metals(3), ceramics(4) and polymers(5) using computeraided designs. This level of flexibility and customizability(6) cannot be achieved through traditional manufacturing routes. Directed Energy Deposition Additive Manufacturing (DED-AM) is amongst the most promising methods in LAM due to its capabilities from repair applications to direct build of functionallygraded and large freeform components. In contrast to Laser Powder Bed Fusion (LPBF) systems, the DED-AM process (also known as the blown powder process) involves the feeding of powder materials from a nozzle into a laser-heated molten metal pool.", "start_char_idx": 484114, "end_char_idx": 487606, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7b2ba363-2bba-441e-b29f-14115cb825b1": {"__data__": {"id_": "7b2ba363-2bba-441e-b29f-14115cb825b1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ec88e885-f075-4bc5-929d-04679f4ced56", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ba6c37df497219ea553bee19a7ff890cef8de4697142b6bcd93743801cec2665", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "67d74253-1291-4a7f-bf57-013c0405c911", "node_type": "1", "metadata": {}, "hash": "19f2c2dae5addfab32337151141a27114ea09c91e497a8f1c7cadfd3b5a07589", "class_name": "RelatedNodeInfo"}}, "text": "Our results clarify DED-AM process dynamics, illustrating why each alloy builds differently, facilitating the wider application of additive manufacturing to new materials.\n\n\\section*{Introduction}\nLaser Additive Manufacturing (LAM)(1) is transforming modern manufacturing technologies and enabling direct fabrication of complex shapes(2) for metals(3), ceramics(4) and polymers(5) using computeraided designs. This level of flexibility and customizability(6) cannot be achieved through traditional manufacturing routes. Directed Energy Deposition Additive Manufacturing (DED-AM) is amongst the most promising methods in LAM due to its capabilities from repair applications to direct build of functionallygraded and large freeform components. In contrast to Laser Powder Bed Fusion (LPBF) systems, the DED-AM process (also known as the blown powder process) involves the feeding of powder materials from a nozzle into a laser-heated molten metal pool. However, the lack of fundamental understanding of the underlying processstructure-property relationships hinders the utilisation of DED-AM for production. Technical challenges include the accumulation of significant residual stresses(7) and formation of undesirable microstructures(8), which can restrict the mechanical performance of the final product. Detrimental features such as gas porosity, lack of fusion porosity and balling of the melt-track can occur and these can have a deleterious effect on the structural integrity of the final components. Specifically, DED-AM is an immensely attractive route for the manufacture of titanium alloy aerospace parts(9) because customised near-net-shape components can be produced without the need for machining which is both time consuming and wasteful of an expensive metallic alloy. However, it has been widely reported that it is difficult to achieve the structural integrity required and this has proved to be a major barrier to more widespread application.\n\nThe majority of the experimental studies of the DED-AM processes have involved ex situ characterisation of the microstructure(10) and the mechanical properties(11). However, this approach does not provide a fundamental understanding of the mechanisms by which microstructural features form. In situ studies, utilizing infrared imaging, high-speed optical imaging, thermocouples and pyrometers, to develop closed-loop control(12) of the manufacturing process have been reported but these also fail to provide fundamental insights. On the other hand, in situ and operando high-speed X-ray investigations(13) using high-flux third-generation synchrotron radiation sources(14) have enabled researchers to see into the heart of the powder bed AM process(15) and characterise the transient phenomena(16) in\\\\\nthe melt-pool(17) such as flow(18), microstructural feature formation(19) together with phase and strain evolution(20). This capability is due to the ability of X-rays to penetrate through a sufficient depth of dense, optically opaque metallic samples with high spatial and temporal resolution(21). Therefore, such an approach has the potential to help elucidate the phenomena occurring on the time and length scales associated with DED-AM. Although synchrotron radiography has been employed to study laser powder bed fusion (LPBF), much less attention has been given to DED-AM process. Wolff et al.(19) simulated some aspects of the blown powder process by using a piezo-driven vibration-assisted powder delivery system to induce a gravitational flow of powders from a syringe-needle; however, their process replicator was vastly different from an industrial DED-AM process due to the low-velocity unfocused powder delivery and very finely focused laser.\n\nIn this work, we perform a high-resolution, time-resolved in situ and operando synchrotron X-ray radiographic study of DED-AM using an AM machine with build capability that directly scales to common industrial DED-AM processes. Here we report the investigation of deposition phenomena in different materials including melt-pool dynamics and the relationship to microstructure formation mechanisms in a multi-layer blown powder build. We successfully capture the laser-matter interactions during DED-AM for SS316 (grade 316 iron-based austenitic stainless steel) and the aerospace titanium alloy Ti6242 (Ti6Al-2Sn-4Zr-2Mo). These observations reveal the vastly different physical phenomena occurring during DED-AM for different materials, including the underlying physics causing melt-track formation mechanisms to be different in the two alloys. Compared with SS316, we uncovered that during the processing of Ti6242, blown powder sinters ahead of, and behind, the melt-pool. The presence of this has a significant influence on the development of the build and on the mechanisms of porosity formation.", "start_char_idx": 486656, "end_char_idx": 491477, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "67d74253-1291-4a7f-bf57-013c0405c911": {"__data__": {"id_": "67d74253-1291-4a7f-bf57-013c0405c911", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7b2ba363-2bba-441e-b29f-14115cb825b1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cfb8335e78c2a70c99965eadd9da2f4c1b7a98ed5cac52c4bed3ae238b23b18c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ba0400ec-9ea1-4e9b-b104-80d2bd4581ca", "node_type": "1", "metadata": {}, "hash": "f27e763d88817d40d544c076e781a402bad52d79a5b4734514be396a3d5ada32", "class_name": "RelatedNodeInfo"}}, "text": "Here we report the investigation of deposition phenomena in different materials including melt-pool dynamics and the relationship to microstructure formation mechanisms in a multi-layer blown powder build. We successfully capture the laser-matter interactions during DED-AM for SS316 (grade 316 iron-based austenitic stainless steel) and the aerospace titanium alloy Ti6242 (Ti6Al-2Sn-4Zr-2Mo). These observations reveal the vastly different physical phenomena occurring during DED-AM for different materials, including the underlying physics causing melt-track formation mechanisms to be different in the two alloys. Compared with SS316, we uncovered that during the processing of Ti6242, blown powder sinters ahead of, and behind, the melt-pool. The presence of this has a significant influence on the development of the build and on the mechanisms of porosity formation. The results presented in this work provide an enhanced fundamental understanding of the DED-AM process with direct relevance to optimising the microstructures of titanium alloy components.\n\n\\section*{Results \\& Discussion}\n\\section*{1. In situ and operando synchrotron X-ray imaging of DED-AM}\nWe performed in situ and operando X-ray imaging on the I12 Joint Engineering, Environmental, and Processing (JEEP) beamline(22) at Diamond Light Source to capture the transient phenomena in the DED-AM of SS316 and Ti6242 (see Supplementary Figure 1). The Blown Powder Additive Manufacturing Process Replicator (BAMPR) was designed to replicate a scaled version of commercial DED-AM systems, enabling integration in synchrotron beamlines, as shown in Figure. 1a (and Suppl. Figure 1). Further details about this bespoke instrument can be found in methods and Supplementary Information. Specifically, the instrument facilitates deposition with a laser power density of up to $6.3710^{3} \\mathrm{~W} \\mathrm{~mm} m^{-2}$ and a corresponding energy density of up to $32 \\mathrm{~J} \\mathrm{~mm}^{-3}$. These specifications were designed to faithfully replicate industrial conditions (see Supplementary Table 1-3 for a detailed comparison to the reported parameters for commercial systems).\n\nA schematic of the X-ray imaging process is shown in Figure. 1b. The synchrotron X-rays are attenuated by the powder and deposited material, which is then converted to visible light via a scintillator and captured as a radiographic video using a fast CCD camera (not shown). As opposed to $\\operatorname{LPBF}(23)$, the weld pool in DED-AM is significantly larger ( $\\mathrm{mm}$ compared to $200 \\mathrm{~mm}$ ) and the traverse speed slower ( $\\mathrm{mm} \\mathrm{s}^{-1}$ as compared to $\\mathrm{m} \\mathrm{s}^{-1}$ ). Furthermore, the melt-pool is stationary with respect to the cameras frame of reference. Therefore, the optimal acquisition speed for imaging the weld pool dynamics was selected as $200 \\mathrm{fps}$ (with $0.0049 \\mathrm{~s}$ exposure time). This framerate provided sufficient signal to noise ratio to resolve the subtle solid-liquid phase contrast boundary. For the experiments capturing the fasttransient influence of powder on melt-pool initiation 2000 fps was used with a subsequent trade-off in signal quality.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_5dd08c8296f7c4d14504g-05}\n\nFigure 1: In situ and operando X-ray imaging of the DED-AM process. (A) The Blown Powder Additive Manufacturing Process Replicator (BAMPR) replicates a commercial DED-AM system. The system is encapsulated within a Class $I$ laser enclosure and comprises an inert environmental chamber, a high precision 3-axis platform, an industrial coaxial DED nozzle and a laser system. (B) Schematic of the in situ and operando X-ray imaging of DED-AM process. The synchrotron X-rays are attenuated by the deposited materials and then are converted to visible light with a scintillator to capture as a radiographic video on a fast CCD camera (not shown). The resulting videos reveal the underlying mechanism and dynamics of the process. Scale bars on the radiographs $=1000 \\mu m$.", "start_char_idx": 490604, "end_char_idx": 494653, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ba0400ec-9ea1-4e9b-b104-80d2bd4581ca": {"__data__": {"id_": "ba0400ec-9ea1-4e9b-b104-80d2bd4581ca", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "67d74253-1291-4a7f-bf57-013c0405c911", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8568a4457877b7bc62384a38afa883ebde0c919509b4a461e0fa3cd8de692bc1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "38bb20b2-ea08-42b0-b0bb-8fd9ffe900a1", "node_type": "1", "metadata": {}, "hash": "168d17c172646bb5a031e488a3e4c09a9c027c2d1b8e3c1ad7ec6c696ae6d8b1", "class_name": "RelatedNodeInfo"}}, "text": "(A) The Blown Powder Additive Manufacturing Process Replicator (BAMPR) replicates a commercial DED-AM system. The system is encapsulated within a Class $I$ laser enclosure and comprises an inert environmental chamber, a high precision 3-axis platform, an industrial coaxial DED nozzle and a laser system. (B) Schematic of the in situ and operando X-ray imaging of DED-AM process. The synchrotron X-rays are attenuated by the deposited materials and then are converted to visible light with a scintillator to capture as a radiographic video on a fast CCD camera (not shown). The resulting videos reveal the underlying mechanism and dynamics of the process. Scale bars on the radiographs $=1000 \\mu m$. (C) Time-resolved radiographs acquired during DED-AM at the start of a melt-track on SS316 (Supplementary Video 1) and Ti6242\n\n(Supplementary Video 2). SS316 build is under laser power density $(P)=6.3710^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}$, scanning\n\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_5dd08c8296f7c4d14504g-06}\\\\\n$v=1 \\mathrm{~mm} \\mathrm{~s}{ }^{-1}$, laser spot size $=400 \\mu \\mathrm{m}$. Both captured at $200 \\mathrm{fps}$, Scale bar $=500 \\mu \\mathrm{m}$. Three radiographs were selected as representative of the building process. The time since the build started is marked on each radiograph. Agglomerated/sintered particles can be observed on top of the Ti6242 melt-track during the building process. (D) Time-series radiographs acquired during DED of an SS316 (Supplementary Video 3) and a Ti6242 (Supplementary Video 4) multi-layer build. Three radiographs were selected as representative of the building process of layer 1, layer 2 and layer 5, respectively. A pore (broken circle) is observed in layer 5 of the SS316 build and numerous pores are observed in the Ti6242 build. The sintered layer caused lack of fusion between layers of Ti6242. Scale bar $=500 \\mu m$. The melt-pool boundary in (C) and (D) are marked by monitoring the solid-liquid moving boundary.\n\n\\section*{2. Melt-track Initiation}\nTo reveal the initial establishment of a melt-track at the onset of the build was captured at varying laser powers of $50 \\mathrm{~W}, 100 \\mathrm{~W}$ and $200 \\mathrm{~W}$ (laser power density $1.5910^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}, 3.1810^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}$ and $6.3710^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}$, respectively with a laser spot size of $200 \\mu \\mathrm{m}$ ) (Figure 2a, b \\& c and Supplementary Videos 5, 6 \\& 7 respectively) at an image acquisition rate of $2000 \\mathrm{fps}$. We applied a local-temporal background subtraction to emphasise the moving objects in the radiographs detailed in the supplementary information. In Figure 2a, with a laser power of $50 \\mathrm{~W}$, a melt-track was not observed to form, little thermal expansion of the substrate was evident, and powder particles were not seen to adhere to the substrate surface. In contrast, as shown in Figure 2b, upon increasing the laser power to $100 \\mathrm{~W}$ the initiation of the particle incorporation process becomes evident. Powder particles are observed to adhere onto the substrate plate commencing at $1.065 \\mathrm{~s}$ after the laser was turned on, suggesting the surface is molten. These powder particles coalesce and form a melt-pool after $1.125 \\mathrm{~s}$. With a further increase of laser power to $200 \\mathrm{~W}$, as shown in Figure 2c, the radiographs show that just $0.0695 s$ after the laser was turned on, a powder particle was captured and incorporated into the melted substrate area and formed a melt-pool after just $0.131 s$.", "start_char_idx": 493953, "end_char_idx": 497549, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "38bb20b2-ea08-42b0-b0bb-8fd9ffe900a1": {"__data__": {"id_": "38bb20b2-ea08-42b0-b0bb-8fd9ffe900a1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ba0400ec-9ea1-4e9b-b104-80d2bd4581ca", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "49005c263cc45100e9cf2cb884508786bf1bddc85079eed9fedde934616e3cd1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "10ce3e50-30b0-4683-b167-5502c00120fc", "node_type": "1", "metadata": {}, "hash": "6c24a3646ac0e0c261f18913486b84e0797238283217c4e81695693967b7335f", "class_name": "RelatedNodeInfo"}}, "text": "In contrast, as shown in Figure 2b, upon increasing the laser power to $100 \\mathrm{~W}$ the initiation of the particle incorporation process becomes evident. Powder particles are observed to adhere onto the substrate plate commencing at $1.065 \\mathrm{~s}$ after the laser was turned on, suggesting the surface is molten. These powder particles coalesce and form a melt-pool after $1.125 \\mathrm{~s}$. With a further increase of laser power to $200 \\mathrm{~W}$, as shown in Figure 2c, the radiographs show that just $0.0695 s$ after the laser was turned on, a powder particle was captured and incorporated into the melted substrate area and formed a melt-pool after just $0.131 s$. It is evident at both powers that the adhesion of the powder particles significantly increases the absorption of the laser energy. We hypothesise this is due to the increased surface area.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5dd08c8296f7c4d14504g-07(1)}\n\\end{center}\n\nd\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5dd08c8296f7c4d14504g-07}\n\\end{center}\n\nFigure 2: Time-series radiographs acquired during DED-AM revealing the mechanism of melttrack formation. Material is SS316. All radiographs were captured at $2000 \\mathrm{fps}$ and revealed by localtemporal background subtraction. (A) $\\mathrm{P}=6.3710^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}, \\mathrm{v}=1.67 \\mathrm{~mm} \\mathrm{~s}^{-1}$. See Supplementary Video 5. Scale bar $=1000 \\mu m$. (B) $\\mathrm{P}=3.18 \\quad 10^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}$. See Supplementary Video 6. Scale bar $=500 \\mu \\mathrm{m}$. The powder particles agglomerated/sintered under laser radiation and eventually forming a melt-track via surface wetting. Powder particles were wetted onto the melted substrate plate separately and deposited onto the substrate surface at $1.065 \\mathrm{~s}$ after the laser was turned on. Three powder particles coalesced at $1.065 s$ and formed a melt-track at $1.125 s$ with more powder particles coalesced with the melt-track. (C) $\\mathrm{P}=1.59 \\quad 10^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}$. See Supplementary Video 7. Scale bar $=500 \\mu \\mathrm{m}$. (D) The relationship between the time a melt-track needs to form after the laser turns on and laser power density.\n\nThe DED-AM process exhibits a complex laser-matter interaction dependent upon multiple factors such\\\\\nas; surface roughness, angle of incidence and the presence of surface oxides(24). The melt-track initiation mechanism is a transient process which occurs when the absorbed power density exceeds a critical power density threshold. While the melt-track development mechanism here is based on laser power density which operates in the melting region(25). The relationship between the time a melt-track needs to form after the laser turns on and laser power density is plotted in Figure 2d. When the laser illuminates the substrate surface with a power density of $6.3710^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}$, instead of forming a cavity(19) or keyhole(26), as can often occur in the $\\operatorname{LPBF}(27)$ process, the substrate surface is melted to give a conduction mode(28) melt-pool. In the present set-up, the powder particle flow is concentric with the laser beam and therefore the powder particles are directly deposited into the region the melted region. Some of these particles can be incorporated into the melt-pool, driven by surface tension and capillary forces, however, others rebounded where they impact solid material. Decreasing the laser power density slows the met-track initiation process as the molten area of the substrate is both narrower and shallower reducing both the probability of a powder particle impacts the molten area and that the powder particle is in-turn incorporated into the pool.", "start_char_idx": 496866, "end_char_idx": 500661, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "10ce3e50-30b0-4683-b167-5502c00120fc": {"__data__": {"id_": "10ce3e50-30b0-4683-b167-5502c00120fc", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "38bb20b2-ea08-42b0-b0bb-8fd9ffe900a1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "fdb5ba3777ed2ab034e427adfaca7fdb288356bcb8b5ccf7c729ddab22b9f6c6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "11b9a688-947b-4e9b-ab5d-0c78fbec0802", "node_type": "1", "metadata": {}, "hash": "a50aad93f136039e3bea3b14eb46251b42beb1111808ce70f5db7c15bd1a75db", "class_name": "RelatedNodeInfo"}}, "text": "In the present set-up, the powder particle flow is concentric with the laser beam and therefore the powder particles are directly deposited into the region the melted region. Some of these particles can be incorporated into the melt-pool, driven by surface tension and capillary forces, however, others rebounded where they impact solid material. Decreasing the laser power density slows the met-track initiation process as the molten area of the substrate is both narrower and shallower reducing both the probability of a powder particle impacts the molten area and that the powder particle is in-turn incorporated into the pool. The reduction of laser powder density therefore, directly results in a corresponding reduction of powder capture efficiency.\n\n\\section*{3. Powder sinter}\nThe time-resolved evolution of the multi-layer melt-track morphology of an SS316 track on an SS304 substrate and a Ti6242 track on a titanium Ti-6Al-2Sn-4Zr-6Mo (Ti6246) substrate, respectively, were captured by X-ray at $200 \\mathrm{fps}$ during the DED-AM laser deposition process (Figure 3c \\& d and Supplementary Videos 1-4). Single melt-tracks were deposited in an alternating bi-directional strategy up to 10 layers in height, with the melt-pool measuring 1 to $3 \\mathrm{~mm}$ in diameter (see Supplementary info). Figure 1c shows a time-series of radiographs taken from the start of the deposition process. The laser beam is shown to melt the substrate surface and consolidate the powder particles into a melt-pool and form a continuous deposited track during the deposition of the first layer. The extent of the melt-pool is marked with a dotted line in Figure 3c-d, and can be observed clearly in Supplementary Videos 1-4 since the liquid is less dense and hence brighter than the solid in radiography; there is also a phase-contrast fringe at the solid-liquid boundary. It should be noted that the shape of the melt-pool is reversed from that of\\\\\na classic convex pool penetrating the track below (as in the SS316 case), to pool resembling a saddle (see Supplementary Figure 5). The saddle shape leads to the appearance of 2-3 phase contrast fringes generated by the local saddle-points through projection in the X-ray direction.\n\nAn additional significant difference in the melt-track morphology between SS316 and Ti6242 can be observed from the radiographs, as shown in Figure 1c and 1d, in that sintered powder particles are observed covering the melt-track and around the melt-pool during the multi-layer build of Ti6242. The thickness of the sintered powder can reach several times that of the melt-track itself as shown in more detail in Figure 3e and Supplementary Video 8. The extent of the sintering appears to depend strongly on the input laser power density. In subsequent layers of the build, the slow percolation of the melt-pool through the sintered powder layer further exacerbates the inversion of melt-pool, causing it to form a saddle shape. This phenomenon is captured in Figure $3 \\mathrm{~b}$ where the front of the melt-pool exhibits a crocodiles mouth shape during the second layer of the build. This key difference between SS316 and Ti6242, i.e. the formation of sinter, is illustrated schematically in Figure 3c and d where infiltration of the Ti6242 melt into the porous powder layer is emphasised and compared.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_5dd08c8296f7c4d14504g-10}\n\nFigure 3: Understanding the powder sintering phenomenon in Ti6242. (A) Time-resolved radiograph acquired during an SS316 build revealing the convex shape of the melt-pool surface, Laser power density $=6.3710^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}, \\mathrm{v}=1.67 \\mathrm{~mm} \\mathrm{~s}^{-1}$ captured at $200 \\mathrm{fps}$. Scale bar $=1000 \\mu \\mathrm{m}$.", "start_char_idx": 500031, "end_char_idx": 503809, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "11b9a688-947b-4e9b-ab5d-0c78fbec0802": {"__data__": {"id_": "11b9a688-947b-4e9b-ab5d-0c78fbec0802", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "10ce3e50-30b0-4683-b167-5502c00120fc", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "62cf78c92ef31dbff7e052beb711acd6dca7db939bf80f4893492e1a90313556", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "cc2ca4c5-6d1d-4cb2-97e8-dd1e33612718", "node_type": "1", "metadata": {}, "hash": "3b7fd7b4f686d1c7d8c101a4a21c2ad0ab3d1cccd3b7f6dd1070a24888b5ff7d", "class_name": "RelatedNodeInfo"}}, "text": "the formation of sinter, is illustrated schematically in Figure 3c and d where infiltration of the Ti6242 melt into the porous powder layer is emphasised and compared.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_5dd08c8296f7c4d14504g-10}\n\nFigure 3: Understanding the powder sintering phenomenon in Ti6242. (A) Time-resolved radiograph acquired during an SS316 build revealing the convex shape of the melt-pool surface, Laser power density $=6.3710^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}, \\mathrm{v}=1.67 \\mathrm{~mm} \\mathrm{~s}^{-1}$ captured at $200 \\mathrm{fps}$. Scale bar $=1000 \\mu \\mathrm{m}$. in comparison to (B) Time-resolved radiograph acquired during a Ti6242 build revealing the concave shape of the melt-pool surface due to the sintered powder layer, Laser power density $=1.5910^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}, \\mathrm{v}=$ $1 \\mathrm{~mm} \\mathrm{~s}^{-1}$ captured at $200 \\mathrm{fps}$. Scale bar $=1000 \\mu \\mathrm{m}$. (C) Schematic of (a) showing the convex shape melt-pool in a multi-layer build condition. (D) Schematic of (B) showing the phenomena in a multi-layer build condition, the percolation of the melt-pool through the loosely sintered powder layer distinctively alters the melt-pool geometry. Laser power density $=1.5910^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}, \\mathrm{v}=1 \\mathrm{~mm} \\mathrm{~s}^{-1}$ captured at $200 \\mathrm{fps}$. Scale bar $=1000 \\mu \\mathrm{m}$. (E) Time-resolved radiograph showing significant powder agglomeration/sintering during Ti6242 build, Laser power density $=7.9610^{2} \\mathrm{~W} \\mathrm{~mm}^{-2}, \\mathrm{v}=1 \\mathrm{~mm} \\mathrm{~s}^{-1}$ captured at 200 fps. See Supplementary Video 8. The sintered layer thickness is more than three times the height of the melt-track itself. Scale bar $=1000 \\mu \\mathrm{m}$. (F) Post-mortem SEM image of Ti6242 partially sintered particle necks attached to the melt-track of (E). Diffusion provides the mechanism for the flow of material from regions of low curvature to regions of high curvature i.e. towards the neck or point of contact. Scale bar $=10 \\mu \\mathrm{m}$. (G) Cross-section of the melt-track from the micro-CT scan of Ti6242 melt-track revealing the lack of fusion between layers and the sinter particles surrounded. Scale bar $=100 \\mu \\mathrm{m}$. (H) Post-mortem micro-CT scan of Ti6242 melt-track revealing lack of fusion porosity between layers caused by sintering phenomenon. Scale bar $=500 \\mu m$.\n\nTo understand more about the sintered Ti6242 powder, the partially sintered layer attached to the melttrack was examined in a scanning electron microscope and inter-particle necks are revealed, as shown in Figure $3 \\mathrm{f}$ and Supplementary Figure 7. The capture efficiency by the melt-pool of powder particles heated in the laser beam is less than one(29). Particles that are not captured by the melt-pool can potentially stick to the surface of the substrate/solidified track; a physical phenomenon that is known to occur\n\nin other processes for the particle sizes $(\\sim 50 \\mu \\mathrm{m})$ and the velocities $\\left(\\sim 5 \\mathrm{~m} \\mathrm{~s}^{-1}\\right)$ similar to those in DED (30). However, with Ti6242 it appears to actually sinter. One hypothesis for the formation of Ti6242 powder sinter is that their surface oxide dissolves into the alloy as the powder surface heats due to the increased solid solubility of oxygen at temperatures over $1000{ }^{\\circ} \\mathrm{C}(31)$.", "start_char_idx": 503198, "end_char_idx": 506633, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "cc2ca4c5-6d1d-4cb2-97e8-dd1e33612718": {"__data__": {"id_": "cc2ca4c5-6d1d-4cb2-97e8-dd1e33612718", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "11b9a688-947b-4e9b-ab5d-0c78fbec0802", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2f09421b26753b9238ad0cf1a798e4fafc300ee4c7a28b933a9363cbf1736c6f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "17e7e34d-13ce-4f20-a7d9-6584822752da", "node_type": "1", "metadata": {}, "hash": "6a13e9af28c8361691ff0d338868dc964d7f596990214d15342e781cdd13eb15", "class_name": "RelatedNodeInfo"}}, "text": "The capture efficiency by the melt-pool of powder particles heated in the laser beam is less than one(29). Particles that are not captured by the melt-pool can potentially stick to the surface of the substrate/solidified track; a physical phenomenon that is known to occur\n\nin other processes for the particle sizes $(\\sim 50 \\mu \\mathrm{m})$ and the velocities $\\left(\\sim 5 \\mathrm{~m} \\mathrm{~s}^{-1}\\right)$ similar to those in DED (30). However, with Ti6242 it appears to actually sinter. One hypothesis for the formation of Ti6242 powder sinter is that their surface oxide dissolves into the alloy as the powder surface heats due to the increased solid solubility of oxygen at temperatures over $1000{ }^{\\circ} \\mathrm{C}(31)$. The exposed high temperature alloy bonds quickly to other particles as seen during Ti alloy sinter treatments (32), while for SS316, the powder has a thin chromia-type oxide that is strongly adherent and chemically stable(33) even when heated. I.e. the SS316 oxide acts as a barrier to sticking and interdiffusion between particles. Hence impinging Ti6242 particles are very likely to stick to one another and, without an oxide diffusion barrier, interdiffusion will occur across clean metal interfaces causing a particle neck to form, as shown in Figure $3 \\mathrm{~d}$.\n\nThe lightly sintered, very porous layer can potentially causes lack of fusion porosity between layers in a multi-layer DED build, Figure 3d, Figure 3g and h. Detailed examples of the formation of porosity and lack of fusion features can be found in Supplementary Figure 8. In situ radiography shows that the sinter layer can alter melt-pool, affect both surface roughness and lack of fusion porosity in the titanium alloy builds.\n\n\\section*{4. Porosity formation}\nPorosity can occur in DED-AM builds and can be categorised into lack of fusion and gas entrapped pores(34). We have already discussed lack of fusion pores. With regards to gas entrapped pores, previous research has suggested they are generated via two sources: laser-induced keyhole porosity and gas entrapped porosity due to absorption of gas from the feedstock powder(19). It is reported that a keyhole can trap shielding gas during DED-AM and contribute to gas entrapped pore formation(19,26). However,\n\nDED-AM is not normally associated with keyhole mode and this phenomenon was not observed in our experiments. Here, we report that entrained porosity (Figure 4a and $4 \\mathrm{~b}$ and Supplementary video 9 \\& 10) is related to gas in the feed powder (entrained and soluble) and the influence of Marangoni flow.\n\nA times series of radiographs (Figure 4a) suggest a potential mechanism of sole pore formed during a 10 layer SS316 build. At $\\mathrm{t}=0.01 s$ into the build, a cluster of 3-4 agglomerated powder particles hits the leading edge of the pool and melts into it. A pore then appears to form at the same location $(t=$ $0.015 \\mathrm{~s}$ ), perhaps entrained from this powder cluster. This gas pore then swirls around several times in the melt-pool, probably following the Marangoni flow streamlines. After a third of a second, the pore reaches the rear of the pool, and is entrained in the semi-solid, forming a pore in the solid track $(t=0.315$ $s$, Figure 4a).\n\nIn contrast, in Ti6242 many pores are formed, as is typical for Ti alloy welds. We hypothesise that there was trapped gas within the sintered powder layer which originated from either the powder particles themselves(35) or from the porous sinter layer. Interestingly, unlike the pore in SS316, when the pores in Ti6242 reach the back, they are pushed along rather than captured by the solid. The actual flow is quite complex, as the pores are in the rear of the two pools on either side of the saddle shape (see Supplementary Figure 5), one larger and deeper than the other. These two clusters of pores hover in the pool below the surface, as the downward Marangoni flow pushes them down balanced against the buoyancy force.", "start_char_idx": 505898, "end_char_idx": 509879, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "17e7e34d-13ce-4f20-a7d9-6584822752da": {"__data__": {"id_": "17e7e34d-13ce-4f20-a7d9-6584822752da", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "cc2ca4c5-6d1d-4cb2-97e8-dd1e33612718", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b35d1812a7542e297c5fe475986c943320de7dd56a623741590d514028fd6805", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ad28ed43-fe21-4608-b53b-5108cd5868c6", "node_type": "1", "metadata": {}, "hash": "b8f35e5730b85bc1ae7ad8f7b46d12a46e98686c7fb04df59648749b4f829237", "class_name": "RelatedNodeInfo"}}, "text": "In contrast, in Ti6242 many pores are formed, as is typical for Ti alloy welds. We hypothesise that there was trapped gas within the sintered powder layer which originated from either the powder particles themselves(35) or from the porous sinter layer. Interestingly, unlike the pore in SS316, when the pores in Ti6242 reach the back, they are pushed along rather than captured by the solid. The actual flow is quite complex, as the pores are in the rear of the two pools on either side of the saddle shape (see Supplementary Figure 5), one larger and deeper than the other. These two clusters of pores hover in the pool below the surface, as the downward Marangoni flow pushes them down balanced against the buoyancy force. We hypothesise that these pores are pushed by the solidification front rather than entrained due to Ti6242s very narrow freezing range $(\\sim 5 K)(36)$, which favours a planar solidification front $(36)$ at the traverse speed of $1 \\mathrm{~mm} \\mathrm{~s}^{-1}-10 \\mathrm{~mm} \\mathrm{~s}^{-1}$ (see Figure 4c and Supplementary Figure S6). The planar solidification front (which cannot be resolved in the present experiments and is not preserved to room temperature due to the solid-state phase transformation(37)) effectively prevents the pores from being engulfed into the solidifying track and instead results in pore pushing. The pores are thus swept along with the melt-pool at its back wall (Figure 4b) until the end of the track is reached, as shown in the XCT scans in the Supplementary Figure S7.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_5dd08c8296f7c4d14504g-13}\n\nb\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_5dd08c8296f7c4d14504g-13(1)}\n\nFigure 4: Porosity formation and pore pushing mechanisms captured during X-ray imaging. (A) SS316: A pore appears to form via gas entrainment from a cluster of powder particles melted into the pool. A pore flow trajectory revealed on a radiograph. See Supplementary Video 9. The Marangoni-\\\\\ndriven flow forces the pore to flow in the melt-pool at an average velocity of $\\sim 43 \\mathrm{~mm} \\mathrm{~s}^{-1}$. Scale bar $=$ $1000 \\mu \\mathrm{m}$. (B) Ti6242: a pore appears to form via gas entrainment from the sintered particles ahead of the melt-pool. See Supplementary Video 10. Pores are being swept along with the melt-pool following the convection flow. Scale bar $=1000 \\mu \\mathrm{m}$. (C) Schematic of the pore formation mechanisms with a comparison between Ti6242 and SS316. The planar/cellular front in Ti6242 effectively prevents the pores from being engulfed into the solidifying track. As a result, the pores at the solid/liquid interface at the back of the melt-pool are swept along with it. In SS316, a cellular colony solidification structure develops which engulfs the pores during solidification. This results in the formation of a series of pores that are regularly distributed along the length of the melt-track.\n\nIn contrast to Ti6242, SS316 has a much wider freezing range $(\\sim 110 K)(38)$ and therefore has a cellular colonies solidification morphology. This morphology tends to allow pores to be engulfed by the solidification front and not pushed towards the end of the track, as shown in Figure 4c and Supplementary Figure S6. In SS316, this gives rise to the formation of pores that are entrained shortly after they enter the melt pool, and hence are more regularly distributed along the length of the melt-track, unlike Ti6242 where end of track agglomeration occurs (Supplementary Figure S8).\n\n\\section*{Summary}\nWe have used fast time-resolved synchrotron X-ray imaging to uncover fundamental physical phenomena during the multi-layer DED-AM process in situ and operando in that dramatically alter the behaviour of different key engineering alloys. We reveal insights into the underlying mechanisms governing melttrack formation, melt-pool dynamics and transient porosity formation. We show these mechanisms are highly material dependent, differing significantly between SS316 and Ti6242.", "start_char_idx": 509155, "end_char_idx": 513189, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ad28ed43-fe21-4608-b53b-5108cd5868c6": {"__data__": {"id_": "ad28ed43-fe21-4608-b53b-5108cd5868c6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "17e7e34d-13ce-4f20-a7d9-6584822752da", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "94a303af42bdc20ff6c11ba15782f49a8a6c0f24bbe9a43e286f0a498fffbeff", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "648b6d6a-2d0d-4222-97c7-32db4a353a9d", "node_type": "1", "metadata": {}, "hash": "e1c6174ffe79708816c068ad650eefd55641b731110e30c09d8436dd3f55b208", "class_name": "RelatedNodeInfo"}}, "text": "This morphology tends to allow pores to be engulfed by the solidification front and not pushed towards the end of the track, as shown in Figure 4c and Supplementary Figure S6. In SS316, this gives rise to the formation of pores that are entrained shortly after they enter the melt pool, and hence are more regularly distributed along the length of the melt-track, unlike Ti6242 where end of track agglomeration occurs (Supplementary Figure S8).\n\n\\section*{Summary}\nWe have used fast time-resolved synchrotron X-ray imaging to uncover fundamental physical phenomena during the multi-layer DED-AM process in situ and operando in that dramatically alter the behaviour of different key engineering alloys. We reveal insights into the underlying mechanisms governing melttrack formation, melt-pool dynamics and transient porosity formation. We show these mechanisms are highly material dependent, differing significantly between SS316 and Ti6242. Using different laser power densities, we demonstrate that the mechanism for initiation and formation of a melt-track involves laserinduced surface wetting driven by capillary forces. We observed a significant difference between SS316 and Ti6242; the latter forms an agglomerated/sintered powder layer on the surface of a track. We conclude that the formation of a sintered layer in Ti6242, which is not found in SS316, is due to differences in the behaviour of their surface oxides. The alteration of the melt-pool spreading due to the presence of the loosely sintered layer is the main cause of high surface roughness and lack of fusion pores in the final product of Ti6242.\n\nWe capture the different pore formation mechanisms in SS316 and Ti6242 builds and conclude that porosity is by gas entrainment from the powder feedstock. In Ti6242 pores are observed to swirl in the melt-pool and are not entrained into the solidification front most probably due to it being planar. Instead, the pores are pushed, forming a cluster of pores at the end of the track. In contrast, SS316 has a much wider freezing range giving a dendritic solidification morphology which readily entrains the pores rather than pushing them, resulting in a more even distribution of pores along the length of the track.\n\nOverall, our results clarify the key fundamental physics behind DED-AM process and can be used to design processing strategies for enhanced quality and performance of additively manufactured parts in stainless steel, titanium and other alloys.\n\n\\section*{Materials and Methods}\n\\section*{1. In situ and operando synchrotron X-ray imaging}\nThe BAMPR (Blown Powder Additive Manufacturing Process Replicator) has been developed to faithfully replicate a commercial DED-AM system which used industrial power density and energy density standards. The instrument was specifically designed to be integrated into high energy high flux synchrotron beamlines, e.g. I12: Joint Engineering, Environmental, and Processing (JEEP) at Diamond Light Source. $I 12$ is chosen for its high energy range (53-150 keV) and well-suited for the size of the melt-pool and the thickness of the melt-track (1-3 $\\mathrm{mm}$ thick). Due to the industrial scale of the experiment and the limitation on the flux, it is proven difficult to increase to frame-rate to more than 2,000 fps. The system is encapsulated within a Class $I$ laser enclosure and comprises an inert environmental chamber, a high precision 3-axis stage, an industrial coaxial DED nozzle and a laser system. An industrial powder feeder (Oerlikon Metco TWIN-10-C) delivers powder to the system in a stream of argon gas. The powders used were gas atomised Ti6242 and SS316 powders with a size distribution of $45 \\mu \\mathrm{m}$ - $90 \\mu \\mathrm{m}$ and with median particle diameter, $D_{50}$, of $70 \\mu \\mathrm{m}$. The laser is a $1070 \\mathrm{~nm}$ Ytterbium-doped fibre laser beam (continuous-wave $(C W)$ mode, laser power $(P)$ of $0 \\mathrm{~W}-200 \\mathrm{~W}$ ) which is coupled with tuneable optics to facilitate a focused spot size of between 200-700 $\\mu \\mathrm{m}$. The laser is positioned to\\\\\nbe concentric with the powder delivery stream blown from the nozzle and normal to the substrate plate (1-2.5 $\\mathrm{mm}$ thick).", "start_char_idx": 512248, "end_char_idx": 516465, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "648b6d6a-2d0d-4222-97c7-32db4a353a9d": {"__data__": {"id_": "648b6d6a-2d0d-4222-97c7-32db4a353a9d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ad28ed43-fe21-4608-b53b-5108cd5868c6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "432e7f3fc09a3eddfd116a591df8ea344228a3b5ae7909fd9929219122e04e7f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "843e3e54-77d4-475d-afd3-2bc427d3f723", "node_type": "1", "metadata": {}, "hash": "bd1ce0b7effdf7c39e2460e9741d7ade2cd5e13b575eac327801d0a3e1f8a949", "class_name": "RelatedNodeInfo"}}, "text": "The powders used were gas atomised Ti6242 and SS316 powders with a size distribution of $45 \\mu \\mathrm{m}$ - $90 \\mu \\mathrm{m}$ and with median particle diameter, $D_{50}$, of $70 \\mu \\mathrm{m}$. The laser is a $1070 \\mathrm{~nm}$ Ytterbium-doped fibre laser beam (continuous-wave $(C W)$ mode, laser power $(P)$ of $0 \\mathrm{~W}-200 \\mathrm{~W}$ ) which is coupled with tuneable optics to facilitate a focused spot size of between 200-700 $\\mu \\mathrm{m}$. The laser is positioned to\\\\\nbe concentric with the powder delivery stream blown from the nozzle and normal to the substrate plate (1-2.5 $\\mathrm{mm}$ thick). As a result, the melt-pool is steadily placed in the centre of the X-ray beam during material deposition process. This provides huge advantages in observing melt-pool dynamics. Ultra-high time resolution is not necessary for our experiments due to its disadvantage in recording powder flow and over-shadow the melt-pool. In this work, the 3-axis stage was able to translate through $25 \\mathrm{~mm}$ in length, $50 \\mathrm{~mm}$ in width, and $50 \\mathrm{~mm}$ in height. The powder used was gas atomised Ti6242 and SS316 powders with a size distribution of $45 \\mu m$ - $90 \\mu m$ with median particle diameter, $D_{50}$, of $70 \\mu m$. The substrate plate is positioned inside the environmental build chamber with Kapton film (X-ray transparent) windows under a flowing argon atmosphere of $6 \\mathrm{~L} \\mathrm{~min}^{-1}$. The speed of the sample stages in both cases was controlled to be 1-5 $\\mathrm{mm} \\mathrm{s}^{-1}$ to enable a continuous track to be formed for this condition as indicated by preliminary laboratory trials.\n\n\\section*{2. Image processing and quantification}\nThe acquired images are corrected to form a Flat-Field Corrected (FFC) image by dividing by an average of 100 flat field images using ImageJ and Matlab(c). To increase the image contrast and signal-to-noise ratio, we applied a local-temporal background subtraction to reveal key information in the X-ray images following equation:\n\n\n\\begin{equation*}\nL T B S=\\frac{F F C}{I_{l a v g}} \\tag{1}\n\\end{equation*}\n\n\nWhere $L T B S$ is the local-temporal background-subtracted image, FFC is the flat field corrected image, and $I_{\\text {lavg }}$ is a local average of 50 of the nearest neighbour images ( 25 before and 25 after). The local-temporal background subtraction method is chosen to reveal the subtle solid-liquid interface at the boundary of the melt-pool in sacrifice of time resolution. In the high image resolution experiment, 200 fps was used to maximise the spatial resolution in the experimental set-up and to avoid the smudge of images from the fast-moving powder particles.\n\n\\section*{Acknowledgments}\nGeneral: The authors also would like to thank Dr. Ali Dehghan-manshadi for performing the microstructure characterization on SS316 samples.\n\nFunding: This research was supported under MAPP: EPSRC Future Manufacturing Hub in Manufacture using Advanced Powder Processes (EP/P006566/1), a Royal Academy of Engineering Chair in Emerg-\n\ning Technology, and Rolls-Royce plc. via the Horizon 2020 Clean Sky 2 WP5.8.1 programs and through support of L.S.s studentship. S.C. was supported by the Office for Naval Research under grant number N62909-19-1-2109.\n\nAuthor contributions: P.D.L. conceived the project. Y.C., S.C. and S.M., led the design of the Blown Powder Additive Manufacturing Process Replicator (BAMPR). Y.C. and S.C. designed and performed the experiments, with all authors contributing. Y.C. performed the data analysis with S.C contributing. Y.C and P.D.L. led the results interpretation and paper writing, with all authors contributing.\n\n\\section*{References}\n\\begin{enumerate}\n  \\item T. Debroy, H.L. Wei, J.S. Zuback, T. Mukherjee, J.W.", "start_char_idx": 515844, "end_char_idx": 519616, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "843e3e54-77d4-475d-afd3-2bc427d3f723": {"__data__": {"id_": "843e3e54-77d4-475d-afd3-2bc427d3f723", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "648b6d6a-2d0d-4222-97c7-32db4a353a9d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7fef2b5cf0bba39c4f0d5c23433a31e75dc5fa128b945e8c2ca1014a9f33e5b4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6f0c1950-388a-475c-99df-efcb343de95d", "node_type": "1", "metadata": {}, "hash": "d78e432b74f62f3155c14d1c496b109a554bee8e73b9a3effcdb48bfe6ce25a6", "class_name": "RelatedNodeInfo"}}, "text": "S.C. was supported by the Office for Naval Research under grant number N62909-19-1-2109.\n\nAuthor contributions: P.D.L. conceived the project. Y.C., S.C. and S.M., led the design of the Blown Powder Additive Manufacturing Process Replicator (BAMPR). Y.C. and S.C. designed and performed the experiments, with all authors contributing. Y.C. performed the data analysis with S.C contributing. Y.C and P.D.L. led the results interpretation and paper writing, with all authors contributing.\n\n\\section*{References}\n\\begin{enumerate}\n  \\item T. Debroy, H.L. Wei, J.S. Zuback, T. Mukherjee, J.W. Elmer, J.O. Milewski, A.M. Beese, A. Wilson-Heid, A. De, W. Zhang, Prog. Mater. Sci. 92, 112-224 (2018).\n\n  \\item J. Beuth, J. Fox, J. Gockel, C. Montgomery, R. Yang, H. Qiao, E. Soylemez, P. Reeseewatt, A. Anvari, S. Narra, N. Klingbeil, 24th Int. SFF Symp. - An Addit. Manuf. Conf. SFF 2013, 655-665 (2013).\n\n  \\item T. B. Sercombe, G. B. Schaffer, Science 301, 12251227 (2003).\n\n  \\item Z. C. Eckel, C. Zhou, J. H. Martin, A. J. Jacobsen, W. B. Carter, T. A. Schaedler, Science 351, 58-62 (2016).\n\n  \\item M. Schmid, K. 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A mean X-ray energy of approximately $53 \\mathrm{keV}$ was used for all experiments. The X-ray imaging system consisted of a $200 \\mu \\mathrm{m}$ thick LuAg:Ce scintillator and a 4 magnification long working distance objective lens ( 0.21 numerical aperture). The X-ray images were captured by a high-resolution imaging camera (PCO.edge 5.5, PCO) at 200 and at up to 2,000 fps using a lower resolution high-speed camera (MIRO 310M, Vision Research Inc.). Unlike laser powder bed fusion, the weld pool in DED-AM is much larger and the translations are much slower $\\left(\\mathrm{mm} \\mathrm{s}^{-1}\\right.$ compared to $m \\mathrm{~s}^{-1}$ ). Therefore, we optimised the number of frames per second for two situations.", "start_char_idx": 522802, "end_char_idx": 525383, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "e23028db-8f94-4bcd-b893-19ee7357ab81": {"__data__": {"id_": "e23028db-8f94-4bcd-b893-19ee7357ab81", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d1a4129d-3dca-4168-b689-386bb77fa41a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2866921ff9a52c18dbb86c3a080f47608fb6420c976bad802e11d6dfb58c78fb", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5471900a-16b5-4428-a97e-722ec394ef6c", "node_type": "1", "metadata": {}, "hash": "e554e4fa27fb05735645e48853abac15b150d242b638cb67b8e3b649cefb26b1", "class_name": "RelatedNodeInfo"}}, "text": "A mean X-ray energy of approximately $53 \\mathrm{keV}$ was used for all experiments. The X-ray imaging system consisted of a $200 \\mu \\mathrm{m}$ thick LuAg:Ce scintillator and a 4 magnification long working distance objective lens ( 0.21 numerical aperture). The X-ray images were captured by a high-resolution imaging camera (PCO.edge 5.5, PCO) at 200 and at up to 2,000 fps using a lower resolution high-speed camera (MIRO 310M, Vision Research Inc.). Unlike laser powder bed fusion, the weld pool in DED-AM is much larger and the translations are much slower $\\left(\\mathrm{mm} \\mathrm{s}^{-1}\\right.$ compared to $m \\mathrm{~s}^{-1}$ ). Therefore, we optimised the number of frames per second for two situations. Firstly, to capture pool phenomena we found 200 fps was sufficient to capture the key phenomena, while enabling a long exposure time of $0.0049 s$ and a very small off-load time $(0.0001$ $s)$ that gave excellent signal to noise $(S / N)$ ratio. We also used $2000 \\mathrm{fps}$ for experiments where faster phenomena were occurring, trading off $S / N$ for speed.\n\n\\section*{2. Supplementary figures}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5dd08c8296f7c4d14504g-22(2)}\n\\end{center}\n\nFigure S1: Experimental setup for the in situ laser additive manufacturing process using Blown Powder Additive Manufacturing Process Replicator (BAMPR). (A) Class I laser enclosure. (B) DED process replicator mounted inside the laser enclosure. (C) Powder feeder.\n\na\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5dd08c8296f7c4d14504g-22(1)}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5dd08c8296f7c4d14504g-22}\n\\end{center}\n\nFigure S2: Powder analysis. SEM image of (A) SS316L powder. Scale bar $=200 \\mu m$; (B) Ti6242 powder. Scale bar $=100 \\mu \\mathrm{m}$. Gas atomised powders was used in the experiments with a size distribution of 45 - $90 \\mu \\mathrm{m}$ and a $D_{50}$ (median diameter) of $70 \\mu \\mathrm{m}$. Particle size distribution is analysed using same method in Leung et als paper(1).\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5dd08c8296f7c4d14504g-23(1)}\n\\end{center}\n\nFigure S3: Microstructure analysis of DED-AM SS316 samples from the imaging experiment. Optical microscope image of SS316L DED-AM microstructure from BAMPR experiment under $P=6.37$ $10^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}$, scanning speed $v=1.67 \\mathrm{~mm} \\mathrm{~s}^{-1}$. Scale bar $=250 \\mu \\mathrm{m}$; (A) cross-section of a ten layer thin wall build and the schematic of the cross-section direction is shown in (B). Scale bar $=1 \\mathrm{~mm}$. (C) Enlarged view of (A) showing microstructure of the third layer and the surrounding re-melt layer. Scale bar $=500 \\mu m$. (D) Enlarged view of (C) showing detailed microstructure of the melt track and re-melt area. Grain size is $\\sim 10 \\mu \\mathrm{m}$. Scale bar $=50 \\mu \\mathrm{m}$. (F) Cross-section along the build direction of the same sample and the schematic of the cross-section direction is shown in (E). Scale bar $=500 \\mu \\mathrm{m}$. (G) Enlarged view of $(\\mathrm{F})$ showing detailed microstructure of the melt track. Scale bar $=50 \\mu \\mathrm{m}$.", "start_char_idx": 524666, "end_char_idx": 527887, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5471900a-16b5-4428-a97e-722ec394ef6c": {"__data__": {"id_": "5471900a-16b5-4428-a97e-722ec394ef6c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e23028db-8f94-4bcd-b893-19ee7357ab81", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "fde6dd824a8a3dceb8dd9a26d6668ac2c028f030cfa1f893920f153789e40561", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7a2915c3-3081-4dab-b441-1a998a74b4fd", "node_type": "1", "metadata": {}, "hash": "dff036ae566eaa66e3d0b3917b0da9032aafea297f24c9a74eb8e909b57adb8d", "class_name": "RelatedNodeInfo"}}, "text": "Scale bar $=1 \\mathrm{~mm}$. (C) Enlarged view of (A) showing microstructure of the third layer and the surrounding re-melt layer. Scale bar $=500 \\mu m$. (D) Enlarged view of (C) showing detailed microstructure of the melt track and re-melt area. Grain size is $\\sim 10 \\mu \\mathrm{m}$. Scale bar $=50 \\mu \\mathrm{m}$. (F) Cross-section along the build direction of the same sample and the schematic of the cross-section direction is shown in (E). Scale bar $=500 \\mu \\mathrm{m}$. (G) Enlarged view of $(\\mathrm{F})$ showing detailed microstructure of the melt track. Scale bar $=50 \\mu \\mathrm{m}$. Elongated grains following the laser path can be observed.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_5dd08c8296f7c4d14504g-23}\n\n\\section*{Build direction}\nFigure S4: Microstructure analysis of DED-AM Ti6242 samples from the imaging experiments. EBSD images of SS316L DED-AM microstructure from BAMPR experiment under $P=1.59 \\quad 10^{3}$ $W m^{-2}, v=1 \\mathrm{~mm} \\mathrm{~s}^{-1}$. Cross-section along the build direction. Long columnar grains and small equiaxed grain in the re-melt area can be observed. Scale bar $=250 \\mu \\mathrm{m}$ and $100 \\mu \\mathrm{m}$ for normal view and expanded view, respectively.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5dd08c8296f7c4d14504g-24}\n\\end{center}\n\nFigure S5: Melt pool morphology of DED-AM from the imaging experiments. The melt pool area is defined as liquid and solid-liquid boundary is marked by observing the moving boundaries. A double melt pool sometimes can be observed showing moving porosity outside of the defined melt pool area during Ti6242 build, as shown in the radiograph revealed by local-temporal background subtraction. It is due to a concave shape at the bottom of the melt pool, as shown in the cross-section view of the post-mortem xCT scan. In Ti6242: (A) Post-mortem xCT cross-section shows the concave shape of the bottom of the melt pool. (B) Schematic shows the mechanism behind double melt pool under X-ray imaging. (C) 3D schematic shows the porosity in the double melt pool are sitting on the two edges of the concave melt pool edge. (D) Corresponding filtered radiograph shows the boundary of double melt pool and the porosity inside. In the contrary, the convex shape of the bottom of the melt pool in SS316 results in a single tear drop shape melt pool: (A) Post-mortem microstructure analysis reveal the convex shape of the bottom of the melt pool. (B) Schematic shows the mechanism behind single tear drop shape melt pool. (C) Corresponding radiograph.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5dd08c8296f7c4d14504g-25(1)}\n\\end{center}\n\nFigure S6: Porosity analysis in SS316. Optical microscope image of a cross-section of SS316 build. It reveals a gas entrapped pore embedded in the cellular colonies. $P=6.3710^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}, v=1.67$ $m m s^{-1}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5dd08c8296f7c4d14504g-25}\n\\end{center}\n\nFigure S7: Power agglomeration in Ti6242. Optical microscope image of a cross-section of SS316 build. It reveals a gas entrapped pore embedded in the cellular colonies. $P=1.5910^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}, v=1$ $m m s^{-1}$.", "start_char_idx": 527287, "end_char_idx": 530547, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7a2915c3-3081-4dab-b441-1a998a74b4fd": {"__data__": {"id_": "7a2915c3-3081-4dab-b441-1a998a74b4fd", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5471900a-16b5-4428-a97e-722ec394ef6c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "00eeb433aa9298ab6f20d3e9c70978401e50b2177b5279c67a17fe4a2990dced", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "310d1e8e-3d33-479e-9432-8d1265794e23", "node_type": "1", "metadata": {}, "hash": "1699d210365e162febe7fd67cad97d993f5d953a8f36bfe3139f6ca4e0a45547", "class_name": "RelatedNodeInfo"}}, "text": "Optical microscope image of a cross-section of SS316 build. It reveals a gas entrapped pore embedded in the cellular colonies. $P=6.3710^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}, v=1.67$ $m m s^{-1}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5dd08c8296f7c4d14504g-25}\n\\end{center}\n\nFigure S7: Power agglomeration in Ti6242. Optical microscope image of a cross-section of SS316 build. It reveals a gas entrapped pore embedded in the cellular colonies. $P=1.5910^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}, v=1$ $m m s^{-1}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5dd08c8296f7c4d14504g-26}\n\\end{center}\n\nFigure S8: Porosity and lack of fusion features in Ti6242. Micro-CT and SEM scans reveal (a) lack of fusion between layers, (b) sintered particles on top of the track, and (b) end of track pores. $P=1.59 \\quad 10^{3}$ $W \\mathrm{~mm}^{-2}, v=1 \\mathrm{~mm} \\mathrm{~s}^{-1}$. Scale bar $=1 \\mathrm{~mm}$.\n\n\\section*{3. Supplementary tables}\n\\begin{center}\n\\begin{tabular}{|l|l|l|l|l|l|l|l|l|}\n\\hline\n\\multicolumn{8}{|c|}{Powder material: SS316L} &  \\\\\n\\hline\nTest No.", "start_char_idx": 530015, "end_char_idx": 531121, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "310d1e8e-3d33-479e-9432-8d1265794e23": {"__data__": {"id_": "310d1e8e-3d33-479e-9432-8d1265794e23", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7a2915c3-3081-4dab-b441-1a998a74b4fd", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "83887f51f5fdd350772b56ff96c6eaa5f182f05a4c6d0265a848a0fd3439cb72", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0ab58cd3-588f-4c5c-8b23-7600f6043e84", "node_type": "1", "metadata": {}, "hash": "3d860e81ce50d5c9a0b71464c8abc720e6bf924689cf312b7bc67e4c874618d5", "class_name": "RelatedNodeInfo"}}, "text": "Micro-CT and SEM scans reveal (a) lack of fusion between layers, (b) sintered particles on top of the track, and (b) end of track pores. $P=1.59 \\quad 10^{3}$ $W \\mathrm{~mm}^{-2}, v=1 \\mathrm{~mm} \\mathrm{~s}^{-1}$. Scale bar $=1 \\mathrm{~mm}$.\n\n\\section*{3. Supplementary tables}\n\\begin{center}\n\\begin{tabular}{|l|l|l|l|l|l|l|l|l|}\n\\hline\n\\multicolumn{8}{|c|}{Powder material: SS316L} &  \\\\\n\\hline\nTest No. & \\begin{tabular}{l}\nSpot \\\\\nsize \\\\\n$(\\mu \\mathrm{m})$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nPower \\\\\n$(\\mathrm{W})$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nScan \\\\\nspeed \\\\\n$\\left(\\mathrm{mm} \\mathrm{s}^{-1}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nShield \\\\\ngas \\\\\nflowrate \\\\\n$\\left(\\mathrm{min}^{-1}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nCarrier \\\\\ngas \\\\\nflowrate \\\\\n$\\left(\\mathrm{min}^{-1}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nPowder \\\\\nfeedrate \\\\\n$\\left(\\mathrm{g} \\mathrm{min}^{-1}\\right)$ \\\\\n\\end{tabular} & Hatch & Camera \\\\\n\\hline\nSS1 & 200 & 200 & 1.67 & 6 & 6 & 5 & 1 & Miro \\\\\n\\hline\nSS2 & 200 & 200 & 1.67 & 6 & 6 & 5 & 1 & Miro \\\\\n\\hline\nSS3 & 200 & 200 & 1.67 & 6 & 6 & 5 & 1 & Miro \\\\\n\\hline\nSS4 & 200 & 200 & 1.67 & 6 & 6 & 5 & 1 & Miro \\\\\n\\hline\nSS5 & 200 & 200 & 10 & 6 & 6 & 5 & 1 & Miro \\\\\n\\hline\nSS6 & 200 & 200 & 5 & 6 & 6 & 5 & 1 & Miro \\\\\n\\hline\nSS7 & 200 & 200 & 3 & 6 & 6 & 5 & 1 & Miro \\\\\n\\hline\nSS8 & 200 & 200 & 1.67 & 8 & 6 & 5 & 1 & Miro \\\\\n\\hline\nSS9 & 200 & 200 & 1.67 & 0 & 8 & 5 & 1 & Miro \\\\\n\\hline\nSS10 & 200 & 200 & 1.67 & 6 & 2 & 5 & 1 & Miro \\\\\n\\hline\nSS11 & 200 & 200 & 1.67 & 6 & 6 & 3 & 1 & Miro \\\\\n\\hline\nSS12 & 200 & 200 & 1.67 & 6 & 6 & 3.5 & 1 & Miro \\\\\n\\hline\nSS13 & 200 & 200 & 1.67 & 6 & 6 & 6 & 1 & Miro \\\\\n\\hline\nSS14 & 200 & 200 & 1.67 & 6 & 6 & 7.5 & 1 & Miro \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable S1: Experimental list using SS316L Listed parameters including laser power, laser spot size, gas flow rate, powder feedrate and substrate traverse speed.\n\n\\begin{center}\n\\begin{tabular}{|l|l|l|l|l|l|l|l|l|}\n\\hline\n\\multicolumn{7}{|c|}{Powder material: Ti6242} &  &  \\\\\n\\hline\nTest No.", "start_char_idx": 530713, "end_char_idx": 532790, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0ab58cd3-588f-4c5c-8b23-7600f6043e84": {"__data__": {"id_": "0ab58cd3-588f-4c5c-8b23-7600f6043e84", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "310d1e8e-3d33-479e-9432-8d1265794e23", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b011dc56ed199d2bdf9c576f0ab75a3f86ecc63a637b385c9c1d6a2a2365af77", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "78fa1c53-d24c-4f40-8384-3f0d1d316d59", "node_type": "1", "metadata": {}, "hash": "2c720f5ecb030af731b00197913cdb2ac5cb5b83e00e144a9cbd07fc7b561922", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\begin{tabular}{|l|l|l|l|l|l|l|l|l|}\n\\hline\n\\multicolumn{7}{|c|}{Powder material: Ti6242} &  &  \\\\\n\\hline\nTest No. & \\begin{tabular}{l}\nSpot \\\\\nsize \\\\\n$(\\mu \\mathrm{m})$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nPower \\\\\n$(\\mathrm{W})$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nScan \\\\\nspeed \\\\\n$\\left(\\mathrm{mm} \\mathrm{s}^{-1}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nShield \\\\\ngas \\\\\nflowrate \\\\\n$\\left(\\mathrm{min}^{-1}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nCarrier \\\\\ngas \\\\\nflowrate \\\\\n$\\left(\\mathrm{min}^{-1}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nPowder \\\\\nfeedrate \\\\\n$\\left(\\mathrm{g} \\mathrm{min}^{-1}\\right)$ \\\\\n\\end{tabular} & Hatch & Camera \\\\\n\\hline\nTi1 & 200 & 200 & 1 & 6 & 6 & 0.25 & 1 & Edge \\\\\n\\hline\nTi2 & 200 & 200 & 1 & 6 & 6 & 1 & 1 & Edge \\\\\n\\hline\nTi3 & 400 & 200 & 0.5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi4 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi5 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi6 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi7 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi8 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi9 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi10 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi11 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi12 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi13 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi14 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\n &  &  &  &  &  & Continued on next page &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable S2- - continued from previous page\n\n\\begin{center}\n\\begin{tabular}{|l|l|l|l|l|l|l|l|l|}\n\\hline\nTi15 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi16 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi17 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi18 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi19 & 200 & 200 & 5 & 6 & 6 & 0.", "start_char_idx": 532661, "end_char_idx": 534607, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "78fa1c53-d24c-4f40-8384-3f0d1d316d59": {"__data__": {"id_": "78fa1c53-d24c-4f40-8384-3f0d1d316d59", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0ab58cd3-588f-4c5c-8b23-7600f6043e84", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "06e3f67a7928993b4248cca5a3b7934a2a29c03222d1710ff80d7c8847735395", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "aed3f5d5-018e-4324-b88d-0e54e3ba65b9", "node_type": "1", "metadata": {}, "hash": "ad969ce01f3f53401cdb0525a9e6425ec4497c8dd27167b5b58f10a86880dde9", "class_name": "RelatedNodeInfo"}}, "text": "125 & 1 & Miro \\\\\n\\hline\nTi16 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi17 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi18 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi19 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi20 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi21 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi22 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi23 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi24 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi25 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi26 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi27 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi28 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi29 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi30 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi31 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi32 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi33 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi34 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi35 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi36 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi37 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi38 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi39 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi40 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\n &  &  &  &  &  &  &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable S2:Experimental list using Ti6242. Listed parameters including laser power, laser spot size, gas flow rate, powder feedrate and substrate traverse speed.", "start_char_idx": 534375, "end_char_idx": 536072, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "aed3f5d5-018e-4324-b88d-0e54e3ba65b9": {"__data__": {"id_": "aed3f5d5-018e-4324-b88d-0e54e3ba65b9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "78fa1c53-d24c-4f40-8384-3f0d1d316d59", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "10b2402c29e515d2dcae7b944d2f94cf0f84a83f13e10cbde6a7756d44ad86b2", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "cd560d73-12e5-48d3-a58b-04796655a233", "node_type": "1", "metadata": {}, "hash": "8a82956eeb0d7223cf43a4e8efe921f4fae63437d0db17001e25aff82e5a518c", "class_name": "RelatedNodeInfo"}}, "text": "125 & 1 & Miro \\\\\n\\hline\nTi38 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi39 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\nTi40 & 200 & 200 & 5 & 6 & 6 & 0.125 & 1 & Miro \\\\\n\\hline\n &  &  &  &  &  &  &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable S2:Experimental list using Ti6242. Listed parameters including laser power, laser spot size, gas flow rate, powder feedrate and substrate traverse speed.\n\n\\begin{center}\n\\begin{tabular}{|l|l|l|l|l|l|l|}\n\\hline\n\\begin{tabular}{l}\nLaser \\\\\npower \\\\\n\\end{tabular} & \\begin{tabular}{l}\nSpot \\\\\nsize \\\\\n\\end{tabular} & \\begin{tabular}{l}\nPower den- \\\\\nsity \\\\\n\\end{tabular} & Scan speed & \\begin{tabular}{l}\nPowder \\\\\nfeedrate \\\\\n\\end{tabular} & \\begin{tabular}{l}\nEnergy \\\\\ndensity \\\\\n\\end{tabular} & References \\\\\n\\hline\n$(W)$ & $(\\mathrm{mm})$ & $\\left(\\mathrm{W} \\mathrm{mm}^{-2}\\right)$ & $\\left(\\mathrm{mm} \\mathrm{s}^{-1}\\right)$ & $\\left(\\mathrm{g} \\mathrm{s}^{-1}\\right)$ & $\\left(\\mathrm{J} \\mathrm{mm}^{-3}\\right)$ &  \\\\\n\\hline\n1400 & 3 & 198 & 16.6 & 0.23 & 19.40 & $(2)$ \\\\\n\\hline\n$130-210$ & 0.1 & $1655-2674$ & $300-1300$ &  & $33-233$ & $(3)$ \\\\\n\\hline\n2300,4000 &  &  & $8.5,23$ & $0.3,0.38$ & 81,66 & $(4)$ \\\\\n\\hline\n$100-3000$ &  &  & $5-20$ & $0.1-1$ & $2-150$ & $(5)$ \\\\\n\\hline\n$50-200$ & $0.2,0.4$ & $398-6366$ & $1-5$ & $0.017-0.16$ & $0.16-32$ & Our work \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable S3: Laser energy density and power density. Experimental parameters in comparison to literature.", "start_char_idx": 535651, "end_char_idx": 537133, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "cd560d73-12e5-48d3-a58b-04796655a233": {"__data__": {"id_": "cd560d73-12e5-48d3-a58b-04796655a233", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "aed3f5d5-018e-4324-b88d-0e54e3ba65b9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c17c806a6b534d0c109111d2eda44bea4572d35c237615b356a23e68d7b16ceb", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "005f7646-7601-4616-a9fd-07fc5440d839", "node_type": "1", "metadata": {}, "hash": "93056e9d59e29174722446143fb1c31b41d3477cc52dcdd8d69676212c429f78", "class_name": "RelatedNodeInfo"}}, "text": "Experimental parameters in comparison to literature.\n\n\\begin{center}\n\\begin{tabular}{|l|l|l|l|l|l|l|}\n\\hline\nMaterials & \\begin{tabular}{l}\nLaser \\\\\npower \\\\\n\\end{tabular} & \\begin{tabular}{l}\nScan \\\\\nspeed \\\\\n\\end{tabular} & \\begin{tabular}{l}\nPowder \\\\\nfeedrate \\\\\n\\end{tabular} & \\begin{tabular}{l}\nMelt pool \\\\\nvolume \\\\\n\\end{tabular} & \\begin{tabular}{l}\nMelt pool \\\\\nlength \\\\\n\\end{tabular} & \\begin{tabular}{l}\nMelt pool \\\\\ndepth \\\\\n\\end{tabular} \\\\\n\\cline { 2 - 7 }\n$\\left(\\mathrm{mm} \\mathrm{s}^{-1}\\right)$ & $\\left(g s^{-1}\\right)$ & $\\left(\\mathrm{mm}^{3}\\right)$ & $(\\mu \\mathrm{m})$ & $(\\mu \\mathrm{m})$ & $(\\mu \\mathrm{m})$ &  \\\\\n\\hline\n\\multirow{5}{*}{SS316L} & 100 & 1.67 & 5 & $0.65 \\pm 0.08$ & $1759 \\pm 13$ & $514 \\pm 5$ \\\\\n\\cline { 2 - 7 }\n & 150 & 1.67 & 5 & $1.41 \\pm 0.17$ & $2215 \\pm 17$ & $713 \\pm 4$ \\\\\n\\cline { 2 - 7 }\n & 200 & 1.67 & 5 & $1.64 \\pm 0.11$ & $2356 \\pm 11$ & $719 \\pm 6$ \\\\\n\\cline { 2 - 7 }\n & 200 & 3.3 & 5 & $0.61 \\pm 0.02$ & $1836 \\pm 9$ & $447 \\pm 3$ \\\\\n\\cline { 2 - 7 }\n & 200 & 5 & 5 & $0.49 \\pm 0.02$ & $1832 \\pm 8$ & $514 \\pm 3$ \\\\\n\\cline { 2 - 7 }\n & 200 & 1.67 & 3 & $0.85 \\pm 0.01$ & $2168 \\pm 3$ & $431 \\pm 2$ \\\\\n\\cline { 2 - 7 }\n & 200 & 1.67 & 7.5 & $4.8 \\pm 0.12$ & $3000 \\pm 41$ & $1187 \\pm 21$ \\\\\n\\hline\n & 100 & 1 & 1 & N/A & $148 \\pm 11$ & $27 \\pm 3$ \\\\\n\\cline { 2 - 7 }\n & 200 & 1 & 1 & N/A & $493 \\pm 18$ & $178 \\pm 5$ \\\\\n\\cline { 2 - 7 }\n & 200 & 2.5 & 1 & N/A & $351 \\pm 9$ & $18 \\pm 1$ \\\\\n\\cline { 2 - 7 }\n & 200 & 5 & 1 & N/A & $306 \\pm 32$ & $98 \\pm 6$ \\\\\n\\cline { 2 - 7 }\n & 200 & 1 & 0.5 & 2 &  & $189 \\pm 1$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable S4: Melt pool geometry measured from experiments. Melt pool volumes and profiles variation across powder feed-rate, laser power and traverse speed. Error is $S D$. SS316 melt pool is regarded as an elliptical-cap shape for the volume calculation. The melt pool length and depth of Ti6242 melt pool is measured as the bigger value from the double melt pool shape. Due to the complex melt pool shape of the TI6242, its volume is not calculated.\n\n\\section*{4. Supplementary movies}\nMovie S1 Time-resolved radiographs acquired during DED-AM at the start of a melt track on SS316.", "start_char_idx": 537081, "end_char_idx": 539279, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "005f7646-7601-4616-a9fd-07fc5440d839": {"__data__": {"id_": "005f7646-7601-4616-a9fd-07fc5440d839", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "cd560d73-12e5-48d3-a58b-04796655a233", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1b800562b9c4aef8cb03d5765ee41116d42e4149397a44a02e51a5435a3ded1d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "36429e29-d9c2-4ef5-bb46-908b08e5b38d", "node_type": "1", "metadata": {}, "hash": "5a9c106cbc5978b2a1eccf9592a478e33fd93786cd693d5309cd0089aaa84b14", "class_name": "RelatedNodeInfo"}}, "text": "Melt pool volumes and profiles variation across powder feed-rate, laser power and traverse speed. Error is $S D$. SS316 melt pool is regarded as an elliptical-cap shape for the volume calculation. The melt pool length and depth of Ti6242 melt pool is measured as the bigger value from the double melt pool shape. Due to the complex melt pool shape of the TI6242, its volume is not calculated.\n\n\\section*{4. Supplementary movies}\nMovie S1 Time-resolved radiographs acquired during DED-AM at the start of a melt track on SS316. SS316 build is under laser power density $P=6.3710^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}$, scanning speed $v=1.67$ $\\mathrm{mm} \\mathrm{s}^{-1}$, powder feedrate $3 \\mathrm{~g} \\mathrm{~min}^{-1}$, captured at $200 \\mathrm{fps}$. Experiment Number SS11.\n\nMovie S2 Time-resolved radiographs acquired during DED-AM at the start of a melt track on Ti6242. Ti6242 build is under $P=1.5910^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}, v=1 \\mathrm{~mm} \\mathrm{~s}^{-1}$, powder feedrate $1 \\mathrm{~g} \\mathrm{~min}^{-1}$, captured at 200 fps. Experiment Number Ti2.\n\nMovie S3 Time-series radiographs acquired during DED of a SS316 multi-layer build. SS316 build is under laser power density $P=6.3710^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}$, scanning speed $v=1.67 \\mathrm{~mm} \\mathrm{~s}^{-1}$, powder feedrate $3 \\mathrm{~g} \\mathrm{~min}^{-1}$, captured at $200 \\mathrm{fps}$. Experiment Number $S S 11$.\n\nMovie S4 Time-series radiographs acquired during DED of a Ti6242 multi-layer build. Ti6242\\\\\nbuild is under $P=1.5910^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}, v=1 \\mathrm{~mm} \\mathrm{~s}^{-1}$, powder feedrate $1 \\mathrm{~g} \\mathrm{~min}^{-1}$, captured at $200 \\mathrm{fps}$. Experiment Number Ti2.\n\nMovie S5 The initial establishment of a melt track at the onset of a build was captured to reveal the mechanism at laser powers of $50 \\mathrm{~W}, P=\\mathbf{1 . 5 9} \\mathbf{1 0}^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}$. Scanning speed $v=1.67 \\mathrm{~mm} \\mathrm{~s}^{-1}$, powder feedrate $3 \\mathrm{~g} \\mathrm{~min}^{-1}$, captured at $200 \\mathrm{fps}$. Experiment Number SS4.\n\nMovie S6 The initial establishment of a melt track at the onset of a build was captured to reveal the mechanism at laser powers of $100 \\mathrm{~W}, P=\\mathbf{3 . 1 8} \\mathbf{1 0}^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}$. Scanning speed $v=1.67 \\mathrm{~mm} \\mathrm{~s}^{-1}$, powder feedrate $3 \\mathrm{~g} \\mathrm{~min}^{-1}$, captured at $200 \\mathrm{fps}$. Experiment Number $S S 3$.\n\nMovie S7 The initial establishment of a melt track at the onset of a build was captured to reveal the mechanism at laser powers of $200 \\mathrm{~W}, P=\\mathbf{6 . 3 7} \\mathbf{1 0}^{3} \\mathrm{~W} \\mathrm{mm^{-2 }}$. Scanning speed $v=1.67 \\mathrm{~mm} \\mathrm{~s}^{-1}$, powder feedrate $3 \\mathrm{~g} \\mathrm{~min}^{-1}$, captured at $200 \\mathrm{fps}$. Experiment Number $S S 1$.", "start_char_idx": 538754, "end_char_idx": 541609, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "36429e29-d9c2-4ef5-bb46-908b08e5b38d": {"__data__": {"id_": "36429e29-d9c2-4ef5-bb46-908b08e5b38d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "005f7646-7601-4616-a9fd-07fc5440d839", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a112d1d09a7693abf6acf41fb45e1ca6d75f400e8142c41f4da3a7d1eb5182fd", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5f8cabdf-efab-49d7-bf95-19258075fbd7", "node_type": "1", "metadata": {}, "hash": "e3f1944d87776d2ed9ec3f2b4469934681d1a13ec3a020910b6abb87b76f2514", "class_name": "RelatedNodeInfo"}}, "text": "Experiment Number $S S 3$.\n\nMovie S7 The initial establishment of a melt track at the onset of a build was captured to reveal the mechanism at laser powers of $200 \\mathrm{~W}, P=\\mathbf{6 . 3 7} \\mathbf{1 0}^{3} \\mathrm{~W} \\mathrm{mm^{-2 }}$. Scanning speed $v=1.67 \\mathrm{~mm} \\mathrm{~s}^{-1}$, powder feedrate $3 \\mathrm{~g} \\mathrm{~min}^{-1}$, captured at $200 \\mathrm{fps}$. Experiment Number $S S 1$.\n\nMovie S8 The sintering phenomenon during DED-AM of Ti6242. The sintered layer thickness is more than three times the height of the melt track itself. $P=7.9610^{2} \\mathrm{~W} \\mathrm{~mm}^{-2}, v=1 \\mathrm{~mm} \\mathrm{~s}^{-1}$, powder feedrate $1 \\mathrm{~g} \\mathrm{~min}^{-1}$, captured at $200 \\mathrm{fps}$. Experiment Number Ti18.\n\nMovie S9 SS316: A pore appears to form via gas entrainment from agglomerated powder particles. A pore flow trajectory revealed on radiographs. SS316 build is under laser power density $P=$ $1.5910^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}$, scanning speed $v=1.67 \\mathrm{~mm} \\mathrm{~s}^{-1}$, powder feedrate $3 \\mathrm{~g} \\mathrm{~min}^{-1}$, captured at $200 \\mathrm{fps}$. Experiment Number $S S 11$.\n\nMovie S10 Ti6242: pores are shown being pushed along in the melt pool. SS316 build is under\n\nlaser power density $P=6.3710^{3} \\mathrm{~W} \\mathrm{~mm}^{-2}$, scanning speed $v=1.67 \\mathrm{~mm} \\mathrm{~s}^{-1}$, powder feedrate 3 $g \\mathrm{~min}^{-1}$, captured at $200 \\mathrm{fps}$. Experiment Number SS11.\n\n\\section*{References}\n\\begin{enumerate}\n  \\item C. L. A. Leung, S. Marussi, R. C. Atwood, M. Towrie, P. J. Withers, P. D. Lee, Nat. Commun. 9, $1-9(2019)$.\n\n  \\item Z. E. Tan, J. H. L. Pang, J. Kaminski, H. Pepin, Addit. Manuf. 25, 286-296 (2019).\n\n  \\item Z. A. Mierzejewska, Materials. 12, 2331 (2019).\n\n  \\item Z. Wang, T. A. Palmer, A. M. Beese, Acta Mater. 110, 226235 (2016).\n\n  \\item T. Debroy, H.L. Wei, J.S. Zuback, T. Mukherjee, J.W. Elmer, J.O. Milewski, A.M. Beese, A. Wilson-Heid, A. De, W. Zhang, Prog. Mater. Sci. 92, 112-224 (2018).\n\n\\end{enumerate}\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\n\\title{Understanding Crack Formation Mechanisms of Ti-48Al-2Cr-2Nb Single Tracks During Laser Powder Bed Fusion }", "start_char_idx": 541199, "end_char_idx": 543762, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5f8cabdf-efab-49d7-bf95-19258075fbd7": {"__data__": {"id_": "5f8cabdf-efab-49d7-bf95-19258075fbd7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "36429e29-d9c2-4ef5-bb46-908b08e5b38d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c6be657cc4dab9509939225978b456daef45c382938556927ab8348c0d5b1b80", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a722adc3-9450-46ca-9704-1aa9580bbb5f", "node_type": "1", "metadata": {}, "hash": "a6843e4bdfe45ed4cc104a0660f7d06fea9adde02821a577d5cd09373794c5f8", "class_name": "RelatedNodeInfo"}}, "text": "Mater. Sci. 92, 112-224 (2018).\n\n\\end{enumerate}\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\n\\title{Understanding Crack Formation Mechanisms of Ti-48Al-2Cr-2Nb Single Tracks During Laser Powder Bed Fusion }\n\n\n\\author{Seulbi Lee ${ }^{1}$ $\\cdot$ Jaewoong Kim ${ }^{1} \\cdot$ Jungho Choe $^{2}$ $\\cdot$ Seong-Woong Kim ${ }^{3}$. Jae-Keun Hong ${ }^{3} \\cdot$ Yoon Suk Choi ${ }^{10}$}\n\\date{}\n\n\n%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?]{%\n  \\if\\relax#1\\relax%\n    \\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n  \\else%\n    \\if?#1\\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n    \\else\\svfootnotetext[#1]{#2}\\fi%\n  \\fi\n}\n\n\\begin{document}\n\\maketitle\nReceived: 21 April 2020 / Accepted: 12 May 2020 / Published online: 2 June 2020\n\n(C) The Korean Institute of Metals and Materials 2020\n\n\\begin{abstract}\nThe crack formation mechanisms of $\\mathrm{Ti}-48 \\mathrm{Al}-2 \\mathrm{Cr}-2 \\mathrm{Nb}$ single tracks processed by laser powder bed fusion were extensively investigated in a wide range of laser powers and scan speeds. The crack patterns were categorized by their directionalities, which were parallel (longitudinal crack) and/or perpendicular (transverse crack) to the scan direction. For the representative process conditions of the keyhole, transition, and conduction modes, cracking behaviors were characterized by combining the fractography and the microstructural analysis. Further, thermal-mechanical finite element method simulations were performed to predict the distribution of temperatures and thermal stresses during the melt pool formation. On the basis of the combined results, the cracks formed in keyhole, transition, and conduction modes were clarified as a solidification crack and/or a thermal crack. In addition, the formation of these cracks was thoroughly understood in terms of thermal stresses and microstructural factors that affect the crack susceptibility. Finally, comprehensive mechanisms responsible for cracking of $\\mathrm{Ti}-48 \\mathrm{Al}-2 \\mathrm{Cr}-2 \\mathrm{Nb}$ single tracks under laser powder bed fusion were proposed for different process conditions (the keyhole, transition and conduction modes).", "start_char_idx": 543182, "end_char_idx": 546093, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a722adc3-9450-46ca-9704-1aa9580bbb5f": {"__data__": {"id_": "a722adc3-9450-46ca-9704-1aa9580bbb5f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5f8cabdf-efab-49d7-bf95-19258075fbd7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8c322893aa2f6131622de24ed74e546f0591125be40106b39302fd3f99ac9845", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0667cbbe-c3cb-4108-8bad-e5a354cb9701", "node_type": "1", "metadata": {}, "hash": "018fd1d8ec7d386b3bdd043b8a34fc6d6d2d8ac41725fe08d61235de664277d1", "class_name": "RelatedNodeInfo"}}, "text": "For the representative process conditions of the keyhole, transition, and conduction modes, cracking behaviors were characterized by combining the fractography and the microstructural analysis. Further, thermal-mechanical finite element method simulations were performed to predict the distribution of temperatures and thermal stresses during the melt pool formation. On the basis of the combined results, the cracks formed in keyhole, transition, and conduction modes were clarified as a solidification crack and/or a thermal crack. In addition, the formation of these cracks was thoroughly understood in terms of thermal stresses and microstructural factors that affect the crack susceptibility. Finally, comprehensive mechanisms responsible for cracking of $\\mathrm{Ti}-48 \\mathrm{Al}-2 \\mathrm{Cr}-2 \\mathrm{Nb}$ single tracks under laser powder bed fusion were proposed for different process conditions (the keyhole, transition and conduction modes).\n\\end{abstract}\n\nKeywords Additive manufacturing (AM) $\\cdot$ Titanium aluminide (TiAl) alloy $\\cdot$ Melt pool $\\cdot$ Crack formation $\\cdot$ Fractography $\\cdot$ Thermal stress\n\n\\section*{1 Introduction}\nTitanium aluminide (TiAl) alloys have been considered to be one of the most advanced structural materials in aerospace, automotive, and energy industries, due to their low density (in the range of $3.9-4.2 \\mathrm{~g} / \\mathrm{cm}^{3}$ ), superior mechanical properties such as elastic stiffness, strength and creep, and oxidation resistance up to $750{ }^{\\circ} \\mathrm{C}[1-5]$. However, the processing of TiAl alloys has been deemed challenging because of their intrinsically low plasticity at room temperature and poor hot formability. As an alternative method, additive manufacturing (AM) process has received attention to get over the processing drawbacks of TiAl alloys. The AM\n\\footnotetext{Yoon Suk Choi\n\n\\href{mailto:choiys@pusan.ac.kr}{choiys@pusan.ac.kr}\n\n1 School of Materials Science and Engineering, Pusan National University, Busan 46241, Republic of Korea\n\n2 3D Printing Materials Center, Korea Institute of Material Science (KIMS), Changwon 51508, Republic of Korea\n\n3 Titanium Alloys Department, Korea Institute of Material Science (KIMS), Changwon 51508, Republic of Korea\n}\n\nprocess offers many key benefits, that can alter the industrial paradigm in various fields as a tool-free, cost-efficient, and digital approach with short lead times [6]. It is noteworthy that the design freedom of the AM process [7] facilitates manufacturing of TiAl-alloy products with new concept designs, which are difficult to be produced using conventional methods but are required to improve the performance of these products in various industries.\n\nSecuring the reliability of additively manufactured TiAl alloys is still problematic because of their high crack susceptibility and $\\mathrm{Al}$ vaporization phenomena (especially in electron beam melting (EBM) process due to its vacuum environment). In particular, the high crack susceptibility of $\\mathrm{TiAl}$ alloys originates from the rapid solidification involved in the AM process as well as the intrinsic brittleness of TiAl alloys. The latter is attributed to intermetallic characteristics of TiAl alloys by an insufficient slip system, grain boundary weakness, restricted cross slip, difficulty in twinning, and so on. To overcome the problems associated with cracking, the majority of studies have employed the EBM process because it employs a high-temperature process using the preheated powder bed and offers low oxidation potential\\\\\nunder high-vacuum environment [8-12]. In the most EBM processes, the thermal stress accumulated during the AM process has been relieved through the preheating up to 1100 ${ }^{\\circ} \\mathrm{C}[8,9,12]$. In the laser metal deposition (LMD) technique, which is the earliest adopted AM process of TiAl alloys [13], cracks can be prevented by employing the local heating $[14,15]$ and preheating the substrate [16]. Sharman et al. [14] fabricated crack-free samples by defocusing the laser on the deposition plane. Thomas et al. [15] used a secondary heat source for performing the local preheating and partial post-heating. Even in the laser powder bed fusion (LPBF) process, known to be difficult to apply the preheating, an attempt was made to preheat the fabrication module (by the furnace integrated inside of the LPBF system) up to $450^{\\circ} \\mathrm{C}$ to avoid crack formation [17].", "start_char_idx": 545138, "end_char_idx": 549596, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0667cbbe-c3cb-4108-8bad-e5a354cb9701": {"__data__": {"id_": "0667cbbe-c3cb-4108-8bad-e5a354cb9701", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a722adc3-9450-46ca-9704-1aa9580bbb5f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6cbfea0711456b68c91cc853ddbe670ce4f675caa63dd660f67cb7b2f98c19f8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "e2a9006d-dc8d-4c59-9f86-c76901786ead", "node_type": "1", "metadata": {}, "hash": "4dc7a1f125efbf2a73389be1b7142391a68448ee6db3838874dcd6ca8e20379e", "class_name": "RelatedNodeInfo"}}, "text": "In the laser metal deposition (LMD) technique, which is the earliest adopted AM process of TiAl alloys [13], cracks can be prevented by employing the local heating $[14,15]$ and preheating the substrate [16]. Sharman et al. [14] fabricated crack-free samples by defocusing the laser on the deposition plane. Thomas et al. [15] used a secondary heat source for performing the local preheating and partial post-heating. Even in the laser powder bed fusion (LPBF) process, known to be difficult to apply the preheating, an attempt was made to preheat the fabrication module (by the furnace integrated inside of the LPBF system) up to $450^{\\circ} \\mathrm{C}$ to avoid crack formation [17].\n\nEven though it is well known that the preheating is necessary to prevent cracking in the AM process of TiAl alloys; the fundamental analysis to understand the crack formation mechanisms has not been established (i.e. amount of the heat required to prevent cracks under different process conditions, quantitative evaluation of the cracks, elucidation of crack formation mechanisms depending on solidification conditions or process conditions, and so on). In the welding process of TiAl alloys, which has similar sequences as those in the AM process in terms of melting and solidification, crack formation mechanisms were reported in previous studies [18-20]. These studies suggested that crack formation is related to the brittleness of the $\\alpha_{2}$ phase, which is a hightemperature phase, but stabilized even at room temperature because of rapid cooling. Therefore, the cracking during the welding of TiAl alloys can be avoided by the formation of relatively ductile microstructures (such as $\\gamma$ grains and $\\gamma / \\alpha_{2}$ lamellar structures) by decomposing the $\\alpha_{2}$ phase via the preheating [19,21], the secondary heat source [18], and the control of the interpass temperature [20].\n\nHowever, the cracking mechanisms of the AM process are somewhat different from those of welding process; this is because the AM process is accompanied by severe heating, solidification and cooling in milliseconds at a microscale. Recently, numerous studies have been conducted to understand the crack formation mechanisms during the AM process. The majority of these studies were conducted on Ni-based superalloys by using the EBM [22] and LMD [23-25] processes. Although the cracking mechanisms were identified as solidification cracking [22, 24, 25], liquation cracking [23], and ductility dip cracking [23], these results suggested that the microstructural factors affecting the crack susceptibility were the misorientation angle and grain morphology. For tungsten and its alloys, which are one of the brittle materials used in the AM process, the cracks were attributed to the residual stress in combination with the ductile-to-brittle transition (DBT) [26]. Vrancken et al. [26, 27] conducted in-situ monitoring to capture the exact moment of the crack initiation during the LPBF process. Wang et al. [27] analyzed the crack patterns in multi-layered samples, showing the crack propagation along the grain boundaries. Recently, Gao et al. [28] established the cracking mechanism of TiAl alloy (Ti-40Al-9V-0.5Y) via the LPBF process by comparing the cooling rates and the resultant phase transformation depending on scan speeds. However, their study was conducted for multi-layered deposited samples, which involve the indirect heating effect [29] (i.e. re-melting and reheating), thereby rendering it difficult to identify the cause of crack formation. Although the AM process is composed of multi-layer depositions, understanding the crack behaviors through single track analysis is needed since the crack formation, especially for brittle materials, is closely related with the process parameters and resultant microstructure evolution during the melt pool formation [26, 27].\n\nIn this study, single tracks in a wide range of LPBF process conditions were comprehensively analyzed for understanding the crack formation mechanisms as a function of the process parameters. Accordingly, single tracks were intentionally generated without preheating to clarify the cracking behavior in their virgin states. The crack formation behavior was experimentally and computationally analyzed to investigate the nature of crack occurrence in the melt pool scale and to predict the distributions of temperature and thermal stresses. The results obtained herein assist our understanding of the cracking behavior in terms of microstructure evolution and its susceptibility to thermal stress during the melt pool formation.", "start_char_idx": 548910, "end_char_idx": 553520, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "e2a9006d-dc8d-4c59-9f86-c76901786ead": {"__data__": {"id_": "e2a9006d-dc8d-4c59-9f86-c76901786ead", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0667cbbe-c3cb-4108-8bad-e5a354cb9701", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "12e75cd86a7c9152853d0b351814525e92bd4c420555ca9b80dca5018446b54a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7f103f70-ae3c-424e-83a4-6afd5d4e6e3a", "node_type": "1", "metadata": {}, "hash": "cd71d1f4ba33925b0c85b1e53f9c05a6118e461f717d11781548993320380629", "class_name": "RelatedNodeInfo"}}, "text": "re-melting and reheating), thereby rendering it difficult to identify the cause of crack formation. Although the AM process is composed of multi-layer depositions, understanding the crack behaviors through single track analysis is needed since the crack formation, especially for brittle materials, is closely related with the process parameters and resultant microstructure evolution during the melt pool formation [26, 27].\n\nIn this study, single tracks in a wide range of LPBF process conditions were comprehensively analyzed for understanding the crack formation mechanisms as a function of the process parameters. Accordingly, single tracks were intentionally generated without preheating to clarify the cracking behavior in their virgin states. The crack formation behavior was experimentally and computationally analyzed to investigate the nature of crack occurrence in the melt pool scale and to predict the distributions of temperature and thermal stresses. The results obtained herein assist our understanding of the cracking behavior in terms of microstructure evolution and its susceptibility to thermal stress during the melt pool formation.\n\n\\section*{2 Experimental and Numerical Analysis}\nThe nominal compositions of the substrate and the powders used in this study are $\\mathrm{Ti}-48 \\mathrm{Al}-2 \\mathrm{Cr}-2 \\mathrm{Nb}$ and $\\mathrm{Ti}-49 \\mathrm{Al}-2 \\mathrm{Cr}-2 \\mathrm{Nb}$ (in at\\%), respectively. Considering the $\\mathrm{Al}$ losses during the laser irradiations, powders were designed to have additional 1 at $\\% \\mathrm{Al}$ as compared to the target compositions (Ti-48Al-2Cr-2Nb) [30]. As shown in Fig. 1a, b, pre-alloyed spherical powders (supplied by ATI Specialty Materials, Ltd.) were used to fabricate single tracks, having a mean size of $31 \\mu \\mathrm{m}$ and the powder size distribution of 15 $\\mu \\mathrm{m}\\left(\\mathrm{D}_{10}\\right), 32 \\mu \\mathrm{m}\\left(\\mathrm{D}_{50}\\right)$, and $46 \\mu \\mathrm{m}\\left(\\mathrm{D}_{90}\\right)$. The substrate with a thickness of $12 \\mathrm{~mm}$ was cut from the vacuum pressurized cast product. Figure 1c shows the fully lamellar microstructures of the substrate, which are the typical microstructure of TiAl alloys composed of $\\alpha_{2} / \\gamma$ constituents.\n\nThe LPBF system used in this study was the Mlab-Cusing system (Concept laser $\\mathrm{GmbH}$ ), which was equipped with a maximum laser power of $100 \\mathrm{~W}$. As shown in Table 1, the LPBF process window was set under the range of laser powers (from 50 to $95 \\mathrm{~W}$ in the steps of $15 \\mathrm{~W}$ ) and scan speeds (from 200 to $1000 \\mathrm{~mm} / \\mathrm{s}$ in the steps of $200 \\mathrm{~mm} / \\mathrm{s}$ ) with the\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-03}\n\nFig. 1 a SEM image and $\\mathbf{b}$ particle size distribution of $\\mathrm{Ti}-49 \\mathrm{Al}-2 \\mathrm{Cr}-2 \\mathrm{Nb}$ powders and $\\mathbf{c}$ backscattered electron SEM image of Ti-48Al-2Cr$2 \\mathrm{Nb}$ substrate, showing a fully lamellar microstructure with $\\boldsymbol{\\alpha}_{2} / \\gamma$ phases\n\nTable 1 LPBF process parameters for $\\mathrm{Ti}-48 \\mathrm{Al}-2 \\mathrm{Cr}-2 \\mathrm{Nb}$ single tracks\n\n\\begin{center}\n\\begin{tabular}{ll}\n\\hline\nProcessing parameter & Value \\\\\n\\hline\nPower $(\\mathrm{W})$ & $50,65,80,95$ \\\\\nScan speed $(\\mathrm{mm} / \\mathrm{s})$ & $200,400,600,800,1000$ \\\\\nBeam diameter $(\\mu \\mathrm{m})$ & 50 \\\\\nPowder layer thickness $(\\mu \\mathrm{m})$ & 50 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nlayer thickness of $50 \\mu \\mathrm{m}$. Single tracks were deposited along a rectangular path $(5 \\mathrm{~mm} \\times 35 \\mathrm{~mm})$ for 20 combinations of laser powers and scan speeds.", "start_char_idx": 552366, "end_char_idx": 556066, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7f103f70-ae3c-424e-83a4-6afd5d4e6e3a": {"__data__": {"id_": "7f103f70-ae3c-424e-83a4-6afd5d4e6e3a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e2a9006d-dc8d-4c59-9f86-c76901786ead", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f4a121aca3715dbba3a21b1c699f18ee935b286a08664a38ad8abf6918b36b2a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "8cbfb0c2-9591-4d01-8fc3-24299ed802c7", "node_type": "1", "metadata": {}, "hash": "acaffd37e71ccd780595f9dc4cba43f9178e927751ee557049a068a4e995bb90", "class_name": "RelatedNodeInfo"}}, "text": "Single tracks were deposited along a rectangular path $(5 \\mathrm{~mm} \\times 35 \\mathrm{~mm})$ for 20 combinations of laser powers and scan speeds. All processes were performed at room temperature in an inert argon atmosphere.\n\nMicrostructures were prepared at the cross-sections in the middle of the $35-\\mathrm{mm}$ long single tracks. The cross-sections were polished down to a $0.04-\\mu \\mathrm{m}$ finish using colloidal silica, and then analyzed by employing an optical microscope (OM) and scanning electron microscope (SEM) that was equipped with electron backscatter diffraction (EBSD). Here, melt pool geometries, such as width and depth, were measured for all single tracks via image analysis, and these values were used to calibrate the laser penetration depth $\\left(d_{p}\\right)$ and absorptivity $(A)$ for performing the finite element method (FEM) based thermal analysis [31].\n\nIn order to identify the crack patterns, single track surfaces were observed using the focus-variation $\\mathrm{OM}$. The crack patterns were categorized with respect to the scan direction (SD). The cracks parallel and perpendicular to the SD were defined as longitudinal crack (L-crack) and transverse crack (T-crack), respectively. To quantify the $\\mathrm{T}$-cracking frequency, an average $\\mathrm{T}$-crack spacing was determined from more than $30 \\mathrm{~T}$-crack spacings measured along the single track. To observe the morphologies of the crack surfaces generated under different LPBF conditions ( $80 \\mathrm{~W}-200,600$ and $1000 \\mathrm{~mm} / \\mathrm{s}$ ), the substrate deposited with single tracks was cut into $2.5 \\mathrm{~mm}$-thick plates. For each plate, the cracks and their surfaces in the single track were carefully located and delicately retrieved by thinning the plate through manual polishing of the bottom face (the other side of the surface with the single track) of the plate until the plate automatically fell apart due to the presence of cracks. Subsequently, fractorgraphy was performed using the SEM by observing the crack surfaces from those thinned\\\\\npieces in order to identify the crack type and crack initiation and propagation and to understand the nature and cause of the cracks. To the authors' knowledge, it is the first time to observe crack surfaces of $\\mathrm{Ti}-48 \\mathrm{Al}-2 \\mathrm{Cr}-2 \\mathrm{Nb}$ single tracks processed by different LPBF conditions. Here, cracks were classified as L- and T-cracks by their directionalities, and as solidification and thermal cracks by the nature of their occurrence. A solidification crack can be categorized as a crack formed at the last moment of the solidification process due to the lack of liquid feeding along the micro-scale paths of the last solidification [32]. Its surface can be typified as an intact morphology of last solidification structures. A thermal crack can be defined as a crack formed by thermal stresses in the solid state. For brittle intermetallic materials, like TiAl alloys, thermal cracking typically occurs at temperatures below the ductile-brittle transition temperature (DBTT), and exhibits cleavage-type fracture surfaces.\n\nFEM simulations for the weakly coupled thermo-mechanical analysis were performed using a commercial FEM solver, ABAQUS ${ }^{\\text {TM }}$ for the conditions of $80 \\mathrm{~W}-200,600$, and $1000 \\mathrm{~mm} / \\mathrm{s}$. In the FE model, the dimensions of the substrate and the powder bed were designed to be $1000 \\times 500 \\times$ $1000 \\mu^{3}$ and $1000 \\times 500 \\times 50 \\mu \\mathrm{m}^{3}$, respectively, as shown in Fig. 2a. In Fig. 2a, uniform fine meshes were applied for the powder bed, compared to coarse gradient meshes for the surrounding substrate. Herein, the number of elements for the powder bed was set to be $80 \\times 40 \\times 4$ along the $x$-, $y$-, and $\\mathrm{z}$ - axes, respectively.\n\nAs shown in Fig. 2b, the Goldak heat source Q model [33] was used to simulate a heat input as a double ellipsoidal heat source model.", "start_char_idx": 555918, "end_char_idx": 559920, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "8cbfb0c2-9591-4d01-8fc3-24299ed802c7": {"__data__": {"id_": "8cbfb0c2-9591-4d01-8fc3-24299ed802c7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7f103f70-ae3c-424e-83a4-6afd5d4e6e3a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c1a80ea23b67c45d5f88f5c62529d228a1b4ea6783b9b688b35df1f08bf2e83e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7fdba35a-8f90-4966-b0ca-f2c210696656", "node_type": "1", "metadata": {}, "hash": "622db89ec6cacd1c3d6bbd0b0ce76e17e1042023d00c5ce9e9c3809388be1df9", "class_name": "RelatedNodeInfo"}}, "text": "In the FE model, the dimensions of the substrate and the powder bed were designed to be $1000 \\times 500 \\times$ $1000 \\mu^{3}$ and $1000 \\times 500 \\times 50 \\mu \\mathrm{m}^{3}$, respectively, as shown in Fig. 2a. In Fig. 2a, uniform fine meshes were applied for the powder bed, compared to coarse gradient meshes for the surrounding substrate. Herein, the number of elements for the powder bed was set to be $80 \\times 40 \\times 4$ along the $x$-, $y$-, and $\\mathrm{z}$ - axes, respectively.\n\nAs shown in Fig. 2b, the Goldak heat source Q model [33] was used to simulate a heat input as a double ellipsoidal heat source model. The following equations were used:\n\n$\\mathrm{Q}=\\mathrm{P} \\cdot \\mathrm{A}$\n\n$Q_{f}(\\mathrm{x}, \\mathrm{y}, \\mathrm{z})=\\frac{6 \\sqrt{3} f_{f} P}{a_{f} b c \\pi \\sqrt{\\pi}} \\exp ^{-\\left[\\frac{3 x^{2}}{a_{f}^{2}}+\\frac{3 y^{2}}{b^{2}}+\\frac{3 z^{2}}{c^{2}}\\right]}$\n\n$Q_{r}(\\mathrm{x}, \\mathrm{y}, \\mathrm{z})=\\frac{6 \\sqrt{3} f_{r} P}{a_{r} b c \\pi \\sqrt{\\pi}} \\exp ^{-\\left[\\frac{3 x^{2}}{a_{r}{ }^{2}}+\\frac{3 y^{2}}{b^{2}}+\\frac{3 z^{2}}{c^{2}}\\right]}$\n\nIn Eqs. (1)-(3), $\\mathrm{Q}$ is the heat flux ( $\\mathrm{J} / \\mathrm{ms}), P$ is the input laser power and $\\mathrm{A}$ is the laser absorptivity, determining a fraction of the input power actually absorbed by the powder bed and substrate. Also, $Q_{f}$ and $Q_{r}$ are the heat flux located in the front and rear section of the ellipsoid heat source, respectively, and $f_{f}$ and $f_{r}$ are the proportion coefficients\\\\\nFig. 2 a Finite element mesh model and $\\mathbf{b}$ schematic illustration of Goldak heat source model used in FEM analysis. Here, the temperature contour at $80 \\mathrm{~W}-600 \\mathrm{~mm} / \\mathrm{s}$ is shown in a, captured in the middle of the FEM simulation.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-04(1)}\n\\end{center}\n\n(b)\n\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-04}\\\\\nrepresenting heat apportionment in the front and rear sections of the heat source $\\left(f_{f}+f_{r}=2\\right)$. Here, $f_{f}$ and $f_{r}$ were set as 0.6 and 1.4, respectively, by adopting the values used in [33]. Also, x, y, and $\\mathrm{z}$ are the local coordinates; $a_{f}, a_{r}, \\mathrm{~b}$, and $c$ are the parameters defining the three dimensional shape of the heat source (see Fig. 2b). For the current simulations, $a_{f}$, $a_{r}$, and $\\mathrm{b}$ were set as $25 \\mu \\mathrm{m}, 50 \\mu \\mathrm{m}$ and $25 \\mu \\mathrm{m}$, respectively, and $c$ corresponds to the laser penetration depth $\\left(d_{p}\\right)$. Here, note that $d_{p}$ and $\\mathrm{A}$ values were calibrated using an algorithm proposed by the authors in the previous study [31] to depict the actual melt pool dimension under different process conditions.", "start_char_idx": 559291, "end_char_idx": 562106, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7fdba35a-8f90-4966-b0ca-f2c210696656": {"__data__": {"id_": "7fdba35a-8f90-4966-b0ca-f2c210696656", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8cbfb0c2-9591-4d01-8fc3-24299ed802c7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6d7933ad36fbf344634890a913fc749eceaa3298adf613a5ada2e3af1d11e8de", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9c8fc250-d695-4074-aede-44f2415b0ed8", "node_type": "1", "metadata": {}, "hash": "468ed204c7b3c67ef314b0d05802a35f7b0d91ec281b692fe5c8fa6bdd4c5255", "class_name": "RelatedNodeInfo"}}, "text": "Also, x, y, and $\\mathrm{z}$ are the local coordinates; $a_{f}, a_{r}, \\mathrm{~b}$, and $c$ are the parameters defining the three dimensional shape of the heat source (see Fig. 2b). For the current simulations, $a_{f}$, $a_{r}$, and $\\mathrm{b}$ were set as $25 \\mu \\mathrm{m}, 50 \\mu \\mathrm{m}$ and $25 \\mu \\mathrm{m}$, respectively, and $c$ corresponds to the laser penetration depth $\\left(d_{p}\\right)$. Here, note that $d_{p}$ and $\\mathrm{A}$ values were calibrated using an algorithm proposed by the authors in the previous study [31] to depict the actual melt pool dimension under different process conditions. In the present study, $d_{p}$ and A values for 200, 600, and $1000 \\mathrm{~mm} / \\mathrm{s}$ at $80 \\mathrm{~W}$ were calibrated to be 405,205 , and $130 \\mu \\mathrm{m}$ and $0.7,0.7$, and 0.6 , respectively. The heat source was set to move along the $\\mathrm{x}$-axis for a distance of $800 \\mu \\mathrm{m}$. The initial temperature was set $30^{\\circ} \\mathrm{C}$, and the convection and radiation were neglected because the primary heat transfer mode was conduction and heating time was relatively short [34]. The temperature-dependent thermal properties (including the density) and mechanical properties for the TiAl alloy were taken from previous studies $[35,36]$ and are listed in Tables 2 and 3, respectively. Also, the latent heat effect was accounted for during melting and solidification. The thermal conductivity in the powder bed was set as $1 \\%$ of that of the substrate, which was adopted from an analytical result done in [37]. For the simulation, the nodal constraint of substrate edges was applied at the bottom face. Thermal stresses were predicted during the melt pool formation based on the temperature fields, which were obtained in the thermal analysis.\n\n\\section*{3 Results and Discussion}\nFigure 3 shows the metallographs of the melt pool crosssections in the power-scan speed process window. The melt pool width-to-depth ratio $(\\mathrm{R})$ and the energy density $\\left(E_{\\rho}\\right)$, which is expressed by $E_{\\rho}=\\frac{P}{v \\cdot t}\\left(\\mathrm{~J} / \\mathrm{mm}^{2}\\right)$, where $P, v$ and $t$ are the laser power, scan speed, and thickness of the powder bed, were provided in the bottom right and bottom left\\\\\nTable 3 Mechanical properties used in thermal-mechanical FEM simulations $[35,36,38]$\n\n\\begin{center}\n\\begin{tabular}{lllll}\n\\hline\n\\begin{tabular}{l}\nTem- \\\\\nperature \\\\\n$\\left({ }^{\\circ} \\mathrm{C}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nYoung's \\\\\nmodulus \\\\\n$(\\mathrm{GPa})$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nYield \\\\\nstrength $(\\mathrm{N} /$ \\\\\n$\\left.\\mathrm{mm}^{2}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nThermal \\\\\nexpansion \\\\\n$\\left(10^{-6} /{ }^{\\circ} \\mathrm{C}\\right)$ \\\\\n\\end{tabular} & Poisson's ratio \\\\\n\\hline\n25 & 172 & 359 & 11.0 & 0.22 \\\\\n150 & - & - & 11.7 & 0.22 \\\\\n300 & 162 & 358 & 12.3 & 0.22 \\\\\n450 & - & - & - & - \\\\\n600 & 153 & - & - & - \\\\\n900 & - & 259 & 15.0 & - \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nof each micrograph in Fig. 3, respectively.", "start_char_idx": 561486, "end_char_idx": 564553, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9c8fc250-d695-4074-aede-44f2415b0ed8": {"__data__": {"id_": "9c8fc250-d695-4074-aede-44f2415b0ed8", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7fdba35a-8f90-4966-b0ca-f2c210696656", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6d37598e8dab2c9debd5c3dbce498a038edc959af16f342670f334c5a017e655", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9a883803-5e32-4f93-a1f7-e2bd954c21d8", "node_type": "1", "metadata": {}, "hash": "46595ce8b6f862c9e5f0d4d866a9ca48e8c1dfe19d90fe404958e101c2bf413f", "class_name": "RelatedNodeInfo"}}, "text": "3, respectively. The melt pool geometries changed from conduction $(R \\leq 0.5)$ to transition $(0.5<\\mathrm{R} \\leq 1.0)$ and then keyhole $(\\mathrm{R}>1.0)$ modes, with increasing energy density $\\left(E_{\\rho}\\right)$. This confirms that single tracks in this study were generated in a variety of melt pool modes. In particular, deep cracks were observed in the high $E_{\\rho}$ domain (i.e., $95 \\mathrm{~W}-200 \\mathrm{~mm} / \\mathrm{s}, 80 \\mathrm{~W}-200 \\mathrm{~mm} / \\mathrm{s}$, and 65 $\\mathrm{W}-200 \\mathrm{~mm} / \\mathrm{s}$ ) and found to be vertically penetrating across the melt pool.\n\nIn Fig. 4, surface images of single tracks show various cracking behaviors. It can be seen that the cracks were formed for all process conditions. In particular, two types of cracks, L-crack and T-crack, were observed in the present process window, as indicated by the arrows in Fig. 4. Here, L-cracks were formed in the high $E_{\\rho}$ domain ( $95 \\mathrm{~W}$-200 and $400 \\mathrm{~mm} / \\mathrm{s}, 80 \\mathrm{~W}-200 \\mathrm{~mm} / \\mathrm{s}$, and $65 \\mathrm{~W}-200 \\mathrm{~mm} / \\mathrm{s}$ ), revealing the crack propagation along the centerline of the single track. On the other hand, T-cracks were observed for all process conditions. In the high $E_{\\rho}$ domain, T-cracks tended to cross the single track asymmetrically depending on the presence of L-cracks. In the low $E_{\\rho}$ domain, however, T-cracks tended to completely cross the single track.\n\nThe surfaces of L- and T-cracks observed in the single tracks at $80 \\mathrm{~W}-200,600$, and $1000 \\mathrm{~mm} / \\mathrm{s}$ conditions (keyhole, transition, and conduction modes, respectively) were presented in Figs. 5 and 6. Figure 5 shows the surfaces of a L-crack and a T-crack observed at $80 \\mathrm{~W}-200 \\mathrm{~mm} / \\mathrm{s}$\n\nTable 2 Thermal properties used in thermal-mechanical FEM simulations [35, 36, 38]\n\n\\begin{center}\n\\begin{tabular}{lllllll}\n\\hline\n\\begin{tabular}{l}\nTemperature \\\\\n$\\left({ }^{\\circ} \\mathrm{C}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nDensity \\\\\n$\\left(\\mathrm{Kg} / \\mathrm{m}^{3}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nSpecific heat \\\\\n$\\left(\\mathrm{J} / \\mathrm{Kg}{ }^{\\circ} \\mathrm{C}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nThermal conduc- \\\\\ntivity $\\left(\\mathrm{W} / \\mathrm{m}{ }^{\\circ} \\mathrm{C}\\right)$ \\\\\n\\end{tabular} & Solidus temperature $\\left({ }^{\\circ} \\mathrm{C}\\right)$ & Liquidus temperature $\\left({ }^{\\circ} \\mathrm{C}\\right)$ & Latent heat $(\\mathrm{kJ} / \\mathrm{Kg})$ \\\\\n\\hline\n25 & 3900 & 610 & 10.5 & 1457 & 1522 & 380 \\\\\n127 & - & 635 & - &  &  &  \\\\\n327 & 3879 & - & 21.0 &  &  &  \\\\\n527 & - & 695 & - & - &  &  \\\\\n727 & 3853 & - & - & 28.0 &  &  \\\\\n927 & 3840 & - & 770 & - &  &  \\\\\n1457 &  &  &  &  &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nFig. 3 Metallographs showing melt pool geometries under different laser powers and scan speeds.", "start_char_idx": 564537, "end_char_idx": 567450, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9a883803-5e32-4f93-a1f7-e2bd954c21d8": {"__data__": {"id_": "9a883803-5e32-4f93-a1f7-e2bd954c21d8", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9c8fc250-d695-4074-aede-44f2415b0ed8", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2c7824e7559736a4f2d0ad0e1e5dbddca1ae571328bb769e9f117109bbbeae5d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "360d644c-d2cf-4838-a24c-6bc0597d44de", "node_type": "1", "metadata": {}, "hash": "24a47f4bb1029da0ba005704b4b8bda97b530087843803782fdb8453cc96b877", "class_name": "RelatedNodeInfo"}}, "text": "3 Metallographs showing melt pool geometries under different laser powers and scan speeds. Melt pool boundaries are outlined by the yellow dashed line, and R and $\\boldsymbol{E}_{\\rho}(\\mathrm{J} /$ $\\mathrm{mm}^{2}$ ) values are provided in the bottom right and bottom left of each micrograph, respectively. (Color figure online)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-06(7)}\n\\end{center}\n\n(a) L-crack\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-06(6)}\n\n(c) L-crack\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-06(2)}\n\n$600 \\mathrm{~mm} / \\mathrm{s}$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-06(9)}\n\\end{center}\n\n$800 \\mathrm{~mm} / \\mathrm{s}$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-06(1)}\n\n(b) L-crack\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-06(4)}\n\\end{center}\n\n(d)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-06(5)}\n\\end{center}\n\n$200 \\mathrm{~mm} / \\mathrm{s}$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-06(3)}\n\\end{center}\n\n$400 \\mathrm{~mm} / \\mathrm{s}$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-06(8)}\n\\end{center}\n\n$600 \\mathrm{~mm} / \\mathrm{s}$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-06}\n\\end{center}\n\n$800 \\mathrm{~mm} / \\mathrm{s}$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-06(10)}\n\\end{center}\n\nFig. 4 Surface images showing crack patterns under different scan speeds at a $95 \\mathrm{~W}$, b $80 \\mathrm{~W}$, c $65 \\mathrm{~W}$, and d $50 \\mathrm{~W}$\n\n(keyhole mode). Using the delicate manual polishing technique described in the previous section, we were able to safely retrieve the surfaces of both L- and T-cracks at the same time, as shown in Fig. 5a. Figure 5b is the front view of the L-crack surface in Fig. 5a. In Fig.5b, the L-crack was found to be a typical solidification crack, which shows inter-columnar crack propagations across the region. In the middle of Fig. 5b, horizontal topology transition (indicated by the dashed line) was observed due to the change of the solidification direction. Figure $5 \\mathrm{c}, \\mathrm{d}$ are the magnified fractographs from the upper part and lower part of the L-crack surfaces of Fig. 5b, respectively, separated\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-07(3)}\n\nFig.", "start_char_idx": 567360, "end_char_idx": 570033, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "360d644c-d2cf-4838-a24c-6bc0597d44de": {"__data__": {"id_": "360d644c-d2cf-4838-a24c-6bc0597d44de", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9a883803-5e32-4f93-a1f7-e2bd954c21d8", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2a74a63f15167607ccf428a912118a17038e725b76698b16131e243a2669a8db", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "723ce465-d7ca-4075-821d-3b786788c564", "node_type": "1", "metadata": {}, "hash": "fba964086cef859ad83ea5e3e8c00049d9b95f9ee0f29e31836f2f576d6d03fb", "class_name": "RelatedNodeInfo"}}, "text": "5a. Figure 5b is the front view of the L-crack surface in Fig. 5a. In Fig.5b, the L-crack was found to be a typical solidification crack, which shows inter-columnar crack propagations across the region. In the middle of Fig. 5b, horizontal topology transition (indicated by the dashed line) was observed due to the change of the solidification direction. Figure $5 \\mathrm{c}, \\mathrm{d}$ are the magnified fractographs from the upper part and lower part of the L-crack surfaces of Fig. 5b, respectively, separated\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-07(3)}\n\nFig. 5 a SEM image showing the L- and T-cracks formed in the single track at $80 \\mathrm{~W}-200 \\mathrm{~mm} / \\mathrm{s}$ (keyhole mode); b a front view of the L-crack surface in a; $\\mathbf{c}$ a magnified view of the upper part of the\\\\\nL-crack surface in $\\mathbf{b}$; d a magnified view of the lower part of the L-crack surface in $\\mathbf{b} ; \\mathbf{e}$ a magnified view of the T-crack surface in $\\mathbf{a}$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-07}\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-07(2)}\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-07(1)}\n\nFig. 6 SEM images showing T-cracks at a $80 \\mathrm{~W}-600 \\mathrm{~mm} / \\mathrm{s}$ (transition mode) and $\\mathbf{d} 80 \\mathrm{~W}-1000 \\mathrm{~mm} / \\mathrm{s}$ (conduction mode). b, c, and e, f are the magnified crack surfaces from a and $\\mathbf{d}$, respectively\n\nby the transition line. It can be seen that the solidification direction, viz. the direction of the columnar structure, was changed from $30^{\\circ}$ in the lower part (in Fig. 5d) to $60^{\\circ}$ in the upper part (in Fig. 5c) from the SD. In addition, the keyhole pores were observed in the lower part of the melt pool, as shown in Fig. 5d). It is well known that\\\\\nthe presence of a free surface of the porosity in a liquid acts as a stress riser and allows the strain to be accommodated by a growth of its pre-existing void through the liquid [39-41].\n\nFigure 5e shows the magnified T-crack from Fig. 5a. In Fig. 5e, the cleavage fracture was mainly observed except a local solidification crack trace, which is isolated by the dashed line. Based on the crack propagation (Fig. 5a) and their fracture surfaces (Fig. 5b, e), the overall crack occurrence sequence at $80 \\mathrm{~W}-200 \\mathrm{~mm} / \\mathrm{s}$ (keyhole mode) is that solidification L-crack occurred first, followed by a T-crack as an secondary crack. The T-crack seems to be initiated at the final solidification stage when the most of the melt pool region becomes a solid state, with little liquid coexisting within a solidification region (a local area enclosed by a dashed line in Fig. 5e). Here, the isolated solidification crack does not seem to propagate until the thermal crack in the solid state initiates in the bottom region of the melt pool, as indicated by the arrow, and propagates cross the melt pool.\n\nFigure 6a-f show the T-crack surfaces observed at 80 $\\mathrm{W}-600 \\mathrm{~mm} / \\mathrm{s}$ (transition mode) and at $80 \\mathrm{~W}-1000 \\mathrm{~mm} / \\mathrm{s}$ (conduction mode), respectively. In Fig. 6a, intragranular cleavage fracture was observed on the whole crack surfaces.", "start_char_idx": 569424, "end_char_idx": 572762, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "723ce465-d7ca-4075-821d-3b786788c564": {"__data__": {"id_": "723ce465-d7ca-4075-821d-3b786788c564", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "360d644c-d2cf-4838-a24c-6bc0597d44de", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cf050fb757c9d0d142591fd2473d0999bc8b3045d28cde7c955855bbb5954173", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "923b9103-9ffd-4e78-9325-8d69dff51e97", "node_type": "1", "metadata": {}, "hash": "43fdd6f0ad20cb333bb1b303598153030aa8a13bae52726ffb837887b49b12df", "class_name": "RelatedNodeInfo"}}, "text": "The T-crack seems to be initiated at the final solidification stage when the most of the melt pool region becomes a solid state, with little liquid coexisting within a solidification region (a local area enclosed by a dashed line in Fig. 5e). Here, the isolated solidification crack does not seem to propagate until the thermal crack in the solid state initiates in the bottom region of the melt pool, as indicated by the arrow, and propagates cross the melt pool.\n\nFigure 6a-f show the T-crack surfaces observed at 80 $\\mathrm{W}-600 \\mathrm{~mm} / \\mathrm{s}$ (transition mode) and at $80 \\mathrm{~W}-1000 \\mathrm{~mm} / \\mathrm{s}$ (conduction mode), respectively. In Fig. 6a, intragranular cleavage fracture was observed on the whole crack surfaces. The crack initiated near the right edge of the melt pool/substrate boundary, as indicated by an arrow in Fig. 6a and in the magnified view of Fig. 6b, and propagated across the melt pool. Here, there is a vertical transition line (indicated by the arrow in Fig. 6c) along the center of the melt pool, which shows a change in fracture topology (an indirect indication of the morphological change of grain structures along the transition line). T-cracking at $80 \\mathrm{~W}-1000 \\mathrm{~mm} / \\mathrm{s}$ (conduction mode) formed stepwise cleavage fracture surfaces, as shown in Fig. 6d. The magnified views of those T-cracks are shown in Fig. 6e (for the left side) and Fig. 6f (for the right side). Here, note that T-cracks were initiated at the bottom of the melt pool, as indicated by arrows in Fig. 6e, $f$ and propagated upward.\n\nBased on fractography done for single tracks at $80 \\mathrm{~W}-200$, 600 , and $1000 \\mathrm{~mm} / \\mathrm{s}$ (keyhole, transition, and conduction modes) the crack formation behaviors can be summarized as follows:\n\n\\begin{itemize}\n  \\item The L-crack was formed at the keyhole mode and found to be a solidification crack developed along the centerline of the single track surface.\n\n  \\item T-cracks were formed in all process conditions (keyhole, transition, and conduction modes). The T-crack in the keyhole mode was a mixture of the solidification and thermal crack, while those in the transition and conduction modes were thermal cracks, which were originated from the side edge of the fusion boundary and from the bottom of the melt pool, respectively.\\\\\nIn order to predict the distribution of the temperature and thermal stresses during single track LPBF, thermal-mechanical FEM simulations were conducted for $80 \\mathrm{~W}-200,600$, and $1000 \\mathrm{~mm} / \\mathrm{s}$ (keyhole, transition, and conduction modes). Simulated temperature and thermal stresses $(S)$ in the middle of the single track were recorded as function of time and exported using MATLAB ${ }^{\\circledR}$ for the visualization. Here, the normal stresses in the $\\mathrm{x}$-axis (S11, along the SD) and y-axis (S22, along the transverse direction to the SD) are associated with thermal stresses inducing $\\mathrm{T}$ - and $\\mathrm{L}$-cracking, respectively. Also, these thermal stresses can be used to assess the occurrence for the solidification crack and thermal crack. In general, a solidification crack occurred when a positive (tensile) thermal stress present at the last solidification stage (of course, other physical conditions favourable for solidification cracking, as described in the previous section, should be met as well) [32]. Here, the temperature range susceptible for solidification cracking of Ti-48Al-2Cr-2Nb was estimated to be from 1390 to $1487^{\\circ} \\mathrm{C}$ based on the solid volume fraction $\\left(f_{s}\\right)$ in a range from 0.7 to 0.98 (calculated by Scheil equation [9]). For the thermal crack, the crack occurrence can be assessed by $\\Delta S\\left(\\Delta S=S-S_{Y S}\\right.$, where $S_{Y S}$ is the yield strength) below the ductile-to-brittle transition temperature (DBTT).", "start_char_idx": 572009, "end_char_idx": 575898, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "923b9103-9ffd-4e78-9325-8d69dff51e97": {"__data__": {"id_": "923b9103-9ffd-4e78-9325-8d69dff51e97", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "723ce465-d7ca-4075-821d-3b786788c564", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a8b05afa4478d585c058aba40ae96bfa9a375b60e6fb1c905546d942e38e0a28", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c38f320a-580b-4a7f-9040-e44479826b90", "node_type": "1", "metadata": {}, "hash": "5408d10edcb73f5815701c3b7c10b4f3522fbc0b066166bcab07898bf976876e", "class_name": "RelatedNodeInfo"}}, "text": "In general, a solidification crack occurred when a positive (tensile) thermal stress present at the last solidification stage (of course, other physical conditions favourable for solidification cracking, as described in the previous section, should be met as well) [32]. Here, the temperature range susceptible for solidification cracking of Ti-48Al-2Cr-2Nb was estimated to be from 1390 to $1487^{\\circ} \\mathrm{C}$ based on the solid volume fraction $\\left(f_{s}\\right)$ in a range from 0.7 to 0.98 (calculated by Scheil equation [9]). For the thermal crack, the crack occurrence can be assessed by $\\Delta S\\left(\\Delta S=S-S_{Y S}\\right.$, where $S_{Y S}$ is the yield strength) below the ductile-to-brittle transition temperature (DBTT). In the present study, the temperature range susceptible for the thermal crack of $\\mathrm{Ti}-48 \\mathrm{Al}-2 \\mathrm{Cr}-2 \\mathrm{Nb}$ was estimated to be below $800{ }^{\\circ} \\mathrm{C}$, based on the DBTT measurement previously reported in [42-44]. Therefore, for the assessment of solidification cracking and thermal cracking, simulated $S$ or $\\Delta \\mathrm{S}$ values were used, depending on temperatures of interest.\n\n\\end{itemize}\n\nFigure 7 shows simulated temperature and thermal stress ( $\\mathrm{S}$ and $\\Delta \\mathrm{S}$ ) contours at the last solidification stages for $80 \\mathrm{~W}-200,600$, and $1000 \\mathrm{~mm} / \\mathrm{s}$ (keyhole, transition, and conduction modes). Here, note that $\\mathrm{S}$ and $\\Delta \\mathrm{S}$ contours are separately plotted in the same map for the regions with temperatures between 1390 and $1487^{\\circ} \\mathrm{C}$ (the solidification range) and below $1390{ }^{\\circ} \\mathrm{C}$, respectively. In Fig. 7, depending on the scan speed, simulated $\\mathrm{S} 11$ and $\\mathrm{S} 22$ values show different trends. As the scan speed increases, simulated S11 in last solidification zone increases (maximum values from 117 to $265 \\mathrm{MPa}$ ), while simulated S22 in the same zone decreases (maximum values from 125 to $80 \\mathrm{MPa}$ ). In particular, the maximum $\\mathrm{S} 22$ was higher than the maximum $\\mathrm{S} 11$ at $80 \\mathrm{~W}-200 \\mathrm{~mm} / \\mathrm{s}$ (keyhole mode), while the trend was reversed at $80 \\mathrm{~W}-600$ and $1000 \\mathrm{~mm} / \\mathrm{s}$ (transition and conduction modes).\n\nFigure 8 shows simulated temperature and thermal stress $(\\Delta \\mathrm{S})$ contours at the stage that the temperatures in the bottom of the melt pool are right below BDTT $\\left(800{ }^{\\circ} \\mathrm{C}\\right)$. As the scan speed increases, simulated maximum $\\Delta \\mathrm{S} 11$ tends to increase from 25 to $250 \\mathrm{MPa}$, while simulated maximum $\\Delta \\mathrm{S} 22$ is negligible. Also, these simulated $\\Delta \\mathrm{S} 11$ hot spots are located near the bottom-part of the melt pool for all conditions, which indicates the bottom part of the melt pool as a\n\nTemp.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-09(2)}\n\nS11 \\& $\\Delta$ S11\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-09(1)}\n\n$\\mathbf{S} 22 \\& \\Delta \\mathbf{S} 22$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-09}\n\nFig. 7 Simulated temperature and thermal stress $(\\boldsymbol{S}$ and $\\Delta \\boldsymbol{S}$ ) contours at the solidification stage for all scan speeds simulated.", "start_char_idx": 575156, "end_char_idx": 578549, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c38f320a-580b-4a7f-9040-e44479826b90": {"__data__": {"id_": "c38f320a-580b-4a7f-9040-e44479826b90", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "923b9103-9ffd-4e78-9325-8d69dff51e97", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "85f29b9b5588faeb5e579ca96bf0f1f8b1e54c7a314b398611c5bea3c986fef4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a7ebf1d2-36fd-4efe-be5a-71b85ace2acb", "node_type": "1", "metadata": {}, "hash": "b2506f5c7f329b75a28b66ca888501a888fd9053d0805abdbc791df98ac37bbc", "class_name": "RelatedNodeInfo"}}, "text": "7 Simulated temperature and thermal stress $(\\boldsymbol{S}$ and $\\Delta \\boldsymbol{S}$ ) contours at the solidification stage for all scan speeds simulated. Note that $\\boldsymbol{S}$ and $\\Delta \\boldsymbol{S}$ contours are separately plotted in the same map for the regions with temperatures above and below $1390{ }^{\\circ} \\mathrm{C}$, respectively\n\npreferential 'thermal' crack initiation site, particularly for T-cracks. However, simulated $\\Delta \\mathrm{S} 22$ values seem to be insignificant to trigger 'thermal' L-cracking for all conditions.\n\nThe results of the crack surface observation (Figs. 5, 6) and FEM simulations (Figs. 7, 8) were analyzed together to delineate when and how cracks occur.\n\nIn addition, to identify the effect of microstructures on the cracking, the EBSD results of the melt pool cross-sections are presented in Fig. 9. Inverse pole figure (IPF) maps combined with image quality (IQ) maps in Fig. 9a-c show the solidification structures with the orientation distribution for $80 \\mathrm{~W}-200,600$, and $1000 \\mathrm{~mm} / \\mathrm{s}$ (keyhole, transition, and conduction modes). Also, IPFs with respect to the SD are shown in Fig. 9d-f. Here, only orientations of the $\\alpha$ phase from the melt pool are shown in Fig. $9 \\mathrm{~d}-\\mathrm{f}$ because the melt pool was composed of the $\\alpha$ phase due to fast cooling rates.\n\nFor solidification cracking, the growth direction of solidification structures needs to be considered with respect to the positive (tensile) direction of the thermal stress. If the same value of thermal stress is applied, the solidification structures that are arranged perpendicularly to the thermal stress become a region vulnerable to cracking. In this study, understanding the overall growth directions of solidification structures were determined using the IPF maps of the melt pool cross-sections (Fig. 9a-c) through the orientation analysis with respect to the SD (Fig. 9d-f).\n\nPrevious studies $[45,46]$ reported that favourable grain growth of HCP structure ( $\\alpha$ phase) is $<11 \\overline{2} 0>$ on the basal plane along the thermal gradient. In the case of the 200 and $600 \\mathrm{~mm} / \\mathrm{s}$ (keyhole and transition modes), the highest texture intensities were observed near $\\langle 2 \\overline{1} \\overline{1} 1>$ (indicated by $\\because$ in Fig. 9d, e), implying that the grain growth direction is about 23 degrees away from the SD (refer to the schematic HCP orientation illustrations shown in the boxed region of Fig. 9). it is well matched with the grain growth direction from the fractograph (about $30^{\\circ}$ away from the $\\mathrm{SD}$ ) in Fig. 5d. Here, grains with $<2 \\overline{1} \\overline{1} 1>$ texture colored green in Fig. 9a, b. However, the grains with $<2 \\overline{1} \\overline{1} 5>$ texture were also observed in the keyhole mode, as indicated by ' $x$ ' in Fig. 9d. These grains are colored orange in the IPF map and mostly located in the upper region of the melt pool as shown in Fig. 9a. Theoretically, the grains having $\\langle 2 \\overline{1} \\overline{1} 5>$ texture to the $\\mathrm{SD}$ grow $67^{\\circ}$ away from $\\mathrm{SD}$ (refer to the illustrations shown in the boxed region of Fig. 9). It is consistent with the fractograph of Fig. 5c, showing that the grain growth direction was about $60^{\\circ}$ away from the SD. Considering the\n\n\\section*{Temp.}", "start_char_idx": 578391, "end_char_idx": 581780, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a7ebf1d2-36fd-4efe-be5a-71b85ace2acb": {"__data__": {"id_": "a7ebf1d2-36fd-4efe-be5a-71b85ace2acb", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c38f320a-580b-4a7f-9040-e44479826b90", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "40548d4e48c6c5fdcf4b60766e3f89ce930eee8f225da7f7d4c3eeaa9287b808", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d33a2dd0-2b63-4f99-8f85-9e06bee61eea", "node_type": "1", "metadata": {}, "hash": "d49d9a5980f4b76e3bd573e69d4b19fa08954262e34584207a4a5eb61d0bcade", "class_name": "RelatedNodeInfo"}}, "text": "9a, b. However, the grains with $<2 \\overline{1} \\overline{1} 5>$ texture were also observed in the keyhole mode, as indicated by ' $x$ ' in Fig. 9d. These grains are colored orange in the IPF map and mostly located in the upper region of the melt pool as shown in Fig. 9a. Theoretically, the grains having $\\langle 2 \\overline{1} \\overline{1} 5>$ texture to the $\\mathrm{SD}$ grow $67^{\\circ}$ away from $\\mathrm{SD}$ (refer to the illustrations shown in the boxed region of Fig. 9). It is consistent with the fractograph of Fig. 5c, showing that the grain growth direction was about $60^{\\circ}$ away from the SD. Considering the\n\n\\section*{Temp.}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-10(1)}\n\\end{center}\n\n$\\Delta \\mathbf{S} 11$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-10}\n\n$\\Delta \\mathbf{S 2 2}$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-10(2)}\n\nFig. 8 Simulated temperature and thermal stress $(\\Delta S)$ contours at the stage that the temperatures in the bottom of the melt pool are right below the DBTT $\\left(800^{\\circ} \\mathrm{C}\\right)$\n\nmelt pool microstructures observed at the cross-sections in Fig. 9a, b, solidification structures grew from the fusion boundaries toward the centerline with the aforementioned growth direction with respect to SD. Then, at the last solidification stage, the liquid distributed along the centerline was solidified upward, resulting in grains arranged vertically in the center of the melt pool in Fig. 9a, b. Such solidification sequences, particularly for the melt pools of the keyhole and transition modes, were also reported in the previous studies done for other metallic alloys [47-49]. For 80 W-1000 $\\mathrm{mm} / \\mathrm{s}$ (conduction mode), the high intensities in $\\langle 10 \\overline{1} 0\\rangle$ and $\\langle 2 \\overline{1} \\overline{1} 0\\rangle$ were observed in Fig. 9f, meaning that the grain growth mainly occurred parallel to the SD (refer to the illustrations shown in the boxed region of Fig. 9). Also, the melt pool cross-section in Fig. 9c showed that almost all grains grow from the fusion boundary toward a center of the top surface.\n\nIn Fig. 9a, the grains aligned vertically in the central region of the melt pool are expected to be susceptible to solidification L-cracking when a large positive (tensile) thermal stress, S22, presents, and that was exactly what FEM simulations predicted in the upper right of Fig. 7 (maximum $\\mathrm{S} 22=125 \\mathrm{MPa}$ ). It means that the melt pool at 80\\\\\nW-200 mm/s (keyhole mode) is vulnerable for solidification L-cracking. However, solidification L-cracking did not occur for melt pools at $80 \\mathrm{~W}-600$ and $1000 \\mathrm{~mm} / \\mathrm{s}$ (transition and conduction modes), even if those melt pools showed grains aligned vertically in the central region in Fig. 9b, c. It seems to be due to the lack of liquid feeding for the melt pools of the transition and conduction modes. As shown in Fig. 7, the solidification zone (the region with temperatures between 1390 and $1487^{\\circ} \\mathrm{C}$ ) expands with decreasing scan speed. A wider solidification zone means a longer intercolumnar passageway, which hinders liquid feeding needed to resist cracking [50]. Therefore, no solidification L-cracking in the transition and conduction modes were attributed to the shorter grain boundary channel for liquid feeding, compared to the keyhole mode.", "start_char_idx": 581131, "end_char_idx": 584638, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d33a2dd0-2b63-4f99-8f85-9e06bee61eea": {"__data__": {"id_": "d33a2dd0-2b63-4f99-8f85-9e06bee61eea", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a7ebf1d2-36fd-4efe-be5a-71b85ace2acb", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8f64641d30bf35d5eb96488059f7ffa5523baa16feeb8cb811609e7ab5c65a92", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b9f3976a-97de-4473-b185-c37461348de0", "node_type": "1", "metadata": {}, "hash": "29e0b45dab05b8691147cf37ede9dae668e21bd7697c1a265a1443abb544d6ee", "class_name": "RelatedNodeInfo"}}, "text": "However, solidification L-cracking did not occur for melt pools at $80 \\mathrm{~W}-600$ and $1000 \\mathrm{~mm} / \\mathrm{s}$ (transition and conduction modes), even if those melt pools showed grains aligned vertically in the central region in Fig. 9b, c. It seems to be due to the lack of liquid feeding for the melt pools of the transition and conduction modes. As shown in Fig. 7, the solidification zone (the region with temperatures between 1390 and $1487^{\\circ} \\mathrm{C}$ ) expands with decreasing scan speed. A wider solidification zone means a longer intercolumnar passageway, which hinders liquid feeding needed to resist cracking [50]. Therefore, no solidification L-cracking in the transition and conduction modes were attributed to the shorter grain boundary channel for liquid feeding, compared to the keyhole mode.\n\nFor solidification T-cracking, it is interesting to note that a locally isolated solidification T-crack was observed only at $80 \\mathrm{~W}-200 \\mathrm{~mm} / \\mathrm{s}$ (keyhole mode), as shown in Fig. 5e, although simulated S11 values are relatively high (173 and $265 \\mathrm{MPa}$ ) for $80 \\mathrm{~W}-600$ and $1000 \\mathrm{~mm} / \\mathrm{s}$ (transition and conduction modes) in Fig. 7. In order to understand the effect of the microstructure on the solidification T-cracking, it is necessary to consider the solidification direction (viz. the grain\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-11(2)}\n\\end{center}\n\n(d)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-11}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-11(6)}\n\\end{center}\n\n(e)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-11(5)}\n\\end{center}\n\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-11(4)}\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-11(3)}\n\n** $\\theta$ is misorientation angle between $\\mathrm{SD}$ and basal plane (// favorable grain growth direction of HCP)\n\n\\section*{(f)}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-11(1)}\n\\end{center}\n\nFig. 9 Inverse pole figure (IPF) maps (combined with the image quality (IQ) maps) for the cross-sections of single tracks at a $80 \\mathrm{~W}-200$ $\\mathrm{mm} / \\mathrm{s}, \\mathbf{b} 80 \\mathrm{~W}-600 \\mathrm{~mm} / \\mathrm{s}$ and $\\mathbf{c} 80 \\mathrm{~W}-1000 \\mathrm{~mm} / \\mathrm{s}$. d-f are IPFs corre-\n\nalignment) with respect to the SD (// S11). In Fig. 9a-c, the grains with $\\langle 2 \\overline{1} \\overline{1} 1>,<10 \\overline{1} 0>$ and $\\langle 2 \\overline{1} \\overline{1} 0>$ textures tend to show relatively low susceptibility to solidification T-cracking (even under high S11) since their main growth directions are slightly tilted or almost parallel to the SD. However, for the grains having $<2 \\overline{1} \\overline{1} 5>/ / \\mathrm{SD}$ in the keyhole mode (Fig.", "start_char_idx": 583808, "end_char_idx": 586849, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b9f3976a-97de-4473-b185-c37461348de0": {"__data__": {"id_": "b9f3976a-97de-4473-b185-c37461348de0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d33a2dd0-2b63-4f99-8f85-9e06bee61eea", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "12f51f7969d892583bec56422ae24e038a78c155d454a6ed60474dc1d69b00f6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "02db9c89-fbf5-443a-86cd-91ebc614c681", "node_type": "1", "metadata": {}, "hash": "1b381988cca20ab946c632e8e7eeb7c33e62378b7979e75b9ceac6842fe2b599", "class_name": "RelatedNodeInfo"}}, "text": "d-f are IPFs corre-\n\nalignment) with respect to the SD (// S11). In Fig. 9a-c, the grains with $\\langle 2 \\overline{1} \\overline{1} 1>,<10 \\overline{1} 0>$ and $\\langle 2 \\overline{1} \\overline{1} 0>$ textures tend to show relatively low susceptibility to solidification T-cracking (even under high S11) since their main growth directions are slightly tilted or almost parallel to the SD. However, for the grains having $<2 \\overline{1} \\overline{1} 5>/ / \\mathrm{SD}$ in the keyhole mode (Fig. 9a, d), the solidification direction will be almost perpendicular to ( $67^{\\circ}$ away from) the $\\mathrm{SD}$, which is expected to be susceptible to solidification T-cracking. These almost vertically aligned grains are colored orange and particularly distributed in the upper region of the melt pool, as shown in Fig. 9a.\n\nAt the solid state below the DBTT, FEM simulations in Fig. 8 predicted large $\\Delta \\mathrm{S} 11$, compared to $\\Delta \\mathrm{S} 22$, for 80 $\\mathrm{W}-600$ and $1000 \\mathrm{~mm} / \\mathrm{s}$ (transition and conduction modes), which seems to be responsible for 'thermal' (cleavage) T-cracks observed in Figs. 4b and 6. However, the crack initiation sites were somehow different between the transition (Fig. 6a-c) and conduction (Fig. 6d-e) modes. Thermal T-cracks at $80 \\mathrm{~W}-1000 \\mathrm{~mm} / \\mathrm{s}$ (conduction mode) were initiated near the bottom of the melt pool, as shown in Fig. 6d-e, which is in good agreement with the FEM prediction of sponding to melt pools in a-c, respectively. Orientations of the HCP lattice for different crystallographic directions are schematically illustrated in the boxed region\n\nFig. 8. However, the thermal T-crack at $80 \\mathrm{~W}-600 \\mathrm{~mm} / \\mathrm{s}$ (transition mode) showed an initiation near the right edge of the fusion boundary (indicated by the arrow in Fig. 6a), which is different from the FEM prediction (the crack initiation near the bottom center of the melt pool, as predicted by $\\Delta \\mathrm{S} 11$ hot spot distribution in Fig. 8). The difference between observed and predicted crack initiation sites seems to be associated with the microstructure. The IPF map of the melt pool cross-section for $80 \\mathrm{~W}-600 \\mathrm{~mm} / \\mathrm{s}$ (transition mode) showed a large $<2 \\overline{1} \\overline{1} 1>$-oriented (green-colored) grain in Fig. 9b. Such a large grain is believed to suffer from relatively large thermal stresses, compared to those of small grains, due to the lack of the redistribution of thermal stresses among differently oriented grains [18]. In this case, the crack initiation will depend upon the location of the large grain. However, the reason for the development of a large grain at $80 \\mathrm{~W}-600 \\mathrm{~mm} / \\mathrm{s}$ (transition mode) is still in question. It is generally understood that the development of grain morphologies relies on the shape of the fusion boundary $[48,49,51,52]$, which is determined by complex heat flow inside the melt pool during the laser-powder/substrate interaction. Grain morphologies at melt pool cross-sections for\\\\\n$80 \\mathrm{~W}-200$ and $1000 \\mathrm{~mm} / \\mathrm{s}$ (keyhole and conduction modes) reveal different multidirectional solidification, as shown in Fig. 9a, c, respectively, starting from the fusion boundary. The similar multidirectional solidification was also reported for other alloys [48, 49, 51, 52]. However, for 80 W-600 $\\mathrm{mm} / \\mathrm{s}$ (transition mode), which is between keyhole and conduction modes, heat flow (and the resulting fusion boundary) seems to favour unidirectional solidification starting from the fusion boundary, leading to the development of large grains, as seen in Fig. 9b.", "start_char_idx": 586355, "end_char_idx": 590070, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "02db9c89-fbf5-443a-86cd-91ebc614c681": {"__data__": {"id_": "02db9c89-fbf5-443a-86cd-91ebc614c681", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b9f3976a-97de-4473-b185-c37461348de0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "28bcb3868d0bd02550d34ab2984aadc70f886bede2b19204f6ddbfee88f48707", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9553fada-766c-4b4a-b2cc-a64e614fa65a", "node_type": "1", "metadata": {}, "hash": "3417a13efe5038239e111c63b1da6a75abf73d5c4fe1ce4c68bb65ba23339419", "class_name": "RelatedNodeInfo"}}, "text": "Grain morphologies at melt pool cross-sections for\\\\\n$80 \\mathrm{~W}-200$ and $1000 \\mathrm{~mm} / \\mathrm{s}$ (keyhole and conduction modes) reveal different multidirectional solidification, as shown in Fig. 9a, c, respectively, starting from the fusion boundary. The similar multidirectional solidification was also reported for other alloys [48, 49, 51, 52]. However, for 80 W-600 $\\mathrm{mm} / \\mathrm{s}$ (transition mode), which is between keyhole and conduction modes, heat flow (and the resulting fusion boundary) seems to favour unidirectional solidification starting from the fusion boundary, leading to the development of large grains, as seen in Fig. 9b. The details remain to be a subject for the future clarification.\n\nAverage T-crack spacings were measured under different LPBF process conditions and plotted in Fig. 10 as a function of scan speed (Fig. 10a) and $E_{\\rho}$ (Fig. 10b). In Fig. 10a, the T-crack spacing decreases (conversely, the frequency of T-cracking increases) with increasing scan speed. Also, the dependency of T-crack spacings on the scan speed was reduced upon increasing the power. In particular, its tendency is not effective under $200-600 \\mathrm{~mm} / \\mathrm{s}$, especially in the keyhole mode. Such a trend is clearly revealed when T-crack spacings are plotted as a function of $E_{\\rho}$ in Fig. 10b. Here, as the $E_{\\rho}$ increases, the T-crack spacing sensitively increases in the conduction and transition modes, and then becomes almost insensitive in the keyhole mode. Generally, upon increasing the scan speed, the cooling rate tends to increase. An increase in cooling rate promotes frequent T-crack occurrence (a decrease in T-crack spacing). Thus, in the domain of conduction and transition modes of Fig. 10b, as the $E_{\\rho}$ increases (viz. as the scan speed decreases), the cooling rate decreases, leading to increased T-crack spacing. In the keyhole mode, however, the keyhole phenomenon results in high energy absorption, causing the abnormal temperature increase during the melt pool formation [53]. That is, the dependency of cooling rates on the scan speed (viz. on $E_{\\rho}$ ) is reduced in the keyhole mode and the T-cracking occurrence is less sensitive to the $E_{\\rho}$ variation than in the conduction and transition modes. It leads to the T-crack spacing nearly insensitive to the $E_{\\rho}$ variation in the keyhole mode as shown in Fig. 10b. Also, T-cracks in the keyhole mode were found to be mostly secondary cracks right after the formation of L-cracks (Fig. 4). Perhaps, those secondary T-crack spacings show the $E_{\\rho}$ sensitivity different from that of the conduction and transition modes due to the relief of thermal stresses upon primary L-cracking. It seems to give an additional contribution to the different $E_{\\rho}$ sensitivity of the T-crack spacing between the conduction/transition and keyhole mode regimes in Fig. 10b.\n\nFigure 11 shows the final summary of crack formation mechanisms responsible for $\\mathrm{L}-$ and $\\mathrm{T}$-cracking in the keyhole, transition, and conduction modes, based on combined results of the fractography, FEM simulations, and the microstructural analysis performed in the present study. In the keyhole mode, solidification L- and T-cracks were triggered by the presence of the solidification structures (the grain alignment) nearly perpendicular to tensile thermal stresses (S) under the wide solidification zone. In the conduction and transition modes, the occurrence of thermal T-cracks was governed by large thermal stresses along the scan direction $(\\Delta S 11)$ at the solid state below the DBTT. Unlike solidification cracks, which were heavily influenced by solidification microstructures, thermal T-cracks were primarily affected by thermal stresses $(\\Delta S 11)$ with a minor microstructural influence (particularly, the grain size distribution) on the crack initiation.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-12}\n\nFig.", "start_char_idx": 589403, "end_char_idx": 593411, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9553fada-766c-4b4a-b2cc-a64e614fa65a": {"__data__": {"id_": "9553fada-766c-4b4a-b2cc-a64e614fa65a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "02db9c89-fbf5-443a-86cd-91ebc614c681", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "17dbbe0d27a63c3ca44e5d5747413a4879071ea3fb7222668845e35ef0598d56", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7d35bfd2-fb1b-4436-a1f0-0325b27528c6", "node_type": "1", "metadata": {}, "hash": "c03cadd40a1f05d2d6cb861abc8795d979d6ea3a36a6dc95b66a4f2164a1c57c", "class_name": "RelatedNodeInfo"}}, "text": "In the keyhole mode, solidification L- and T-cracks were triggered by the presence of the solidification structures (the grain alignment) nearly perpendicular to tensile thermal stresses (S) under the wide solidification zone. In the conduction and transition modes, the occurrence of thermal T-cracks was governed by large thermal stresses along the scan direction $(\\Delta S 11)$ at the solid state below the DBTT. Unlike solidification cracks, which were heavily influenced by solidification microstructures, thermal T-cracks were primarily affected by thermal stresses $(\\Delta S 11)$ with a minor microstructural influence (particularly, the grain size distribution) on the crack initiation.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_a65eb47b4d7ef04a43d9g-12}\n\nFig. 10 T-crack spacings as a function of $\\mathbf{a}$ scan speed and $\\mathbf{b}$ energy density ( $\\left.\\boldsymbol{E}_{\\boldsymbol{\\rho}}\\right)$\n\nFig. 11 Schematic illustration for crack formation mechanisms in the keyhole, conduction and transition modes\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-13(1)}\n\\end{center}\n\n\\section*{Conduction \\& Transition Modes}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_a65eb47b4d7ef04a43d9g-13}\n\\end{center}\n\nT-crack frequency sensitive to the laser power and scan speed\n\n4-...-. Solidification Directions\n\nThermal Stress $(S \\& \\Delta S$ ) Directions\n\n\\begin{center}\n\\begin{tabular}{c|c|c|l}\n\\hline\nProcess Condition & \\begin{tabular}{c}\nCrack \\\\\nPattern \\\\\n\\end{tabular} & Crack Type & \\multicolumn{1}{c}{Causes} \\\\\n\\hline\nKeyhole Mode & L-crack & Solidification & \\begin{tabular}{l}\nSolidification direction (grain alignment) \\\\\nnormal to the tensile thermal stress $(S)$ \\\\\nunder the wide solidification zone \\\\\n\\end{tabular} \\\\\n\\cline { 2 - 2 }\n\\begin{tabular}{c}\n \\\\\nTransition Modes \\\\\n\\end{tabular} & T-crack & \\begin{tabular}{c}\nThermal \\\\\nCrack \\\\\n\\end{tabular} & \\begin{tabular}{l}\nLarge thermal stress $(\\Delta S 11)$ below \\\\\nDBTT; a minor effect of grain size on \\\\\nthe crack initiation \\\\\n\\end{tabular} \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\section*{4 Conclusions}\nThe crack formation mechanisms of Ti-48Al-2Cr $-2 \\mathrm{Nb}$ single tracks processed by laser powder bed fusion were thoroughly investigated depending on the keyhole, transition, and conduction modes. The fractography, microstructural analysis, and thermal-mechanical FEM simulations were conducted to clarify crack formation mechanisms. On the basis of the results, the following conclusions were drawn.\n\n1 Depending on process conditions (the laser power and scan speed), different types of L- and T-cracks by their directionality, and solidification and thermal cracks were observed by the nature of their occurrence.\n\n2 In the keyhole mode, the solidification L- and T-cracks were observed. The formation of solidification cracks was associated with directionally developed grain structures along with tensile thermal stresses loaded perpendicularly to those grains.\n\n3 In the transition and conduction modes, thermal T-cracks were formed by large thermal stresses $(\\Delta \\mathrm{S} 11)$ predicted along the scan direction at the temperature below the ductile-to-brittle transition. The microstructure did not seem to give a major influence on the formation of thermal T-cracks, except its minor effect on the crack initiation, particularly for large grains.\\\\\n4 The variation of T-crack spacings with the energy density showed different trends with the melting modes. In the conduction and transition modes, the T-crack spacing proportionally increased with increasing energy density, while the T-crack spacing was nearly insensitive to the variation of the energy density in the keyhole mode.", "start_char_idx": 592623, "end_char_idx": 596398, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7d35bfd2-fb1b-4436-a1f0-0325b27528c6": {"__data__": {"id_": "7d35bfd2-fb1b-4436-a1f0-0325b27528c6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9553fada-766c-4b4a-b2cc-a64e614fa65a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9c057dafba3a2c97ec458087da0948fbf8e297bedd54d6854865071c53a3c67c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "39be47d3-579d-430e-9215-8f56ddd729ac", "node_type": "1", "metadata": {}, "hash": "8fee74e7147af9428c587f6012cc8220308feafce8b2a1a43744c67064c3b838", "class_name": "RelatedNodeInfo"}}, "text": "2 In the keyhole mode, the solidification L- and T-cracks were observed. The formation of solidification cracks was associated with directionally developed grain structures along with tensile thermal stresses loaded perpendicularly to those grains.\n\n3 In the transition and conduction modes, thermal T-cracks were formed by large thermal stresses $(\\Delta \\mathrm{S} 11)$ predicted along the scan direction at the temperature below the ductile-to-brittle transition. The microstructure did not seem to give a major influence on the formation of thermal T-cracks, except its minor effect on the crack initiation, particularly for large grains.\\\\\n4 The variation of T-crack spacings with the energy density showed different trends with the melting modes. In the conduction and transition modes, the T-crack spacing proportionally increased with increasing energy density, while the T-crack spacing was nearly insensitive to the variation of the energy density in the keyhole mode. The proportional relationship between the scan speed and the cooling rate (hence, the T-crack frequency), and the abnormal temperature rise by the keyhole phenomenon (which disturbs the relationship between the scan speed and the T-crack frequency) seemed to be responsible for the former and latter, respectively.\n\nFunding This research was supported by the Industrial Strategic Technology Development Program (10077677) and the Technology Innovation Program (20000201) funded by the Ministry of Trade, Industry and Energy (MOTIE, Korea). This work was also supported by Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government (MOTIE) (20193310100050, Technology development of gas turbine blade reengineering specialized for domestic operating environment).\n\n\\section*{Compliance with Ethical Standards}\nConflict of interest The authors declare that they have no conflict of interest.\n\n\\section*{References}\n\\begin{enumerate}\n  \\item H. Clemens, S. Mayer, Mater. High Temp. 33, 560 (2016)\n\n  \\item M. Thomas, T. Malot, P. Aubry, C. Colin, T. Vilaro, P. Bertrand, Mater. High Temp. 33, 571 (2016)\n\n  \\item W. Chen, Z. Li, Additive Manufacturing of Titanium Aluminides (Elsevier, Amsterdam, 2019)\n\n  \\item P.L. Narayana, C.L. Li, J.K. Hong, S.W. Choi, C.H. Park, S.W. Kim, S.E. Kim, N.S. Reddy, J.T. Yeom, Met. Mater. Int. 25, 1063 (2019)\n\n  \\item J. Qiu, Z. Fu, B. Liu, Y. Liu, J. Yan, D. Pan, W. Zhang, Met. Mater. Int. 25, 1564 (2019)\n\n  \\item S. Gorsse, C. 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Manuf. 30, 100835 (2019)\n\n\\end{enumerate}\n\nPublisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{bbold}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\\usepackage{multirow}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\n\\title{Rapid Alloy Development of Extremely High-Alloyed Metals Using Powder Blends in Laser Powder Bed Fusion }", "start_char_idx": 601395, "end_char_idx": 603541, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f4d28d7d-2c07-4100-85bb-3fe3ff3bcc87": {"__data__": {"id_": "f4d28d7d-2c07-4100-85bb-3fe3ff3bcc87", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "80d15132-a466-4c27-b6e3-8bfcdc73f35b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "66e61f1e185ce4683efa5803f4c6d500a6369727524c04164e1bd030f99bd291", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ea102622-6740-4615-8519-80aa1fc0d08e", "node_type": "1", "metadata": {}, "hash": "3c7f2d3ff1f5da28439d0fd3304999411086d6544e08127451fa3f7039212c23", "class_name": "RelatedNodeInfo"}}, "text": "\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{bbold}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\\usepackage{multirow}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\n\\title{Rapid Alloy Development of Extremely High-Alloyed Metals Using Powder Blends in Laser Powder Bed Fusion }\n\n\n\\author{Simon Ewald ${ }^{1, *}$, Fabian Kies ${ }^{2}\\left(\\mathbb{D}\\right.$, Steffen Hermsen ${ }^{1}$, Maximilian Voshage ${ }^{1}$, Christian Haase ${ }^{2}$\\\\\nand Johannes Henrich Schleifenbaum 1,3\\\\\n1 Chair of Digital Additive Production, RWTH Aachen University, 52074 Aachen, Germany;\\\\\nsteffen.hermsen@dap.rwth-aachen.de (S.H.); MAXIMILIAN.VOSHAGE@dap.rwth-aachen.de (M.V.);\\\\\nJOHANNES.HENRICH.SCHLEIFENBAUM@dap.rwth-aachen.de (J.H.S.)\\\\\n2 Steel Institute, RWTH Aachen University, 52072 Aachen, Germany; Fabian.Kies@iehk.rwth-aachen.de (F.K.);\\\\\nchristian.haase@iehk.rwth-aachen.de (C.H.)\\\\\n3 Fraunhofer Institute for Laser Technology, 52074 Aachen, Germany\\\\\n* Correspondence: simon.ewald@dap.rwth-aachen.de; Tel.: +49-241-8906-478}\n\\date{}\n\n\n\\begin{document}\n\\maketitle\nArticle\n\nReceived: 8 May 2019; Accepted: 23 May 2019; Published: 26 May 2019\n\n\\begin{abstract}\nThe design of new alloys by and for metal additive manufacturing (AM) is an emerging field of research. Currently, pre-alloyed powders are used in metal AM, which are expensive and inflexible in terms of varying chemical composition. The present study describes the adaption of rapid alloy development in laser powder bed fusion (LPBF) by using elemental powder blends. This enables an agile and resource-efficient approach to designing and screening new alloys through fast generation of alloys with varying chemical compositions. This method was evaluated on the new and chemically complex materials group of multi-principal element alloys (MPEAs), also known as high-entropy alloys (HEAs). MPEAs constitute ideal candidates for the introduced methodology due to the large space for possible alloys. First, process parameters for LPBF with powder blends containing at least five different elemental powders were developed. Secondly, the influence of processing parameters and the resulting energy density input on the homogeneity of the manufactured parts were investigated. Microstructural characterization was carried out by optical microscopy, electron backscatter diffraction (EBSD), and energy-dispersive X-ray spectroscopy (EDS), while mechanical properties were evaluated using tensile testing. Finally, the applicability of powder blends in LPBF was demonstrated through the manufacture of geometrically complex lattice structures with energy absorption functionality.\n\\end{abstract}\n\nKeywords: additive manufacturing; laser powder bed fusion; high-entropy alloys; multi-principal element alloys; powder blends; rapid alloy development\n\n\\section*{1. Introduction}\nAdditive manufacturing (AM) is an emerging production technology with enormous potential to replace and supplement conventional manufacturing processes. Especially in the field of metal $\\mathrm{AM}$, recent developments in equipment as well as improved part quality have allowed advancements from rapid prototyping of single pieces to final part production. Among the various powder-based metal AM techniques, laser powder bed fusion (LPBF) is currently the most widely used method, as it allows for higher geometrical flexibility than laser metal deposition (LMD) and higher resolution compared to electron beam melting (EBM) [1].", "start_char_idx": 602971, "end_char_idx": 606726, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ea102622-6740-4615-8519-80aa1fc0d08e": {"__data__": {"id_": "ea102622-6740-4615-8519-80aa1fc0d08e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f4d28d7d-2c07-4100-85bb-3fe3ff3bcc87", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "136117199c2f1445db12952a3efe54b185a433a236342c4218bdeca5147daf1b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1d9987ce-9b0a-4ee0-b2c3-d8f3bab16293", "node_type": "1", "metadata": {}, "hash": "208de09e44eec144a7c417caf09cce723a6335b3641ff552d0946ee77941600d", "class_name": "RelatedNodeInfo"}}, "text": "Finally, the applicability of powder blends in LPBF was demonstrated through the manufacture of geometrically complex lattice structures with energy absorption functionality.\n\\end{abstract}\n\nKeywords: additive manufacturing; laser powder bed fusion; high-entropy alloys; multi-principal element alloys; powder blends; rapid alloy development\n\n\\section*{1. Introduction}\nAdditive manufacturing (AM) is an emerging production technology with enormous potential to replace and supplement conventional manufacturing processes. Especially in the field of metal $\\mathrm{AM}$, recent developments in equipment as well as improved part quality have allowed advancements from rapid prototyping of single pieces to final part production. Among the various powder-based metal AM techniques, laser powder bed fusion (LPBF) is currently the most widely used method, as it allows for higher geometrical flexibility than laser metal deposition (LMD) and higher resolution compared to electron beam melting (EBM) [1]. Geometrical freedom, reduced material waste, energy usage, and high degrees of automation are additional advantages of LPBF that contribute to meeting global challenges such as increased individualization, environmental friendliness, and digitalization.\n\nFurthermore, elemental segregation can be strongly reduced due to high cooling rates, which makes a large spectrum of materials processable [1-5].\n\nWhereas the various AM techniques enable high degrees of freedom in geometrical design, the methods are rather inflexible with respect to material inputs. So far, mostly pre-alloyed powders or powder blends consisting of two similar materials, e.g., Ti and TiC or TiB, have been utilized to guarantee process stability and chemical and microstructural homogeneity in reproducible properties. Additive manufactured TiC/TiB-reinforced Ti matrix nanocomposites have been used in biomedical applications [6-8]. The use of diversified powder blends would open up new degrees of freedom for powder-based AM, especially in alloy design. Utilizing mixtures of multiple powders would allow for fast and simple variations in chemical composition, which would enable the rapid design and screening of new alloys. Therefore, powder-based AM techniques in combination with powder blends might be a new solution for rapidly designing and screening chemically complex materials such as multi-principal element alloys (MPEAs), also known as high-entropy alloys (HEAs) [9-11].\n\nMPEAs are a relatively new class of alloys, which instead of relying on one base element contain at least three principal elements with fractions of 5-35 at\\% each [9,11,12]. Hence, a vast space for chemical compositions and properties is possible, which has stimulated intensive research in this field. With this concept, mechanical and functional property combinations that cannot be found in conventional alloys may be achievable. These property combinations can be varied within a wide range by varying the concentration of one or more of the elements [9-11,13].\n\nEarlier studies carried out by Haase et al. [14] introduced a robust methodology utilizing thermodynamic modeling and rapid screening using LMD for new MPEAs. The methodology is based on using powder blends as an input material to enable rapid and resource-efficient screening of MPEAs. However, LMD is very limited with respect to producing parts with complex geometry and is prone to defects, which motivates the application of LPBF instead [15]. The possibility of using powder blends as an input material for LPBF has been successful in various previous studies [16,17]. For example, the mechanical properties of high-manganese steels were adjusted by adding elementary $\\mathrm{Al}$ powder to pre-alloyed steel powder $[16,18,19]$. However, this approach was not tested with powder blends consisting of more than two powders or different powder morphologies from their production processes (e.g., inert gas atomization, water atomization, grinding).\n\nThe goal of the present study is the application of the rapid alloy development methodology introduced by Haase et al. [14] for MPEAs in the LPBF process. First, the Al-C-Co-Fe-Mn-Ni system was exemplarily chosen as the considered material in the present study. This chemically complex system demonstrated an extreme case for powder blends in LPBF, since a variety of different elemental powders, both metallic and nonmetallic, with differing morphologies were used. Secondly, a base composition without $C$ was qualified for the LPBF process to produce fully dense parts. Different energy densities were selected to investigate the homogeneity of the produced samples.", "start_char_idx": 605724, "end_char_idx": 610384, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1d9987ce-9b0a-4ee0-b2c3-d8f3bab16293": {"__data__": {"id_": "1d9987ce-9b0a-4ee0-b2c3-d8f3bab16293", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ea102622-6740-4615-8519-80aa1fc0d08e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "464c3a00640db84375c0e29bfcbc096ee35fe426781028637a128676dc925363", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2a845235-dd46-40d1-977e-348a756a8b12", "node_type": "1", "metadata": {}, "hash": "b96edc06bdb7e29d14d01298ef39ac86c857cad31a8abd9072031922f84fffd5", "class_name": "RelatedNodeInfo"}}, "text": "However, this approach was not tested with powder blends consisting of more than two powders or different powder morphologies from their production processes (e.g., inert gas atomization, water atomization, grinding).\n\nThe goal of the present study is the application of the rapid alloy development methodology introduced by Haase et al. [14] for MPEAs in the LPBF process. First, the Al-C-Co-Fe-Mn-Ni system was exemplarily chosen as the considered material in the present study. This chemically complex system demonstrated an extreme case for powder blends in LPBF, since a variety of different elemental powders, both metallic and nonmetallic, with differing morphologies were used. Secondly, a base composition without $C$ was qualified for the LPBF process to produce fully dense parts. Different energy densities were selected to investigate the homogeneity of the produced samples. Thirdly, the fabricated alloys were evaluated regarding their processability, microstructure, and mechanical properties by using optical microscopy, electron backscatter diffraction (EBSD), energy-dispersive X-ray spectroscopy (EDS), and tensile testing. Finally, parts with complex geometry, i.e. lattice structures, were produced to demonstrate the applicability of powder blends in LPBF. The lattice structures were subsequently compression-tested to evaluate their energy absorption capability. Based on the findings, the correlation between process, microstructure, and mechanical properties is discussed, and the application of elemental powder blends in LPBF is critically evaluated.\n\n\\section*{2. Materials and Methods}\n\\subsection*{2.1. Rapid Alloy Development Methodology Using Powder Blends in LPBF}\nIn Figure 1, the rapid alloy development methodology using powder blends in LPBF of the present study is schematically shown. The approach was divided into three steps. First, a base alloy was created by dry-mixing elemental powders. Secondly, to screen the alloy system, the base alloy was\\\\\nadapted by adding additional elemental powders, e.g., C. Finally, the various created powder blends were processed by LPBF and evaluated by microstructure analysis and mechanical properties.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_14ad84a6f46bf5697b9dg-03}\n\\end{center}\n\nFigure 1. Schematic illustration of the rapid alloy development methodology using powder blends for the laser powder bed fusion (LPBF) process, where \"...n\" is a placeholder for additional elements.\n\n\\subsection*{2.2. LPBF Processing}\nThe morphology and powder characteristics of the different elemental powders are shown in Figure 2 and Table 1, respectively. The used elemental powders had a purity $>99.6 \\mathrm{wt} \\%$ of the respective element. To achieve homogeneously mixed powder blends for the LPBF process, the elemental powders were mixed for $45 \\mathrm{~min}$ in a Turbula 2F tumbler mixer (Willy A. Bachofen AG, Basel, Switzerland). The two investigated alloy combinations are shown in Table 2. The base alloy was defined as equiatomic CoFeMnNi with the addition of $3 \\mathrm{wt} \\% \\mathrm{Al}$ (referred to as BASE or $\\mathrm{Al}_{0.26} \\mathrm{CoFeMnNi}$ in at $\\%$ ) and was further alloyed with $0.6 \\mathrm{wt} \\% \\mathrm{C}$ (referred to as BASE + 0.6C or $\\mathrm{C}_{0.12} \\mathrm{Al}_{0.26} \\mathrm{CoFeMnNi}$ in at\\%). An LPBF process parameter qualification was carried out for BASE and was then transferred to BASE + 0.6C.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_14ad84a6f46bf5697b9dg-03(1)}\n\\end{center}\n\nFigure 2. Secondary electron (SE) micrographs showing the different morphologies of the used powders: (a) $\\mathrm{Al}$, (b) $\\mathrm{C}$, (c) $\\mathrm{Co}$, (d) $\\mathrm{Fe},(\\mathbf{e}) \\mathrm{Mn}$, and (f) Ni.\n\nTable 1. Overview of the characteristics of the different elemental powders.", "start_char_idx": 609496, "end_char_idx": 613339, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2a845235-dd46-40d1-977e-348a756a8b12": {"__data__": {"id_": "2a845235-dd46-40d1-977e-348a756a8b12", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1d9987ce-9b0a-4ee0-b2c3-d8f3bab16293", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "692b2aa2ddefcecb9e81b975a055506fba6af0f66895bca8c2dcf07c9c34f15f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "104c5c45-a4a5-478a-a091-80d09b1a7920", "node_type": "1", "metadata": {}, "hash": "808e35474966fa0ca13b177fe3cc464f9b8ca86263bd17a5d4a2023aae707718", "class_name": "RelatedNodeInfo"}}, "text": "An LPBF process parameter qualification was carried out for BASE and was then transferred to BASE + 0.6C.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_14ad84a6f46bf5697b9dg-03(1)}\n\\end{center}\n\nFigure 2. Secondary electron (SE) micrographs showing the different morphologies of the used powders: (a) $\\mathrm{Al}$, (b) $\\mathrm{C}$, (c) $\\mathrm{Co}$, (d) $\\mathrm{Fe},(\\mathbf{e}) \\mathrm{Mn}$, and (f) Ni.\n\nTable 1. Overview of the characteristics of the different elemental powders.\n\n\\begin{center}\n\\begin{tabular}{ccccccc}\n\\hline\nPowder & \\begin{tabular}{c}\nManufacturing \\\\\nMethod \\\\\n\\end{tabular} & \\begin{tabular}{c}\nParticle Size \\\\\nDistribution \\\\\n$(\\boldsymbol{\\mu m})$ \\\\\n\\end{tabular} & Form & \\begin{tabular}{c}\nFlowability as \\\\\nAvalanche \\\\\nAngle $\\left.\\mathbf{(}^{\\circ}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nLaser \\\\\nAbsorption for \\\\\n$\\mathbf{1 0 6 4} \\mathbf{~ n m} \\mathbf{( \\% )}$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\nBulk \\\\\nDensity \\\\\n$\\mathbf{( g \\cdot \\mathbf { m l } ^ { - 1 } )}$ \\\\\n\\end{tabular} \\\\\n\\hline\n$\\mathrm{Al}$ & gas-atomized (Ar) & $10-45$ & spherical & $58 \\pm 0.18$ & $48 \\pm 0.33$ & $1.31 \\pm 0.02$ \\\\\n$\\mathrm{C}$ & ground & up to 45 & flake-shaped & $62 \\pm 0.18$ & $90 \\pm 0.29$ & $0.54 \\pm 0.02$ \\\\\n$\\mathrm{Co}$ & water-atomized & $15-45$ & splash-shaped & $48 \\pm 0.10$ & $73 \\pm 0.06$ & $3.40 \\pm 0.02$ \\\\\n$\\mathrm{Fe}$ & gas-atomized (Ar) & $10-45$ & spherical & $56 \\pm 0.18$ & $74 \\pm 0.65$ & $4.03 \\pm 0.03$ \\\\\n$\\mathrm{Mn}$ & ground & up to 45 & flake-shaped & $52 \\pm 0.09$ & $73 \\pm 0.09$ & $2.50 \\pm 0.02$ \\\\\n$\\mathrm{Ni}$ & gas-atomized (Ar) & $15-45$ & spherical & $55 \\pm 0.19$ & $65 \\pm 0.34$ & $4.55 \\pm 0.02$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 2. Nominal chemical composition of the investigated alloys.\n\n\\begin{center}\n\\begin{tabular}{cccccccc}\n\\hline\nAlloy & Element & Al & C & Co & Fe & Mn & Ni \\\\\n\\hline\n\\multirow{2}{*}{BASE} & $(\\mathrm{at} \\%)$ & 6.14 & - & 23.46 & 23.46 & 23.46 & 23.46 \\\\\n & $(\\mathrm{wt} \\%)$ & 3.00 & - & 25.03 & 23.72 & 23.33 & 24.93 \\\\\nBASE + 0.6C & $(\\mathrm{at} \\%)$ & 6.01 & 2.70 & 22.82 & 22.82 & 22.82 & 22.82 \\\\\n & $(\\mathrm{wt} \\%)$ & 3.00 & 0.60 & 24.87 & 23.57 & 23.19 & 24.77 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nThe LPBF experiments were performed on an AconityMINI system designed by Aconity3D (Herzogenrath, Germany), which was specifically developed for laboratory use.", "start_char_idx": 612833, "end_char_idx": 615248, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "104c5c45-a4a5-478a-a091-80d09b1a7920": {"__data__": {"id_": "104c5c45-a4a5-478a-a091-80d09b1a7920", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2a845235-dd46-40d1-977e-348a756a8b12", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7a168d6482f9ea5013fe9404040ab56953f3a22e7a37f3f56c55e183e6e21a76", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7e2aa30d-a9d2-4611-830f-134031d4171e", "node_type": "1", "metadata": {}, "hash": "a1307bcbd07be8edd66191cfacfc648269f006098b58a98dca1b4ed69b1664fb", "class_name": "RelatedNodeInfo"}}, "text": "This system is characterized by a small building space (diameter $=50 \\mathrm{~mm}$, with a height of $200 \\mathrm{~mm}$ ) to reduce powder consumption, because the powder blends cannot be separated again after powder-mixing. The beam source was a single-mode fiber laser (wavelength of $1064 \\mathrm{~nm}$ ) with up to $400 \\mathrm{~W}$ of power output. Samples for microstructure and process parameter development were synthesized on a 45 substrate plate using a bidirectional scanning strategy with $90^{\\circ}$ rotations between consecutive layers to keep the vector length constant. A vector length of $5 \\mathrm{~mm}$ resulted from the used samples' geometry (cuboids with dimensions of $5 \\times 5 \\times 10 \\mathrm{~mm}^{3}$ ). The energy input during exposure was controlled by the selected process parameters (laser power $\\left(P_{L}\\right)$, layer thickness $\\left(D_{S}\\right)$, scanning speed $\\left(v_{S}\\right)$, and hatch distance $\\left(\\Delta y_{s}\\right)$ ). The volume energy density $\\left(E_{V}\\right)$ was calculated by Equation (1) [20]:\n\n\n\\begin{equation*}\nE_{V}=\\frac{P_{L}}{D_{S} \\cdot v_{s} \\cdot \\Delta y_{s}} \\tag{1}\n\\end{equation*}\n\n\nWithin the scope of this work, all specimens were manufactured with a constant layer thickness of $30 \\mu \\mathrm{m}$. The investigated process parameter combinations, including the corresponding calculated $E_{V}$, are shown in Figure 3. First, the relative densities of the BASE specimens were analyzed. Relative densities above $99.5 \\%$ were considered to be appropriate for the LPBF process [20]. Based on those results, process parameter sets with low $\\left(<100 \\mathrm{~J} \\mathrm{~mm}^{-3}\\right.$ ), middle $\\left(100-200 \\mathrm{~J} \\mathrm{~mm}^{-3}\\right)$, and high ( $>200 \\mathrm{~J}$ $\\mathrm{mm}^{-3}$ ) $E_{V}$ were selected to manufacture the BASE and BASE $+0.6 \\mathrm{C}$ samples.\n\nSamples for mechanical testing were produced on a C45 substrate plate, with a bidirectional scanning strategy, a scanning vector rotation of $33^{\\circ}$ between consecutive layers, and a scanning vector length of $5 \\mathrm{~mm}$. The mechanical properties of the bulk material were investigated with tensile tests. Therefore, cylindrical rods $6 \\mathrm{~mm}$ in diameter and $60 \\mathrm{~mm}$ in length were manufactured. For lattice compression tests, $\\mathrm{f}_{2} \\mathrm{cc}$ lattice structure specimens were manufactured [21] with $10 \\times 10 \\times 14$ cells, a cell width of $3 \\mathrm{~mm}$, dimensions of $30 \\times 30 \\times 42 \\mathrm{~mm}^{3}$, and a strut diameter of $500 \\mu \\mathrm{m}$.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_14ad84a6f46bf5697b9dg-05}\n\nFigure 3. Investigated hatch process parameter combinations with corresponding $E_{V}$. The used parameter sets for further samples are marked in blue.\n\n\\subsection*{2.3. Sample Preparation and Characterization Techniques}\nSpecimens for microstructure analysis were mechanically removed from the baseplate and ground with up to $1200 \\mathrm{SiC}$ grit paper followed by polishing using 6 and $1 \\mu \\mathrm{m}$ diamond suspension on a plane parallel to the build-up direction. Furthermore, samples were electrolytically polished using a voltage between 25 and $30 \\mathrm{~V}$ (depending on the chemical composition) for $15 \\mathrm{~s}$ in A2 electrolyte (Struers, Birmensdorf, Switzerland). Various etchants were tested to make microstructural features visible for optical microscopy. Reasonable results were only obtained with V2A etchant (a mixture consisting of equal parts water and hydrochloric acid with $5 \\%$ nitric acid) at $70{ }^{\\circ} \\mathrm{C}$.", "start_char_idx": 615249, "end_char_idx": 618881, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7e2aa30d-a9d2-4611-830f-134031d4171e": {"__data__": {"id_": "7e2aa30d-a9d2-4611-830f-134031d4171e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "104c5c45-a4a5-478a-a091-80d09b1a7920", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "fafbe007e11e7759d12d3ab378a141169d9c60ce5ad0616033cb9b2022f28df6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "91bc19dc-8b54-4309-8dc6-5fedc763c7ce", "node_type": "1", "metadata": {}, "hash": "198ad6fc6741e9f3633923b3826e2b7eead57b14102e008b3854613321416f54", "class_name": "RelatedNodeInfo"}}, "text": "\\subsection*{2.3. Sample Preparation and Characterization Techniques}\nSpecimens for microstructure analysis were mechanically removed from the baseplate and ground with up to $1200 \\mathrm{SiC}$ grit paper followed by polishing using 6 and $1 \\mu \\mathrm{m}$ diamond suspension on a plane parallel to the build-up direction. Furthermore, samples were electrolytically polished using a voltage between 25 and $30 \\mathrm{~V}$ (depending on the chemical composition) for $15 \\mathrm{~s}$ in A2 electrolyte (Struers, Birmensdorf, Switzerland). Various etchants were tested to make microstructural features visible for optical microscopy. Reasonable results were only obtained with V2A etchant (a mixture consisting of equal parts water and hydrochloric acid with $5 \\%$ nitric acid) at $70{ }^{\\circ} \\mathrm{C}$.\n\nScanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDS), and electron backscatter diffraction (EBSD) were performed on a field emission gun (FEG) SEM (Zeiss Sigma, Jena, Germany) with EDS and EBSD detectors (Oxford Instruments, Tubney Woods, Abingdon, UK). Combined EDS and EBSD area mappings were recorded with the voltage at $15 \\mathrm{kV}$ with the high-current mode enabled, a working distance between 8.5 and $9 \\mathrm{~mm}$, and a step size of $0.2 \\mu \\mathrm{m}$. Analysis and noise reduction of the data were carried out with the MATLAB\u00aeR-based MTEX toolbox [22,23].\n\nThe manufactured cylinders were machined to obtain round dog bone tensile specimens with B4 $\\times 20$ dimensions after DIN 50125. The mechanical properties were then determined through quasi-static uniaxial tensile tests on a Z4204 device (Zwick/Roell, Ulm, Germany) at room temperature and a strain rate of $2.510^{-4} \\cdot \\mathrm{s}^{-1}$. The lattice structures were removed from the baseplate by electrical discharge machining and were then compression-tested at room temperature on a servo-hydraulic universal mechanical testing machine (Schenk, Darmstadt, Germany) equipped with a $400 \\mathrm{kN}$ load cell and a constant strain rate of $10^{-3} \\mathrm{~s}^{-1}$. The specimens were tested according to DIN 50134:2008 and were interpreted after Tancogne et al. and Ashby et al. [24,25]. The specific energy absorption $\\left(E_{s 40 \\%}\\right)$ was used to evaluate energy absorption potential, which was calculated by integrating the force-displacement curve up until $40 \\%$ compression $\\left(E_{40 \\%}\\right)$ and dividing by the respective weight of the lattice structure $[18,26]$.\n\n\\section*{3. Results}\n\\subsection*{3.1. Process Development}\nThe measured relative densities corresponding to the calculated $E_{V}$ in Figure 3 for BASE and BASE $+0.6 \\mathrm{C}$ are shown in Figure 4. The densest specimens were manufactured with a laser power $P_{L}$ of $120 \\mathrm{~W}$, a scanning speed $v_{S}$ of $350 \\mathrm{~mm} \\cdot \\mathrm{s}^{-1}$, and hatch distances between 70 and $90 \\mu \\mathrm{m}$. The other area of the dense samples was manufactured with a $P_{L}$ of $200 \\mathrm{~W}, v_{S}$ of $450 \\mathrm{~mm} \\cdot \\mathrm{s}^{-1}$, and hatch distances between 60 and $80 \\mu \\mathrm{m}$. The parameter sets for further sample production were selected accordingly and are marked in Figure 4.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_14ad84a6f46bf5697b9dg-06}\n\nFigure 4. Color-coded relative densities dependent on different process parameters for (a) BASE and (b) BASE + 0.6C. The selected parameter sets for further production of samples are marked in blue.\n\n\\subsection*{3.2. Meltpool Size Depending on the Energy Input}\nAn analysis of the microstructure using optical microscopy on selected samples with high relative densities (see Figure 4) is shown in Figure 5.", "start_char_idx": 618071, "end_char_idx": 621800, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "91bc19dc-8b54-4309-8dc6-5fedc763c7ce": {"__data__": {"id_": "91bc19dc-8b54-4309-8dc6-5fedc763c7ce", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7e2aa30d-a9d2-4611-830f-134031d4171e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2024e21291fb77a2be75717bf9a55cff7bf2b5de75628e64d4f95e7e43730844", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "016858b9-203b-424e-ab0c-34dbcc368da1", "node_type": "1", "metadata": {}, "hash": "cf003c216cdb56a44ed0e64441e3e9c42eaa4895cb08c5aa5d8f46fbd0b22b14", "class_name": "RelatedNodeInfo"}}, "text": "The parameter sets for further sample production were selected accordingly and are marked in Figure 4.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_14ad84a6f46bf5697b9dg-06}\n\nFigure 4. Color-coded relative densities dependent on different process parameters for (a) BASE and (b) BASE + 0.6C. The selected parameter sets for further production of samples are marked in blue.\n\n\\subsection*{3.2. Meltpool Size Depending on the Energy Input}\nAn analysis of the microstructure using optical microscopy on selected samples with high relative densities (see Figure 4) is shown in Figure 5. In the micrographs, inhomogeneous regions from partially or unmelted powder particles were more intensely etched, resulting in black regions in the images. With increasing energy densities from 68 to 173 to $247 \\mathrm{~J} \\mathrm{~mm}^{-3}$ (Figure 5a,c,e), the amount of inhomogeneity was reduced, where the sample was fully homogeneous and uniformly etched with the highest energy density. To show the development of the melt pools in these samples, the uppermost layers of the respective specimens are shown in Figure 5b,d,f. The diameter of the previous melt pool increased from 111 to 195 to $424 \\mu \\mathrm{m}$, while the depth increased from 85 to 185 to $577 \\mu \\mathrm{m}$.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_14ad84a6f46bf5697b9dg-07}\n\nFigure 5. Optical micrographs of etched BASE alloy samples manufactured with energy densities of $(\\mathbf{a}, \\mathbf{b}) 68,(\\mathbf{c}, \\mathbf{d}) 173$, and $(\\mathbf{e}, \\mathbf{f}) 247 \\mathrm{~J} \\mathrm{~mm}^{-3}$. Microstructure development is shown $(\\mathrm{a}, \\mathrm{c}, \\mathrm{e})$ in the center of the sample and $(b, d, f)$ on the uppermost layer of the respective samples. White and orange dotted lines denote the sample surface and the shape of the former melt pool, respectively.\n\n\\subsection*{3.3. Chemical Homogeneity}\nThe chemical homogeneity after processing with different energy densities is shown in Figure 6 with EBSD and EDS area maps. At an energy density of $143 \\mathrm{~J} \\mathrm{~mm}^{-3}$ (Figure 6a), multiple areas of the microstructure were strongly enriched in $\\mathrm{Co}, \\mathrm{Fe}$, and $\\mathrm{Ni}$ below the prior melt pool boundaries. These were caused by partially melted powder particles during LPBF processing. When the energy density was sufficiently high, a more homogeneous elemental distribution was obtained (Figure 6b), where slight local differences in composition resulted from dendritic solidification. A low fraction of Al-oxides can be observed in Figure 6, where the dots represent oxide clusters.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_14ad84a6f46bf5697b9dg-08}\n\nFigure 6. Electron backscatter diffraction (EBSD) and energy-dispersive X-ray spectroscopy (EDS) area maps for the BASE multi-principal element alloys (MPEAs) manufactured with energy densities of (a) 143 and (b) $247 \\mathrm{~J} \\mathrm{~mm}^{-3}$. Lower energy densities resulted in regions locally enriched in $\\mathrm{Co}, \\mathrm{Fe}$, and $\\mathrm{Ni}$, while higher values produced a more homogeneous elemental distribution. The color-coding of the EBSD maps refers to an inverse pole figure with the build-up direction (BD) as a reference axis.\n\n\\subsection*{3.4. Mechanical Properties}\nThe results of tensile tests on samples manufactured with different energy densities are shown in Figure 7. At lower energy densities of 88 and $127 \\mathrm{~J} \\mathrm{~mm}^{-3}$, both investigated compositions showed drastically reduced elongation and slightly increased strength compared to a higher energy density state of $173 \\mathrm{~J} \\mathrm{~mm}^{-3}$.", "start_char_idx": 621203, "end_char_idx": 624884, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "016858b9-203b-424e-ab0c-34dbcc368da1": {"__data__": {"id_": "016858b9-203b-424e-ab0c-34dbcc368da1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "91bc19dc-8b54-4309-8dc6-5fedc763c7ce", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6a222f5c968519131161d7d0318889941003a19a7f6147e451d3c72bad154747", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9866c2de-9557-4c3d-a72e-59a51bc5272d", "node_type": "1", "metadata": {}, "hash": "5218ba4b137be4a0f64cb491489a6b45dd6ada1c463754b7e2f96b75c69c58fa", "class_name": "RelatedNodeInfo"}}, "text": "Lower energy densities resulted in regions locally enriched in $\\mathrm{Co}, \\mathrm{Fe}$, and $\\mathrm{Ni}$, while higher values produced a more homogeneous elemental distribution. The color-coding of the EBSD maps refers to an inverse pole figure with the build-up direction (BD) as a reference axis.\n\n\\subsection*{3.4. Mechanical Properties}\nThe results of tensile tests on samples manufactured with different energy densities are shown in Figure 7. At lower energy densities of 88 and $127 \\mathrm{~J} \\mathrm{~mm}^{-3}$, both investigated compositions showed drastically reduced elongation and slightly increased strength compared to a higher energy density state of $173 \\mathrm{~J} \\mathrm{~mm}^{-3}$. Additionally, overall strength and ductility was increased with the addition of 0.6 $\\mathrm{wt} \\% \\mathrm{C}$ to the alloy.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_14ad84a6f46bf5697b9dg-09}\n\nFigure 7. Engineering stress-strain curves of the (a) BASE and (b) BASE +0.6 C alloys processed with the shown energy densities. Total elongation was drastically reduced, whereas strength increased slightly at low energy densities. The addition of $0.6 \\mathrm{wt} \\% \\mathrm{C}$ led to strongly increased strength and ductility.\n\nBased on the mechanical properties from tensile testing (Figure 7), the alloy and processing parameters with the highest combinations of strength and ductility were used to manufacture the lattice structure. Consequently, BASE $+0.6 \\mathrm{C}$ was chosen at an energy density of $173 \\mathrm{~J} \\mathrm{~mm}^{-3}$. The corresponding force-strain curve obtained by compression testing of the produced lattice structure and comparisons with other materials are shown in Figure 8. After yielding, the force increased to $46 \\mathrm{kN}$ at around $30 \\%$ compression. Further loading led to decreased force, indicating the failure of some load-bearing struts in the structure. At around $60 \\%$ compression, the compaction region was reached, where the lattice was fully compressed. With $40 \\%$ strain, the lattice structure absorbed an energy of $712 \\mathrm{~J}\\left(E_{40 \\%}\\right)$, resulting in a specific energy absorption of $15.2 \\mathrm{~J} \\mathrm{~g}^{-1}$ when taking the weight of the specimen into account. Compared to lattice structures with the same geometry but a different alloy, the energy absorption of the MPEAs was higher than that of 316L, while it was on a similar level to high-Manganese steels.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_14ad84a6f46bf5697b9dg-10}\n\nFigure 8. (a) Force-engineering strain curve of the BASE + 0.6C lattice structure during compression testing. The sample was manufactured using an energy density of $173 \\mathrm{~J} \\mathrm{~mm}^{-3}$. (b) Comparison of the specific absorbed energy to lattice structures [18] of the same geometry ( $\\mathrm{f}_{2} \\mathrm{Cc}_{\\mathrm{z}}$ type, $500 \\mu \\mathrm{m}$ struts, $3 \\mathrm{~mm}$ cell width) but different material.\n\n\\section*{4. Discussion}\nIn the following, the adaption of the rapid alloy development methodology from LMD to LPBF as well as the processability of powder blends and the influence of process parameters on the mechanical properties are discussed.\n\nAfter process parameter optimization, several parameter sets with relative densities above $99.5 \\%$ and a homogenous elemental distribution were determined for BASE and BASE + 0.6C (Figures 4-6). These results showed the successful transition of the rapid alloy development methodology first applied in LMD [14] to LPBF. With LPBF, less elemental segregation takes place during solidification due to the higher cooling rates compared to LMD [18,27]. Therefore, the possibility of processable materials is larger than in LMD, and better mechanical properties can be achieved because of grain refinement [28-30]. However, the powder consumption in LPBF is higher compared to LMD due to the necessity of filling the building chamber.", "start_char_idx": 624176, "end_char_idx": 628147, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9866c2de-9557-4c3d-a72e-59a51bc5272d": {"__data__": {"id_": "9866c2de-9557-4c3d-a72e-59a51bc5272d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "016858b9-203b-424e-ab0c-34dbcc368da1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1b8390af4af99e91ef4f8cf80703f18b613391fd0bbcdbefec7f8027a9e8cac8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "75bc4064-c4ab-4e79-9165-50191ebf8ecd", "node_type": "1", "metadata": {}, "hash": "d21b8f4aab0eb3658945463160beac85c8a530530d22fef99c58f41dc13a091a", "class_name": "RelatedNodeInfo"}}, "text": "Discussion}\nIn the following, the adaption of the rapid alloy development methodology from LMD to LPBF as well as the processability of powder blends and the influence of process parameters on the mechanical properties are discussed.\n\nAfter process parameter optimization, several parameter sets with relative densities above $99.5 \\%$ and a homogenous elemental distribution were determined for BASE and BASE + 0.6C (Figures 4-6). These results showed the successful transition of the rapid alloy development methodology first applied in LMD [14] to LPBF. With LPBF, less elemental segregation takes place during solidification due to the higher cooling rates compared to LMD [18,27]. Therefore, the possibility of processable materials is larger than in LMD, and better mechanical properties can be achieved because of grain refinement [28-30]. However, the powder consumption in LPBF is higher compared to LMD due to the necessity of filling the building chamber. With respect to flexible alloy modification, LMD enables in-situ mixing of various powders, chemical gradients within specimens/parts, and efficient powder consumption $[1,31]$. Overall, LPBF is more suitable for alloy design due to higher reproducibility and lower defect density compared to LMD.\n\nThe powder blends utilized in the process contained up to six different elemental powders with varying morphology. The $\\mathrm{Ni}, \\mathrm{Al}$, and $\\mathrm{Fe}$ powders were inert gas-atomized, which is the most used production technology for the synthesis of powders used in LPBF. The characteristics of inert gas-atomized powders are a spherical shape, high flowability, and high purity [32]. Mn and C were produced by grinding, resulting in flake-shaped particles with poor flowability and thus poor recoating behavior during LPBF [32]. The Co powder was water-atomized and revealed an irregular splash-shaped morphology. Nevertheless, the Co powder still retained reasonable flowability. The bulk density of the powders was in the range between $0.544 \\mathrm{~g} \\mathrm{ml}^{-1}(\\mathrm{C})$ and $4.545 \\mathrm{~g} \\mathrm{ml}^{-1}(\\mathrm{Ni})$. The particle size distribution (PSD) for all powders was in the range of 10 and $45 \\mu \\mathrm{m}$, except for $\\mathrm{Mn}$ and C, where particles with a diameter below $10 \\mu \\mathrm{m}$ were present, which reduced the flowability and thus influenced powder recoating behavior. The flowability (defined by the average avalanche angle) was between $48^{\\circ}$ for $\\mathrm{Co}$ and $62^{\\circ}$ for $\\mathrm{C}$. As evidenced by the high relative densities achieved (Figure 4), the powder\\\\\nblends revealed a suitable recoating behavior. Therefore, the poor flowability of powders ( $\\mathrm{C}, \\mathrm{Mn})$ could be compensated for by blending them with powders characterized by high flowability ( $\\mathrm{Fe}, \\mathrm{Ni}$, and $\\mathrm{Al}$ ).\n\nThe absorption tested for the used wavelength of $1064 \\mathrm{~nm}$ was determined to be $48 \\%$ for $\\mathrm{Al}$ and up to $90 \\%$ for C. Therefore, the energy input into the powder varied significantly between the different powders. This could cause overheating of powders with higher absorption as well as incomplete melting of powders with low absorption. However, once the melt pool was fully developed, the absorption remained constant and the influence of the different absorption coefficients vanished due to a preflowing melt pool [33]. The use of elemental powders led to higher evaporation, since the elements with lower melting temperatures melted first and could overheat, whereas the elements with higher melting temperatures showed delayed transformation into the liquid phase [34] (Table 3). Consequently, Mn and Co had the highest and lowest evaporation rates due to their evaporation temperatures, respectively. This behavior was validated by EDS mapping, as shown in Figure 6. The used elemental manganese powder showed high oxidation and therefore a high oxygen content due to the production process. The oxygen introduced by the manganese powder resulted in the formation of Al-oxides due to the high affinity of $\\mathrm{Al}$ to oxygen [35]. A low fraction of Al-oxides could be observed in the EDS element mapping, as shown in Figure 6. The Al-oxide clusters are shown as small white dots in the aluminum mapping.", "start_char_idx": 627181, "end_char_idx": 631497, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "75bc4064-c4ab-4e79-9165-50191ebf8ecd": {"__data__": {"id_": "75bc4064-c4ab-4e79-9165-50191ebf8ecd", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9866c2de-9557-4c3d-a72e-59a51bc5272d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3109aa59b3b5d320865994728c837a90c10e12d6a3b6c8edfeb4bc8810b1d64d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7f9219dd-f952-450c-ba94-7ecb86bb826e", "node_type": "1", "metadata": {}, "hash": "75514f781503e5f711d8673c1365e5f65d6492109b0c3d3027afc710e5e71ba0", "class_name": "RelatedNodeInfo"}}, "text": "The use of elemental powders led to higher evaporation, since the elements with lower melting temperatures melted first and could overheat, whereas the elements with higher melting temperatures showed delayed transformation into the liquid phase [34] (Table 3). Consequently, Mn and Co had the highest and lowest evaporation rates due to their evaporation temperatures, respectively. This behavior was validated by EDS mapping, as shown in Figure 6. The used elemental manganese powder showed high oxidation and therefore a high oxygen content due to the production process. The oxygen introduced by the manganese powder resulted in the formation of Al-oxides due to the high affinity of $\\mathrm{Al}$ to oxygen [35]. A low fraction of Al-oxides could be observed in the EDS element mapping, as shown in Figure 6. The Al-oxide clusters are shown as small white dots in the aluminum mapping. Nevertheless, an overall homogenous element distribution could be observed in the LPBF-produced samples using powder blends. This proved in general the applicability of powder blends in LPBF, even for complex powder blends consisting of up to six different powders with varying morphologies and PSDs.\n\nTable 3. Evaporation and melting temperatures of the used elements $[19,20]$.\n\n\\begin{center}\n\\begin{tabular}{ccccccc}\n\\hline\nElement & Al & C & Co & Fe & Mn & Ni \\\\\n\\hline\nMelting temperature $\\left({ }^{\\circ} \\mathrm{C}\\right)$ & 660 & - & 1495 & 1538 & 1246 & 1455 \\\\\nEvaporation temperature $\\left({ }^{\\circ} \\mathrm{C}\\right)$ & 2470 & 4827 & 2870 & 2862 & 2061 & 2732 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nThe results showed that dense parts could be produced using a broad spectrum of process parameters. This allowed for the application of a wide processing window, with $E_{V}$ in the range between 60 and $240 \\mathrm{~J} \\mathrm{~mm}^{-3}$ for the investigated alloying system. A higher energy input resulted in higher homogeneity of the elemental distribution due to enlargement of the melt pool size by means of width and depth, which resulted in a higher number of powder particles in the melt pool [36]. The calculated particle amount contained in the melt pools shown in Figure 5 was 15 for Figure 5b, 57 for Figure 5d, and 386 for Figure 5f. This enlarged melt pool enabled the enhanced mixing of elements and at the same time facilitated the remelting of previously solidified layers. Hence, the higher the energy density was, the higher the homogeneity of the elemental distribution due to complete melting and mixing of the various elemental powder particles was. In Figure 6a, partially molten particles and heterogeneously composed areas can be found. Furthermore, the increased energy input also promoted higher homogeneity due to a higher melt pool temperature [36]. As a consequence, less nonfused material was observed (Figures 5 and 6).\n\nHomogeneity also affected the mechanical properties. Whereas specimens produced with a higher $E_{V}$ resulted in increased elongation, samples manufactured with a lower $E_{V}$ revealed reduced fracture strain (Figure 7). Presumably, the loss of ductility was associated with locally heterogeneous deformation behavior, as well as notch effects in the vicinity of unmolten particles [37]. Since the process development allowed for the production of samples with similarly high relative densities, the detrimental effects of the remaining porosity could be ruled out as a cause of reduced ductility. However, it must also be noted that very high energy densities may result in pronounced evaporation/gas entrapment and thus more gas pores [38]. These pores usually contribute to deteriorated mechanical properties [39]. Hence, an optimum process window avoids the effects associated with very low and very high input energies.\n\nFurthermore, the rapid alloy development methodology introduced was used for material screening. As an example, $\\mathrm{C}$ was added to the BASE alloy to tailor the mechanical properties. $\\mathrm{C}$ was\\\\\nchosen because it is known as a very efficient solid solution strengthening element in fcc alloys. By adding $0.6 \\mathrm{wt} \\% \\mathrm{C}$, the mechanical properties of the BASE alloy were improved with respect to both strength and ductility (Figure 7).", "start_char_idx": 630607, "end_char_idx": 634859, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7f9219dd-f952-450c-ba94-7ecb86bb826e": {"__data__": {"id_": "7f9219dd-f952-450c-ba94-7ecb86bb826e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "75bc4064-c4ab-4e79-9165-50191ebf8ecd", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "fd904bbdc0206277627fadf8157d3a054c0f53d70340d89e5b150fa525fced73", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "27dd3b36-c82d-4c61-be10-eb8c83e1b7cb", "node_type": "1", "metadata": {}, "hash": "c78ee38fb698865270da19c35289f5a4d026a37bacd1e982e2db9bc0f23fc6b6", "class_name": "RelatedNodeInfo"}}, "text": "However, it must also be noted that very high energy densities may result in pronounced evaporation/gas entrapment and thus more gas pores [38]. These pores usually contribute to deteriorated mechanical properties [39]. Hence, an optimum process window avoids the effects associated with very low and very high input energies.\n\nFurthermore, the rapid alloy development methodology introduced was used for material screening. As an example, $\\mathrm{C}$ was added to the BASE alloy to tailor the mechanical properties. $\\mathrm{C}$ was\\\\\nchosen because it is known as a very efficient solid solution strengthening element in fcc alloys. By adding $0.6 \\mathrm{wt} \\% \\mathrm{C}$, the mechanical properties of the BASE alloy were improved with respect to both strength and ductility (Figure 7). To exclude further microstructural modifications, the process parameters were kept constant for both BASE and BASE + 0.6C. A usable parameter set was determined within the process parameter development (Figures 3 and 4). The development showed similar results for relative density for both alloys using the same process parameter sets. Nevertheless, a negligible influence of the process parameters on the relative density was determined. Surprisingly though, the application of powder blends containing elemental $\\mathrm{C}$ powder with poor flowability and flake-shaped morphology did not deteriorate processability. Furthermore, pure $\\mathrm{C}$ particles and large carbides were not observed, which suggested the complete dissolution and homogeneous distribution of interstitial C atoms. Therefore, the usage of complex powder blends to tailor material properties to design materials by and for AM can be confirmed.\n\nTo demonstrate the potential to produce geometrically complex structures with powder blends, $\\mathrm{f}_{2} \\mathrm{Cc}_{\\mathrm{Z}}$ lattice structures were synthesized. These delicate structures are a suitable measure for the reliability of the material produced from powder blends due to the sensitivity of the thin struts to material homogeneity. For instance, most common strut sizes for LPBF-manufactured lattice structures are $500 \\mu \\mathrm{m}$ in diameter [21,40], which means that a laser beam melts approximately 350 particles on the top layer per strut. An energy input of $173 \\mathrm{~J} \\mathrm{~mm}^{-3}$, considered to be the optimal value for the BASE + 0.6C alloy, was chosen, resulting in ductile and homogeneous deformation behavior (Figure 8). Compared to the results of Kies et al. [18], where high-manganese transformation-induced plasticity (TRIP) and twinning-induced plasticity (TWIP) steels were tested, a similar specific energy absorption was achieved. Furthermore, compared to the benchmark material 316L, the specific energy absorption of the tested MPEAs was increased by approximately $75 \\%[18,31]$. Therefore, the usability of the rapid alloying methodology was additionally validated due to successfully manufacturing lattice structure specimens with reliable deformation behavior.\n\n\\section*{5. Conclusions}\nThe present study showed that fully dense and chemically homogenous MPEAs could be successfully manufactured by using elemental powder blends in LPBF. This enables a rapid and resource-efficient approach to screen and design novel materials. The following conclusions could be drawn:\n\n\\begin{enumerate}\n  \\item Complex powder blends consisting of up to six elemental powders with different morphologies, size distributions, and amounts could be applied to the LPBF process. Therefore, rapid alloy development of chemically complex metallic alloys is possible, which was demonstrated on C-Al-Co-Fe-Mn-Ni MPEAs. Compared to other metal AM processes, higher cooling rates facilitated improved material properties, e.g., high strength, high energy absorption capacity, and less elemental segregation.\n\n  \\item Chemical homogeneity was strongly dependent on the energy input and resulting size of the melt pool formed during LPBF. On the one hand, insufficient energy input resulted in inhomogeneous elemental distribution, as powders with high melting points were only partially melted. On the other hand, small melt pool sizes prohibited sufficient elemental mixing. Optimal energy input resulted in alloys with high chemical homogeneity.\n\n  \\item The mechanical properties of the investigated $\\mathrm{Al}_{0.26} \\mathrm{CoFeMnNi}$ system were significantly improved by the addition of $0.6 \\mathrm{wt} \\% \\mathrm{C}$, resulting in both increased strength and ductility. Therefore, the methodology of combining powder blending and LPBF was proven to be a promising method to produce high-quality material containing significant nonmetallic additions, such as $\\mathrm{C}$.", "start_char_idx": 634067, "end_char_idx": 638802, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "27dd3b36-c82d-4c61-be10-eb8c83e1b7cb": {"__data__": {"id_": "27dd3b36-c82d-4c61-be10-eb8c83e1b7cb", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7f9219dd-f952-450c-ba94-7ecb86bb826e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4834332ac2c1eda0f8a8f307a6c0e9143a04cbfbfa2266bd2db7bb436a1c8924", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f70f7c61-d578-48ad-9ef7-0271754f81af", "node_type": "1", "metadata": {}, "hash": "740aa5809067dba542ed702bd7a485500b6804af2dee2ca974ae7d759f9a2fee", "class_name": "RelatedNodeInfo"}}, "text": "\\item Chemical homogeneity was strongly dependent on the energy input and resulting size of the melt pool formed during LPBF. On the one hand, insufficient energy input resulted in inhomogeneous elemental distribution, as powders with high melting points were only partially melted. On the other hand, small melt pool sizes prohibited sufficient elemental mixing. Optimal energy input resulted in alloys with high chemical homogeneity.\n\n  \\item The mechanical properties of the investigated $\\mathrm{Al}_{0.26} \\mathrm{CoFeMnNi}$ system were significantly improved by the addition of $0.6 \\mathrm{wt} \\% \\mathrm{C}$, resulting in both increased strength and ductility. Therefore, the methodology of combining powder blending and LPBF was proven to be a promising method to produce high-quality material containing significant nonmetallic additions, such as $\\mathrm{C}$.\n\n  \\item LPBF using powder blends enables manufacturing of parts with complex geometry, e.g., lattice structures, and reliable mechanical properties. The produced lattice structures indicated a higher energy absorption capacity compared to the commonly used 316L and were comparable to high-Manganese steel samples.\n\n\\end{enumerate}\n\nAuthor Contributions: The research work presented in this manuscript was planned and carried out as a collaboration of the authors listed above. S.E. and M.V. produced the samples and performed the experiments; F.K. performed the microstructural and mechanical analysis; S.E., F.K., S.H., and M.V. analyzed the data. S.E., F.K., and S.H. wrote the paper; supervision and conceptualization were perfomed by C.H. and J.H.S.; all authors contributed to the scientific design of the study and a discussion of the results and have seen and approved the final manuscript.\n\nFunding: This research was funded by the German Research Foundation DFG within the Cluster of Excellence Internet of Production (IOP) Project-ID: 390621612-Cluster Research Domain B1 and C2. This research was also funded by Hans Hermann Voss-Stiftung from the RWTH Aachen Seed-Fund project OPSF406.\n\nConflicts of Interest: The authors confirm that there are no known conflicts of interest associated with this publication and that there has been no significant financial support for this work that could have influenced its outcome.\n\n\\section*{References}\n\\begin{enumerate}\n  \\item Gibson, I.; Rosen, D.W.; Stucker, B. Additive Manufacturing Technologies; Springer US: Boston, MA, USA, 2010; ISBN 978-1-4419-1119-3.\n\n  \\item Schleifenbaum, H.; Meiners, W.; Wissenbach, K.; Hinke, C. Individualized production by means of high power Selective Laser Melting. CIRP J. Manuf. Sci. Technol. 2010, 2, 161-169. [CrossRef]\n\n  \\item Wen, P.; Jauer, L.; Voshage, M.; Chen, Y.; Poprawe, R.; Schleifenbaum, J.H. Densification behavior of pure Zn metal parts produced by selective laser melting for manufacturing biodegradable implants. J. Mater. Process. Technol. 2018, 258, 128-137. 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[CrossRef]\n\n  \\item Kies, F.; K\u00f6hnen, P.; Wilms, M.B.", "start_char_idx": 641109, "end_char_idx": 643908, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "85f8035e-de7e-4157-8b48-ea155ca33b12": {"__data__": {"id_": "85f8035e-de7e-4157-8b48-ea155ca33b12", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f70f7c61-d578-48ad-9ef7-0271754f81af", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9e5916ce2da4ce3aeff338af2079f2f151bf3e7f6fb82e75f97b206a91d9c5e2", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7d5fd6a8-de2e-4446-9dd9-979662c55b07", "node_type": "1", "metadata": {}, "hash": "71239d4905d87c29700fcc99e59bfc1109d51e984db3085571f29609b9abd2ed", "class_name": "RelatedNodeInfo"}}, "text": "[CrossRef]\n\n  \\item Ewald, S.; Schaukellis, M.; Koehnen, P.; Schleifenbaum, J.H. Laser Powder Bed Fusion of Advanced High-Strength Steels-Modification of Deformation Mechanisms by Increasing Stacking Fault Energy. BHM Berg 2019, 10, 2. [CrossRef]\n\n  \\item Liu, Z.H.; Zhang, D.Q.; Sing, S.L.; Chua, C.K.; Loh, L.E. Interfacial characterization of SLM parts in multi-material processing: Metallurgical diffusion between 316L stainless steel and C18400 copper alloy. Mater. Charact. 2014, 94, 116-125. [CrossRef]\n\n  \\item Kies, F.; K\u00f6hnen, P.; Wilms, M.B.; Brasche, F.; Pradeep, K.G.; Schwedt, A.; Richter, S.; Weisheit, A.; Schleifenbaum, J.H.; Haase, C. Design of high-manganese steels for additive manufacturing applications with energy-absorption functionality. Mater. Des. 2018, 160, 1250-1264. [CrossRef]\n\n  \\item Li, W.; Chen, X.; Yan, L.; Zhang, J.; Zhang, X.; Liou, F. Additive manufacturing of a new Fe-Cr-Ni alloy with gradually changing compositions with elemental powder mixes and thermodynamic calculation. Int. J. Adv. Manuf. 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Laser Additive Manufacturing of High-Performance Materials; Springer: Berlin/Heidelberg, Germany, 2015; ISBN 978-3-662-46088-7.", "start_char_idx": 643356, "end_char_idx": 646155, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7d5fd6a8-de2e-4446-9dd9-979662c55b07": {"__data__": {"id_": "7d5fd6a8-de2e-4446-9dd9-979662c55b07", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "85f8035e-de7e-4157-8b48-ea155ca33b12", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8f455baf025fb9cf39e3c027171fb2687992df1ee51e096eee44e972a65c8ce8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "525678cd-c498-4581-b47d-dda650871046", "node_type": "1", "metadata": {}, "hash": "474974e52b865ac2c2bd69e2e45f8c41625f510282f631060d57aab0e031b13a", "class_name": "RelatedNodeInfo"}}, "text": "; Bleck, W. Mechanical properties and deformation behavior of additively manufactured lattice structures of stainless steel. Mater. Des. 2018, 145, 205-217. [CrossRef]\n\n  \\item Yap, C.Y.; Chua, C.K.; Dong, Z.L.; Liu, Z.H.; Zhang, D.Q.; Loh, L.E.; Sing, S.L. Review of selective laser melting: Materials and applications. Appl. Phys. Rev. 2015, 2, 41101. [CrossRef]\n\n  \\item Gu, D. Laser Additive Manufacturing of High-Performance Materials; Springer: Berlin/Heidelberg, Germany, 2015; ISBN 978-3-662-46088-7.\n\n  \\item Marchese, G.; Garmendia Colera, X.; Calignano, F.; Lorusso, M.; Biamino, S.; Minetola, P.; Manfredi, D. Characterization and Comparison of Inconel 625 Processed by Selective Laser Melting and Laser Metal Deposition. Adv. Eng. Mater. 2017, 19, 1600635. [CrossRef]\n\n  \\item Calleja, A.; Tabernero, I.; Ealo, J.A.; Campa, F.J.; Lamikiz, A.; Lopez de Lacalle, L.N. Feed rate calculation algorithm for the homogeneous material deposition of blisk blades by 5 -axis laser cladding. Int. 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Cellular Design for Laser Freeform Fabrication, 1st ed.; Cuvillier Verlag: G\u00f6ttingen, Germany, 2010; ISBN 9783736932739.", "start_char_idx": 645647, "end_char_idx": 648478, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "525678cd-c498-4581-b47d-dda650871046": {"__data__": {"id_": "525678cd-c498-4581-b47d-dda650871046", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7d5fd6a8-de2e-4446-9dd9-979662c55b07", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "22f5e0a1089c4425a2ecc343b4f7afe3f1098d6fa758f8a53816496b3bdb9da0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9797bfa4-3997-4a4c-8832-3e2db91dd7e1", "node_type": "1", "metadata": {}, "hash": "bdb5cab8dd1165f3ac65ff2855ec0b8b6e3757b498ac8dd736f73f8fddb1c650", "class_name": "RelatedNodeInfo"}}, "text": "\\item Voshage, M.; Wen, P.; Schaukellis, M.; Schleifenbaum, J.H. Formation Quality, Mechanical Properties, and Processing Behavior of Pure Zinc Parts Produced by Laser-Based Manufacturing for Biodegradable Implants. BHM Berg. 2019, 87, 1. [CrossRef]\n\n  \\item Xu, Z.; Wen, W.; Zhai, T. Effects of Pore Position in Depth on Stress/Strain Concentration and Fatigue Crack Initiation. Metall. Mat. Trans. A 2012, 43, 2763-2770. [CrossRef]\n\n  \\item Rehme, O. Cellular Design for Laser Freeform Fabrication, 1st ed.; Cuvillier Verlag: G\u00f6ttingen, Germany, 2010; ISBN 9783736932739.\n\n\\end{enumerate}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_14ad84a6f46bf5697b9dg-15}\n\\end{center}\n\n(C) 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (\\href{http://creativecommons.org/licenses/by/4.0/}{http://creativecommons.org/licenses/by/4.0/}).\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\n\\title{Controlling crack formation and porosity in laser powder bed fusion: Alloy design and process optimisation }\n\n\n\\author{Hossein Eskandari Sabzi ${ }^{\\mathrm{a}}$, Suhyun Maeng ${ }^{\\mathrm{a}, \\mathrm{b}}$, Xingzhong Liang ${ }^{\\mathrm{a}, \\mathrm{c}}$, Marco Simonelli ${ }^{\\mathrm{d}}$,\\\\\nNesma T. Aboulkhair ${ }^{\\mathrm{d}}$, Pedro E.J. Rivera-D\u00edaz-del-Castillo ${ }^{\\mathrm{a}, *}$\\\\\n${ }^{a}$ Department of Engineering, Engineering Building, Lancaster University, LA1 4YW, United Kingdom\\\\\n${ }^{\\mathrm{b}}$ The Wolfson School of Mechanical, Electrical and Manufacturing Engineering, Loughborough University, LE11 3TU, United Kingdom\\\\\n${ }^{\\mathrm{c}}$ Department of Engineering, University of Leicester, Leicester LE1 7RH, UK\\\\\n${ }^{\\mathrm{d}}$ Centre for Additive Manufacturing (CFAM), Faculty of Engineering, University of Nottingham, NG8 1BB, United Kingdom}\n\\date{}\n\n\n%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?]{%\n  \\if\\relax#1\\relax%\n    \\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n  \\else%\n    \\if?#1\\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n    \\else\\svfootnotetext[#1]{#2}\\fi%\n  \\fi\n}\n\n\\begin{document}\n\\maketitle", "start_char_idx": 647905, "end_char_idx": 650855, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9797bfa4-3997-4a4c-8832-3e2db91dd7e1": {"__data__": {"id_": "9797bfa4-3997-4a4c-8832-3e2db91dd7e1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "525678cd-c498-4581-b47d-dda650871046", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "fda32dcd6b32f42b529b1c9b1389ee374a544fef55ebff7289ffde1a8c098444", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0f87108c-f70d-42cc-9750-b431a5cc59a3", "node_type": "1", "metadata": {}, "hash": "7117e3886ffcdffed43a82a2ac19d4b760ffe7cea71e5996e59b82662bf4b0fb", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{A R T I C L E I N F O}\n\\section*{Keywords:}\nAdditive manufacturing\n\nLaser powder bed fusion\n\nSolidification cracking\n\nPorosity\n\nAustenitic stainless steel\n\n\\begin{abstract}\nA B S T R A C T A computational method is presented to design alloys of lower susceptibility to solidification cracking, while preventing the formation of porosity and defects during laser powder bed fusion (LPBF). The method is developed for austenitic stainless steels, on which a wealth of data are available as various conditions for crack and pore/defect formation have been reported. The model is based on an alloy design approach combining thermodynamic calculations with a genetic algorithm to discover novel austenitic stainless steel compositions; the new alloys are expected to be crack-free whilst showing improved strength. A new crack prevention factor is proposed to relate composition to solidification crack formation. The factor incorporates quantitative criteria for the solidification temperature range, the performance index (ratio between yield stress and coefficient of thermal expansion) and the solidification path. Overall, the design methodology is validated by literature data on 316L austenitic stainless steel. Although cracking is not an issue during LPBF of 316L stainless steel, this material is a good choice to show under which conditions the cracks form. As for porosity and defect prevention, it is shown how this can be achieved by providing a sufficient amount of energy to melt the powder bed, and by controlling the melt pool geometry; such criteria are dissimilar to those reported in the literature. Process maps have been developed to show the effects of process parameters on the formation of pores and defects based on the proposed criteria. The model is applied to optimise such parameters to produce 316L austenitic stainless steel, and it is shown that a defect-free LPBFed stainless steel can be achieved, performing better under tensile testing compared to its wrought counterpart. The conditions for the application of such model to other alloy families displaying cracking, such as marageing steels and nickel alloys, are discussed.\n\\end{abstract}\n\n\\section*{1. Introduction}\nAustenitic stainless steels have widespread usage in marine, energy, aerospace, nuclear and medical devices as they exhibit attractive strength and corrosion resistance [1]. Laser powder bed fusion (LPBF) is a type of additive manufacturing (AM) process with great potential for the production of austenitic stainless steel components, as there is a wide availability of relatively inexpensive feedstock of such materials for AM [2]. However, it is challenging to produce crack- and porosityfree austenitic stainless steel components via LPBF, due to the complex thermal cycles of its associated processing, which lead to high residual stresses, variations in the settings of the different LPBF machines as well as a range of powder characteristics, which can affect the formation of cracks and porosity [3-7]. The presence of defects (cracks and pores) has the most adverse effect on mechanical properties [4]. The challenges to reduce them in LPBF as-built parts comes from the variability of different machines, complex processing conditions and variance in local thermal histories that can have a significant impact on defect formation $[8,9]$.\n\nA key challenge for researchers working on LPBF of austenitic stainless steels is to determine key process parameters to reduce the probability of the formation of defects. Experimental advances have been achieved via trial and error approaches, which are expensive and time consuming. One approach is the in situ detection of defect formation, using imaging techniques as a strategy to monitor the LPBF process [10]. This approach may be useful to detect crack and porosity\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author.\n\\end{itemize}\n\nE-mail address: \\href{mailto:p.rivera1@lancaster.ac.uk}{p.rivera1@lancaster.ac.uk} (P.E.J. Rivera-D\u00edaz-del-Castillo).\n}\nformation, but it neglects the impact of variations in process parameters in LPBF machines and in feedstock compositions, which have been adjusted by trial and error. An attractive alternative to such approach is to predict the formation of defects using numerical models that consider both the properties of the material and the process parameters, as this leads to cost reduction.\n\nCracks developing during LPBF of austenitic stainless steels form in the presence of liquid films [11,12]. The combination of liquid films and thermal stresses arising from LPBF leads to the development of solidification cracks [13]. Therefore, not only process parameters can affect cracking but also the solidification sequence.", "start_char_idx": 650858, "end_char_idx": 655604, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0f87108c-f70d-42cc-9750-b431a5cc59a3": {"__data__": {"id_": "0f87108c-f70d-42cc-9750-b431a5cc59a3", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9797bfa4-3997-4a4c-8832-3e2db91dd7e1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8ad16529e2eb595aa737b7cc62df5e6e937ab7c899f222971c4985801e96e1cf", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a7905e7b-a6d1-4323-b0ac-ad5aa95a35ca", "node_type": "1", "metadata": {}, "hash": "01f4c30dafde59803904f944c3817962b4f0be7f7a7fedc16d563f8726b4dc81", "class_name": "RelatedNodeInfo"}}, "text": "\\end{itemize}\n\nE-mail address: \\href{mailto:p.rivera1@lancaster.ac.uk}{p.rivera1@lancaster.ac.uk} (P.E.J. Rivera-D\u00edaz-del-Castillo).\n}\nformation, but it neglects the impact of variations in process parameters in LPBF machines and in feedstock compositions, which have been adjusted by trial and error. An attractive alternative to such approach is to predict the formation of defects using numerical models that consider both the properties of the material and the process parameters, as this leads to cost reduction.\n\nCracks developing during LPBF of austenitic stainless steels form in the presence of liquid films [11,12]. The combination of liquid films and thermal stresses arising from LPBF leads to the development of solidification cracks [13]. Therefore, not only process parameters can affect cracking but also the solidification sequence. It follows that optimisation of the chemical composition of the alloy can lead to a reduction in solidification cracking susceptibility in austenitic stainless steels. In contrast with nickel superalloys that are susceptible to more cracking variations such as liquation cracking or environmentally-assisted cracking (such as oxygen-induced cracks) [14,15], solidification cracking is the only crack type that has been observed during LPBF of austenitic stainless steels.\n\nIt is customary to adopt the concept of volumetric energy to estimate the heat input transferred to the melt pool by a scanning laser [16]. The volumetric energy is defined as\n\n$E_{v}=\\frac{P}{v \\cdot h \\cdot t}$\n\nwhere $P$ is the laser power, $v$ is the laser scan speed, $h$ is the hatch distance and $t$ is the layer thickness. Several attempts have been made to correlate $E_{v}$ with the defect density [6,17-19]. However, it has been proved that such estimation is not precise as it does not consider process parameters such as the laser spot size, the materials properties related to melting or the powder absorptivity [20]. Thomas et al. [21] normalised each parameter in Eq. (1) proposing dimensionless process parameters. Based on these parameters, a process map was developed to predict the formation of defects in general. Nevertheless, such maps cannot exactly predict the conditions leading to the presence of cracks and porosity.\n\nProcess-induced defects such as pores in LPBF can be categorised as lack of fusion, keyhole, and balling [22]. Each defect and pore type has a different origin dictated by the melt pool geometry [23,24]. Numerous attempts have been made to simulate and predict the melt pool geometry using computational approaches such as the finite element method (FEM) [24-26]. Using FEM provides a simplified and efficient approach to the problem of finding a solution for a single energy-balance equation. However, some of its disadvantages include that assumptions and simplifications have to be made about how the laser heat source is mathematically described; in addition, only a rough approximation of the melt pool and the convective flow is possible [27]. Moreover, it is a significant challenge to simulate the whole process due to its complexity and the associated computational cost [28]. Therefore, most of the associated studies are limited to a single track build [29].\n\nThere are some analytical models such as the Rosenthal solution [30] and the Eagar-Tsai model [31] that have originally been developed to describe fusion welding, and can be used for AM technology as well. Although due to the many simplifying assumptions followed by them, their accuracy is not sufficient to predict the melt pool geometry precisely, they can be used as efficient means to estimate the boundaries for melt pool geometry. In this paper, we combine a collection of computationally efficient models to estimate the melt pool geometry in order to predict the formation of different types of defects and porosity. In our model it has been assumed that the powder layer is spread homogeneously so its impact on the formation of defects is neglected. Heat input, which can be determined by the process parameters and the material's properties, has a major impact on the melt pool geometry. Insufficient laser power or high scan speeds can lead to Plateau-Rayleigh instability, which results in balling formation [11]. If the heat input is low, lack of fusion occurs [32]. On the other hand, above a certain heat input threshold, the laser melting changes from conduction to keyhole mode [33]. In here, the concept of normalised enthalpy has been applied to measure the heat input transferred to the powder bed by the laser beam.", "start_char_idx": 654755, "end_char_idx": 659333, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a7905e7b-a6d1-4323-b0ac-ad5aa95a35ca": {"__data__": {"id_": "a7905e7b-a6d1-4323-b0ac-ad5aa95a35ca", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0f87108c-f70d-42cc-9750-b431a5cc59a3", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "27d5d16880a9b42f458f4c3bcec6c5b0b127e9cac94c8081185fbd802b1c18e9", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9b910684-e1e2-42ef-b496-3211e0aec9f0", "node_type": "1", "metadata": {}, "hash": "f918a08a4acc350fe884d4614402da860f8dd3eb7c9befeea888806593e90c23", "class_name": "RelatedNodeInfo"}}, "text": "In this paper, we combine a collection of computationally efficient models to estimate the melt pool geometry in order to predict the formation of different types of defects and porosity. In our model it has been assumed that the powder layer is spread homogeneously so its impact on the formation of defects is neglected. Heat input, which can be determined by the process parameters and the material's properties, has a major impact on the melt pool geometry. Insufficient laser power or high scan speeds can lead to Plateau-Rayleigh instability, which results in balling formation [11]. If the heat input is low, lack of fusion occurs [32]. On the other hand, above a certain heat input threshold, the laser melting changes from conduction to keyhole mode [33]. In here, the concept of normalised enthalpy has been applied to measure the heat input transferred to the powder bed by the laser beam.\n\nIt has been reported that the presence of pores and defects deteriorate the mechanical properties of the as-built parts both in powder bed fusion and directed energy deposition (DED) processes. Mierzejewska showed that changing the LPBF process parameters will lead to a change in the volume fraction of pores in Ti-6Al-4V. They found that reducing the porosity percentage to $0.16 \\%$ leads to superior mechanical properties compared to the wrought counterparts [34]. Reduction in porosity and defects also improve the fatigue behaviour of the LPBF as-built components [35]. The same type of improvements in mechanical properties and fatigue behaviour are also reported by a reduction in crack and pore contents during the DED process $[36,37]$.\n\nA less developed, but more promising approach from a materials point of view is to design alloys less susceptible to LPBF variations, and subsequently less prone to defect formation. In this paper, we firstly propose a framework to design alloys of optimised solidification and controlled thermal stress formation. For this purpose, a number of metallurgical criteria for crack prevention have been introduced. This resulted in a crack prevention factor to define safe regions in compositional space for microcrack prevention upon austenitic stainless steels LPBF. A genetic algorithm (GA), combined with thermodynamic calculations was used to optimise and choose the new alloys. Then, a comprehensive analytical model is proposed to estimate safe process parameters for defect-free LPBF. This incorporates the material properties to avoid the formation of process-induced porosity in the as-built part. The methodology presented in this work can be considered as one more contribution to a growing body of literature [24,22,38] aimed at addressing the important problems of cracking, defects and porosity in metal AM.\n\nFollowing this, the application of the proposed models will be compared with the existing data on LPBF of 316L alloy in literature for crack prevention. The defect and porosity prevention model is validated for LPBF to describe the conditions leading to crack resistant 316L stainless steels. The effect of using optimised processing parameters on the production of a defect-free LPBF part is discussed. In the last part of this work, the mechanical properties of a defect-free LPBF-produced 316L stainless steel will be compared to those containing defects, and also to wrought alloys to show the effectiveness of the suggested approach.\n\n\\section*{2. Modelling}\n\\subsection*{2.1. Alloy design for crack prevention}\nThe microstructural and mechanical requirements for austenitic stainless steels and their relation with alloy composition are firstly discussed. Solidification cracking occurs when an insufficient amount of liquid in the melt pool covers the space between the solidifying metal as a result of high residual stresses [39]. Three criteria to decrease the occurrence of solidification cracks during LPBF are outlined next.\n\n\\subsection*{2.1.1. Solidification temperature range (STR)}\nComposition affects solidification cracking through the solidification temperature range (STR), defined as the liquidus and solidus temperature difference for a given alloy composition. As low melting point constituents are rejected by solidifying dendrites, a thin film of solute-rich liquid remains even at low temperatures. When this cannot bear the shrinkage strain, a crack is formed [40]. Some elements such as $\\mathrm{S}, \\mathrm{P}, \\mathrm{Si}$ and $\\mathrm{N}$ can increase the solidification cracking likelihood by increasing the STR [41-43]. Therefore, the alloy composition should be optimised to minimise STR.\n\n\\subsection*{2.1.2.", "start_char_idx": 658433, "end_char_idx": 663046, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9b910684-e1e2-42ef-b496-3211e0aec9f0": {"__data__": {"id_": "9b910684-e1e2-42ef-b496-3211e0aec9f0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a7905e7b-a6d1-4323-b0ac-ad5aa95a35ca", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a551cacf8826b3124106edfa21fca6b05eac6429cb755704a1ca8e0bb56fc069", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b3df4ab1-1bcf-4587-affa-5ecf77550789", "node_type": "1", "metadata": {}, "hash": "db5c8edc6204ecdeb19cb10b33aadd6ce29163649ea3f4436d689f89c4d61d22", "class_name": "RelatedNodeInfo"}}, "text": "Three criteria to decrease the occurrence of solidification cracks during LPBF are outlined next.\n\n\\subsection*{2.1.1. Solidification temperature range (STR)}\nComposition affects solidification cracking through the solidification temperature range (STR), defined as the liquidus and solidus temperature difference for a given alloy composition. As low melting point constituents are rejected by solidifying dendrites, a thin film of solute-rich liquid remains even at low temperatures. When this cannot bear the shrinkage strain, a crack is formed [40]. Some elements such as $\\mathrm{S}, \\mathrm{P}, \\mathrm{Si}$ and $\\mathrm{N}$ can increase the solidification cracking likelihood by increasing the STR [41-43]. Therefore, the alloy composition should be optimised to minimise STR.\n\n\\subsection*{2.1.2. Performance index (PI)}\nThe layer-by-layer nature of the LPBF imposes severe temperature\\\\\nvariations from the melting region to the far-field powder bed temperature; therefore, as-built components are subjected to the effects of strong thermal stresses. The contraction resulting from thermal stresses leads to deformation and the formation of residual stresses, which can cause microcracks in the as-built part [44]. Thermal stresses generated during LPBF can be estimated via Eq. (2) [45]:\n\n$\\sigma_{\\text {Thermal }}=\\left[\\frac{E \\cdot \\alpha_{\\text {CTE }}}{2(1-v)}\\right] \\Delta T$\n\nwhere $E$ is the Young's modulus, $\\alpha_{C T E}$ is the coefficient of thermal expansion near the melting point of the alloy, $\\nu$ is the Poisson's ratio, and $\\Delta T$ is the temperature difference between the melt pool and the powder bed. The purpose of the proposed model is alloy design through composition tailoring. Changes in composition of the alloy reflect only moderately in the variation of the modulus. In contrast with this, in the thermal stress generation during LPBF, the coefficient of thermal expansion has a much larger influence in performance index changes. Therefore, the alloys with lower $\\alpha_{C T E}$ induce lower thermal stress. Conversely, alloys with higher yield strength $\\left(\\sigma_{y}\\right)$ at high temperature perform better under high cooling and heating rates. Performance index thus shows the ability of different alloys to endure cracking; therefore, maximising $P I$ is the second criterion for LPBF alloy design:\n\n$\\mathrm{PI}=\\frac{\\sigma_{y}}{\\alpha_{\\mathrm{CTE}}}$\n\n\\subsection*{2.1.3. Solidification path}\nThe solidification path of austenitic stainless steels also varies with alloy composition. The alloys undergoing the reaction $L \\rightarrow \\delta+\\gamma$, display a primary phase formed from the liquid transforming into austenite or $\\delta$-ferrite, which chiefly depends on the ratio between chromium and nickel contents. Multicomponent systems adopt the ratio of chromium and nickel equivalent, $C r_{e q}$ and $N i_{e q}$, respectively, as criterion for solidification path. The expressions for $\\mathrm{Cr}_{e q}$ and $\\mathrm{Ni}_{e q}$ have been presented by Hull [46]:\n\n\n\\begin{align*}\n\\mathrm{Cr}_{\\mathrm{eq}}= & W_{\\mathrm{Cr}}+1.21 W_{\\mathrm{Mo}}+0.48 W_{\\mathrm{Si}}+0.14 W_{\\mathrm{Nb}}+2.2 W_{\\mathrm{Ti}}+0.72 W_{\\mathrm{W}} \\\\\n& +0.21 W_{\\mathrm{Ta}}+2.27 W_{\\mathrm{V}}+2.48 W_{\\mathrm{Al}}  \\tag{4}\\\\\n\\mathrm{Ni}_{\\mathrm{eq}}= & W_{\\mathrm{Ni}}+0.11 W_{\\mathrm{Mn}}+24.5 W_{\\mathrm{C}}+18.4 W_{\\mathrm{N}}+0.44 W_{\\mathrm{Cu}}+0.41 W_{\\mathrm{Co}} \\tag{5}\n\\end{align*}\n\n\nwhere $W_{i}$, with $i=\\mathrm{Cr}$, Mo, $\\mathrm{Si}, \\mathrm{W}, \\mathrm{Nb}, \\ldots$ is the wt.\\% of element $i$.", "start_char_idx": 662242, "end_char_idx": 665808, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b3df4ab1-1bcf-4587-affa-5ecf77550789": {"__data__": {"id_": "b3df4ab1-1bcf-4587-affa-5ecf77550789", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9b910684-e1e2-42ef-b496-3211e0aec9f0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0459a0dae29ddb597c056c8c4f226e0a03ccc691b0bb2e5df6e4d426371abf7a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ca70b7e1-910f-46c5-9c90-5b8ad37b1252", "node_type": "1", "metadata": {}, "hash": "5a6f0d4297a195d84fccbe7b6ce64d3e8e8ed5a51cb95e1d5214d87fc5909f3c", "class_name": "RelatedNodeInfo"}}, "text": "where $W_{i}$, with $i=\\mathrm{Cr}$, Mo, $\\mathrm{Si}, \\mathrm{W}, \\mathrm{Nb}, \\ldots$ is the wt.\\% of element $i$.\n\nEven small amounts of $\\delta$-ferrite in the austenite matrix are known to alleviate the deleterious effects of impurity elements such as Si, P, and $\\mathrm{S}$, which have a higher solubility in $\\delta$-ferrite than in austenite; this results in lower segregation to grain boundaries once solidification is completed [47]. Moreover, $\\delta$-ferrite pins the austenite grain boundaries making the potential paths for cracking more complicated than in fully austenitic structures [48]. A two-phase solidification front of $\\delta$-ferrite/ austenite essentially increases the interphase interfaces between austenite and ferrite, while it minimises the area of austenite/austenite and ferrite/ferrite grain boundaries during solidification. As austenite and ferrite have different crystal structures, the phase boundaries between them are not wetted by liquid as easily as grain boundaries between two similar lattices such as austenite/austenite boundaries. Therefore, crack propagation in a material solidifying in a ferritic-austenitic mode is more difficult than in a material with austenitic mode of solidification [49]. These beneficial effects of $\\delta$-ferrite is the basis of the third criterion for alloy design against cracking.\n\nAs seen in Fig. 1, which shows a $70 \\mathrm{wt}$ \\% iron isopleth of the ternary system of $\\mathrm{Fe}-\\mathrm{Cr}-\\mathrm{Ni}$, the solidifying paths of austenitic stainless steels are divided into four modes: austenitic (A), austenitic-ferritic or primary austenite (AF), ferritic-austenitic or primary ferritic (FA), and ferritic (F). Although, LPBF kinetics do not follow the equilibrium conditions, a threshold for the presence of $\\delta$-ferrite during solidification can be approximated from Fig. 1. For $\\mathrm{Cr}_{e q} / N i_{e q}<1.3$, mode A is activated. When $C r_{e q} / N i_{e q}>1.3$, the presence of $\\delta$-ferrite is ensured [50]. It should be noted that the presence of more than $60 \\%$ of $\\delta$-ferrite is undesired for crack prevention [49]. The very fast cooling rates of LPBF, originally increase the stability of austenite during solidification [51], therefore, no upper limit for $\\mathrm{Cr}_{e q} / N i_{e q}$ is applied in the alloy design methodology. Therefore the third criterion for alloy design is that $\\mathrm{Cr}_{e q} / N i_{e q}>1.3$.\n\n\\subsection*{2.1.4. Computational alloy design approach}\nThe computational alloy design approach is summarised here. This study employed ThermoCalc software coupled with the TCFE9 database accessed through TC Matlab toolbox [52]. The optimisation algorithm used ThermoCalc as input to limit the composition of alloys and keep their constitution within design specifications. A multiobjective genetic algorithm has been used to optimise composition. GA works with a population of individuals (alloy compositions), whereby each represents a potential solution. A randomly generated population of individuals (alloys), undergoes a repeated process of selection, crossover and mutation. Each cycle leads to a new generation. The objective is to find the individuals that, over a certain number of generations, approach an optimal solution [53].\n\nSTR and PI constitute the fitness scores. To find metrics for these scores to be applied as constraints for our alloy design approach, compositions of printed 316L austenitic stainless steels reported in the literature are listed in Table 1. However, this methodology can be applied to other alloying systems such as marageing steels and high carbon steels, which are prone to crack formation during LPBF. The first three alloys (shown in bold) display microcracks in the as-built part as is shown in Fig. 2. However, the rest have been printed successfully by modifying the chemical composition using a trial and error approach.", "start_char_idx": 665692, "end_char_idx": 669611, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ca70b7e1-910f-46c5-9c90-5b8ad37b1252": {"__data__": {"id_": "ca70b7e1-910f-46c5-9c90-5b8ad37b1252", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b3df4ab1-1bcf-4587-affa-5ecf77550789", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e92a613ba06084b1d6c53c4c1a8a11adeaf50ed694a8ef10750bf823663e0da7", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "26f58245-abed-4dfa-83fc-e7dd770d160b", "node_type": "1", "metadata": {}, "hash": "9641a91c92d7deed5b5f614c2892b26b0c93b3f7cbb10655fef1653aa1a5a988", "class_name": "RelatedNodeInfo"}}, "text": "A randomly generated population of individuals (alloys), undergoes a repeated process of selection, crossover and mutation. Each cycle leads to a new generation. The objective is to find the individuals that, over a certain number of generations, approach an optimal solution [53].\n\nSTR and PI constitute the fitness scores. To find metrics for these scores to be applied as constraints for our alloy design approach, compositions of printed 316L austenitic stainless steels reported in the literature are listed in Table 1. However, this methodology can be applied to other alloying systems such as marageing steels and high carbon steels, which are prone to crack formation during LPBF. The first three alloys (shown in bold) display microcracks in the as-built part as is shown in Fig. 2. However, the rest have been printed successfully by modifying the chemical composition using a trial and error approach. The minimum STR that has been obtained is $32 \\mathrm{~K}$, and the maximum PI is $1.46 \\times 10^{6} \\mathrm{MPa} \\mathrm{K}$. Therefore, for each candidate solution: (1) STR (as calculated by ThermoCalc) should be less than $32 \\mathrm{~K}$; (2) PI (Eq. (3)) should be higher than $1.46 \\times 10^{6} \\mathrm{MPa} \\mathrm{K}$ and (3) $\\mathrm{Cr}_{e q} / \\mathrm{Ni}_{e q}$ (Eqs. (4) and (5)) should be higher than 1.3. These criteria have been defined as go/ no-go. The algorithm of the model rooted in these considerations is presented in Fig. 3. It should be noted that Thermo-Calc databases can also be used for prediction of presence of $\\delta$-ferrite instead of using Eqs. (4) and (5) for $C r_{e q} / N i_{e q}$ calculation. However, this leads to a much longer computation time; with the current algorithm it already takes the optimisation more than three days to be completed.\n\nIn order to calculate the PI, the yield strength and the coefficient of thermal expansion for each alloy should be calculated. $\\sigma_{y}$ is expressed as:\n\n$\\sigma_{y}=\\Delta \\sigma_{\\mathrm{gb}}+\\Delta \\sigma_{\\mathrm{pr}}+\\Delta \\sigma_{\\mathrm{ss}}$\n\nwhere $\\sigma_{g b}$ is the grain boundary strengthening, which depends on the grain size, $\\sigma_{p r}$ is the precipitation hardening, and $\\sigma_{s s}$ is the solid solution strengthening. In the absence of precipitates and for coarse grain sizes upon solidification, the most important term for alloy design is $\\sigma_{s s}$, which is calculated via Eq. (7) [65]:\n\n$\\Delta \\sigma_{\\mathrm{ss}}=\\left[\\sum_{i}\\left(k_{\\mathrm{ss}, i}^{3 / 2} c_{i}\\right)\\right]^{2 / 3}$\n\nwhere $k_{s s, i}$ is the coefficient of solid solution strengthening for element $i$, and $c_{i}$ is its concentration. $k_{s s}$ for different elements in the austenitic matrix is shown in Table 2 [66]. $\\alpha_{C T E}$ of the alloy can be calculated from a rule of mixtures [67]. $\\alpha_{\\text {CTE }}$ values for different elements near their melting points are also shown in Table 2.\n\nThe alloy system considered in the calculations is based on 10 alloying elements: C, Cr, Ni, Mn, Mo, Si, W, N, P, and S, where P and S amounts are fixed. The concentration ranges employed for each element in the optimisation procedure are in Table 3. The model scans the full composition ranges in Table 3, employing the optimisation criteria presented in this section.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_6467a9d8d19c4db3d666g-04}\n\\end{center}\n\nFig. 1. Pseudobinary section of the Fe-Cr-Ni ternary phase diagram at $70 \\mathrm{wt} \\%$ iron, showing different solidification paths (A, AF, FA, and F), based on the relevant $C r_{e q} / N i_{e q}$ values [52].", "start_char_idx": 668699, "end_char_idx": 672317, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "26f58245-abed-4dfa-83fc-e7dd770d160b": {"__data__": {"id_": "26f58245-abed-4dfa-83fc-e7dd770d160b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ca70b7e1-910f-46c5-9c90-5b8ad37b1252", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "403401387cce2e3064fd21ebf6f2f9a0deed6cedbd20ab437d4eabf492a349b1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f07bb606-e351-48b2-9c72-d636e8aea9cc", "node_type": "1", "metadata": {}, "hash": "8858cdaecda0a74d874daa4d725d93f48ebffb11a5ab7155609aa13a85fe1cb4", "class_name": "RelatedNodeInfo"}}, "text": "The concentration ranges employed for each element in the optimisation procedure are in Table 3. The model scans the full composition ranges in Table 3, employing the optimisation criteria presented in this section.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_6467a9d8d19c4db3d666g-04}\n\\end{center}\n\nFig. 1. Pseudobinary section of the Fe-Cr-Ni ternary phase diagram at $70 \\mathrm{wt} \\%$ iron, showing different solidification paths (A, AF, FA, and F), based on the relevant $C r_{e q} / N i_{e q}$ values [52].\n\n\\subsection*{2.1.5. Crack prevention factor}\nBased on the factors affecting solidification cracking in austenitic stainless steels, a crack prevention factor $(F)$ is defined and calculated for the alloys reported in literature and shown in Table 1:\n\n$F=\\sqrt{1500\\left(\\mathrm{STR}^{-1}\\right)^{2}+\\mathrm{PI}^{2}}$.\n\nThis is, based on a Pythagorean relationship between the reciprocal of the STR (as lower STRs are more favourable) and the PI. This relationship has been proposed to fit the data from literature (Table 1), and to provide a rule of the thumb approach to alloy selection for printability. Based on Eq. (8), a material less prone to crack formation will be obtained by maximising the crack prevention factor. Based on the experimental results on LPBF of 316L stainless steels (Table 1), a threshold value $F=1.6$ for crack susceptibility resistance is suggested. Austenitic stainless steels with $F>1.6$ produced by LPBF are crackfree. However, in addition to this, the solidification path plays an important role in crack resistance. Alloys that have an $F<1.6$, but $\\mathrm{Cr}_{e q} /$ $N i_{e q}>1.69$ prevent crack formation upon LPBF. Therefore, a process map for $F$ vs. $\\mathrm{Cr}_{e q} / N i_{e q}$ from literature data (Table 1) is presented in Fig. 4. The alloy that will be used in this study to validate this approach is highlighted in Fig. 4.\n\nTable 1\n\nChemical compositions of 316L stainless steel in wt.\\%, produced by LPBF. The units of STR and PI are K and MPa K, respectively. Fe value are balanced. $F$ is the crack prevention factor.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n$\\mathrm{Cr}$ & $\\mathrm{Ni}$ & $\\mathrm{Mn}$ & Mo & C & $\\mathrm{N}$ & $\\mathrm{Si}$ & $\\mathrm{P}$ & $S$ & STR & $P I \\times 10^{6}$ & $C r_{e q} / N i_{e q}$ & $F$ & Ref. \\\\\n\\hline\n16.17 & 12.57 & 0.23 & 2.33 & 0.09 & - & 0.6 & 0.014 & 0.014 & 50 & 1.32 & 1.28 & 1.53 & $[5]$ \\\\\n\\hline\n17 & 12 & 2 & 2.5 & 0.03 & 0.1 & 1 & 0.045 & 0.03 & 60 & 1.45 & 1.51 & 1.58 & $[6]$ \\\\\n\\hline\n17.26 & 11.48 & 1.41 & 2.32 & 0.01 & - & 0.71 & 0.01 & 0.01 & 39 & 1.19 & 1.68 & 1.54 & [7] \\\\\n\\hline\n17.34 & 10.74 & 1.14 & 2.28 & 0.01 & 0.1 & 0.63 & 0.026 & 0.014 & 43 & 1.36 & 1.57 & 1.63 & [54] \\\\\n\\hline\n17.5 & 11.", "start_char_idx": 671782, "end_char_idx": 674565, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f07bb606-e351-48b2-9c72-d636e8aea9cc": {"__data__": {"id_": "f07bb606-e351-48b2-9c72-d636e8aea9cc", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "26f58245-abed-4dfa-83fc-e7dd770d160b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "61d5faeab190f29f3812ea06c1fc458791116ca6ad5ac4e01751bbe7eb5b2f79", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "241f9574-a763-4653-8b1e-415bdeba9a52", "node_type": "1", "metadata": {}, "hash": "e4fb6a4f59f596d3127e7c921393ce7dfef79032ee1bac41f22cb85bfe3d3af1", "class_name": "RelatedNodeInfo"}}, "text": "5 & 0.03 & 0.1 & 1 & 0.045 & 0.03 & 60 & 1.45 & 1.51 & 1.58 & $[6]$ \\\\\n\\hline\n17.26 & 11.48 & 1.41 & 2.32 & 0.01 & - & 0.71 & 0.01 & 0.01 & 39 & 1.19 & 1.68 & 1.54 & [7] \\\\\n\\hline\n17.34 & 10.74 & 1.14 & 2.28 & 0.01 & 0.1 & 0.63 & 0.026 & 0.014 & 43 & 1.36 & 1.57 & 1.63 & [54] \\\\\n\\hline\n17.5 & 11.5 & 2 & 2.25 & 0.03 & 0.11 & 1 & 0.045 & 0.03 & 57 & 1.45 & 1.54 & 1.6 & [55] \\\\\n\\hline\n17.42 & 12.53 & 0.6 & 2.36 & 0.02 & 0.06 & 0.51 & 0.01 & 0.01 & 32 & 1.36 & 1.45 & 1.82 & [56] \\\\\n\\hline\n17 & 12 & 1 & 2.5 & 0.01 & 0.05 & 0.5 & 0.023 & 0.01 & 38 & 1.35 & 1.51 & 1.69 & [57] \\\\\n\\hline\n17.75 & 12.75 & 1.5 & 2.4 & 0.02 & - & - & 0.01 & 0.001 & 33 & 1.24 & 1.49 & 1.7 & [58] \\\\\n\\hline\n16.7 & 11.9 & 0.6 & 2.5 & 0.02 & - & 0.6 & 0.01 & 0.02 & 33 & 1.22 & 1.61 & 1.69 & [59] \\\\\n\\hline\n16.7 & 10.3 & 0.99 & 2.2 & 0.01 & - & 0.69 & 0.02 & 0.05 & 37 & 1.12 & 1.85 & 1.53 & [60] \\\\\n\\hline\n17.9 & 12.8 & 1.15 & 2.35 & 0.01 & 0.09 & 0.66 & 0.01 & 0.004 & 33 & 1.42 & 1.4 & 1.82 & [61] \\\\\n\\hline\n17.5 & 11.2 & 2.2 & 2.3 & 0.03 & - & - & 0.05 & 0.03 & 61 & 1.22 & 1.67 & 1.37 & [62] \\\\\n\\hline\n16.3 & 10.3 & 1.31 & 2.09 & 0.02 & - & 0.49 & 0.026 & 0.006 & 44 & 1.14 & 1.72 & 1.44 & [63] \\\\\n\\hline\n18.43 & 12.2 & 1.86 & 2.46 & 0.02 & - & 0.75 & 0.032 & 0.01 & 54 & 1.26 & 1.69 & 1.44 & [64] \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_6467a9d8d19c4db3d666g-05}\n\\end{center}\n\nFig. 2. Microstructures of the samples underwent cracking during LPBF of 316L stainless steels [5-7].\n\n\\subsection*{2.2. Model for defect and porosity prevention}\n\\subsection*{2.2.1.", "start_char_idx": 674268, "end_char_idx": 675871, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "241f9574-a763-4653-8b1e-415bdeba9a52": {"__data__": {"id_": "241f9574-a763-4653-8b1e-415bdeba9a52", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f07bb606-e351-48b2-9c72-d636e8aea9cc", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a9063a70fe6c880b0aeb3f57453e166b3403732e4189f0625f44782803d835d6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0413e6ee-f4ab-45b7-bcad-1ab131fd60c4", "node_type": "1", "metadata": {}, "hash": "fe21af99fb6538fddea2df94396c595bd81bc18de0461c47b6d46295a1af2017", "class_name": "RelatedNodeInfo"}}, "text": "14 & 1.72 & 1.44 & [63] \\\\\n\\hline\n18.43 & 12.2 & 1.86 & 2.46 & 0.02 & - & 0.75 & 0.032 & 0.01 & 54 & 1.26 & 1.69 & 1.44 & [64] \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_6467a9d8d19c4db3d666g-05}\n\\end{center}\n\nFig. 2. Microstructures of the samples underwent cracking during LPBF of 316L stainless steels [5-7].\n\n\\subsection*{2.2. Model for defect and porosity prevention}\n\\subsection*{2.2.1. Keyholes}\nKeyholes are caused by a high laser energy input on a small volume, this results in the formation of a melt pool with a narrow and deep shape. The melt pool geometry criterion for keyhole prevention is $W /$ $D>2$, where $W$ is the melt pool width and $D$ is the melt pool depth [69]. Moreover, the energy transferred to melt the powder should be optimised: low energies lead to lack of fusion, whilst high energies lead to keyhole formation. A way to consider both LPBF process parameters and the material's properties to optimise the energy is to adopt the normalised enthalpy concept, introduced by King et al. [70]:\n\n$\\frac{\\Delta H}{h_{s}}=\\frac{\\mathrm{AP}}{h_{s} \\sqrt{\\pi \\mathrm{dv} \\sigma^{3}}}$\n\nwhere $\\frac{\\Delta H}{h_{s}}$ is the normalised enthalpy, $A$ is the absorptivity, $h_{s}$ is the enthalpy at the melting temperature, $d$ is the thermal diffusivity and $\\sigma$ is the laser spot size. The condition for preventing keyhole formation adopting the normalised enthalpy concept for 316-type of stainless steels is:\n\n$\\frac{\\Delta H}{h_{s}} \\leq \\frac{\\pi T_{b}}{T_{m}}=5.5$\n\nwhere $T_{b}$ is the boiling temperature and $T_{m}$ is the melting temperature of the alloy.\\\\\nTable 2\n\nCoefficients of solid solution strengthening for different elements (i) in austenitic matrix [65] and their thermal expansion coefficient near their melting points [68].\n\n\\begin{center}\n\\begin{tabular}{lllllllll}\n\\hline\n$i$ & $\\mathrm{Cr}$ & $\\mathrm{Ni}$ & $\\mathrm{Mo}$ & $\\mathrm{W}$ & $\\mathrm{C}$ & $\\mathrm{N}$ & $\\mathrm{Si}$ & $\\mathrm{Fe}(\\mathrm{FCC})$ \\\\\n\\hline\n$k_{s s, i}\\left[\\mathrm{MPa} \\mathrm{Ma}^{-3 / 2}\\right]$ & 101.71 & 112 & 637 & 826 & 1984 & 1984 & - & - \\\\\n$\\alpha_{C T E}\\left[10^{-6} \\mathrm{~K}^{-1}\\right]$ & 19 & 20.3 & 16.5 & 11.6 & - & - & 3.8 & 23.3 \\\\\n\\end{tabular}\n\\end{center}\n\nTable 3\n\nConcentration ranges of all components employed in the optimisation (wt.\\%).", "start_char_idx": 675419, "end_char_idx": 677784, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0413e6ee-f4ab-45b7-bcad-1ab131fd60c4": {"__data__": {"id_": "0413e6ee-f4ab-45b7-bcad-1ab131fd60c4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "241f9574-a763-4653-8b1e-415bdeba9a52", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3d86ee9e26968623968ce5b11792ee9901873ecf64cc44c760a371732573f6e6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9f5415e2-0938-47c1-aafb-4608a45d97b4", "node_type": "1", "metadata": {}, "hash": "b5a63a6d508d2222f58ed46d35685927dc86316151f9a09d5fd3b44fb23e9c4d", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\begin{tabular}{lllllllllll}\n\\hline\n & $\\mathrm{Cr}$ & $\\mathrm{Ni}$ & $\\mathrm{Mo}$ & $\\mathrm{W}$ & $\\mathrm{C}$ & $\\mathrm{N}$ & $\\mathrm{Si}$ & $\\mathrm{Mn}$ & $\\mathrm{P}$ & $\\mathrm{S}$ \\\\\n\\hline\nMin & 12 & 8 & 0.3 & 0 & 0.01 & 0 & 0.1 & 0.2 & 0.03 & 0.001 \\\\\nMax & 21 & 13 & 2.5 & 1 & 0.03 & 0.11 & 0.5 & 2.2 & 0.03 & 0.001 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\subsection*{2.2.2. Lack of fusion}\nLack of fusion signals insufficient melting between two adjacent layers, both in the width and height directions. Two criteria have therefore been proposed [22,16] to avoid lack of fusion based on the melt pool geometry: (1) $D / t>1.5$ and (2) $h / W<1$ (where $D$ is the melt pool depth, $t$ is the layer thickness, $h$ is the hatch distance and $W$ is the melt pool width). In order to predict the maximum hatch distance for LPBF process, the width of the melt pool can be estimated via [69]:\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_6467a9d8d19c4db3d666g-05(1)}\n\\end{center}\n\nFig. 3. Algorithm of the thermodynamic calculations and criteria evaluation.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_6467a9d8d19c4db3d666g-06}\n\\end{center}\n\nFig. 4. The process map, showing the safe region from solidification cracks for LPBF produced austenitic stainless steels. The alloy used in this study is also shown. The red triangles show the alloys that underwent solidification cracking during LPBF and the green circles show no-crack alloys; references shown in Table 1.\n\n$W=\\sqrt{\\frac{8}{\\pi \\cdot e} \\frac{\\mathrm{AP}}{\\rho C_{p} v\\left(T_{m}-T_{0}\\right)}}$\n\nwhere $\\rho$ is the density, $C_{p}$ is the heat capacity and $T_{0}$ is the powder bed temperature. As mentioned in Section 2.2.1, in order to prevent the formation of keyholes, the maximum depth of the melt pool must not exceed half of the melt pool width. Therefore, the maximum layer thickness can also be predicted based on the first criterion defined for lack of fusion.\n\n\\subsection*{2.2.3. Balling}\nBalling is caused by the laser energy inducing a non-stabilised melt pool. Balling defects are believed to form both in low and high laser energies. They may result in the formation of discontinuous scan lines, which will significantly affect the melt pool overlapping between such scan lines. The melt pool geometry criterion for balling prevention is $L /$ $W<2.3$, where $L$ is the melt pool length and $W$ is the melt pool width [22]. For melt pool length prediction, Rubenchik et al. [71] presented a numerical equation. The melt pool length is a function of the laser spot size and two dimensionless parameters ( $a$ and $b$ ), which depend on the materials properties. The dimensionless parameter of $a$ is defined as the ratio between thermal diffusivity, laser scan speed and laser spot size:\n\n$a=\\sqrt{\\frac{d}{v \\sigma}}$\n\nFor $a<1$ the thermal diffusion depth $(D / v)$ during the laser dwell time is smaller than the beam size. Therefore, the melt pool is shallow and elongated. This condition is typical of materials with low thermal conductivity such as stainless steels. For these materials, $b$ is a fraction of the normalised enthalpy:\n\n$b=\\frac{\\Delta H}{2^{3 / 4} \\pi h_{s}}$.\n\nThe melt pool length $(L)$ is estimated from [71]:", "start_char_idx": 677786, "end_char_idx": 681066, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9f5415e2-0938-47c1-aafb-4608a45d97b4": {"__data__": {"id_": "9f5415e2-0938-47c1-aafb-4608a45d97b4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0413e6ee-f4ab-45b7-bcad-1ab131fd60c4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "fa50b333fddff8fbe3cadaf8f0bb659576f0ed9d49196bd09c0750eb09162802", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0ba0612f-174d-4171-ae60-4f21c66205b8", "node_type": "1", "metadata": {}, "hash": "860b300d631149c2d0934bea13352702ec7ef1f2c4893c2e4079acd68b8b3103", "class_name": "RelatedNodeInfo"}}, "text": "[71] presented a numerical equation. The melt pool length is a function of the laser spot size and two dimensionless parameters ( $a$ and $b$ ), which depend on the materials properties. The dimensionless parameter of $a$ is defined as the ratio between thermal diffusivity, laser scan speed and laser spot size:\n\n$a=\\sqrt{\\frac{d}{v \\sigma}}$\n\nFor $a<1$ the thermal diffusion depth $(D / v)$ during the laser dwell time is smaller than the beam size. Therefore, the melt pool is shallow and elongated. This condition is typical of materials with low thermal conductivity such as stainless steels. For these materials, $b$ is a fraction of the normalised enthalpy:\n\n$b=\\frac{\\Delta H}{2^{3 / 4} \\pi h_{s}}$.\n\nThe melt pool length $(L)$ is estimated from [71]:\n\n\n\\begin{align*}\nL= & \\frac{\\sigma}{a^{2}}\\left[0.0053-0.21 a+1.3 a^{2}+(-0.11-0.17 b) a^{2} \\ln a\\right. \\\\\n& \\left.+b\\left(-0.0062+0.23 a+0.075 a^{2}\\right)\\right] \\tag{14}\n\\end{align*}\n\n\n\\section*{3. Experimental procedure}\nThe material used for model validation is a crack resistant 316L stainless steel. The pre-alloyed powder was produced by gas atomisation and provided by Carpenter Additive. The chemical composition of the powder used for LPBF is reported in wt.\\% in Table 4. The STR, PI, and $\\mathrm{Cr}_{e q} / \\mathrm{Ni}_{e q}$ for this commercial alloy are $44 \\mathrm{~K}, 1.48 \\times 10^{6} \\mathrm{MPa} \\mathrm{K}$, and\\\\\nTable 4\n\nChemical composition of the powders used in the present investigation in wt.\\%.\n\n\\begin{center}\n\\begin{tabular}{lllllllllll}\n\\hline\n$\\mathrm{Fe}$ & $\\mathrm{Cr}$ & $\\mathrm{Ni}$ & $\\mathrm{Mo}$ & $\\mathrm{Mn}$ & $\\mathrm{Si}$ & $\\mathrm{P}$ & $\\mathrm{S}$ & $\\mathrm{N}$ & $\\mathrm{C}$ & $\\mathrm{Cu}$ \\\\\n\\hline\nBal. & 17.75 & 12.75 & 2.38 & 2 & 0.75 & 0.025 & 0.01 & 0.1 & 0.03 & 0.5 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n1.35, respectively. It locates in the safe region from cracking (\"This study\" in Fig. 4). The as-received powder exhibits mostly a spherical morphology with some satellites. Particles have an average size of $D_{90}=38 \\mu \\mathrm{m}$.\n\nThe physical properties of the alloy used in this study have been calculated using ThermoCalc software making use of the TCFE9 database dedicated to steels and $\\mathrm{Fe}$ alloys at the melting temperature (liquidus temperature) and provided in Table 5.\n\nTensile samples with dimensions shown in Fig. 5 were built in a Renishaw plc (UK) AM125 LPBF machine with a laser spot size of $35 \\mu \\mathrm{m}$. All the samples were built at $5^{\\circ}$ over the substrate (ISO/ASTM 52921 standard [72]) to minimise the scan vector length and for support application. The platform is equipped with a $200 \\mathrm{~W}$ D-series redPOWER ytterbium fibre continuous wavelength (CW) laser from SPI laser (UK) with a near infrared wavelength of $1070 \\mathrm{~nm}$. The AM125 has a build volume of $125 \\mathrm{~mm}^{3}$ with a base plate heater, set to $80^{\\circ} \\mathrm{C}$, which was maintained throughout the build process. A vacuum and argon purge was performed in order to keep oxygen content below a maximum of $900 \\mathrm{ppm}$; however, in the actual processing conditions, the oxygen content was below 100 ppm. Mild steel (304 stainless steel) was used as substrate.", "start_char_idx": 680307, "end_char_idx": 683544, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0ba0612f-174d-4171-ae60-4f21c66205b8": {"__data__": {"id_": "0ba0612f-174d-4171-ae60-4f21c66205b8", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9f5415e2-0938-47c1-aafb-4608a45d97b4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "88ab96a01d9a7fcec4df88890c1f59ab7c1617a5750de0eddb6116f2c197266d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b46bf07f-db16-419a-90a7-3312873eaf2e", "node_type": "1", "metadata": {}, "hash": "642a9f1021f1d223a3ef34f723a4fdb3caff7746e5f516bd752a4308065776aa", "class_name": "RelatedNodeInfo"}}, "text": "All the samples were built at $5^{\\circ}$ over the substrate (ISO/ASTM 52921 standard [72]) to minimise the scan vector length and for support application. The platform is equipped with a $200 \\mathrm{~W}$ D-series redPOWER ytterbium fibre continuous wavelength (CW) laser from SPI laser (UK) with a near infrared wavelength of $1070 \\mathrm{~nm}$. The AM125 has a build volume of $125 \\mathrm{~mm}^{3}$ with a base plate heater, set to $80^{\\circ} \\mathrm{C}$, which was maintained throughout the build process. A vacuum and argon purge was performed in order to keep oxygen content below a maximum of $900 \\mathrm{ppm}$; however, in the actual processing conditions, the oxygen content was below 100 ppm. Mild steel (304 stainless steel) was used as substrate.\n\nThree different sets of experiments have been carried out with different processing parameters, which are shown in Table 6. The first batch parameter set was intuitively chosen to promote keyhole and lack of fusion defects. The second batch is produced with a layer thickness slightly larger than the predicted optimised maximum layer thickness.\n\n\\section*{Table 5}\nMaterial properties used in the physical model for porosity prevention in 316L stainless steel. All the thermophysical properties have been calculated using ThermoCalc at liquidus temperature [52].\n\n\\begin{center}\n\\begin{tabular}{ll}\n\\hline\nMaterial properties & Value at liquidus temperature \\\\\n\\hline\n$A$ & 0.36 \\\\\n$h_{s}\\left(\\mathrm{~J} / \\mathrm{m}^{3}\\right)$ & $7.764 \\times 10^{9}$ \\\\\n$d\\left(\\mathrm{~m}^{2} / \\mathrm{s}\\right)$ & $6.052 \\times 10^{-6}$ \\\\\n$T_{b}(\\mathrm{~K})$ & 2885 \\\\\n$T_{m}(\\mathrm{~K})$ & 1647 \\\\\n$\\rho\\left(\\mathrm{kg} / \\mathrm{m}^{3}\\right)$ & 6922 \\\\\n$C_{p}(\\mathrm{~J} / \\mathrm{kg} \\mathrm{K})$ & 663.614 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_6467a9d8d19c4db3d666g-07(1)}\n\\end{center}\n\nFig. 5. The geometry of the tensile specimens produced by LPBF. All the values shown are in $\\mathrm{mm}$.\n\nTable 6\n\nLPBF main process parameters that have been used for 316L stainless steel builds.\n\n\\begin{center}\n\\begin{tabular}{lllll}\n\\hline\n & $P(\\mathrm{~W})$ & $v(\\mathrm{~m} / \\mathrm{s})$ & $h(\\mu \\mathrm{m})$ & $t(\\mu \\mathrm{m})$ \\\\\n\\hline\nBatch 1 & 200 & 1 & 110 & 50 \\\\\nBatch 2 & 100 & 1 & 70 & 30 \\\\\nBatch 3 & 100 & 1 & 70 & 20 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nThe third batch has been produced with the optimised process parameters, based on what will be discussed in the next section. The scan strategy used in this study was meander, with $67^{\\circ}$ rotation at each layer, to minimise residual stresses.\n\nFor cracks/porosity characterisation, the longitudinal section of the as-built samples were ground on $\\mathrm{SiC}$ paper with increasingly finer grit, followed by mechanical polishing. Optical microscopy images were acquired using Leica DFC295. The porosity measurements have been performed by image analysis using ImageJ software [73], over micrographs taken from different locations for each sample.\n\nTo investigate the mechanical properties of the LPBF-produced 316L and compare the results with the wrought 316L alloy, tensile tests were performed at room temperature using an Instron 3382 universal testing machine at a strain rate of $10^{-4} \\mathrm{~s}^{-1}$ [74], with the load axis parallel to the building direction.\n\n\\section*{4. Results and discussion}\n\\subsection*{4.1.", "start_char_idx": 682782, "end_char_idx": 686215, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b46bf07f-db16-419a-90a7-3312873eaf2e": {"__data__": {"id_": "b46bf07f-db16-419a-90a7-3312873eaf2e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0ba0612f-174d-4171-ae60-4f21c66205b8", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c33f68d15618d205af411057167b6475fd1d5c089ffdfc8a4845c58a5a2801c0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a87fa0a9-7adc-4514-9a05-10f2abe7f827", "node_type": "1", "metadata": {}, "hash": "8f8dd345c9f9e3c035d2dcb2d6b598ccaf1a76d8c90046aa16baac64c4f9aaa5", "class_name": "RelatedNodeInfo"}}, "text": "For cracks/porosity characterisation, the longitudinal section of the as-built samples were ground on $\\mathrm{SiC}$ paper with increasingly finer grit, followed by mechanical polishing. Optical microscopy images were acquired using Leica DFC295. The porosity measurements have been performed by image analysis using ImageJ software [73], over micrographs taken from different locations for each sample.\n\nTo investigate the mechanical properties of the LPBF-produced 316L and compare the results with the wrought 316L alloy, tensile tests were performed at room temperature using an Instron 3382 universal testing machine at a strain rate of $10^{-4} \\mathrm{~s}^{-1}$ [74], with the load axis parallel to the building direction.\n\n\\section*{4. Results and discussion}\n\\subsection*{4.1. Crack-free high strength austenitic stainless steels}\nThree new austenitic stainless steels are proposed, aimed at solidification within lower temperature ranges, displaying higher strengths and lower thermal expansion, whilst solidifying with the appropriate solidification path. Within these properties and characteristics, the designed alloys should offer improved performance compared with the most common austenitic stainless steel, namely 316L, which is the baseline alloy. After running GA optimisation for Table 3 compositional changes, 38 optimised alloys are obtained. Fig. 6 shows a comparison between the optimised alloys and the three 316L stainless steels that have been printed with microcracks in the literature [5-7], from the point of view of the three criteria mentioned before. All the designed alloys have STR lower than $32 \\mathrm{~K}$ and a PI higher than $1.46 \\times 10^{6} \\mathrm{MPa} \\mathrm{K}$, and solidify in ferrite + austenite manner; therefore, they should act better compared with the three typical existing 316L alloys. Within these 38 optimum alloys, three alloy examples are proposed: (i) Alloy 1 optimised for the minimum STR; (ii) Alloy 2: optimised for the maximum PI; (iii) Alloy 3: optimised for a compromise between the three criteria. The compositions of each of the proposed alloys are provided in Table 7.\n\nIn order to clarify the impact of each of the three criteria provided in this paper on crack susceptibility resistance, Scheil simulations have been carried out for the designed alloys and three cracked 316L alloy to show the solidification path, assuming constitutive segregation (Fig. 7).\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_6467a9d8d19c4db3d666g-07}\n\\end{center}\n\nFig. 6. Comparison between the optimal space and the baseline alloys. Three proposed alloys have been shown as alloys 1-3. Alloys [5-7] show cracking as depicted in Fig. 2.\n\nIn these simulations, $\\mathrm{C}$ and $\\mathrm{N}$ are considered as the fast diffusers. Considering the effects of element segregation, the STR is expanded to bigger ranges. The STR for alloys 1-3 are 147, 157, and $153 \\mathrm{~K}$ respectively. The STR for the three variations of $316 \\mathrm{~L}$, is $143 \\mathrm{~K}$ for [5], $172 \\mathrm{~K}$ for [6], and $113 \\mathrm{~K}$ for [7].\n\nFor [5], despite the fact that the STR in paraequilibrium conditions is lower than the designed alloys, the solidification mode is mainly dominated by austenite phase (because its $\\mathrm{Cr}_{e q} / N i_{e q}$ is less than 1.3). Moreover, the detrimental MnS phase will be stable for more than $100 \\mathrm{~K}$ during solidification, which cannot be dissolved very well in austenite. For 316L alloy printed by [6], the STR is very high both in equilibrium and non-equilibrium conditions, and this cannot be compensated by high values for $\\mathrm{Cr}_{e q} / \\mathrm{Ni}_{e q}$. Therefore, it led to the formation of cracks during LPBF. The third alloy, which was printed by [7], presents a very low STR in non-equilibrium condition. However, it is very low PI $\\left(1.19 \\times 10^{6} \\mathrm{MPaK}\\right)$ is the reason for formation of cracks during LPBF.", "start_char_idx": 685430, "end_char_idx": 689398, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a87fa0a9-7adc-4514-9a05-10f2abe7f827": {"__data__": {"id_": "a87fa0a9-7adc-4514-9a05-10f2abe7f827", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b46bf07f-db16-419a-90a7-3312873eaf2e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "04abb75207c58e72b21303c9832dd71f0742d884b98d48ee61617048dddf6714", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "981df132-dde1-4f5f-a186-d83e25894761", "node_type": "1", "metadata": {}, "hash": "e355fe2b8d53acd899b27ebc7b1abd14b73a9606a05920e783a8e1e688ad2178", "class_name": "RelatedNodeInfo"}}, "text": "Moreover, the detrimental MnS phase will be stable for more than $100 \\mathrm{~K}$ during solidification, which cannot be dissolved very well in austenite. For 316L alloy printed by [6], the STR is very high both in equilibrium and non-equilibrium conditions, and this cannot be compensated by high values for $\\mathrm{Cr}_{e q} / \\mathrm{Ni}_{e q}$. Therefore, it led to the formation of cracks during LPBF. The third alloy, which was printed by [7], presents a very low STR in non-equilibrium condition. However, it is very low PI $\\left(1.19 \\times 10^{6} \\mathrm{MPaK}\\right)$ is the reason for formation of cracks during LPBF. Therefore, to reach a crack-free austenitic stainless steel there should be a compromise between the criteria proposed here. Although the STR in non-equilibrium condition is not very low for the three designed alloys, their higher performance index, and the lower stability of MnS during solidification of these alloys, make them more resistant to crack formation during LPBF.\n\nPhase field (PF) modelling can also be performed and it may lead to more precise results, but as our aim is alloy design and several of the PF variables have unknown compositional dependence such as the interfacial energy or the diffuse interface thickness, PF may not constitute a computationally feasible tool for alloy design.\n\n\\subsection*{4.2. Porosity-free $316 \\mathrm{~L}$ stainless steel}\nTo produce a part without defects and porosity, the first step is to find the right normalised enthalpy (the energy transferred to the powder bed) for different laser powers, and scan speeds to find the safe regions without the formation of keyholes. Using Eq. (9), with the material properties input from Table 5, two areas of safe and keyhole regions can be determined and shown in Fig. 8. The normalised enthalpy threshold for this 316L alloy is about 5.5 (based on Eq. (10)). This shows that all the combinations of $P$ and $v$ which result in normalised enthalpies less than 5.5, are safe from keyhole formation for a constant laser spot size of $35 \\mu \\mathrm{m}$. A wide range of laser powers $(100-300 \\mathrm{~W})$ and scan speeds $(0.1-2.5 \\mathrm{~m} / \\mathrm{s})$ have been used for plotting the process maps. Using higher powers and lower scan speeds increases\n\nTable 7\n\nComposition of the designed alloys. All the contents are provided in wt.\\%. In all three alloys, P and S are 0.03 and 0.001 wt.\\%, respectively. STR and PI are in K and MPa K, respectively.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\nAlloy & $\\mathrm{C}$ & $\\mathrm{Cr}$ & $\\mathrm{Ni}$ & Mn & Mo & $\\mathrm{Si}$ & $\\mathrm{W}$ & $\\mathrm{N}$ & STR & $P I \\times 10^{6}$ & $C r_{e q} / N i_{e q}$ \\\\\n\\hline\nAlloy 1 & 0.02 & 14.50 & 10.37 & 1.08 & 0.88 & 0.43 & 0.36 & 0.07 & 28.13 & 1.68 & 1.31 \\\\\n\\hline\nAlloy 2 & 0.01 & 15.03 & 10.88 & 1.92 & 1.45 & 0.23 & 0.92 & 0.06 & 31.64 & 2.11 & 1.40 \\\\\n\\hline\nAlloy 3 & 0.02 & 15.83 & 11.23 & 1.06 & 1.09 & 0.3 & 0.44 & 0.07 & 29.88 & 1.87 & 1.35 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nthe possibility of formation of keyholes due to overheating, which makes the temperature of the powder bed exceed the boiling temperature of the alloy. Based on Fig.", "start_char_idx": 688767, "end_char_idx": 691976, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "981df132-dde1-4f5f-a186-d83e25894761": {"__data__": {"id_": "981df132-dde1-4f5f-a186-d83e25894761", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a87fa0a9-7adc-4514-9a05-10f2abe7f827", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1c3e2689623af50e7ddeea14497298e7c386a8e062578741556ccd490387a53c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b2549b99-ac34-49e5-acac-4dae2d009f0e", "node_type": "1", "metadata": {}, "hash": "a781ee8f5c8e34bd65497e8b5f3cf586d67d6d2da89c6cf907db8d9ff736b5ca", "class_name": "RelatedNodeInfo"}}, "text": "Based on Fig. 8, laser powers exceeding $150 \\mathrm{~W}$ cannot be used for LPBF of 316L stainless steel for a machine with spot size of $35 \\mu \\mathrm{m}$. In order to increase the productivity of the process (using higher laser powers), machines with higher spot size should be used. In here, the first experimental set were chosen to be in the keyhole region $(P=200 \\mathrm{~W}$ and $v=1 \\mathrm{~m} / \\mathrm{s})$. The second and third batches have been produced with a safe combination of $P$ and $v(100 \\mathrm{~W}$ and $1 \\mathrm{~m} / \\mathrm{s}$, respectively).\n\nThe second step is to avoid lack of fusion defects, which depends on the hatch distance and layer thickness of the process. Based on the second criterion for lack of fusion prevention, the maximum hatch distance $(h)$ of the process is the melt pool width $(W)$. Therefore, using Eq. (11), the maximum $h$ for different combinations of $P$ and $v$ is presented in Fig. 9a. It can be seen that using higher powers and lower scan speeds, the hatch distance can be larger. However, in here, for the first batch, the maximum hatch distance is calculated to be $105 \\mu \\mathrm{m}$. To induce lack of fusion in this sample, the experimental $h$ is chosen to be $110 \\mu \\mathrm{m}$. Reducing $P$ to $100 \\mathrm{~W}$ for the next two batches, decreases the maximum $h$ to $75 \\mu \\mathrm{m}$. Therefore, for these two batches, a hatch distance of $70 \\mu \\mathrm{m}$ has been used. Based on the first criterion for lack of fusion, an optimum layer thickness should be chosen by knowing the depth of the melt pool. Based on the criterion for keyhole formation, $W / D$ should be higher than 2. Therefore, the maximum $D$ is half $W$. As $D / t$ should be higher than 1.5, the maximum layer thickness for LPBF of 316L in this study for a machine with laser spot size of $35 \\mu \\mathrm{m}$ is plotted for different combinations of $P$ and $v$ and shown in Fig. 9b. Clearly, layer thicknesses lower than $80 \\mu \\mathrm{m}$ are suitable for laser power of $100 \\mathrm{~W}$. In here, for $P=200 \\mathrm{~W}$ (first batch), the maximum allowable layer thickness is $35 \\mu \\mathrm{m}$. Therefore, a $t=50 \\mu \\mathrm{m}$ has been used for this batch to induce lack of fusion. For $P=100 \\mathrm{~W}$ (second and third batches), the maximum $t$ is $25 \\mu \\mathrm{m}$. For second batch, a $t=30 \\mu \\mathrm{m}$ is used to induce lack of fusion but without keyhole formation, and for the third batch, a $t=20 \\mu \\mathrm{m}$ is used to guarantee sufficient melting.\n\nThe third step is to ensure balling prevention. Balling occurs when $L / W$ is higher than 2.3. Fig. 10a shows the predicted melt pool length $(L)$ for the different combinations of $P$ and $v$. $L$ decreases with increasing the scan speed and decreasing the laser power. The balling criterion for the different combinations of $P$ and $v$ is also presented in Fig. 10b. Balling is thus not a serious problem during LPBF of 316L using a machine with $\\sigma=35 \\mu \\mathrm{m}$. Even at high powers and scan speeds, the melt pool stability is high enough to prevent any balling defects. Therefore, the process parameters remain the same as introduced\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_6467a9d8d19c4db3d666g-08}\n\nFig. 7. (a)-(c) Scheil simulation for the designed, and (d)-(f) for three cracked 316L stainless steels. In all simulations, C and N are assumed as fast diffusers. Calculations performed using ThermoCalc, relying on TCFE9 database.", "start_char_idx": 691963, "end_char_idx": 695462, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b2549b99-ac34-49e5-acac-4dae2d009f0e": {"__data__": {"id_": "b2549b99-ac34-49e5-acac-4dae2d009f0e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "981df132-dde1-4f5f-a186-d83e25894761", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "df4e65ae8c9f4fae080e303d44f4307f01b47c553ade6731a954a5fc5f95e7a0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "47f20f05-4ef6-480a-aeb6-72682557c2f1", "node_type": "1", "metadata": {}, "hash": "156dc46b05a029090e0199ffbd96b41d53b13421f625db8f4a1cf9d1bcb1db8a", "class_name": "RelatedNodeInfo"}}, "text": "The balling criterion for the different combinations of $P$ and $v$ is also presented in Fig. 10b. Balling is thus not a serious problem during LPBF of 316L using a machine with $\\sigma=35 \\mu \\mathrm{m}$. Even at high powers and scan speeds, the melt pool stability is high enough to prevent any balling defects. Therefore, the process parameters remain the same as introduced\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_6467a9d8d19c4db3d666g-08}\n\nFig. 7. (a)-(c) Scheil simulation for the designed, and (d)-(f) for three cracked 316L stainless steels. In all simulations, C and N are assumed as fast diffusers. Calculations performed using ThermoCalc, relying on TCFE9 database.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_6467a9d8d19c4db3d666g-09}\n\\end{center}\n\nFig. 8. Keyhole/safe regions for different combinations of $P$ and $v$ with a laser spot size of $35 \\mu \\mathrm{m}$ for the experimental 316L stainless steel.\n\nbefore for the three mentioned batches.\n\nIt should be noted that as the powder was gas atomised with argon, internal porosity in the powder particles is often observed. If argon is given enough time to escape from the melt, this type of porosity can be eliminated [75]. However, as these types of pores have no detrimental effects on mechanical properties [76], in the present work no attempts have been made to describe the formation of these type of pores.\n\nAfter building the samples using LPBF, optical microscopy is used to reveal the crack/porosity contents. Using ImageJ software, a black and white contrast of the optical micrographs are provided and shown in Fig. 11. The micrographs show no solidification cracks after LPBF, as was expected from the high $F(F=1.72)$ of the alloy. As expected, the micrographs from the sample built in batch one with unoptimised process parameters indicate the presence of keyholes and lack of fusion defects (Fig. 11a). The average porosity content in this specimen is $1.11 \\pm 0.4 \\%$. The normalised enthalpy for this set of experiment is 10.2, which is higher than the threshold value for keyhole formation (the threshold is 5.5). This leads to overheating of the powder bed and\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_6467a9d8d19c4db3d666g-09(1)}\n\nFig. 9. (a) Maximum hatch distance, and (b) maximum layer thickness for the experimental 316L stainless steel for different combinations of $P$ and $v$ with a laser spot size of $35 \\mu \\mathrm{m}$.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_6467a9d8d19c4db3d666g-10}\n\nFig. 10. (a) Melt pool length and (b) balling criterion for different combinations of $P$ and $v$ with a laser spot size of $35 \\mu \\mathrm{m}$ for the experimental $316 \\mathrm{~L}$ stainless steel.\n\nevaporation of some of alloying elements with lower boiling points such as $\\mathrm{Mn}, \\mathrm{Cr}$, and Ni. This is the cause for the formation of keyholes. The smallest detected keyhole, based on its near-circular morphology is about $3 \\mu \\mathrm{m}$. It was also expected to produce some lack of fusion defects with layer thickness and hatch distances higher than the maximum values predicted by our model. The smallest lack of fusion defect that has been characterised in this work is about $10 \\mu \\mathrm{m}$. As lack of fusion defects are bigger than keyholes, it is expected that they have more detrimental effects on mechanical properties. Gas entrapment pores are also characterised in this sample and they are much smaller, about $1 \\mu \\mathrm{m}$. As shown in Figs. 10b and c, there is no evidence of keyholes by optimising the process parameters and reducing the normalised enthalpy value to 5.1.", "start_char_idx": 694766, "end_char_idx": 698448, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "47f20f05-4ef6-480a-aeb6-72682557c2f1": {"__data__": {"id_": "47f20f05-4ef6-480a-aeb6-72682557c2f1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b2549b99-ac34-49e5-acac-4dae2d009f0e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7324c7ecf0e8b8dd1d5813d9ba0ef78dd2be82f50b0d1ce7e11e78b40735ccfd", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "de6482c9-cb82-45eb-a6d6-693ea0c57daa", "node_type": "1", "metadata": {}, "hash": "f552ee524c0bbfa7551ae9deb27285974f7df617dbbdbd95381a67799566e362", "class_name": "RelatedNodeInfo"}}, "text": "This is the cause for the formation of keyholes. The smallest detected keyhole, based on its near-circular morphology is about $3 \\mu \\mathrm{m}$. It was also expected to produce some lack of fusion defects with layer thickness and hatch distances higher than the maximum values predicted by our model. The smallest lack of fusion defect that has been characterised in this work is about $10 \\mu \\mathrm{m}$. As lack of fusion defects are bigger than keyholes, it is expected that they have more detrimental effects on mechanical properties. Gas entrapment pores are also characterised in this sample and they are much smaller, about $1 \\mu \\mathrm{m}$. As shown in Figs. 10b and c, there is no evidence of keyholes by optimising the process parameters and reducing the normalised enthalpy value to 5.1. The average porosity levels in both samples from batch two and three is $0.03 \\pm 0.02 \\%$, which is lower than any reported before in 316 LPBF processing. In Fig. 11b, some lack of fusion defects are recognisable, which is because of the unoptimised layer thickness that had been chosen for production of this batch. However, that unoptimised layer thickness did not cause any changes in total population of pores and can be neglected. Looking into Fig. 11c reveals that the only pores that are present in the as-built part are gas-entrapped pores that could be related to the powder atomisation method. Using the full optimised process parameters by this method presented here, leads to production of porosity-free components, for a variety of machine parameters and alloy compositions.\n\nThis study also shows that the volumetric energy (heat input) is not a proper tool to predict the density of the LPBF-produced parts, However, it can be used as a good means for quantitatively estimating the heat input for the as-built bulk, as it considers the effects of layer thickness and hatch distance. Using Eq. (1), the $E_{v}$ for the batches 1-3 produced in here are $36,47.61$, and $71.42 \\mathrm{~J} / \\mathrm{mm}^{3}$, respectively. The least heat input estimated by this approach leads to evaporation and formation of the keyholes. Moreover, the average porosity contents in batches two and three are the same, however, the $E_{v}$ is totally different for these two conditions. These show that to reach fully-dense LPBF asbuilt parts, the proposed model works well in comparison with previous approaches reported in the literature $[77,78,20]$.\n\n\\subsection*{4.3. Mechanical properties}\nFig. 12 shows the tensile properties of the LPBF-built 316L samples, varying the process parameters. The mechanical properties requirements for 316L stainless steels in two states of cold-finished wrought (black dashes in Fig. 12) and hot-finished wrought (blue dashes in Fig. 12) based on ASM standard [79] are also shown in Fig. 12. It is worth noting that samples with similar void density have very close tensile performances. Among the samples, the sample from batch 1 has the lowest yield and tensile strength and elongation values owing to its relatively high porosity. However, its yield and ultimate tensile strength meets the requirements for 316L standard, but its elongation is poor (10\\% lower than the cold-finished wrought and $32.5 \\%$ lower than the hot-finished wrought alloy). Interestingly, the fully dense samples from batch two and three exhibit higher strength and comparable ductility, even with the hot-finished wrought samples. These samples also have better strength and ductility compared to the high porosity sample. The yield and ultimate tensile strength is increased in fully dense LPBF-built samples compared to the wrought samples by $47 \\%$ and $12 \\%$. It is also interesting that the ductility values for full dense LPBF-built samples are even better than the cold-finished wrought alloy and is slightly lower than the hot-finished wrought alloy.", "start_char_idx": 697645, "end_char_idx": 701524, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "de6482c9-cb82-45eb-a6d6-693ea0c57daa": {"__data__": {"id_": "de6482c9-cb82-45eb-a6d6-693ea0c57daa", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "47f20f05-4ef6-480a-aeb6-72682557c2f1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "11aa28bea399f6b4b09233bc3dd1c23810c30cc806971c3e415b38719a5767f5", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "be7f1431-835b-412b-9ca8-b407afaf4dec", "node_type": "1", "metadata": {}, "hash": "504167449456ea6d98dc8e84a344f2199e1bb5cd735d67fda9e72b7448e31455", "class_name": "RelatedNodeInfo"}}, "text": "Among the samples, the sample from batch 1 has the lowest yield and tensile strength and elongation values owing to its relatively high porosity. However, its yield and ultimate tensile strength meets the requirements for 316L standard, but its elongation is poor (10\\% lower than the cold-finished wrought and $32.5 \\%$ lower than the hot-finished wrought alloy). Interestingly, the fully dense samples from batch two and three exhibit higher strength and comparable ductility, even with the hot-finished wrought samples. These samples also have better strength and ductility compared to the high porosity sample. The yield and ultimate tensile strength is increased in fully dense LPBF-built samples compared to the wrought samples by $47 \\%$ and $12 \\%$. It is also interesting that the ductility values for full dense LPBF-built samples are even better than the cold-finished wrought alloy and is slightly lower than the hot-finished wrought alloy.\n\nThe present study reveals that the formability of 316L stainless steel\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_6467a9d8d19c4db3d666g-11(3)}\n\n(b)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_6467a9d8d19c4db3d666g-11(2)}\n\n(c)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_6467a9d8d19c4db3d666g-11}\n\nFig. 11. Micrographs from three different locations of the tensile samples: (a) sample from batch 1, showing keyholes and lack of fusion defects, (b) sample from batch two, showing some lack of fusion defects, (c) sample from batch three, showing neither keyholes nor lack of fusion defects. The only type of pores in this sample are gas-entrapped pores.\n\ncan be enhanced via LPBF processing using the optimised compositions for the alloy and optimised process parameters. The yield strength of the both defect-free and high porosity samples produced by LPBF is better than that of the wrought alloys, due to a higher dislocation density resulting from the high cooling rates and thermal strain during LPBF [80]. Solidification-enabled cellular structures with average submicron sizes that could develop during LPBF is another possible reason for the superior yield strength of the LPBF components [80]. Moreover, it was expected to obtain high yield strength, due to usage of a high PI alloy in this study. The ultimate tensile strength and ductility of the defect-free LPBF-built samples are better than the sample with porosity. The presence of keyholes and lack of fusion are assumed to be detrimental to both tensile strength and ductility of the material. Moreover, the presence of pores led to a decrease in the yield strength of the LPBF-built samples. Comparing the samples from batch two and three reveals the effects of lack of fusion on mechanical properties. Even low contents of lack of fusion (less than $0.03 \\%$ ) can lead to a decrease in the yield and ultimate tensile strength, as well as strain hardening capacity, but it does not change the elongation in such low contents.\n\nComparing the formability index (ultimate tensile strength $\\times$ elongation) [81] of the LPBF-built samples with the wrought alloy also shows a significant increase from 18,690 to $19,200 \\mathrm{MPa} \\%$ for wrought alloys to $27,800-28,280 \\mathrm{MPa} \\%$ for batches two and three, respectively.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_6467a9d8d19c4db3d666g-11(1)}\n\\end{center}\n\nFig. 12. Engineering stress-strain graphs for various LPBFbuilt 316L samples. The requirements for the tensile properties (the yield strength, ultimate tensile strength, and elongation) for cold-finished and hot-finished wrought samples are indicated in black and blue dashes, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)\n\nIt is believed that the deformation mechanism of the wrought $316 \\mathrm{~L}$ alloys is governed by dislocation slip and deformation twinning, due to its moderate stacking fault energy [82].", "start_char_idx": 700572, "end_char_idx": 704594, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "be7f1431-835b-412b-9ca8-b407afaf4dec": {"__data__": {"id_": "be7f1431-835b-412b-9ca8-b407afaf4dec", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "de6482c9-cb82-45eb-a6d6-693ea0c57daa", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "04dbe01d6b2ed7f0dbc2e397060f57438f606ba712cc7f939d0cafa86688a931", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fefa719b-e8fa-4456-a3fc-eabb037a2368", "node_type": "1", "metadata": {}, "hash": "265d3a13ba00f348d46a64c49f9d7e17321e996f00541c05e208cc2b151e0636", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_6467a9d8d19c4db3d666g-11(1)}\n\\end{center}\n\nFig. 12. Engineering stress-strain graphs for various LPBFbuilt 316L samples. The requirements for the tensile properties (the yield strength, ultimate tensile strength, and elongation) for cold-finished and hot-finished wrought samples are indicated in black and blue dashes, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)\n\nIt is believed that the deformation mechanism of the wrought $316 \\mathrm{~L}$ alloys is governed by dislocation slip and deformation twinning, due to its moderate stacking fault energy [82]. In here, although formation of deformation twins does not lead to high strain hardening rate, the high ductility of full-dense LPBF-built samples can be attributed to the deformation twins. This significant increase in formability index shows the effectiveness of optimisation of both composition and process parameters of LPBF can lead to production of remarkably better alloys and reduce the cost of heat treatments and forming processes significantly.\n\n\\subsection*{4.4. Novelty of the new crack and defect prevention criteria}\nThis work combines a number of factors to prevent crack formation. The performance index, $P I$ has been proposed by Hunt et al. [45], and the solidification temperature range STR has been proposed in welding literature [43]; in the present work, the values of $P I=1.46 \\times 10^{6} \\mathrm{MPa} \\mathrm{K}$ and $S T R=32 \\mathrm{~K}$ are for the first time proposed for 316L. Moreover, the relationship for $F=\\left(1500\\left(\\mathrm{STR}^{-1}\\right)^{2}+\\mathrm{PI}^{2}\\right)^{1 / 2}$ is new and shows a compromise in $\\mathrm{F}-\\mathrm{Cr}_{e q} / N i_{e q}$ space which has not been envisioned before; this indicates a trade between the ability to prevent cracks and the need to follow a certain solidification path.\n\nReferring to defect prevention, the geometry constraints listed in Section 2.2 are listed below and contrasted with previous literature:\n\n\\begin{itemize}\n  \\item For keyhole formation $\\Delta H / h_{s}$, the proposed threshold value of 5.5 is significantly lower than that of $30 \\pm 4$ reported by King et al. [70]. The value of $W / D>2$ differs that the values of 1.5 suggested in [22].\n  \\item Lack of fusion includes criteria for $D / t>1.5$ are similar to previous values of 1.0, 1.1 and 1.2 suggested by Mukherjee et al. [24] and 1.5 as proposed by Johnson et al. [22]. $h / W<1$, it comes from the work of Tang et al. [16] and has never been used before in combination with $D / t$.\n\\end{itemize}\n\n\\subsection*{4.5. Application to other alloy systems}\nMarageing steels are another family of alloys on which increasing attention is being focused. Two grades are worth of notice:\n\n\\begin{itemize}\n  \\item 17-4 precipitation hardened stainless steel, where the compromise of ( $F$ ) with $C r_{e q} / N i_{e q}$ can be adopted, but a different value for $F$ is to be considered and $C r_{e q} / N i_{e q}$ would be different as $\\delta$-ferrite is undesired if produced under LPBF due to the rapid solidification.\n\n  \\item The recently patented Formetrix family of steels [83], where the crack prevention-solidification path has to be reviewed, and the precipitate hardening capability has to be reviewed as part of postprocessing schedules.\n\n\\end{itemize}\n\nNickel alloys such as IN738 or CM247 require further attention, as the modelling strategy suggested in this work has to be complemented to incorporate the effects of liquation and strain-age cracking [84-86].\n\n\\section*{5. Conclusions}\nA general theory-guided computational alloy design methodology is presented, together with a physics-based model, to predict printability of austenitic stainless steels.", "start_char_idx": 703873, "end_char_idx": 707720, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fefa719b-e8fa-4456-a3fc-eabb037a2368": {"__data__": {"id_": "fefa719b-e8fa-4456-a3fc-eabb037a2368", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "be7f1431-835b-412b-9ca8-b407afaf4dec", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "987b49191c166a91fb15776e960028a8f854a0b712030febccdeecb19c133b9e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "088ea332-e7a1-41cb-985a-bb3127032300", "node_type": "1", "metadata": {}, "hash": "73cdf326e96c685bcda0578169ca554973294695d371a00f29bc59d879029b80", "class_name": "RelatedNodeInfo"}}, "text": "\\item The recently patented Formetrix family of steels [83], where the crack prevention-solidification path has to be reviewed, and the precipitate hardening capability has to be reviewed as part of postprocessing schedules.\n\n\\end{itemize}\n\nNickel alloys such as IN738 or CM247 require further attention, as the modelling strategy suggested in this work has to be complemented to incorporate the effects of liquation and strain-age cracking [84-86].\n\n\\section*{5. Conclusions}\nA general theory-guided computational alloy design methodology is presented, together with a physics-based model, to predict printability of austenitic stainless steels. Three variables have been controlled to prevent the formation of solidification cracks: solidification temperature range, performance index and the solidification path. Three austenitic stainless steels were designed to minimise the formation of solidification cracks during laser powder bed fusion and compared to the existing 316L alloys. Moreover, a new crack prevention factor has been defined to predict the susceptibility to crack formation.\n\nTo prevent formation of defects and porosity during laser powder bed fusion, physics-based models have been combined to estimate the melt pool geometry, and optimise the process parameters, considering the physical properties of the material. Process maps have been drawn to indicate the safe regions from different types of pores and defects in different combinations of laser powder bed fusion process parameters. The value of the proposed parameters is contrasted with those proposed in the literature.\n\nA 316L alloy with an optimised composition (high crack prevention factor) has been chosen to validate the printability model. It has been shown that the formability of the defect-free selective laser melted 316L alloy has been significantly improved compared to samples with pores and wrought versions of the same alloy. The findings of the present work will be of significance to laser powder bed fusion of other types of metallic parts into high-performance parts. Optimisation of chemical composition of the alloy as well as optimisation of process parameters is a promising method to overcome the long-standing strength-ductility dilemma in metallic materials. With enhanced formability capacity, the metallic parts or components produced by laser powder bed fusion will become safer when used in heavy load-bearing structures, and less material without the post-processing cost will be needed to achieve the same goal. This paper can help metal additive manufacturing find broader industrial applications.\n\nThe conditions to extend this strategy to other alloying systems such as marageing steels and nickel alloys have been overviewed.\n\n\\section*{Authors' contribution}\nPedro E.J. Rivera: conceptualisation, methodology, supervision and administration. writing and reviewing and editing. Hossein Eskandari: experimental data interpretation, metallography, writing original draft. Suhyun Maeng: computational modelling. Nesma Abulkhair, Marco Simonelli: printing of specimens. Xingzhong Liang: mechanical testing.\n\n\\section*{Data availability}\nThe raw and processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.\n\n\\section*{Conflict of interest}\nNone declared.\n\n\\section*{Acknowledgment}\nThe authors are grateful to Carpenter additive for useful discussions, and to the Royal Academy of Engineering for chair funding (RCSRF1718/5/32), and to theEPSRCfor funding via DARE grant (EP/ L025213/1). The authors are also grateful to Dr. Will Herbert from Carpenter Additive for useful discussions.\n\n\\section*{References}\n[1] G.T. Gray III, V. Livescu, P. Rigg, C.P. Trujillo, C.M. Cady, S.-R. Chen, J.S. Carpenter, T.J. Lienert, S.J. Fensin, Structure/property (constitutive and spallation response) of additively manufactured 3161 stainless steel, Acta Mater. 138 (2017) 140-149.\n\n[2] H.D. Carlton, A. Haboub, G.F. Gallegos, D.Y. Parkinson, A.A. 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Garlea, Effect of laser power on defect, texture, and microstructure of a laser powder bed fusion processed 3161 stainless steel, Mater. Des. 164 (2019) 107534.\n\n[79] A.H. Committee, et al., Properties and selection: stainless steels, tool materials and special-purpose metals, Metals Handbook, 9th ed., (1980), p. 3.\n\n[80] D. Wang, C. Song, Y. Yang, Y. Bai, Investigation of crystal growth mechanism during selective laser melting and mechanical property characterization of 3161 stainless steel parts, Mater. Des. 100 (2016) 291-299.\n\n[81] H.E. Sabzi, A.Z. Hanzaki, H. Abedi, R. Soltani, A. Mateo, J. Roa, The effects of bimodal grain size distributions on the work hardening behavior of a transformation-twinning induced plasticity steel, Mater. Sci. Eng. A 678 (2016) 23-32.\n\n[82] Z. Sun, X. Tan, S.B. Tor, C.K. Chua, Simultaneously enhanced strength and ductility for 3d-printed stainless steel 3161 by selective laser melting, NPG Asia Mater. 10 (4) (2018) 127.\n\n[83] C.D. Tuffile, H. Lemke, 3d printable hard ferrous metallic alloys for powder bed fusion, US Patent App. 16/393,194 (2019).\n\n[84] S. Catchpole-Smith, N. Aboulkhair, L. Parry, C. Tuck, I. Ashcroft, A. Clare, Fractal scan strategies for selective laser melting of 'unweldable'nickel superalloys, Addit. Manuf. 15 (2017) 113-122.\n\n[85] J.H. Boswell, D. Clark, W. Li, M.M. Attallah, Cracking during thermal post-processing of laser powder bed fabricated cm247lc ni-superalloy, Mater. Des. 174 (2019) 107793.\n\n[86] C. Qiu, H. Chen, Q. Liu, S. Yue, H. Wang, On the solidification behaviour and cracking origin of a nickel-based superalloy during selective laser melting, Mater. Charact. 148 (2019) 330-344.\n\n\\begin{itemize}\n  \\item \n\\end{itemize}", "start_char_idx": 724644, "end_char_idx": 727302, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b3583547-6f93-4db3-bf72-34080c93564d": {"__data__": {"id_": "b3583547-6f93-4db3-bf72-34080c93564d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "49b6e976-f23d-4142-a028-18ee8dbf2bbd", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6bd37196a677d54a792091897ce988d5c7ad982616492190f0944b2aa539be6a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "77d34ac9-6750-4ea9-959a-71eef4f0534a", "node_type": "1", "metadata": {}, "hash": "04a0e8d7684edb38f6d02937df1999533480872fc35be2775b8e5c28d5c64e38", "class_name": "RelatedNodeInfo"}}, "text": "Manuf. 15 (2017) 113-122.\n\n[85] J.H. Boswell, D. Clark, W. Li, M.M. Attallah, Cracking during thermal post-processing of laser powder bed fabricated cm247lc ni-superalloy, Mater. Des. 174 (2019) 107793.\n\n[86] C. Qiu, H. Chen, Q. Liu, S. Yue, H. Wang, On the solidification behaviour and cracking origin of a nickel-based superalloy during selective laser melting, Mater. Charact. 148 (2019) 330-344.\n\n\\begin{itemize}\n  \\item \n\\end{itemize}\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\\usepackage{multirow}\n\n\\title{Laser powder bed fusion of AA7075 alloy: Influence of process parameters on porosity and hot cracking }\n\n\n\\author{Wojciech Stopyra*, Konrad Gruber, Irina Smolina, Tomasz Kurzynowski, Bogumi\u0142a Ku\u017anicka\\\\\nWroc\u0142aw University of Science and Technology, Faculty of Mechanical Engineering, Centre for Advanced Manufacturing Technologies (CAMT/FPC), 5 \u0141ukasiewicza st. 50-\\\\\n371 Wroc\u0142aw, Poland}\n\\date{}\n\n\n%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?]{%\n  \\if\\relax#1\\relax%\n    \\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n  \\else%\n    \\if?#1\\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n    \\else\\svfootnotetext[#1]{#2}\\fi%\n  \\fi\n}\n\n\\begin{document}\n\\maketitle\nResearch Paper\n\n\n\n\\section*{A R T I C L E I N F O}\n\\section*{Keywords:}\nHot cracking\n\nAdditive manufacturing\n\nAluminium alloys\n\nLPBF\n\nMicrosegregation\n\n\\begin{abstract}\nA B S T R A C T Laser powder bed fusion (LPBF) is an attractive technology of manufacturing high-strength aluminium alloy parts for the aircraft and automobile industries, limited by poor processability of these alloys. This work was aimed at finding the process window for the LPBF manufacturing of defect-free components of AA7075 alloy. Optimization of the parameters was performed at each stage of the multi-stage research, i.e. for single tracks, thin walls and volumetric specimens. At each stage, the relation between LPBF parameters and defect formation with a focus on hot cracking was investigated and discussed. Due to the optimization of process parameters, the density of volumetric specimens above $99 \\%$ was reached and vaporization losses of the alloying elements were significantly reduced, but solidification cracks could not be eliminated. It was found that solidification cracks were formed by the liquid film rupture mode, mainly along columnar grain boundaries. The EDS microanalysis showed intergranular microsegregation, not only of the main alloying elements $(\\mathrm{Zn}, \\mathrm{Mg}, \\mathrm{Cu})$ but also of minor elements such as Si.", "start_char_idx": 726863, "end_char_idx": 730130, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "77d34ac9-6750-4ea9-959a-71eef4f0534a": {"__data__": {"id_": "77d34ac9-6750-4ea9-959a-71eef4f0534a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b3583547-6f93-4db3-bf72-34080c93564d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "925ec2cd17e9c558e45578b193d611777f0cfa3586570b4d2f55c630d89d4d49", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3839cae5-9b37-4333-9ba0-b0881e27738d", "node_type": "1", "metadata": {}, "hash": "21cbe89d91aecebf5ccedb3186c708efbace89aecaaafcdfef5c6c15a715ac89", "class_name": "RelatedNodeInfo"}}, "text": "This work was aimed at finding the process window for the LPBF manufacturing of defect-free components of AA7075 alloy. Optimization of the parameters was performed at each stage of the multi-stage research, i.e. for single tracks, thin walls and volumetric specimens. At each stage, the relation between LPBF parameters and defect formation with a focus on hot cracking was investigated and discussed. Due to the optimization of process parameters, the density of volumetric specimens above $99 \\%$ was reached and vaporization losses of the alloying elements were significantly reduced, but solidification cracks could not be eliminated. It was found that solidification cracks were formed by the liquid film rupture mode, mainly along columnar grain boundaries. The EDS microanalysis showed intergranular microsegregation, not only of the main alloying elements $(\\mathrm{Zn}, \\mathrm{Mg}, \\mathrm{Cu})$ but also of minor elements such as Si. Silicon may play a significant role in increasing susceptibility to cracking by increasing the stability of the liquid film. Reduction in the silicon impurity content in the AA7075 powder gives a chance to reduce susceptibility to cracking with no change of the alloy specification.\n\\end{abstract}\n\n\\section*{1. Introduction}\n\\subsection*{1.1. Laser powder bed fusion}\nLaser powder bed fusion (LPBF), often also named selective laser melting (SLM), belongs to one of the seven categories of additive manufacturing processes specified in ASTM F2792-12a. In the LPBF technology, semi-finished parts with complex geometry are fabricated by the selective melting and consolidating of metallic powder in a layerby-layer manner using a laser beam controlled directly from a 3D CAD file.\n\nAn advantage of LPBF technology is the possibility of manufacturing customized parts without the need for part-specific tooling, dies or casting moulds. On account of these advantages, LPBF is currently a widely accepted new way of designing and producing high performance components for applications in the automotive and aerospace industry $[1]$.\n\nAluminium alloys, as construction materials, are very attractive for manufacturing parts that are characterized by an excellent strength-toweight ratio, a relatively low cost-to-specific strength ratio and corrosion resistance [2]. The application of LPBF technology would add to the advantages of using high strength aluminium alloys for the manufacturing of complex parts by introducing topology optimization, thin walls and internal structures [3]. However, there is a problem that the printability of aluminium alloys is low [4] in comparison to alloys such as stainless steel $316 \\mathrm{~L}$, Inconel 718 or Ti6Al4V [5]. Only the neareutectic casting alloys like AlSi12 and AlSi10Mg are relatively easy to process [6] due to the small difference between their liquidus and solidus temperatures in comparison to that of the $2 \\mathrm{xxx}, 6 \\mathrm{xxx}$, and $7 \\mathrm{xxx}$ series of wrought alloys [7]. Therefore, one of the solutions of this problem is developing new Al alloys, specifically designed for the LPBF process, mainly by an addition of silicon [8].\n\n\\subsection*{1.2. Processability of $A A 7075$ alloy}\nPrecipitation hardened wrought aluminium alloys have higher mechanical properties than eutectic alloys, and therefore alloys such as AA6061 and AA7075, which are important in the aircraft industry, are the objects of research works focused on poor LPBF processability of these, considered as difficult to weld and cast, alloys [9]. Due to properly selected ratios between the three main alloying elements $(\\mathrm{Zn}$, $\\mathrm{Mg}$ and $\\mathrm{Cu}$ ), the AA7075 alloy achieves a high level of strength after\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author.\n\\end{itemize}\n\nE-mail address: \\href{mailto:wojciech.stopyra@pwr.edu.pl}{wojciech.stopyra@pwr.edu.pl} (W. Stopyra).\n}\n\nTable 1\n\nPhysical properties of the AA7075 alloy [MatWeb-Material Property Data].", "start_char_idx": 729185, "end_char_idx": 733165, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3839cae5-9b37-4333-9ba0-b0881e27738d": {"__data__": {"id_": "3839cae5-9b37-4333-9ba0-b0881e27738d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "77d34ac9-6750-4ea9-959a-71eef4f0534a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "58c29423d753f77f6116d956d7a133a704ae45aa16c72793ee048e19ae49dfa8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bd827a1f-a159-4fe7-a671-15bf65089dd4", "node_type": "1", "metadata": {}, "hash": "02e680b2f51ec66e70cdd18ecbc780ac5460fa23a71ff684b59fd3d8d0d26ebe", "class_name": "RelatedNodeInfo"}}, "text": "Due to properly selected ratios between the three main alloying elements $(\\mathrm{Zn}$, $\\mathrm{Mg}$ and $\\mathrm{Cu}$ ), the AA7075 alloy achieves a high level of strength after\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author.\n\\end{itemize}\n\nE-mail address: \\href{mailto:wojciech.stopyra@pwr.edu.pl}{wojciech.stopyra@pwr.edu.pl} (W. Stopyra).\n}\n\nTable 1\n\nPhysical properties of the AA7075 alloy [MatWeb-Material Property Data].\n\n\\begin{center}\n\\begin{tabular}{ll}\n\\hline\nDensity & $2.81 \\mathrm{~g} / \\mathrm{cm}^{3}$ \\\\\nCTE (average for $20-300{ }^{\\circ} \\mathrm{C}$ ) & $25.2 \\mu \\mathrm{m} / \\mathrm{m} \\cdot{ }^{\\circ} \\mathrm{C}$ \\\\\nSpecific heat capacity & $0.96 \\mathrm{~J} / \\mathrm{g} \\cdot{ }^{\\circ} \\mathrm{C}$ \\\\\nThermal conductivity & $130 \\mathrm{~W} / \\mathrm{m} \\cdot \\mathrm{K}$ \\\\\nMelting range & $477-635{ }^{\\circ} \\mathrm{C}$ \\\\\nViscosity (in the liquid range) & $0.4-0.5 \\mathrm{~mm}^{2} / \\mathrm{s}$ \\\\\nVolumetric shrinkage & $6-8 \\%$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nsolutioning and peak-aging (T6). However, from the viewpoint of the processability by LPBF, the AA7075 composition and its physical properties (Table 1) are the reason for the strong tendency of the alloy to form defects during processing. These defects are due to the wide range of solidification temperatures, which are extended by the tendency of microsegregation occurring [10].\n\nGaly et al. [11] classified the defects observed in the LPBF-ed parts of aluminium alloys, distinguishing four main types: porosity, hot cracking, low surface quality and anisotropy. If surface quality and anisotropy are defects dependent on process parameters, the tendency to form pores and hot cracks is strongly affected by both the process parameters and the chemical composition of the alloy. The porosity of aluminium alloys can be minimized by the quality of the powder, as well as by the proper selection of the laser power and scanning speed. According to Louvis et al. [12], the phenomenon of the rapid creation of thin oxide films on both solid and liquid surfaces must also be taken into consideration. This requires a suitably high laser power and scanning speed to be selected due to the high thermal conductivity of aluminium alloys and the necessity to break the oxide films. In the case of AA7075, the selection of process parameters must additionally consider the high susceptibility of the alloy to hot cracking, i.e. solidification cracking and, to a lesser degree, liquation cracking.\n\n\\subsection*{1.3. Solidification and liquation cracking}\nCracking during solidification is generally believed to result from the uniaxial tensile fracture of the semisolid film at the grain boundaries [10]. Tension in the semisolid film is induced by volumetric shrinkage and by the thermal contraction of the semisolid and its neighbouring solids at a temperature in which the solid fraction exceeds 0.9 [13].\n\nThe AA7075 alloy has poor processability by LPBF due to its high solidification shrinkage and high susceptibility to solidification cracking. Eskin et al. [13] reported that solidification shrinkage of aluminium alloys amounts from 6 to 8 vol\\% as opposed to ca. 3 vol\\% for titanium alloys and steels [14]. According to the Kou's criterion [15], the cracking susceptibility of AA7075, measured by the maximum value of the index $\\left|\\mathrm{dT} /\\left(\\mathrm{df}_{\\mathrm{s}}\\right)^{1 / 2}\\right|$ at nearly $\\mathrm{f}_{\\mathrm{s}}{ }^{1 / 2} \\approx 1$ (where $\\mathrm{f}_{\\mathrm{s}}$ is the solid fraction and $\\mathrm{T}$ is the temperature of the mushy zone), is higher than for the other high strength Al alloys, e.g.", "start_char_idx": 732724, "end_char_idx": 736370, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bd827a1f-a159-4fe7-a671-15bf65089dd4": {"__data__": {"id_": "bd827a1f-a159-4fe7-a671-15bf65089dd4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3839cae5-9b37-4333-9ba0-b0881e27738d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ef0379d80b32c5989b569df52f79d30b1c16861c6746cb9d575cc6ca70c32039", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a0b8f650-69eb-4c22-b35f-f7608d07e48d", "node_type": "1", "metadata": {}, "hash": "33f1f8d2cbf994be1da4aa0089fa684e40f5793f6dd628027c5caa3b5e640847", "class_name": "RelatedNodeInfo"}}, "text": "The AA7075 alloy has poor processability by LPBF due to its high solidification shrinkage and high susceptibility to solidification cracking. Eskin et al. [13] reported that solidification shrinkage of aluminium alloys amounts from 6 to 8 vol\\% as opposed to ca. 3 vol\\% for titanium alloys and steels [14]. According to the Kou's criterion [15], the cracking susceptibility of AA7075, measured by the maximum value of the index $\\left|\\mathrm{dT} /\\left(\\mathrm{df}_{\\mathrm{s}}\\right)^{1 / 2}\\right|$ at nearly $\\mathrm{f}_{\\mathrm{s}}{ }^{1 / 2} \\approx 1$ (where $\\mathrm{f}_{\\mathrm{s}}$ is the solid fraction and $\\mathrm{T}$ is the temperature of the mushy zone), is higher than for the other high strength Al alloys, e.g. AA2024 and AA2219, but lower than for AA6061 [16]. During the LPBF process, rapid solidification of the thin layers of the molten powder consists of cellular-dendritic and epitaxial growth of columnar grains [4]. This directional growth of columnar grains, proceeding across multiple build layers, creates the conditions that are conducive to solidification cracking. Because of the slow lateral growth and the much slower bridging than the forward growth of cell-dendrites, long grain boundary channels are created that are hard for liquid feeding and which act as very sharp notches. In addition, susceptibility to cracking is increased by interdendritic microsegregation of alloying elements, which results in constitutional undercooling [10].\n\nLiquation cracking is a consequence of constitutional liquation, i.e. non-equilibrium eutectic melting of the intermetallic-phase particles present at grain boundaries at temperatures above the eutectic temperature of the matrix-intermetallic phase system and below the equilibrium solidus temperature of the alloy [17]. This phenomenon occurs during rapid heating of a multi-phase alloy to the solution temperature, when the time before reaching the eutectic temperature is too short for dissolving the intermetallic-phase particles [18]. The liquid film produced by constitutional liquation at grain boundaries initiates cracks under tensile stresses. Therefore, it cannot be excluded that, during the LPBF of AA7075, liquation cracking interferes with solidification cracking. As was found by Ghaini et al. [19], liquation cracks can strongly affect the initiation of solidification cracks in the AA2024 alloy.\n\n\\subsection*{1.4. Current status of research on high-strength aluminium alloys processed by $L P B F$}\nDifficulties in processing aluminium alloys are the reason for the interest of scientists in investigating the feasibility of introducing high strength wrought aluminium alloys to the LPBF process [20]. This particularly concerns the alloy series $6 \\mathrm{xxx}$ and $7 \\mathrm{xxx}$, which have a very high crack susceptibility index [16].\n\nA way to prevent the formation of cracks in these alloys during LPBF is by controlling the nucleation and growth of crystals, so that small equiaxed grains are obtained instead of columnar grains [21]. One approach to manufacturing grain-refined alloys is to control the thermal gradient and solidification velocity in order to induce the large undercooling required for the nucleation and growth of equiaxed grains, which is in accordance with the Hunt criterion for the columnar-toequiaxed transition [22]. This demands appropriate manipulation of the LPBF process parameters. In the case of aluminium alloys, it is extremely difficult to obtain critical undercooling because of the high thermal conductivity of aluminium and the large liquid diffusivities of alloying elements. Nevertheless, it is possible that the equiaxed grains can be originated by the breakdown and fragmentation of the columnar dendrites, induced by melt movement [23] or by acoustic cavitation [24].\n\nEven though Reschetnik et al. [25] used the best experimentally determined set of process parameters ( $350 \\mathrm{~W} / 930 \\mathrm{~mm} / \\mathrm{s}$ ) for manufacturing the AA7075 specimens, they did not achieve a success. The specimens contained a dense network of long cracks, initiated mostly in the track fusion zone parallel to the building direction.\n\nMartin et al. [9] succeeded in producing the AA7075 alloy by LPBF with no cracks by reducing the undercooling threshold for equiaxed grain growth with the introduction of low-energy-barrier heterogeneous nucleants ahead of the solidification front.", "start_char_idx": 735641, "end_char_idx": 740068, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a0b8f650-69eb-4c22-b35f-f7608d07e48d": {"__data__": {"id_": "a0b8f650-69eb-4c22-b35f-f7608d07e48d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bd827a1f-a159-4fe7-a671-15bf65089dd4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "fa2eb2150f6bd2e7ef90b0510e426a0e4bf92f56260c7d5a9e34f1da48c51289", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "e2104c32-36e7-4412-a165-8d1eebd8bc98", "node_type": "1", "metadata": {}, "hash": "ad5c4b991f04fa0bdc50d75e68971f0ea609e6a2d1cd10aae1a5186653a3d6ae", "class_name": "RelatedNodeInfo"}}, "text": "Nevertheless, it is possible that the equiaxed grains can be originated by the breakdown and fragmentation of the columnar dendrites, induced by melt movement [23] or by acoustic cavitation [24].\n\nEven though Reschetnik et al. [25] used the best experimentally determined set of process parameters ( $350 \\mathrm{~W} / 930 \\mathrm{~mm} / \\mathrm{s}$ ) for manufacturing the AA7075 specimens, they did not achieve a success. The specimens contained a dense network of long cracks, initiated mostly in the track fusion zone parallel to the building direction.\n\nMartin et al. [9] succeeded in producing the AA7075 alloy by LPBF with no cracks by reducing the undercooling threshold for equiaxed grain growth with the introduction of low-energy-barrier heterogeneous nucleants ahead of the solidification front. They developed a method of \"nano-functionalization\" of powder with hydrogen-stabilized zirconium nanoparticles that, after decomposition at the melt, created the $\\mathrm{Al}_{3} \\mathrm{Zr}$ nucleant phase. However, use of hydrogen as a stabilizer is questionable due to aluminium alloys being susceptible to hydrogen embrittlement. Moreover, the much lower solubility of hydrogen in solid than in liquid aluminium causes the additional problem of porosity for the fabricated parts.\n\nQi et al. [26] focused on investigating the effect of scanning speed and defocusing distance on the melting mode transition and cracking in LPBF of the AA7050 powder using a $200 \\mathrm{~W}$ laser power. They stated that using the optimal scanning speed can only reduce, but not eliminate the cracks, induced by the process. By manipulating the scanning speed and defocusing distance, it is possible to change the keyholemode to the conduction mode of melting and to therefore influence the hot crack sensitivity of the alloy.\n\nAnother approach to preventing the forming of solidification cracks is to preheat the base plate in order to decrease thermal gradients during LPBF and thus reduce thermal stresses and decrease undercooling. Using high-power platform preheating at $200{ }^{\\circ} \\mathrm{C}$ and a set of process parameters of $500 \\mathrm{~W} / 1200 \\mathrm{~mm} / \\mathrm{s}$, Kaufmann et al. [27] obtained a $99.8 \\%$ density of the AA7075 alloy, but were not able to reduce cracking.\n\nDuring the manufacturing of AA7075 alloy parts, Mertens et al. [28]\\\\\nused platform preheating at $400{ }^{\\circ} \\mathrm{C}$ with process parameters of $270 \\mathrm{~W} /$ $1200 \\mathrm{~mm} / \\mathrm{s}$, obtaining a reduction in crack formation and a change in crack morphology. However, they were not able to completely prevent cracking.\n\nUddin et al. [29] used $500{ }^{\\circ} \\mathrm{C}$ preheating in combination with parameters: $400 \\mathrm{~W} / 1400 \\mathrm{~mm} / \\mathrm{s}$, obtaining a result in the form of crack-free cubic specimens of the Al6061 alloy. Judging by the presence of divorced eutectic particles in the as-built microstructure, a disadvantage of this method, which is a result of non-equilibrium melting, can be the inability to achieve elongations of over $5 \\%$ in the aging condition.\n\nThe above-presented results demonstrate that finding the optimal LPBF process parameters for the manufacturing of pore-free and crackfree parts of AA6061 and AA7075 alloys is a very difficult task. As is stressed in the subject literature, the reason for this is the insufficient understanding of the behaviour of these alloys during LPBF fabrication and also the insufficient identification of the processing parameters that are responsible for hot crack formation.\n\nThe presented work aimed to find the process window for the production of defect-free components of the high-strength AA7075 alloy. Selection of the parameters was made at each stage of the multi-stage experiment, i.e. for single tracks, thin walls, and for volumetric specimens. In addition, the relation between the process parameters and defect formation was investigated, with a focus on hot cracking. It was assumed that the obtained results would broaden the knowledge about defects, and in particular the hot cracks created during the LPBF fabrication of AA7075, and also explain whether hot isostatic pressing (HIP) can be used to reduce defects and to heal cracks.\n\n\\section*{2. Materials and methods}\n\\subsection*{2.1.", "start_char_idx": 739261, "end_char_idx": 743571, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "e2104c32-36e7-4412-a165-8d1eebd8bc98": {"__data__": {"id_": "e2104c32-36e7-4412-a165-8d1eebd8bc98", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a0b8f650-69eb-4c22-b35f-f7608d07e48d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "84cf3f4cc1012faaed3e17a0f892f2d27cd60fef912bd32eede4f76a85a95191", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "61afcbc3-d14f-42e4-bf47-a468eea34b5a", "node_type": "1", "metadata": {}, "hash": "bd00827b96f35a309eb2a447cc7ad5612c4be6babd0eb1b9783f904d5e127d2b", "class_name": "RelatedNodeInfo"}}, "text": "As is stressed in the subject literature, the reason for this is the insufficient understanding of the behaviour of these alloys during LPBF fabrication and also the insufficient identification of the processing parameters that are responsible for hot crack formation.\n\nThe presented work aimed to find the process window for the production of defect-free components of the high-strength AA7075 alloy. Selection of the parameters was made at each stage of the multi-stage experiment, i.e. for single tracks, thin walls, and for volumetric specimens. In addition, the relation between the process parameters and defect formation was investigated, with a focus on hot cracking. It was assumed that the obtained results would broaden the knowledge about defects, and in particular the hot cracks created during the LPBF fabrication of AA7075, and also explain whether hot isostatic pressing (HIP) can be used to reduce defects and to heal cracks.\n\n\\section*{2. Materials and methods}\n\\subsection*{2.1. Aluminium 7075 powder}\nThe quality of parts manufactured by LPBF is significantly influenced by the characteristics of alloy powder as a feedstock material. These characteristics include chemical composition, shape, size distribution, surface morphology, and the fraction of internal pores [30]. The quality of the powder determines its flowability and apparent density [31].\n\nIn the presented research, the commercially available gas-atomised AA7075 powder, supplied by KAMB Import-Export, was used, with the particle shape qualified, according to ASTM B243-11, as nodular (Fig. 1a) with an aspect ratio from 1 to 4, surface satellite defects and internal porosity (Fig. 1b). This morphology negatively affects flowability and packing density [7]. Nevertheless, Reschetnik et al. [25], Kaufmann et al. [27], Montero Sistiaga et al. [32], Aboulkhair et al. [33], while employing in their research the AA7075 and AlSi10Mg gasatomised powders with non-spherical particles, achieved a high density of fabricated parts when an appropriate energy density was used.\n\nChemical composition of the powder (Table 2) was determined using the optical emission spectrometer ARL 4460. Particle size distribution (PSD) was determined using sieve analysis according to EN 24497. The 10th, 50th and 90th weight percentiles of the different size particles were $\\mathrm{D}_{10} \\leq 39.0 \\mu \\mathrm{m}, \\mathrm{D}_{50} \\leq 57.0 \\mu \\mathrm{m}$, and $\\mathrm{D}_{90} \\leq 85.0 \\mu \\mathrm{m}$, with the low span value of 0.8 defined as $\\left(D_{90}-D_{10}\\right) / D_{50}$.\n\nThe Hall Flowmeter Funnel - Copley (Type Upright \\& Stand) and Mitutoyo Absolute Digimatic Heightgage were used to measure angles of repose (ASTM B213) and apparent density of the powder (ASTM B212). Before the process, the virgin powder was dried at $350{ }^{\\circ} \\mathrm{C}$ for $120 \\mathrm{~h}$ inside the process chamber. After drying, the powder was characterised by low angles of repose of 30 to $40^{\\circ}$, meeting the criterion of freely flowing powders [34]. The determined apparent density of 1.23 $\\mathrm{g} / \\mathrm{cm}^{3}$ constituted $44 \\%$ of the solid material density, which is contained within the range of $40-60 \\%$ that is typical for the gas-atomised powders, as is reported in review paper [35]. Considering the findings for the IN738LC alloy presented in paper [36], the determined powder characteristics were acknowledged as acceptable from the viewpoint of their flowability and the fact that there was no influence on cracking susceptibility.\n\n\\subsection*{2.2. Fabrication of specimens}\nSpecimens with various geometries were produced using the LPBF Realizer II 250 (MPC-HEK) system equipped with a $400 \\mathrm{~W}$ pulsed Ytterbium fibre laser with a focused beam diameter of $200 \\mu \\mathrm{m}$. Highpurity argon was used as the protective atmosphere.", "start_char_idx": 742573, "end_char_idx": 746423, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "61afcbc3-d14f-42e4-bf47-a468eea34b5a": {"__data__": {"id_": "61afcbc3-d14f-42e4-bf47-a468eea34b5a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e2104c32-36e7-4412-a165-8d1eebd8bc98", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e45fe2022d10d67bd358c62b95902e390b7513705a6f8a295d4da4ffc3903f5b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3f119e3a-c178-4cd1-9a26-787356f54c9b", "node_type": "1", "metadata": {}, "hash": "8e57ac81e815c31206b4077eda50e5cd25f7619f9c41564b42ff4f3dad718670", "class_name": "RelatedNodeInfo"}}, "text": "The determined apparent density of 1.23 $\\mathrm{g} / \\mathrm{cm}^{3}$ constituted $44 \\%$ of the solid material density, which is contained within the range of $40-60 \\%$ that is typical for the gas-atomised powders, as is reported in review paper [35]. Considering the findings for the IN738LC alloy presented in paper [36], the determined powder characteristics were acknowledged as acceptable from the viewpoint of their flowability and the fact that there was no influence on cracking susceptibility.\n\n\\subsection*{2.2. Fabrication of specimens}\nSpecimens with various geometries were produced using the LPBF Realizer II 250 (MPC-HEK) system equipped with a $400 \\mathrm{~W}$ pulsed Ytterbium fibre laser with a focused beam diameter of $200 \\mu \\mathrm{m}$. Highpurity argon was used as the protective atmosphere.\n\nTaking into account poor processability of the AA7075 powder and strong dependence of quality (including dimensional accuracy) of the final product on quality of each single track and each single layer [37], optimum process parameters were selected for individual steps, i.e. for single tracks, thin walls and volumetric specimens. At each stage, the process stability was evaluated, as well as the strength of influence of individual process parameters on the alloy behaviour in the course of the process. Course of the gradual selection of various LPBF process variables aimed at determining the optimum set of process parameters is shown in Table 3.\n\nThe multi-stage investigations included:\n\n\\begin{itemize}\n  \\item Trial melting of substrate in the form of single tracks on the surface of the hot-rolled plate of the alloy AA7075-T6 (165 HV0.5). The plate was $8 \\mathrm{~mm}$ thick, a laser power of $200 \\mathrm{~W}$ and $400 \\mathrm{~W}$ was used, and various scanning speeds set by a combination of the point distances and varying exposure time of one point, were adopted. The cross sections of the tracks were examined and correlated with the process parameters.\n  \\item Trial manufacturing of thin walls at various sets of process\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_b6298c9a4a3486463622g-03}\n\\end{itemize}\n\nFig. 1. Backscattered Electron Detector (BSD) images of AA7075 powder: (a) globular particles with large amounts of satellites on their surfaces; (b) internal gas pores on the cross-sections of some particles. The aspect ratios of selected particles are given in brackets.\n\nTable 2\n\nChemical composition of AA7075 (AlZn5.5MgCu) powder in wt.\\%.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\n\\hline\nElement & $\\mathrm{Al}$ & $\\mathrm{Zn}$ & $\\mathrm{Mg}$ & $\\mathrm{Cu}$ & $\\mathrm{Cr}$ & Mn & Si & $\\mathrm{Fe}$ \\\\\n\\hline\nPowder & Bal. & 5.54 & 2.40 & 1.56 & 0.25 & 0.26 & 0.4 & 0.11 \\\\\n\\hline\nISO $209-1$ & Bal. & $5.1-6.1$ & $2.1-2.9$ & $1.2-2.0$ & $0.18-0.28$ & $\\max 0.30$ & $\\max 0.40$ & $\\max 0.50$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nparameters, where laser power and scanning speed set by a combination of point distances 20,40, 60 and $80 \\mu \\mathrm{m}$ and varying exposure time of one point $(20-420 \\mu \\mathrm{s})$ were accepted as variables. The walls were built on the plate of the AA7075 alloy with a single track that outlined a square of $7 \\mathrm{~mm} \\times 7 \\mathrm{~mm}$ to the height of $5 \\mathrm{~mm}$. The layer of melted powder was $50 \\mu \\mathrm{m}$ thick. The quality of the walls was evaluated by: determining their thickness measured by width of the last (top) track, and visual, microscopic evaluation of their side surface quality.", "start_char_idx": 745604, "end_char_idx": 749145, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3f119e3a-c178-4cd1-9a26-787356f54c9b": {"__data__": {"id_": "3f119e3a-c178-4cd1-9a26-787356f54c9b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "61afcbc3-d14f-42e4-bf47-a468eea34b5a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "248fc3dccee7818f78aefd2412335107d95482c1c33227524a541b0a610a7c6b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f554b856-d2f8-49b5-a4d8-26cc820d2158", "node_type": "1", "metadata": {}, "hash": "a2a77074cb2bee29f40a93bd1977956d2604fd47f7de211c4f8227dd5cb49740", "class_name": "RelatedNodeInfo"}}, "text": "The walls were built on the plate of the AA7075 alloy with a single track that outlined a square of $7 \\mathrm{~mm} \\times 7 \\mathrm{~mm}$ to the height of $5 \\mathrm{~mm}$. The layer of melted powder was $50 \\mu \\mathrm{m}$ thick. The quality of the walls was evaluated by: determining their thickness measured by width of the last (top) track, and visual, microscopic evaluation of their side surface quality. The variants showing an irregular width of tracks or their discontinuities and side surfaces with \"balling effect\", overlaps and stuck-on agglomerates of powder particle were rejected.\n\nBecause of unsatisfactory results, i.e. obtaining too thick walls in relation to the focused beam diameter, the series of tests was repeated delaying the scanning of each subsequent thin-walled specimen by 1.5 $\\mathrm{s}$. The distance between neighbouring specimens was $10 \\mathrm{~mm}$.\n\n\\begin{itemize}\n  \\item Multivariant trial manufacturing of volumetric specimens of $10 \\mathrm{~mm} \\times 8$ $\\mathrm{mm} \\times 5 \\mathrm{~mm}$ at variable parameters: hatch spacing, scanning speed, negative defocus distance, scanning strategy and the parameter values selected in the previous tests, i.e. a laser power of $200 \\mathrm{~W}$ and a scan delay (SD) of $1.5 \\mathrm{~s}$. The focal offset distance was set by a change of lens position, resulting in a shift of the laser focus in relation to the calibrated zero-plane of the system. A negative shift describes the displacement of focus below the build plane.\n\\end{itemize}\n\nIn order to determine the influence of the scanning strategy on the porosity and hot cracking, four variants of scanning strategy were used: alternating (S1), double scanning (DS), $2.5 \\mathrm{~mm}$ wide stripes alongside (SS2), and chessboard (SS3) with the field size of $2.5 \\mathrm{~mm} \\times 2.5 \\mathrm{~mm}$. The specimens were prepared on support structures without preheating the base plate and with preheating it to $300{ }^{\\circ} \\mathrm{C}$ at the same configuration. Porosity was the main quality criterion of all the specimens.\n\n\\begin{itemize}\n  \\item Tensile tests with the use of cylindrical specimens with a diameter of $4 \\mathrm{~mm}$ on the gauge length of $20 \\mathrm{~mm}$, manufactured using the parameter sets selected at the previous stages. The tensile specimens were built with the tension axis parallel to the build direction. The tensile tests were carried-out on as-built specimens and on the specimens additionally densified by HIP. The HIP process was conducted under conditions: $450^{\\circ} \\mathrm{C} / 2 \\mathrm{~h} / 100 \\mathrm{MPa}$, and cooling to 400 ${ }^{\\circ} \\mathrm{C} / 2 \\mathrm{~h} / 50 \\mathrm{MPa}$.\n\\end{itemize}\n\n\\subsection*{2.3. Examination methods}\nMicrostructure examinations were carried-out on the longitudinal and transverse sections of all the variants of the specimens except thin walls, i.e. single tracks, cuboid-shaped and tensile specimens. The sections were ground with carborundum papers (down to 2000 grit), then polished with suspension of alumina particles $(0.025 \\mu \\mathrm{m})$. The polished surfaces were cleaned in a supersonic washer in order to remove residuals in pores and cracks and then etched with the Kroll's reagent. The optical microscope Olympus LEXT OLS4000 and the scanning electron microscope Zeiss EVO MA25, equipped with an EDS analysis system, were used for microstructure and crack surface examination, as well as for chemical microanalysis.\n\nWall thickness was determined by width measurements of the last track in top view of the specimens left on the base plate, with the digital microscope Keyence VHX-600. The wall thickness representative for a single specimen (composed of four walls) was calculated as the average of thickness measurements of each wall. After removing the specimens from the platform, quality of their side surfaces was evaluated with use of the same digital microscope.\n\nThe relative density of the rectangular specimens was assessed by computer analysis of binarized images obtained for the metallographic xy sections. The percentage of pixels falling on the pores and cracks was determined.", "start_char_idx": 748734, "end_char_idx": 752881, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f554b856-d2f8-49b5-a4d8-26cc820d2158": {"__data__": {"id_": "f554b856-d2f8-49b5-a4d8-26cc820d2158", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3f119e3a-c178-4cd1-9a26-787356f54c9b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "35fa7b3c879111beda462fa176b42017f5824f62d22b3b79ce0110c9f185af46", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "93d52d0b-6e6e-4a72-b3e2-658a222aa758", "node_type": "1", "metadata": {}, "hash": "e7b828c7b2a822e735186a9e75fdb5949dd72d2c33b76042c15e72cc18ca4cf8", "class_name": "RelatedNodeInfo"}}, "text": "The optical microscope Olympus LEXT OLS4000 and the scanning electron microscope Zeiss EVO MA25, equipped with an EDS analysis system, were used for microstructure and crack surface examination, as well as for chemical microanalysis.\n\nWall thickness was determined by width measurements of the last track in top view of the specimens left on the base plate, with the digital microscope Keyence VHX-600. The wall thickness representative for a single specimen (composed of four walls) was calculated as the average of thickness measurements of each wall. After removing the specimens from the platform, quality of their side surfaces was evaluated with use of the same digital microscope.\n\nThe relative density of the rectangular specimens was assessed by computer analysis of binarized images obtained for the metallographic xy sections. The percentage of pixels falling on the pores and cracks was determined. Thus, relative density in this paper was calculated as the difference between $100 \\%$ and the percentage of pores and cracks, which made it possible for it be referred to the results quoted in the references, where density was determined by the Archimedes method [38].\n\nThe three-dimensional distribution of pores and cracks within the gauge length of the tensile specimens was detected and visualized using computed tomography. The system ZEISS METROTOM 1500 was used for the image reconstruction. Resolution of data for the AA7075 specimens was $8 \\mu \\mathrm{m}$ at an X-ray tube voltage of $200 \\mathrm{kV}$ and a current of 40 $\\mu \\mathrm{A}$.\n\nThe static tensile tests were performed on an Instron 3384 testing machine. A Zwick Roell tester was used for the hardness measurements.\n\nTable 3\n\nComparison of fixed and variable LPBF process parameters for manufacture of the specimens used at individual stages of the research.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-04}\n\\end{center}\n\nTable 4\n\nResults of the scan single track melting test.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\n\\hline\n\\multirow[t]{2}{*}{No.}", "start_char_idx": 751971, "end_char_idx": 754059, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "93d52d0b-6e6e-4a72-b3e2-658a222aa758": {"__data__": {"id_": "93d52d0b-6e6e-4a72-b3e2-658a222aa758", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f554b856-d2f8-49b5-a4d8-26cc820d2158", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "030ca3c48508200a1ebd67fa27a0184bc33de2e2ed44ac973d05580fe109082a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "29fb603e-e2fc-4a1d-9a07-722d93794b56", "node_type": "1", "metadata": {}, "hash": "f845655b5bf3af6d4663be2ffa9eb05b034fe8f94e2ca3db2757a4373f0d9b79", "class_name": "RelatedNodeInfo"}}, "text": "The static tensile tests were performed on an Instron 3384 testing machine. A Zwick Roell tester was used for the hardness measurements.\n\nTable 3\n\nComparison of fixed and variable LPBF process parameters for manufacture of the specimens used at individual stages of the research.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-04}\n\\end{center}\n\nTable 4\n\nResults of the scan single track melting test.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\n\\hline\n\\multirow[t]{2}{*}{No.} & \\multirow{2}{*}{}\\begin{tabular}{l}\nLaser power \\\\\n$[\\mathrm{W}]$ \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{l}\nPoint exposure time $t$ \\\\\n$[\\mu s]$ \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{l}\nPoint distance \\\\\ns \\\\\n$[\\mu \\mathrm{m}]$ \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{l}\nScanning speed \\\\\n$\\mathrm{v}=\\mathrm{s} / \\mathrm{t}$ \\\\\n$[\\mathrm{mm} / \\mathrm{s}]$ \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{l}\nEnergy density $\\mathrm{E}_{\\mathrm{L}}$ \\\\\n$[\\mathrm{J} / \\mathrm{mm}]$ \\\\\n\\end{tabular} & \\multicolumn{3}{|c|}{Cross-section of a track} \\\\\n\\hline\n &  &  &  &  &  & \\begin{tabular}{l}\nDepth \\\\\nd \\\\\n$[\\mu \\mathrm{m}]$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nWidth \\\\\n$\\mathrm{w}$ \\\\\n$[\\mu \\mathrm{m}]$ \\\\\n\\end{tabular} & Ratio d/w \\\\\n\\hline\n1 & 400 & 80 & 20 & 250 & 1.6 & $612 \\pm 22$ & $451 \\pm 20$ & 1.36 \\\\\n\\hline\n2 & 200 & 80 & 20 & 250 & 0.8 & $76 \\pm 56$ & $161 \\pm 43$ & 0.47 \\\\\n\\hline\n3 & 200 & 20 & 160 & 8000 & 0.025 & $20 \\pm 4$ & $64 \\pm 7$ & 0.31 \\\\\n\\hline\n4 & 200 & 10 & 80 & 8000 & 0.025 & $22 \\pm 1$ & $66 \\pm 2$ & 0.32 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\section*{3. Results and discussion}\n\\subsection*{3.1. Single track melting of substrate}\nThe first step towards process optimization was single track melting of the AA7075 alloy substrate surface with various combinations of parameters. Trials of single track melting made it possible to assess both the process stability by the prevention of balling and the determination of the threshold for the keyhole-mode melting, as well as the susceptibility of the alloy to solidification and liquation cracking. As was stated by King et al. [39], the melting mode can be changed from keyhole to conduction mode by a combination of laser power and scanning speed, and therefore the depth and width of melting can be controlled and the creation of defects in the form of vapour voids or insufficient melting can be prevented. It results from the above that, to achieve continuous single tracks with shallow semi-circular melt pools suitable for LPBF, an optimum set of process parameters should provide melting that is mainly determined by the thermal conductivity of the material.\n\nThe results of single track melting trials, obtained within the presented research in the form of the cross-sectional dimensions of the tracks (Table 4), are consistent with the conclusions given by [40], i.e. both the depth and width of the melt pools, as well as their corresponding depth to width ratio, decrease with a diminishing energy density.", "start_char_idx": 753534, "end_char_idx": 756613, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "29fb603e-e2fc-4a1d-9a07-722d93794b56": {"__data__": {"id_": "29fb603e-e2fc-4a1d-9a07-722d93794b56", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "93d52d0b-6e6e-4a72-b3e2-658a222aa758", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "97139f81ae44c4088ff210cefdcae5ef78087c03b383057def37a0bd065bf592", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9a64a372-6a4b-4e01-bf5c-b888f2d0ba23", "node_type": "1", "metadata": {}, "hash": "7358f9cb66a5f9793ff975354c695c3a0a0fbe25592f295ad1bb16365d0e3323", "class_name": "RelatedNodeInfo"}}, "text": "As was stated by King et al. [39], the melting mode can be changed from keyhole to conduction mode by a combination of laser power and scanning speed, and therefore the depth and width of melting can be controlled and the creation of defects in the form of vapour voids or insufficient melting can be prevented. It results from the above that, to achieve continuous single tracks with shallow semi-circular melt pools suitable for LPBF, an optimum set of process parameters should provide melting that is mainly determined by the thermal conductivity of the material.\n\nThe results of single track melting trials, obtained within the presented research in the form of the cross-sectional dimensions of the tracks (Table 4), are consistent with the conclusions given by [40], i.e. both the depth and width of the melt pools, as well as their corresponding depth to width ratio, decrease with a diminishing energy density.\n\nIt was found that, for a high enough energy density, the depth to width ratio of the melt pool is bigger than 0.5 , which is due to the transition mode melting that is conducive to the creation of gas pores (Fig. 2a) and to hot cracking (Fig. 2a, b). A reduction of laser power from $400 \\mathrm{~W}$ to $200 \\mathrm{~W}$, but at the same scanning speed of $250 \\mathrm{~mm} / \\mathrm{s}$, undoubtedly reduces metal vaporization. The depth to width ratio of the melt pool decreases due to the increased share of conduction in the melting mode, but this is insufficient to make the melt pool stable. This is demonstrated by the diversification of the dimensions of the melt pool for the tracks fabricated at the same process parameters (Fig. 2b, c) and also by the formation of solidification cracks when $\\mathrm{d} / \\mathrm{w}=0.69$, as can be seen in Fig. 2b. Qi et al. [26] observed a similar phenomenon of unstable keyhole-mode melting in the case of AA7050, for a laser power of $200 \\mathrm{~W}$ and a scanning speed within $250-350 \\mathrm{~mm} / \\mathrm{s}$, recognizing it as the transition mode between the keyhole-mode and the conduction mode of melting.\n\nThe presence of hot cracks in the melted zones of tracks, shown in Fig. 2a, b, confirms the high sensitivity to solidification cracking of the AA7075 alloy and its lower susceptibility to liquation cracking in partially melted zones. The properties of the alloy, given in Table 1, are conducive to this sensitivity. Moreover, a high cooling rate decreases the solidus temperature, favours non-equilibrium solidification with the participation of an eutectic mixture as a result of interdendritic microsegregation, and causes high thermal shrinkage strains, a high stress gradient and a lack of backfilling of the developing cracks [19]. As can be seen in Fig. 2, the crack path is determined by the front of the rapid growth of the columnar grains. When energy density $\\mathrm{E}_{\\mathrm{L}}$ is high and $\\mathrm{d} / \\mathrm{w}$ is much higher than 0.5 , the crack proceeds centrically along the line of straight contact of the rapidly growing columnar grains (Fig. 2a). At lower $\\mathrm{E}_{\\mathrm{L}}$ and d/w close to 0.5 (Fig. 2b), cracking occurs in the zone of the columnar to equiaxed grain transition [21].\n\nTherefore, the test results (Table 4 and Fig. 2) suggest that, in order to minimize susceptibility of the AA7075 alloy to hot cracking, conduction in the melting mode should be increased by reducing the laser energy density, accepting $0.4<\\mathrm{d} / \\mathrm{w}<0.5$ as a threshold.\n\n\\subsection*{3.2. Fabrication of thin wall specimens}\nTrials of thin wall fabrication are the subsequent step of the optimisation of process parameters. In comparison to the single track melting trials, these tests bring additional information, for the assumed layer thickness, about the influence of laser power and scanning speed on the thickness and surface quality of LPBF-fabricated thin walls. The measurement results of wall thickness are shown in Fig. 3a. The\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_b6298c9a4a3486463622g-05}\n\nFig. 2.", "start_char_idx": 755694, "end_char_idx": 759753, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9a64a372-6a4b-4e01-bf5c-b888f2d0ba23": {"__data__": {"id_": "9a64a372-6a4b-4e01-bf5c-b888f2d0ba23", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "29fb603e-e2fc-4a1d-9a07-722d93794b56", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1261cde9d77e896966dce85636ece06920fa41458f9c3ad274b25726745bff7e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "dbf7eb71-290d-4ead-ac6e-6eafe4138ab0", "node_type": "1", "metadata": {}, "hash": "76c921d8ae7c51b621ef40fd6a293e329ce5cee2da1f9909ad8ebf0d15bbb7c2", "class_name": "RelatedNodeInfo"}}, "text": "2) suggest that, in order to minimize susceptibility of the AA7075 alloy to hot cracking, conduction in the melting mode should be increased by reducing the laser energy density, accepting $0.4<\\mathrm{d} / \\mathrm{w}<0.5$ as a threshold.\n\n\\subsection*{3.2. Fabrication of thin wall specimens}\nTrials of thin wall fabrication are the subsequent step of the optimisation of process parameters. In comparison to the single track melting trials, these tests bring additional information, for the assumed layer thickness, about the influence of laser power and scanning speed on the thickness and surface quality of LPBF-fabricated thin walls. The measurement results of wall thickness are shown in Fig. 3a. The\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_b6298c9a4a3486463622g-05}\n\nFig. 2. Cross-sections of single tracks on the AA7075-T6 substrate fabricated with a scanning speed of $250 \\mathrm{~mm} / \\mathrm{s}$ and laser power of: (a) $400 \\mathrm{~W}$, (b) and (c) $200 \\mathrm{~W}$. Solidification cracks are marked with white arrows, a keyhole pore with a yellow arrow and liquation cracks with red arrows.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-06}\n\\end{center}\n\nFig. 3. Wall thickness (average values of 4 measurements) versus laser beam velocity for various combinations of irradiation time (20-420 $\\mu$ s) and distance between irradiation points $(20-80 \\mu \\mathrm{m}$ ): (a) without scan delay, (b) with scan delay of 1-2 s.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_b6298c9a4a3486463622g-06(1)}\n\nFig. 4. Top view of two exemplary thin wall specimens qualified on the grounds of width and continuity of tracks as: (a) good quality, and (b) bad quality. Thickness of each wall was measured by the distance between two white lines drawn along the whole track length. The arrow indicate cracks perpendicular to the tracks.\n\nmethods of measurement and continuity evaluation of the tracks are shown in Fig. 4. As can be seen in Fig. 3a, wall thickness decreases along with the laser power - drastically when scanning speed increases over $200 \\mathrm{~mm} / \\mathrm{s}$, especially in the case of using short $(<100 \\mu \\mathrm{s})$ laser irradiation times and a short $(20 \\mu \\mathrm{m})$ distance between irradiation points. Nevertheless, the smallest thickness of the selected walls was twice as large as the laser spot size and as the hot cracks parallel to the build direction (perpendicular to the scanning direction) that occurred in the walls (arrows in Fig. 4). This was caused by a drop of heat transfer effectiveness from the molten pool into the substrate as the subsequent layers were built, which was demonstrated by increasing size of the melt pool [5]. Thus, to increase the conductive heat loss by the substrate, a time delay was used between scanning the successive specimens. Usage of a 1-2 s delay gave the additional effect of a\\\\\nsignificant reduction of the wall thickness, especially for $200 \\mathrm{~W}$ laser power (see Fig. 3b), but did not eliminate hot cracks completely. This means that the used scan delay did not affect the hot cracking directly, i.e. no simple correlation existed between them and the two factors determining crack initiation: residual stresses and solidification behaviour of this alloy.\n\nThe side surface quality of all the variants of the thin wall specimens was assessed visually using a digital microscope. To link the PBF surface topography with its process parameters, effects of different features, i.e. roughness, waviness, shape distortion, globules (unmelted/partial melted particles, spatter particles) and surface pores, should be taken into consideration. The existing methods of surface parameterization use filtration techniques that do not permit extraction of the abovementioned topographical features [41]. Therefore, with regard to large number of the specimens at this stage of the optimisation process, it was reasonable to accept a quick method of surface quality evaluation instead of strict measurements of traditional profiles or areal surface texture parameters.", "start_char_idx": 758951, "end_char_idx": 763083, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "dbf7eb71-290d-4ead-ac6e-6eafe4138ab0": {"__data__": {"id_": "dbf7eb71-290d-4ead-ac6e-6eafe4138ab0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9a64a372-6a4b-4e01-bf5c-b888f2d0ba23", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a09443ad2cd54c0780f7faa9e78a207a52780802dcbe993ec2895b059b3f9bcf", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f4268a55-c3ef-44f8-8381-01025d145f71", "node_type": "1", "metadata": {}, "hash": "7fa6750c7b53b6f3403dd7491da1dc476b72bf128c4a9c1fee5c8ee21e424de6", "class_name": "RelatedNodeInfo"}}, "text": "This means that the used scan delay did not affect the hot cracking directly, i.e. no simple correlation existed between them and the two factors determining crack initiation: residual stresses and solidification behaviour of this alloy.\n\nThe side surface quality of all the variants of the thin wall specimens was assessed visually using a digital microscope. To link the PBF surface topography with its process parameters, effects of different features, i.e. roughness, waviness, shape distortion, globules (unmelted/partial melted particles, spatter particles) and surface pores, should be taken into consideration. The existing methods of surface parameterization use filtration techniques that do not permit extraction of the abovementioned topographical features [41]. Therefore, with regard to large number of the specimens at this stage of the optimisation process, it was reasonable to accept a quick method of surface quality evaluation instead of strict measurements of traditional profiles or areal surface texture parameters.\n\nFor energy density $\\mathrm{E}_{\\mathrm{L}}$, used in the range from 0.1 to $5.0 \\mathrm{~J} / \\mathrm{mm}$, a tendency of a decreasing surface quality with an increasing scanning speed was visible, especially for the specimens manufactured at a higher laser power of $400 \\mathrm{~W}$. Fig. 5 shows representative examples of the surface morphology of the specimens manufactured at a similar energy density within 0.8 to $0.9 \\mathrm{~J} / \\mathrm{mm}$, but which resulted from various combinations of laser power and scanning speed. With energy densities below $0.5 \\mathrm{~J} / \\mathrm{mm}$, low quality surfaces were formed due to incomplete melting of powder particles or to the balling phenomenon.\n\nOn this basis, for the next stage of the research involving laser power between 200 and $400 \\mathrm{~W}$, the scanning speed threshold was accepted as 200 and $400 \\mathrm{~mm} / \\mathrm{s}$, respectively.\n\n\\subsection*{3.3. Fabrication of volumetric rectangular specimens}\nWhen striving for the minimization of porosity, it was taken into account that alloying elements like $\\mathrm{Zn}$ and $\\mathrm{Mg}$ have lower boiling points and much higher equilibrium vapour pressure than aluminium\\\\\n(Fig. 6a), which results in their significant vaporization during laser melting. This can affect both the porosity and chemical composition of the alloy. A control chemical analysis of the volumetric specimens, fabricated at $200 \\mathrm{~W}$ and $400 \\mathrm{~W}$, but with the same linear energy density, showed a significant loss of $\\mathrm{Zn}$ and $\\mathrm{Mg}$, especially of $\\mathrm{Zn}$ at the higher laser power (Fig. 6b). Comparison of these results with those reported by Kaufmann et al. [27], Martin et al. [9], and Wang et al. [42] suggests that vaporization of these elements is decidedly affected by laser power and, to a lesser degree, by scanning speed. This conclusion is consistent with the results of the numerical parametric study for the AA6061 alloy [43]. A spectral analysis of the AA7075 specimens manufactured with a laser power of $200 \\mathrm{~W}$ showed about a $23 \\%$ loss of $\\mathrm{Zn}$ and about a $14 \\%$ loss of Mg. Increasing the laser power to 400-500 W resulted in about a $30 \\%$ loss of $\\mathrm{Zn}$ and about a $23 \\%$ loss of $\\mathrm{Mg}$. Therefore, at the third stage of fabrication of the volumetric specimens, $\\mathrm{P}=200 \\mathrm{~W}$ was accepted as the fixed parameter, with SD being maintained at $1.5 \\mathrm{~s}$.\n\nThe main problem for AA7075 processing is, apart from porosity, its susceptibility to hot cracking. Therefore, the parameters influencing energy density and the stresses arising during solidification of the alloy were accepted as the variable parameters to be optimised. LPBF is a process that is sensitive to (apart from laser power) scanning strategy, hatch spacing, scanning speed and the negative shift of focal height $(-\\Delta \\mathrm{F})$. The selection of these parameters necessitates a compromise, since a decreased hatch spacing and scanning speed (at a constant laser power and layer thickness) result in a higher energy density, lower porosity and lower stress level, but at the same time in a lower surface quality [5].", "start_char_idx": 762045, "end_char_idx": 766296, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f4268a55-c3ef-44f8-8381-01025d145f71": {"__data__": {"id_": "f4268a55-c3ef-44f8-8381-01025d145f71", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "dbf7eb71-290d-4ead-ac6e-6eafe4138ab0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "abc1d2c6f4d342484e18f4a3d0b2b76a5de29a32a95de10f580b986071070751", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "45e27b05-34d9-4f35-8bf3-ae88bba871b0", "node_type": "1", "metadata": {}, "hash": "dd2f70500195d60df56f9e23c10c13d40a4d967430ab53cc9f38f8dfba091a7c", "class_name": "RelatedNodeInfo"}}, "text": "Therefore, at the third stage of fabrication of the volumetric specimens, $\\mathrm{P}=200 \\mathrm{~W}$ was accepted as the fixed parameter, with SD being maintained at $1.5 \\mathrm{~s}$.\n\nThe main problem for AA7075 processing is, apart from porosity, its susceptibility to hot cracking. Therefore, the parameters influencing energy density and the stresses arising during solidification of the alloy were accepted as the variable parameters to be optimised. LPBF is a process that is sensitive to (apart from laser power) scanning strategy, hatch spacing, scanning speed and the negative shift of focal height $(-\\Delta \\mathrm{F})$. The selection of these parameters necessitates a compromise, since a decreased hatch spacing and scanning speed (at a constant laser power and layer thickness) result in a higher energy density, lower porosity and lower stress level, but at the same time in a lower surface quality [5]. In turn, the laser focus shift $(\\Delta \\mathrm{F})$ changes the melting mode [26], enlarges the spot size and reduces the energy density at the melt pool [45].\n\nThe effective methods of reducing build-up of residual stresses are double scanning and the dividing of the laser-scanned area of each layer into smaller stripes or into square sections referred to as 'islands'. Taking this into account, in this work the rectangular specimens were manufactured using 4 scanning variants (Fig. 7): alternating single scanning (SS1), double scanning (DS; remelting), stripes alongside\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_b6298c9a4a3486463622g-07}\n\nFig. 5. Surface topography of thin wall specimens fabricated with parameters: (a) $P=400 \\mathrm{~W}, \\mathrm{v}=429 \\mathrm{~mm} / \\mathrm{s}, \\mathrm{E}_{\\mathrm{L}}=0.93 \\mathrm{~J} / \\mathrm{mm}, \\mathrm{s}=60 \\mu \\mathrm{m}$; (b) $\\mathrm{P}=200 \\mathrm{~W}, \\mathrm{v}=250$ $\\mathrm{mm} / \\mathrm{s}, E_{\\mathrm{L}}=0.8 \\mathrm{~J} / \\mathrm{mm}, \\mathrm{s}=60 \\mu \\mathrm{m}$.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_b6298c9a4a3486463622g-08(6)}\n\nFig. 6. Vaporization of zinc and magnesium in AA7075 during laser melting: (a) comparison of equilibrium vapour pressure of $\\mathrm{Zn}, \\mathrm{Mg}, \\mathrm{Cu}$ and $\\mathrm{Al}$ at various temperatures (based on [44]); (b) concentration of $\\mathrm{Zn}$ and $\\mathrm{Mg}$ in raw powder and after LPBF with various laser power and constant linear energy $\\mathrm{E}_{\\mathrm{L}}=1 \\mathrm{~J} / \\mathrm{mm}$ : $\\mathrm{P}=$ $200 \\mathrm{~W}, \\mathrm{~s}=20 \\mu \\mathrm{m}, \\mathrm{t}=100 \\mu \\mathrm{s} ; \\mathrm{P}=400 \\mathrm{~W}, \\mathrm{~s}=40 \\mu \\mathrm{m}, \\mathrm{t}=100 \\mu \\mathrm{s}$.\n\n(SS2) and chessboard (SS3).\n\nThe effect of scanning strategy on the quantity and arrangement of pores and cracks in the cross-sections xy and yz of the specimens are shown in Fig. 8. It can be seen that scanning with short scan vectors (Fig. 8d) results in lower porosity in comparison to scanning with longer scan vectors (Fig. 8a, b, c). Similar results were obtained for the AA2618 alloy by Koutny et al. [46]. The strategies SS1, DS and SS2 are conducive to the formation of channel-like pores and gaseous pores with spherical shapes (Fig. 8a, b, c). Application of strategy SS3 not only leads to the reduction of the quantity of pores, but also to the reduction of their sizes (Fig. 8d). This is related to the fact that scanning of small fields with short, parallel vectors results in local overheating and reduction of the thermal gradient, resulting subsequently in better wetting conditions and lower porosity.", "start_char_idx": 765375, "end_char_idx": 768956, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "45e27b05-34d9-4f35-8bf3-ae88bba871b0": {"__data__": {"id_": "45e27b05-34d9-4f35-8bf3-ae88bba871b0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f4268a55-c3ef-44f8-8381-01025d145f71", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "200faf4f6e3528ee892b169cce97a1f7fbb06c8366f1950ebabda51baee399ee", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "cce55f42-4cc0-4026-b321-6fc83480f11d", "node_type": "1", "metadata": {}, "hash": "70ac3e5dc0b90eab9a8cf23e3914aa985b74e53e8329a9634a09800a019e4d9d", "class_name": "RelatedNodeInfo"}}, "text": "8. It can be seen that scanning with short scan vectors (Fig. 8d) results in lower porosity in comparison to scanning with longer scan vectors (Fig. 8a, b, c). Similar results were obtained for the AA2618 alloy by Koutny et al. [46]. The strategies SS1, DS and SS2 are conducive to the formation of channel-like pores and gaseous pores with spherical shapes (Fig. 8a, b, c). Application of strategy SS3 not only leads to the reduction of the quantity of pores, but also to the reduction of their sizes (Fig. 8d). This is related to the fact that scanning of small fields with short, parallel vectors results in local overheating and reduction of the thermal gradient, resulting subsequently in better wetting conditions and lower porosity. In the case of the other strategies (SS1, DC and SS2), longer and successively scanned tracks have more time to cool down, which results in worse wetting conditions and higher porosity. However, cracks occurred irrespective of the strategy.\n\nIn all the specimens, as can be seen in Fig. 8, the solidification cracks have a different width, length and distribution density depending on the scanning variant. The cracks are caused by the action of 2 factors: thermally induced re-strain (volume shrinkage and thermal contraction) and the crack-susceptible microstructure. Their propagation is determined by the distribution of tensile stresses and the persistence of liquid films along the solidification boundaries in the manufactured specimen. It can be seen in Fig. 8d that long cracks propagate along the island borders. The islands were scanned in the sequence every second island area (see Fig. 7d), which inclines to the supposition that the overlapping contour is the preferred location for initiation of liquation cracking in the previously solidified outmost track of the neighbouring island. On cross-sections yz, cracks are parallel to the building direction of the specimens. They are also initiated on the irregularities on the free and side surfaces of the specimens, on the areas between the supports, and on the internal pores. In the case of small cracks initiated inside the specimens, their sources cannot be identified.\n\nAttention is attracted to the reverse correlation between porosity and the observed crack density. The reason for this can be the fact that shrinkage of the material is partially compensated by its higher porosity. In consequence, shrinkage-related residual stresses are reduced, in turn causing the cracks to become thinner and be visible at larger magnifications only (compare Fig. 8c, d).\n\nEven if no success was achieved in the form of the complete elimination of cracks, one scanning pattern, considered as the best, was accepted at the subsequent stage of tests for all the volumetric specimens, i.e. the chessboard scanning strategy with one island size of 2.5 $\\mathrm{mm} \\times 2.5 \\mathrm{~mm}$.\n\nThe results obtained for the selected parameter sets in the form of diagrams of relative density versus scanning speed and defocusing distance are shown in Fig. 9a and b, respectively. The distance and the defocusing sign aff ;ect the size and geometry of the melt pool [47]. In order to increase the width of the melt pool and to reduce its depth a\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-08(2)}\n\\end{center}\n\nC\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-08(4)}\n\\end{center}\n\nLayer $n+1$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-08(1)}\n\\end{center}\n\nLayer $\\mathrm{n}+1$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-08}\n\\end{center}\n\nb\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_b6298c9a4a3486463622g-08(3)}\n\nd\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_b6298c9a4a3486463622g-08(5)}\n\nFig. 7.", "start_char_idx": 768217, "end_char_idx": 772114, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "cce55f42-4cc0-4026-b321-6fc83480f11d": {"__data__": {"id_": "cce55f42-4cc0-4026-b321-6fc83480f11d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "45e27b05-34d9-4f35-8bf3-ae88bba871b0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f17a1966b45a1a9e6d87613ac9bdf26e1e7dc67d1099c27098995b4888a0501c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "feaf4f2f-da47-4721-8db4-3654cab81f62", "node_type": "1", "metadata": {}, "hash": "188a00e6e3bf1b60178d7db244528f89a363fdec5a1d9c10c844b7e079998872", "class_name": "RelatedNodeInfo"}}, "text": "7. Scanning variants: (a) alternating single scanning - SS1; (b) double scanning - DS; (c) stripes alongside (2.5 mm wide) - SS2; (d) chessboard - SS3. Red dots mean start points of the scan path.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-09}\n\\end{center}\n\nFig. 8. Influence of scanning strategy on the quantity and distribution of pores and solidification cracks. Parameters used for all samples: $\\mathrm{P}=200 \\mathrm{~W} ; \\mathrm{h}=140$ $\\mu \\mathrm{m} ; \\mathrm{v}=200 \\mathrm{~mm} / \\mathrm{s} ; \\mathrm{s}=20 \\mu \\mathrm{m}, \\Delta \\mathrm{F}=-1 ; \\mathrm{E}_{\\mathrm{V}}=143 \\mathrm{~J} / \\mathrm{mm}^{3}$.\n\nresulting from lowered power density, negative defocusing was adjusted while taking into account the results obtained by McLouth et al. [45].\n\nAs can be seen in Fig. 9a, none of the specimens fabricated at a constant laser power and focus distance, but which did have a variable hatch spacing and scanning speed, did not achieve a relative density of over $98.5 \\%$. On the other hand, a very strong influence of defocusing distance on the density of the specimens is visible in Fig. 9b. An increase of the defocus distance was accompanied by an increase in density. The highest level of relative density, amounting to about 99.5 $\\%$, was reached for the variant of parameter set: $\\mathrm{P}=200 \\mathrm{~W}, \\mathrm{v}=200$ $\\mathrm{mm} / \\mathrm{s}, \\mathrm{s}=20 \\mu \\mathrm{m}$, hatch spacing $=140 \\mu \\mathrm{m}$ and $\\Delta \\mathrm{F}=-3.5 \\mathrm{~mm}$. However, it was not possible to eliminate hot cracks completely.\n\nAn additional decrease of the level of residual stresses, and thus susceptibility of the alloy to hot cracking, was also expected as a result of preheating the base plate to $300{ }^{\\circ} \\mathrm{C}$ - the maximum temperature possible to be reached in the applied LPBF machine. Even if crack density was reduced this way (compare the images in Fig. 8d and\\\\\nFig. 10), it was still at the expense of relative density (Fig. 9). It is possible that application of preheating with no change of the process parameters (reduction of energy density) creates conducive conditions to transition from the conduction controlled melting to the keyholemode melting that results in increased porosity. Hot cracks were observed for all the variants of the parameter sets, especially between the individual fields of the scanning pattern.\n\nMertens et al. [28] were also unable to eliminate cracks in the AA7075 alloy, even if they applied a higher preheating temperature of $400{ }^{\\circ} \\mathrm{C}$. However, they applied high scanning speeds $(500-1500 \\mathrm{~mm} / \\mathrm{s})$ and a thinner layer in comparison to the parameters used in this work, thus creating favourable conditions for higher residual stresses. Therefore, this does not justify ceasing the trials with the use of preheating as the tool supporting the elimination of hot cracking.\n\n\\subsection*{3.4. Fabrication of tensile specimens}\nBefore tensile testing, the as-built specimens were subjected to CT and microscopic examinations in order to determine their relative density and the presence of cracks. Since it was found that high relative density (see Table 5) and the complete elimination of hot cracks in LPBF-ed AA7075 (Fig. 11a) cannot be assured by adjusting the process parameter window only, HIP treatment was introduced to heal hot cracks, pores and other accidental defects. As the results in Table 5 indicate, HIP resulted in a higher relative density of the specimens and better plastic properties of the alloy. However, in comparison to the properties of the wrought alloy in an annealed condition, the elongation at failure and strength values are lower due to the fact that HIP failed to close the cracks. It can be seen in Fig.", "start_char_idx": 772112, "end_char_idx": 775914, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "feaf4f2f-da47-4721-8db4-3654cab81f62": {"__data__": {"id_": "feaf4f2f-da47-4721-8db4-3654cab81f62", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "cce55f42-4cc0-4026-b321-6fc83480f11d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e4bb81d923c60097f1057b70656faae2e3ba7eb4b5cce780cd113358041b77a3", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c6ab2eef-1af7-4b3c-a938-2ba5bba08d8b", "node_type": "1", "metadata": {}, "hash": "4a36649f162e50d67f648402feb7907dafeabf5525c575ba9aad18b18bed684f", "class_name": "RelatedNodeInfo"}}, "text": "\\subsection*{3.4. Fabrication of tensile specimens}\nBefore tensile testing, the as-built specimens were subjected to CT and microscopic examinations in order to determine their relative density and the presence of cracks. Since it was found that high relative density (see Table 5) and the complete elimination of hot cracks in LPBF-ed AA7075 (Fig. 11a) cannot be assured by adjusting the process parameter window only, HIP treatment was introduced to heal hot cracks, pores and other accidental defects. As the results in Table 5 indicate, HIP resulted in a higher relative density of the specimens and better plastic properties of the alloy. However, in comparison to the properties of the wrought alloy in an annealed condition, the elongation at failure and strength values are lower due to the fact that HIP failed to close the cracks. It can be seen in Fig. 11b that even if the higher density of the specimens indicated the healing of a significant part of the defects during HIP treatment, the large cracks that developed along the boundaries of the columnar grains still remained open.\n\nThe HIP-ing conditions, temperature and pressure (Table 5), were so selected that pores and cracks were closed by plastic flow and creep. From microstructure point of view, they neither changed the shape and size of the columnar grains nor clearly reduced the segregation patterns of scan layers (Fig. 11).\n\nThe results of hardness measurements in Table 5 indicate hardening of the alloy in the as-built condition, similar to the hardening in the T6 condition. After HIP, however, its hardness is close to that of in the state of equilibrium. This demonstrates overaged condition of the alloy.\n\n\\subsection*{3.5. Examination of the formation and healing of hot cracks}\nThe multistage trials to determine a set of LPBF parameters, optimum from the viewpoint of the minimisation of porosity and hot cracking during the manufacture of AA7075 objects, did not bring the expected results with regard to cracks. This is why microscopic examinations of the cracks were taken-up in order to explain, in relation to the models accepted for this type of cracking at traditional casting and welding, the mechanism and the origin of hot cracking in the AA7075 alloy fabricated by LPBF.\n\nAccording to Kou [15] and Liu et al. [48], hot cracking is actuated by insufficient compensation of solidification shrinkage by the melt flow in the presence of thermal stresses. Nevertheless, other factors like pores, surface irregularities or constitutional liquation can be conducive to the initiation and propagation of hot cracks, as the authors of the current study highlighted in their comments concerning Fig. 8. Eskin et al. [49] defined several mechanisms of hot cracking during directchill casting, as well as the conditions that may lead to it. In their opinion, the mechanisms of nucleation, crack propagation and fracture mode are influenced by the range of solidification temperatures and the strength of the semisolid zone, as well as by structure of the alloy. Defects in the form of a liquid film, pores, intermetallic particles and a film of oxides, as well as the structure of defects like vacancy clusters and grain boundary, can have a strong influence on crack initiation\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_b6298c9a4a3486463622g-10(1)}\n\nFig. 9. Relative density of volumetric specimens fabricated with $P=200 \\mathrm{~W}$, chessboard strategy and various variants of the remaining process parameters, versus (a) scanning speed; $\\Delta \\mathrm{F}=-1$ (b) defocusing distance $\\Delta \\mathrm{F}$.\n\nunder specific temperature-stress conditions. Thus, depending on the solid fraction, crack development can be caused by disruption of the liquid film, the brittle fracture of bridges and by an intergranular brittle or ductile fracture.\n\nMicroscopic examinations of the surfaces of long cracks, shown in Figs. 10 and $11 \\mathrm{a}$, indicate solidification cracking by the liquid film rupture mode. As can be seen in Fig. 12a and b, this is evidenced by the dendritic nature of the fracture surfaces covered by the solidified liquid film. Preheating of the base plate to $300^{\\circ} \\mathrm{C}$, in spite of a reduction of the ratio of thermal gradient (G) to growth rate (R), did not change the fracture mode of cracking.\n\nAttention is drawn to the fact that the wide, long cracks shown in Fig.", "start_char_idx": 775051, "end_char_idx": 779463, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c6ab2eef-1af7-4b3c-a938-2ba5bba08d8b": {"__data__": {"id_": "c6ab2eef-1af7-4b3c-a938-2ba5bba08d8b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "feaf4f2f-da47-4721-8db4-3654cab81f62", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "738efa6fd4ad4892a318af7bfdf292aa2cf40d19672e0b5f270fcfc206adcffe", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "e1a3c2f6-5d9b-49ec-9f40-68db1125eeee", "node_type": "1", "metadata": {}, "hash": "671a179b26af9d41f07cd52b6b1199e7aff3d7ccf8619eddafc539f6fa9cec9b", "class_name": "RelatedNodeInfo"}}, "text": "under specific temperature-stress conditions. Thus, depending on the solid fraction, crack development can be caused by disruption of the liquid film, the brittle fracture of bridges and by an intergranular brittle or ductile fracture.\n\nMicroscopic examinations of the surfaces of long cracks, shown in Figs. 10 and $11 \\mathrm{a}$, indicate solidification cracking by the liquid film rupture mode. As can be seen in Fig. 12a and b, this is evidenced by the dendritic nature of the fracture surfaces covered by the solidified liquid film. Preheating of the base plate to $300^{\\circ} \\mathrm{C}$, in spite of a reduction of the ratio of thermal gradient (G) to growth rate (R), did not change the fracture mode of cracking.\n\nAttention is drawn to the fact that the wide, long cracks shown in Fig. 11a occur mostly between high-angle misoriented columnar grains, but not between low-angle misoriented cell-dendrites, inside the columnar grains. The columnar grains are unfavourably (perpendicularly) oriented in relation to the direction of tensile stresses induced by solidification shrinkage and thermal contraction, both of which are obstructed by the solidified bottom layer. The cracks propagate through successive layers, since the healing of the crack by feeding with liquid metal is impeded by a high strain rate.\\\\\nThe reason that the liquid film between the columnar grains persists to lower temperatures in comparison to the liquid film on the subboundaries can be, according to the model of Rappaz et al. [50], due to the higher stability of the liquid film at the high-angle grain boundary during the last stage of solidification. Additionally, the relatively higher concentration of the segregating alloying elements, according to the Scheil-Gulliver model, lowers the solidus temperature. Microsegregation also results in an increase of the alloy susceptibility to liquation cracking, which is due to the rapid heating of the already solidified alloy layer during the subsequent pass of the laser beam [19]. It seems, due to the complex thermal history of the material, i.e. melting, remelting, partial melting and cyclic heat treatment at high speeds of heating and cooling, that liquation cracking interferes with solidification cracking and that their distinction departs from the goal of this work.\n\nThe influence of microsegregation on lowering the AA7075 solidus temperature is related to the low values of partitioning coefficients of both the main and minor alloying elements (Table 6), which results in a higher concentration of these elements in liquid at the final phases of non-equilibrium solidification. In comparison to the AA7075 solidus\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-10}\n\\end{center}\n\nFig. 10. Effect of base plate preheating to $300^{\\circ} \\mathrm{C}$ on the quantity and distribution of pores and solidification cracks in planes xy and yz. Parameter set: $\\mathrm{P}=200 \\mathrm{~W}, \\mathrm{~h}$ $=140 \\mathrm{um}, \\mathrm{v}=200 \\mathrm{~mm} / \\mathrm{s}, \\mathrm{s}=20 \\mu \\mathrm{m}, \\Delta \\mathrm{F}=-1 \\mathrm{~mm}$.\n\nTable 5\n\nComparison of the mechanical properties of the AA7075 alloy in various fabrication conditions.", "start_char_idx": 778667, "end_char_idx": 781887, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "e1a3c2f6-5d9b-49ec-9f40-68db1125eeee": {"__data__": {"id_": "e1a3c2f6-5d9b-49ec-9f40-68db1125eeee", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c6ab2eef-1af7-4b3c-a938-2ba5bba08d8b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "fd0cc0f7c2491cc9606c26d39c7a0f8f67b6143bd0d9bafc6619911c9985d3bc", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "60509f9d-5bd5-4a1e-9eae-79ed0f5e73f1", "node_type": "1", "metadata": {}, "hash": "4b1b7156a60a9f48ccc715b34008c1642a99d0f7a0c5f40d611502a9b1f27fdb", "class_name": "RelatedNodeInfo"}}, "text": "In comparison to the AA7075 solidus\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-10}\n\\end{center}\n\nFig. 10. Effect of base plate preheating to $300^{\\circ} \\mathrm{C}$ on the quantity and distribution of pores and solidification cracks in planes xy and yz. Parameter set: $\\mathrm{P}=200 \\mathrm{~W}, \\mathrm{~h}$ $=140 \\mathrm{um}, \\mathrm{v}=200 \\mathrm{~mm} / \\mathrm{s}, \\mathrm{s}=20 \\mu \\mathrm{m}, \\Delta \\mathrm{F}=-1 \\mathrm{~mm}$.\n\nTable 5\n\nComparison of the mechanical properties of the AA7075 alloy in various fabrication conditions.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline\nTensile specimen & $\\mathrm{R}_{\\mathrm{p} 0.2}[\\mathrm{MPa}]$ & $\\mathrm{R}_{\\mathrm{m}}[\\mathrm{MPa}]$ & $\\varepsilon_{\\mathrm{f}}[\\%]$ & HV0.3 & Density [\\%] \\\\\n\\hline\nAs-built ${ }^{\\mathrm{a}}$ & - & $160 \\pm 12$ & $0.3 \\pm 0.05$ & $137 \\pm 6$ & $96.7 \\pm 2.5$ \\\\\n\\hline\n$\\mathrm{HIP}^{\\mathrm{b}}$ & $97 \\pm 9$ & $159 \\pm 11$ & $3.5 \\pm 0.6$ & $83 \\pm 4$ & $99.1 \\pm 0.5$ \\\\\n\\hline\nWrought, $\\mathrm{T}^{\\mathrm{C}}$ & $372-503$ & $462-572$ & 3-11 & 175 & 100 \\\\\n\\hline\nWrought, annealed ${ }^{c}$ & 95 & 220 & 17 & 60 & 100 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\footnotetext{a Parameter set: $\\mathrm{P}=200 \\mathrm{~W}, \\mathrm{~h}=140 \\mu \\mathrm{m}, \\mathrm{s}=20 \\mu \\mathrm{m}, \\mathrm{v}=200 \\mathrm{~mm} / \\mathrm{s}$, and $\\Delta \\mathrm{F}=-3.5 \\mathrm{~m}$, without preheating.\n\nb HIP parameters: $450{ }^{\\circ} \\mathrm{C} / 2 \\mathrm{~h} / 100 \\mathrm{MPa}$, and cooling to $400{ }^{\\circ} \\mathrm{C} / 2 \\mathrm{~h} / 50 \\mathrm{MPa}$.\n\nc MatWeb-Material Property Data.\n}temperature of $477{ }^{\\circ} \\mathrm{C}$ that is quoted in materials databases (see Table 1), the lowest melting point within the Al-Cu-Mg-Zn system, calculated by G\u00f3mez-Acebo et al. [51] as $338^{\\circ} \\mathrm{C}$, belongs to the ternary system $\\mathrm{Al}-\\mathrm{Mg}-\\mathrm{Zn}$, while the eutectic point for $\\mathrm{Al}-\\mathrm{Cu}-\\mathrm{Mg}$ is $425{ }^{\\circ} \\mathrm{C}$. This means that in the case of a high cooling rate $\\left(10^{4}-10^{6} \\mathrm{~K} / \\mathrm{s}\\right)$, the shapes of the solidification curves can be changed due to the non-equilibrium partition coefficients and reduced back diffusion of solute. Since the susceptibility index of the alloy, i.e. its maximum steepness $\\mid \\mathrm{dT} /\\left(\\mathrm{df}_{\\mathrm{s}}\\right)^{1 /}$ ${ }^{2}$ at nearly $\\mathrm{f}_{\\mathrm{s}}^{1 / 2} \\approx 1$ is highest without back diffusion [48], it is clear that microsegregation at rapid cooling is an important factor for cracking. An increased concentration of segregating alloying elements in interdendritic liquid intensifies remelting and partial melting in individual material layers.", "start_char_idx": 781299, "end_char_idx": 784055, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "60509f9d-5bd5-4a1e-9eae-79ed0f5e73f1": {"__data__": {"id_": "60509f9d-5bd5-4a1e-9eae-79ed0f5e73f1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e1a3c2f6-5d9b-49ec-9f40-68db1125eeee", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "80ec2b8d961311b83d6663e608d81c4ba5c6f0dba755b12abc1fe943baff1d74", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d4b47e8c-bba2-4871-8af1-98f93391fa74", "node_type": "1", "metadata": {}, "hash": "4d617371c77b33a7e6326690dc20326f99c220307c2482467995a7a694c4b905", "class_name": "RelatedNodeInfo"}}, "text": "This means that in the case of a high cooling rate $\\left(10^{4}-10^{6} \\mathrm{~K} / \\mathrm{s}\\right)$, the shapes of the solidification curves can be changed due to the non-equilibrium partition coefficients and reduced back diffusion of solute. Since the susceptibility index of the alloy, i.e. its maximum steepness $\\mid \\mathrm{dT} /\\left(\\mathrm{df}_{\\mathrm{s}}\\right)^{1 /}$ ${ }^{2}$ at nearly $\\mathrm{f}_{\\mathrm{s}}^{1 / 2} \\approx 1$ is highest without back diffusion [48], it is clear that microsegregation at rapid cooling is an important factor for cracking. An increased concentration of segregating alloying elements in interdendritic liquid intensifies remelting and partial melting in individual material layers.\n\nEDS analysis (Fig. 13) of the as-built microstructure showed microsegregation of $\\mathrm{Zn}, \\mathrm{Mg}, \\mathrm{Cu}$ and $\\mathrm{Si}$ (despite its low content) at the grain boundaries. The microstructure of AA7075, shown in Fig. 14, consists of primary solid solution $\\alpha$, dispersed secondary phases and a divorced eutectic phase arranged at low- and high-angle grain boundaries. This eutectic phase, most likely $\\eta-\\mathrm{Mg}(\\mathrm{Zn}, \\mathrm{Cu}, \\mathrm{Al})_{2}$, is the main strengthening phase in the AA7075 alloy [52]. In Fig. 14a and b, micropores distributed close to the eutectic $\\eta$-phase can be seen in addition to a solidification crack. Such a series of micropores, which originated from solidification shrinkage, gas precipitation or vacancy supersaturation, are the potential nuclei of hot cracks. Thus, the main reason for solidification cracking is the persistence of liquid films (rich in $\\mathrm{Zn}, \\mathrm{Mg}, \\mathrm{Cu}$, and $\\mathrm{Si}$ ) between high-angle misorientation grains in the critical temperature range, where strain rate and stress are high. It is highly probable that the presence of minor elements such as silicon in the liquid film significantly contributes to its stability by reducing liquid-solid interface energy $\\gamma_{\\mathrm{sl}}$ in relation to grain boundary energy $\\gamma_{\\mathrm{gb}}$ to the level (acc. to the concept of Rappaz et al. [50]) for that the condition $\\gamma_{\\mathrm{gb}}>2 \\gamma_{\\mathrm{sl}}$ is fulfilled. The high influence of Si on the cracking susceptibility of the Al-xSi binary alloys $(0<x<1)$, as well as of the IN738LC alloy during LPBF, reported respectively by Kimura et al. [53] and Engeli et al. [36], supports this hypothesis.\n\nApart from $\\eta-\\mathrm{Mg}(\\mathrm{Zn}, \\mathrm{Cu}, \\mathrm{Al})_{2}$, fine strengthening precipitates and secondary particles typical in AA7075 (constituent and dispersoid particles of E-phase $\\mathrm{Al}_{18} \\mathrm{Mg}_{3} \\mathrm{Cr}_{2}$ ) do not affect susceptibility to hot cracking, since they are not created as a result of the eutectic reaction.\n\nHIP treatment of the LPBF-ed tensile specimens significantly increased their relative density to $99.1 \\%$ (Table 5), although this is not a satisfactory result. Wide, long cracks (see Fig. 11b) remained open, which was evidenced by the cellular-dendritic structure of their fracture surfaces, similar to those shown in Fig. 12a and b for the specimens in their as-built condition. Nevertheless, it was found that, apart from healing of lack-of-fusion or other pores, the narrow, short microcracks became also closed (Fig. 15a). What is interesting, some discrete secondary phase precipitated along the healed cracks. The EDS analysis showed a concentration of $\\mathrm{Mg}$ inside the healed crack (EDS map in Fig. 15a). This raises the suspicion that a localized liquid film is created during HIP on crack surfaces. Thus, it can be concluded that some cracks and shrinkage pores became closed due to simultaneous presence of a liquid film and a compressive stress field.", "start_char_idx": 783321, "end_char_idx": 787132, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d4b47e8c-bba2-4871-8af1-98f93391fa74": {"__data__": {"id_": "d4b47e8c-bba2-4871-8af1-98f93391fa74", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "60509f9d-5bd5-4a1e-9eae-79ed0f5e73f1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "28c103ce82a0d3197745f2b7043e1998436f069f76479aa9c61753d84bbcd3aa", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "be72216d-4cd5-4444-b32b-a25e7d83709a", "node_type": "1", "metadata": {}, "hash": "27aa7a49d96b90df3f71e3912c9ae47f5078f73b25d9e3cc67879d441f833f71", "class_name": "RelatedNodeInfo"}}, "text": "Wide, long cracks (see Fig. 11b) remained open, which was evidenced by the cellular-dendritic structure of their fracture surfaces, similar to those shown in Fig. 12a and b for the specimens in their as-built condition. Nevertheless, it was found that, apart from healing of lack-of-fusion or other pores, the narrow, short microcracks became also closed (Fig. 15a). What is interesting, some discrete secondary phase precipitated along the healed cracks. The EDS analysis showed a concentration of $\\mathrm{Mg}$ inside the healed crack (EDS map in Fig. 15a). This raises the suspicion that a localized liquid film is created during HIP on crack surfaces. Thus, it can be concluded that some cracks and shrinkage pores became closed due to simultaneous presence of a liquid film and a compressive stress field. Because of microsegregation, the temperature $450{ }^{\\circ} \\mathrm{C}$ during HIP-ing can be locally higher than the melting temperature of the zones along grain boundaries rich in the segregating $\\mathrm{Zn}, \\mathrm{Mg}, \\mathrm{Cu}$ and $\\mathrm{Si}$. In consequence, the liquid film is created by constitutional liquation mechanism, i.e. by dissolution of the primary $\\eta$-phase at grain boundaries and on the crack surface by the eutectic reaction. This is confirmed by the BSD image (Fig. 15b) of the resolidified grain boundary zones with white traces of retained segregation and small shrinkage pores. The similar crack healing mechanism was observed by Kalentics et al. [54], repeatedly applying the laser shock peening during processing the CM247LC alloy by LPBF, as well as by Zhao et al. using HIP after laser solid forming of Rene88DT alloy.\n\nThe results of EDS analysis of fragment of the high-angle boundary with traces of residual microsegregation, decorated by precipitates of the second phases (see Fig. 15b) are shown in Fig. 16. High concentration of $\\mathrm{Mg}$ and $\\mathrm{Si}$ in some precipitates is visible. In the authors' opinion, precipitating of the $\\mathrm{Mg}$ and $\\mathrm{Si}$ rich phase confirms creation of the liquid film at high-angle grain boundaries, which was followed by solidification and precipitation of the $\\eta$-phase and $\\mathrm{Mg}$-Si phase or the $\\eta$ -\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-11}\n\\end{center}\n\nFig. 11. Hot cracks in the gauge length of the tensile specimens in: (a) as-built and (b) HIP-ed condition.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-12}\n\\end{center}\n\nFig. 12. SE-SEM images of the solidification crack surfaces: (a) tensile specimen with cracks, shown in Fig. 11a and fabricated without preheating; (b) cuboidal specimen with cracks, shown in Fig. 10 and fabricated with preheating to $300{ }^{\\circ} \\mathrm{C}$.\n\nTable 6\n\nEquilibrium partition coefficients for alloying elements in aluminium [10].\n\n\\begin{center}\n\\begin{tabular}{lllllllll}\n\\hline\nElement & $\\mathrm{Fe}$ & $\\mathrm{Si}$ & $\\mathrm{Cu}$ & $\\mathrm{Mg}$ & $\\mathrm{Zn}$ & $\\mathrm{Mn}$ & $\\mathrm{Cr}$ & $\\mathrm{Ti}$ \\\\\n\\hline\n$\\mathrm{k}$ & 0.03 & 0.13 & 0.17 & 0.43 & 0.45 & 0.82 & 2.0 & 9.0 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nphase only, depending on local concentration of Si.\n\nConfirmation of these conclusions requires the examinations to be methodically continued with the use of the Atom Probe Tomography (APT), Electron Backscatter Diffraction (EBSD), and Transmission Electron Microscopy (TEM) methods in order to identify small-scale segregation, misorientation angles and phase composition.\n\nIt is highly probable that long cracks, being connected to the surface, made the HIP process ineffective.", "start_char_idx": 786322, "end_char_idx": 790000, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "be72216d-4cd5-4444-b32b-a25e7d83709a": {"__data__": {"id_": "be72216d-4cd5-4444-b32b-a25e7d83709a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d4b47e8c-bba2-4871-8af1-98f93391fa74", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7784a70895a4122967ce33e4774d66986b2f886924a0a1582625a2e75dcd2af9", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c594c249-1777-410a-a0fc-e7073d48d648", "node_type": "1", "metadata": {}, "hash": "3016401fbe5dbf15aef217eb38ebd10c52b6f030a6716d7ed8aa44faba855400", "class_name": "RelatedNodeInfo"}}, "text": "Confirmation of these conclusions requires the examinations to be methodically continued with the use of the Atom Probe Tomography (APT), Electron Backscatter Diffraction (EBSD), and Transmission Electron Microscopy (TEM) methods in order to identify small-scale segregation, misorientation angles and phase composition.\n\nIt is highly probable that long cracks, being connected to the surface, made the HIP process ineffective. It is also possible that there exists a threshold opening of the crack that can be closed as a result of both the liquation mechanism and the HIP densification mechanisms presented by Atkinson et al. [55], i.e. plastic yielding, power-law creep and densification by diffusion creep. This is affected by temperature and pressure, which are selected on the assumption that part of the geometry remains unchanged.\n\n\\section*{4. Conclusions}\nMulti-stage trials to adjust the optimum process parameters for the fabrication of crack-free AA7075 parts using LPBF technology were finished with no success. However, the obtained results make it possible to better understand the causes of the problems related to processing AA7075, as well as to formulate conclusions that will be useful for future research.\n\n1 With regard to optimisation of the process window, the following was concluded:\n\n\\begin{itemize}\n  \\item To avoid keyhole-mode melting and thus to reduce gas pores and the formation of hot cracks, the depth to width ratio of the melt pool should be kept between 0.4 and 0.5 , a laser power of $200 \\mathrm{~W}$ should be used and a scanning speed of $200-250 \\mathrm{~mm} / \\mathrm{s}$ should be adopted. The laser power is of crucial importance in comparison to the scanning speed, and its relatively low value is profitable with respect to the reduction of $\\mathrm{Zn}$ and $\\mathrm{Mg}$ losses by vaporization and for the reduction of surface roughness.\n  \\item Because of the inverse correlation between porosity and crack density (porosity compensates shrinkage), the selection of the optimum process parameters that are based on the maximization\n\\end{itemize}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-12(1)}\n\\end{center}\n\nFig. 13. EDS maps showing the concentration of $\\mathrm{Zn}, \\mathrm{Cu}, \\mathrm{Mg}$ and Si-impurity at the grain boundaries. Cross section (xy plane).\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-13}\n\\end{center}\n\nFig. 14. Microstructure of the as-built tensile specimens, fabricated with the process parameters shown in Table 3: (a) longitudinal section, (b) cross section. Arrows indicate the eutectic $\\eta$-phase particles at grain (orange arrows) and cells (white arrows) boundaries. BSD-SEM images.\n\nof the parts' density is a reasonable optimisation criterion. Accomplishing relative density of the order of $99.5 \\%$ is possible for the following parameters: defocusing distance $\\Delta \\mathrm{F}=-3.5 \\mathrm{~mm}$, chessboard scanning strategy and hatch spacing $=140 \\mu \\mathrm{m}$, whereby pores are almost eliminated, but cracks are only partially reduced. Preventing hot cracking requires a metallurgical approach towards optimization of the chemical composition of the AA7075 powder for LPBF.\n\n\\begin{itemize}\n  \\item The optimum process parameters determined for small specimens do not guarantee that the the same qualilty will be obtained in the case of tensile specimens. Apart from reducing density to $96.7 \\%$, vertical orientation of building tensile specimens is conducive to the development of long cracks along columnar grain boundaries. HIP is an effective method to improve density to $99.1 \\%$ by healing defects and short cracks. However, the method does leave long cracks open.\n\\end{itemize}\n\n2 With regard to the relation between the process and the formation of defects, the following was concluded:\n\n\\begin{itemize}\n  \\item The manufacturing of defect-free parts of AA7075 by LPBF represents a major challenge, since the detrimental defects like pores and solidification cracks are consequences of high volumetric shrinkage and non-equilibrium directional solidification connected with a high cooling rate.\n  \\item Solidification cracks are formed by the liquid film rupture mode.", "start_char_idx": 789573, "end_char_idx": 793841, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c594c249-1777-410a-a0fc-e7073d48d648": {"__data__": {"id_": "c594c249-1777-410a-a0fc-e7073d48d648", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "be72216d-4cd5-4444-b32b-a25e7d83709a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "855005af4e325d3460bf6a1d010496d4279da960f9bc2f9c9a4d2f21970c1248", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c464f7f2-57e6-4078-9c85-ebaa0a4d9847", "node_type": "1", "metadata": {}, "hash": "533a5afcd4b0961a5a75cc99303d559b04aac3c092a25276b5934b5a9ed17b42", "class_name": "RelatedNodeInfo"}}, "text": "Apart from reducing density to $96.7 \\%$, vertical orientation of building tensile specimens is conducive to the development of long cracks along columnar grain boundaries. HIP is an effective method to improve density to $99.1 \\%$ by healing defects and short cracks. However, the method does leave long cracks open.\n\\end{itemize}\n\n2 With regard to the relation between the process and the formation of defects, the following was concluded:\n\n\\begin{itemize}\n  \\item The manufacturing of defect-free parts of AA7075 by LPBF represents a major challenge, since the detrimental defects like pores and solidification cracks are consequences of high volumetric shrinkage and non-equilibrium directional solidification connected with a high cooling rate.\n  \\item Solidification cracks are formed by the liquid film rupture mode. The reason why the liquid film persists to low temperatures at the last solidification stage is due to the microsegregation of $\\mathrm{Zn}, \\mathrm{Cu}$, and $\\mathrm{Mg}$, which results in the presence of the non-equilibrium eutectic form of the main strengthening phase $(\\eta)$ at the grain boundaries.\n  \\item Concentration of silicon detected at grain boundaries indicates that this minor element, with a strong tendency to undergo segregation in $\\mathrm{Al}$, plays a significant role in increasing susceptibility to cracking. This can be explained by the fact that silicon increases the stability of the liquid film by decreasing the liquid-solid interface energy in relation to the energy of the high-angle grain boundary. Lowering the silicon content would decrease the hot cracking tendency of the AA7075 alloy, while at the same time maintaining its specified composition.\n\\end{itemize}\n\n3 HIP is effective in healing only the short cracks, not connected with the surface, by the liquation mechanism, i.e. crack surface melting combined with action of compressive stresses.\n\nTo sum up, the obtained results are an incentive to continue the research aimed at manufacturing crack-free parts with no change of the AA7075 specified composition. Even if the optimum selection of LPBF parameters, determined by the characteristics of the AA7075 powder and susceptibility of $\\mathrm{Zn}$ and $\\mathrm{Mg}$ to vaporization, makes it possible to obtain relative density above $99 \\%$, its effect on solidification cracking is too weak.\n\nTherefore, a new approach to increasing the hot cracking resistance of this alloy uses powders with a concentration of $\\mathrm{Si}$ that is reduced below $0.1 \\mathrm{wt}$ \\% (considering vaporization losses of $\\mathrm{Zn}$ and $\\mathrm{Mg}$ ) and, at the same time, applies powder bed preheating that should activate back diffusion of alloying elements from a liquid to solid solution. Concurrent action of both factors should drastically increase the resistance to cracking by increasing the solidification temperature and reducing shrinkage stresses.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-13(1)}\n\\end{center}\n\nFig. 15. Tensile specimen after HIP treatment with parameters: $\\mathrm{T}=450^{\\circ} \\mathrm{C} / 100 \\mathrm{MPa}$, cooling to $400^{\\circ} \\mathrm{C} / 50 \\mathrm{MPa}$ (a) SE-SEM micrographs of the microstructure with the healed short cracks (white arrows), pores (orange arrow), and EDS map of Mg concentration; (b) BSD-SEM image of the microstructure showing resolidified grain boundary with residual segregation traces, dispersive precipitates and shrinkage pores.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_b6298c9a4a3486463622g-14}\n\\end{center}\n\nFig. 16. Microstructure of the tensile specimen, HIP-ed with parameters: $\\mathrm{T}=450{ }^{\\circ} \\mathrm{C} / 100 \\mathrm{MPa}$, cooling to $400{ }^{\\circ} \\mathrm{C} ; \\mathrm{p}=50 \\mathrm{MPa}$ (a) BSD-SEM image on the cross section; (b) EDS maps of the alloying elements of the selected area.\n\n\\section*{Declaration of competing interest}\nNone.\n\n\\section*{CRediT authorship contribution statement}\nWojciech Stopyra: Conceptualization, Formal analysis, Writing original draft. Konrad Gruber: Data curation, Methodology. Irina Smolina: Resources, Investigation.", "start_char_idx": 793018, "end_char_idx": 797194, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c464f7f2-57e6-4078-9c85-ebaa0a4d9847": {"__data__": {"id_": "c464f7f2-57e6-4078-9c85-ebaa0a4d9847", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c594c249-1777-410a-a0fc-e7073d48d648", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0227aa328cf34aecf2ec70354bf4a83c9466181c80a8e3ac1be399cff09e2aad", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "30d159b9-6bd7-4bce-9ed4-b48dd4c3f50a", "node_type": "1", "metadata": {}, "hash": "cf1611624369b9b9b0d1127999a3e048e3b771cf2053faefe36c8f8d5372a52e", "class_name": "RelatedNodeInfo"}}, "text": "16. Microstructure of the tensile specimen, HIP-ed with parameters: $\\mathrm{T}=450{ }^{\\circ} \\mathrm{C} / 100 \\mathrm{MPa}$, cooling to $400{ }^{\\circ} \\mathrm{C} ; \\mathrm{p}=50 \\mathrm{MPa}$ (a) BSD-SEM image on the cross section; (b) EDS maps of the alloying elements of the selected area.\n\n\\section*{Declaration of competing interest}\nNone.\n\n\\section*{CRediT authorship contribution statement}\nWojciech Stopyra: Conceptualization, Formal analysis, Writing original draft. Konrad Gruber: Data curation, Methodology. Irina Smolina: Resources, Investigation. Tomasz Kurzynowski: Funding acquisition, Project administration. Bogumi\u0142a Ku\u017anicka: Writing - review \\& editing, Supervision.\n\n\\section*{Acknowledgement}\nThis work was financially supported byThe National Centre for Research and Development, Polandwithin the project INNOLOT/I/6/ NCBR/2013, AMpHOra.\n\n\\section*{References}\n[1] N. Guo, M.C. 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Sci. 31 (2000) 2981-3000, \\href{https://doi.org/10.1007/s11661-000-0078-2}{https://doi.org/10.1007/s11661-000-0078-2}.\n\n\\begin{itemize}\n  \\item \n\\end{itemize}\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\n\\title{Modulating laser intensity profile ellipticity for microstructural control during metal additive manufacturing }\n\n\n\\author{Tien T. Roehling a, b, *, Sheldon S.Q. Wu ${ }^{c}$, Saad A. Khairallah ${ }^{\\text {d }}$, John D. Roehling ${ }^{\\text {b, }}$,\\\\\nS. Stefan Soezeri ${ }^{a}$, Michael F. Crumb ${ }^{c}$, Manyalibo J. Matthews ${ }^{\\text {b, }}$.\\\\\na Department of Mechanical Engineering, University of the Pacific, Stockton, CA, USA\\\\\n${ }^{\\mathrm{b}}$ Materials Science Division, Lawrence Livermore National Laboratory, Livermore, CA, USA\\\\\n${ }^{\\text {c }}$ National Ignition Facility, Lawrence Livermore National Laboratory, Livermore, CA, USA\\\\\n${ }^{\\mathrm{d}}$ Weapons and Complex Integration, Lawrence Livermore National Laboratory, Livermore, CA, USA}\n\\date{}", "start_char_idx": 811139, "end_char_idx": 813733, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "4a6e6f90-042d-4f9d-8026-f96aa995b6f2": {"__data__": {"id_": "4a6e6f90-042d-4f9d-8026-f96aa995b6f2", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "cadbea04-f3f0-46ff-950b-99befc6d3296", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c1562d976acd61cffb3f86de618b32fbbc4e769cf241d737f7aac12e79973b94", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9b77c09c-6633-4f3f-96b0-dc0a33ba4479", "node_type": "1", "metadata": {}, "hash": "bd9d994bb1b1619fad7c7294de2b40f8252c1a58a5bc97f27a06212f24e1e2ef", "class_name": "RelatedNodeInfo"}}, "text": "%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?]{%\n  \\if\\relax#1\\relax%\n    \\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n  \\else%\n    \\if?#1\\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n    \\else\\svfootnotetext[#1]{#2}\\fi%\n  \\fi\n}\n\n\\begin{document}\n\\maketitle\nFull length article\n\n\n\n\\section*{A R T I C L E I N F O}\n\\section*{Article history:}\nReceived 16 December 2016\n\nAccepted 7 February 2017\n\nAvailable online 12 February 2017\n\n\\section*{Keywords:}\nAdditive manufacturing\n\nLaser powder-bed fusion\n\nMicrostructure control\n\nLaser modulation\n\nBeam shaping\n\n\\begin{abstract}\nA B S T R A C $T$ Additively manufactured (AM) metals are often highly textured, containing large columnar grains that initiate epitaxially under steep temperature gradients and rapid solidification conditions. These unique microstructures partially account for the massive property disparity existing between AM and conventionally processed alloys. Although equiaxed grains are desirable for isotropic mechanical behavior, the columnar-to-equiaxed transition remains difficult to predict for conventional solidification processes, and much more so for AM. In this study, the effects of laser intensity profile ellipticity on melt track macrostructures and microstructures were studied in 316L stainless steel. Experimental results were supported by temperature gradients and melt velocities simulated using the ALE3D multi-physics code. As a general trend, columnar grains preferentially formed with increasing laser power and scan speed for all beam profiles. However, when conduction mode laser heating occurs, scan parameters that result in coarse columnar microstructures using Gaussian profiles produce equiaxed or mixed equiaxed-columnar microstructures using elliptical profiles. By modulating spatial laser intensity profiles on the fly, sitespecific microstructures and properties can be directly engineered into additively manufactured parts. (C) 2017 Acta Materialia Inc. Published by Elsevier Ltd. This is an open access article under the CC BY-NCND license (\\href{http://creativecommons.org/licenses/by-nc-nd/4.0/}{http://creativecommons.org/licenses/by-nc-nd/4.0/}).\n\\end{abstract}\n\n\\section*{1. Introduction}\nResearch in additive manufacturing (AM) has gained tremendous momentum over the past decade due to the prospect of directly building complex three-dimensional parts from computeraided design (CAD) files. During laser powder-bed fusion (LPBF), processing parameters such as laser power, scan speed, scan pattern, and hatch spacing have typically been optimized to improve geometrical accuracy and reduce defect concentrations. In taking this macroscopic approach, however, the microstructureproperty relationships underlying the performance disparities between conventionally machined and AM parts are often overlooked.\n\nThe ultimate goal of a priori parameter selection for tailored microstructures is in sight, with recent efforts made in e-beam and\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author. Department of Mechanical Engineering, University of the Pacific, Stockton, CA, USA.\n\\end{itemize}\n\nE-mail address: \\href{mailto:roehling2@1lnl.gov}{roehling2@1lnl.gov} (T.T. Roehling).\n}\n\nlaser additive manufacturing [1-6]. Site-specific microstructural control has numerous practical applications, such as in improving the fatigue life of a part by imposing deliberate textures at surfaces or stress-concentrating features, or in manufacturing components with functionally graded mechanical properties. In 2014, K\u00f6rner et al.", "start_char_idx": 813736, "end_char_idx": 817659, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9b77c09c-6633-4f3f-96b0-dc0a33ba4479": {"__data__": {"id_": "9b77c09c-6633-4f3f-96b0-dc0a33ba4479", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "4a6e6f90-042d-4f9d-8026-f96aa995b6f2", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "16a69e81f62dc1a5a0a9e2b956a2087ed3895402f2a832b6852a2cc3df55c0f4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3e244c5b-e4e0-45a8-90e7-0534101c16ec", "node_type": "1", "metadata": {}, "hash": "7fafdf3b6f32bfea6229d663b3111241d1dda5e50074448edb3458686e94fdbb", "class_name": "RelatedNodeInfo"}}, "text": "The ultimate goal of a priori parameter selection for tailored microstructures is in sight, with recent efforts made in e-beam and\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author. Department of Mechanical Engineering, University of the Pacific, Stockton, CA, USA.\n\\end{itemize}\n\nE-mail address: \\href{mailto:roehling2@1lnl.gov}{roehling2@1lnl.gov} (T.T. Roehling).\n}\n\nlaser additive manufacturing [1-6]. Site-specific microstructural control has numerous practical applications, such as in improving the fatigue life of a part by imposing deliberate textures at surfaces or stress-concentrating features, or in manufacturing components with functionally graded mechanical properties. In 2014, K\u00f6rner et al. investigated the effect of varying \"cross snake\" scan patterns every ten versus every single layer in Inconel tensile samples [1]. The authors found that columnar grains are formed when solidification occurs primarily in the building direction, while equiaxed grains are formed when the solidification direction varies frequently. In 2015, Dehoff et al. demonstrated localized microstructural control by developing highly misoriented equiaxed grains surrounded by columnar grains in an Inconel 718 block [2]. The researchers rapidly switched between point and line heat sources to manipulate local thermal gradients and solid/liquid (s/l) interface velocities. Some microstructural control has also been demonstrated in laser additive manufacturing by varying laser power up to $1000 \\mathrm{~W}$ [3], using multiple laser sources [4], and varying scan strategies $[5,6]$.\n\nIn this work, beam ellipticity is pursued as a potential means for microstructural control during laser additive manufacturing. Commercial LPBF systems typically use circular Gaussian intensity profiles, although they may not be ideal for optimizing process control. During a build, beam ellipticity can be modulated on the fly by diverting the laser into a beam shaping optical element (e.g., an anamorphic prism pair). Since local temperature gradients are affected, it may be possible to engineer equiaxed or columnar grains at specified locations by modulating beam shape in situ. Elliptical beams have been explored for laser annealing semiconductors $[7,8]$, but knowledge of their effects on metal solidification remains relatively limited, particularly with respect to metal AM. The present study explores the microstructures produced by circular and elliptical laser intensity profiles in 316L stainless steel single-tracks. Macroscopic features, such as track continuity, roughness, and melt depth are measured and discussed.\n\nSince LPBF is a far-from-equilibrium processing technique, the classic temperature gradient $(G)$ versus solidification rate $(R)$ analysis may not fully capture the complexities of solidification in the aggressively dynamic melt. The Arbitrary Lagrangian-Eulerian 3D (ALE3D) massively-parallel multi-physics code was used to simulate the temperature gradients and melt flow velocities induced by the beam profiles used in this study. The model takes into account Marangoni convection, the recoil pressure, evaporative and radiative cooling. It has been used recently to successfully described several deleterious LPBF phenomena, including spatter, denudation, melt instability, and three mechanisms of pore formation [9-11].\n\nThe objective of this investigation is to determine the microstructures produced by circular and elliptical laser intensity profiles at different beam sizes, laser powers, and scan speeds. The purpose is to judge if changes in beam ellipticity could provide a route for site-specific microstructural control during laser additive manufacturing. ALE3D simulations support analyses of the experimental results.\n\n\\section*{2. Experimental}\n\\subsection*{2.1. Laser powder-bed fusion experiments}\nSingle-track laser melting experiments were completed using 316L stainless steel powder (Concept Laser) on 316L stainless steel substrates (McMaster-Carr). Prior to use, the $\\sim 27-\\mu \\mathrm{m}$ powders were vacuum dried at $623 \\mathrm{~K}$ and stored in a desiccator thereafter. The surfaces of the $3.175-\\mathrm{mm}(1 / 8-$ in) thick substrates were bead blasted. A $50-\\mu \\mathrm{m}$ thick powder layer was manually spread onto each substrate using a glass microscope slide prior to single powder layer melting.", "start_char_idx": 816942, "end_char_idx": 821311, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3e244c5b-e4e0-45a8-90e7-0534101c16ec": {"__data__": {"id_": "3e244c5b-e4e0-45a8-90e7-0534101c16ec", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9b77c09c-6633-4f3f-96b0-dc0a33ba4479", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cf3ee87f692587805bfbd8da18bf1a7f6541370b86c87882faa95f0624acea4e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "906ce5b6-0d63-40ab-a2cc-52ff2745404e", "node_type": "1", "metadata": {}, "hash": "fbe07d698c4fcd8035c7e6f2921e12edfd61bb628f4869646a8ad4d0470bccc4", "class_name": "RelatedNodeInfo"}}, "text": "The purpose is to judge if changes in beam ellipticity could provide a route for site-specific microstructural control during laser additive manufacturing. ALE3D simulations support analyses of the experimental results.\n\n\\section*{2. Experimental}\n\\subsection*{2.1. Laser powder-bed fusion experiments}\nSingle-track laser melting experiments were completed using 316L stainless steel powder (Concept Laser) on 316L stainless steel substrates (McMaster-Carr). Prior to use, the $\\sim 27-\\mu \\mathrm{m}$ powders were vacuum dried at $623 \\mathrm{~K}$ and stored in a desiccator thereafter. The surfaces of the $3.175-\\mathrm{mm}(1 / 8-$ in) thick substrates were bead blasted. A $50-\\mu \\mathrm{m}$ thick powder layer was manually spread onto each substrate using a glass microscope slide prior to single powder layer melting.\n\nIn the LPBF testbed, the output of a $600 \\mathrm{~W}$ fiber laser (JK600 FL, JK Lasers) was first collimated using a $50 \\mathrm{~mm}$ FL lens and then directed through an anamorphic prism pair (Thor Labs) to adjust beam ellipticity. The modified beam was then directed through a $2-$ $5 \\mathrm{x}$ reducer (Thor Labs) which controls the beam size to a galvanometer scanner (Nutfield Technologies), and through the high purity fused silica window of a $15 \\times 15 \\times 15 \\mathrm{~cm}^{3}$ vacuum chamber. For each experiment, the chamber was evacuated using a turbomolecular pump and back-filled with argon. During laser melting, the Ar pressure was maintained at 750 Torr.\n\nThe circular and elliptical beam profiles were studied at three sizes, each (Fig. 1, Table 1). The nominal $1 / e^{2}$ diameters of the circular beams were $w_{b}=100,175,250 \\mu \\mathrm{m}$. These sizes will hereon be referred to as $\\mathrm{S}$ (small), $\\mathrm{M}$ (medium), and $\\mathrm{L}$ (large), respectively. The major and minor axes of the elliptical beams were calculated from $S, M$, and $L$ to deliver equivalent peak irradiances (based on average geometric beam diameters) at an aspect ratio of $\\sim 3.7: 1$. Size $S$ was limited by the smallest minor axis achievable using the current setup. The elliptical beams were scanned with the major axes parallel (\"longitudinal\", LE) and perpendicular (\"transverse\", TE) to the scan direction, and compared to circular (C) beam scans. The intensity profiles are named by geometry and size (e.g., LE-M refers to a longitudinal elliptical beam of Size M)\n\nExperimental parameters were selected based on Kamath et al. [12] and King et al. [13]. An energy density $(Q)$ equation common in laser welding was adapted to scale laser power $(P)$, scan speed $(v)$, powder layer thickness $(t=50 \\mu \\mathrm{m})$, and beam size $\\left(w_{b}\\right)$ :\n\n$Q=\\frac{P}{v t w_{b}}$\n\nThe energy density ranged from 80 to $260 \\mathrm{~J} / \\mathrm{mm}^{3}$ at $60 \\mathrm{~J} / \\mathrm{mm}^{3}$ intervals. Since nominal laser power was varied from 50 to $550 \\mathrm{~W}$ at $100-W$ intervals, scan speed $(15-1375 \\mathrm{~mm} / \\mathrm{s})$ was calculated based on $Q, P, t$, and $w_{b}$. Overall, 216 combinations of beam shape, beam size, power, and scan speed were studied.\n\n\\subsection*{2.2. Characterization}\nWide-field height maps of the single-tracks were generated by laser confocal microscopy (Keyence) to assess macroscopic morphological features. Height and line roughness were measured along the centerline of the middle $\\sim 0.8 \\mathrm{~cm}$ of each $1.0-\\mathrm{cm}$ long track. Track continuity was categorized according to Childs et al. [14], with example tracks shown in the Supporting Information (Table S1).", "start_char_idx": 820487, "end_char_idx": 824068, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "906ce5b6-0d63-40ab-a2cc-52ff2745404e": {"__data__": {"id_": "906ce5b6-0d63-40ab-a2cc-52ff2745404e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3e244c5b-e4e0-45a8-90e7-0534101c16ec", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2ff25e2a4e5a29084ac4bb3ad58fdd58d41ac537703382dc42f4252fd159d84a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "4396db22-3d8d-4335-bb8f-d7d387cac6f2", "node_type": "1", "metadata": {}, "hash": "b0e1b98194f0b04a53102651778f3e8223e29cad3a2b72fedcbaf06d093cdd0d", "class_name": "RelatedNodeInfo"}}, "text": "Since nominal laser power was varied from 50 to $550 \\mathrm{~W}$ at $100-W$ intervals, scan speed $(15-1375 \\mathrm{~mm} / \\mathrm{s})$ was calculated based on $Q, P, t$, and $w_{b}$. Overall, 216 combinations of beam shape, beam size, power, and scan speed were studied.\n\n\\subsection*{2.2. Characterization}\nWide-field height maps of the single-tracks were generated by laser confocal microscopy (Keyence) to assess macroscopic morphological features. Height and line roughness were measured along the centerline of the middle $\\sim 0.8 \\mathrm{~cm}$ of each $1.0-\\mathrm{cm}$ long track. Track continuity was categorized according to Childs et al. [14], with example tracks shown in the Supporting Information (Table S1).\n\nAfter sectioning, the samples were mounted, ground using 120-1200 grit metallographic silicon carbide paper, and then polished with $1-\\mu \\mathrm{m}$ polycrystalline diamond suspension. At this point, the samples were checked by optical microscopy for pores and voids. Immediately before etching, the samples were polished with $0.05 \\mu \\mathrm{m}$ aluminum oxide. The samples were swabbed with a modified Carpenter's reagent, which contained an additional $5 \\mathrm{~mL}$ of $\\mathrm{HNO}_{3}$ for each $100 \\mathrm{~mL}$ of stock solution, for less than $1 \\mathrm{~min}$. The\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c67706ca9b766b63e498g-02}\n\nFig. 1. Numerical fits of measured spatial intensity profiles for the (a) circular Gaussian and (b) elliptical beam shapes at Size L.\n\nTable 1\n\nSize of circular and elliptical beam shapes, including geometric average size for elliptical beams.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline\nSize & Circula $(\\mu \\mathrm{m})$ & Elliptical $(\\mu \\mathrm{m})$ & Elliptical average $(\\mu \\mathrm{m})$ \\\\\n\\hline\n$S$ & 98 & $52 \\times 201$ & 102 \\\\\n\\hline\nM & 187 & $95 \\times 351$ & 183 \\\\\n\\hline\n$\\mathrm{L}$ & 248 & $125 \\times 457$ & 239 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nCarpenter's stock solution contained $8.5 \\mathrm{~g} \\mathrm{FeCl}_{3}, 2.4 \\mathrm{~g} \\mathrm{CuCl}_{2}, 122 \\mathrm{~mL}$ $\\mathrm{HCl}, 6 \\mathrm{~mL} \\mathrm{HNO}_{3}$, and $122 \\mathrm{~mL} \\mathrm{CH}_{3} \\mathrm{CH}_{2} \\mathrm{OH}$.\n\nThe transverse and longitudinal track cross-sections were examined by scanning electron microscopy (TESCAN VEGA3 SEM) at $15-30 \\mathrm{kV}$ using a backscattered electron detector. Specifically, we used SEM to characterize the degree of surface wetting (contact angle, $\\theta$ ) and the depth $(d)$ to width $(w)$ ratio of the melt beads (Fig. 2). Equiaxed and columnar microstructures were characterized in the root of the melt zone, since the region represented by the melt bead would be re-melted and re-solidified with the addition of subsequent layers during an actual LPBF process. Partial re-melting is necessary during LPBF to reach full densities [15,16].\n\n\\subsection*{2.3. Simulations}\nDetails of the ALE3D code and the 316L material properties used in the simulations are published elsewhere [9,17]. Briefly, the simulation used the actual particle size distribution, and random particle packing ( $40 \\%$ density) was modeled using the ALE3D utility code, ParticlePack [18]. A laser ray tracing algorithm was used to simulate laser interaction with the powder bed. The threedimensional model was addressed using a hybrid finite element and finite volume formulation on an unstructured grid.", "start_char_idx": 823344, "end_char_idx": 826765, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "4396db22-3d8d-4335-bb8f-d7d387cac6f2": {"__data__": {"id_": "4396db22-3d8d-4335-bb8f-d7d387cac6f2", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "906ce5b6-0d63-40ab-a2cc-52ff2745404e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0e2fefa1762894c3dc725bef395af4cddcb898c232d9ba529073df321a537c36", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "25808e49-2398-4c6f-823a-c68dc760c0ae", "node_type": "1", "metadata": {}, "hash": "8b6f47d6778a7c989ed8241852b8a29ccb59340f6df23049bafc7e50aead0634", "class_name": "RelatedNodeInfo"}}, "text": "2). Equiaxed and columnar microstructures were characterized in the root of the melt zone, since the region represented by the melt bead would be re-melted and re-solidified with the addition of subsequent layers during an actual LPBF process. Partial re-melting is necessary during LPBF to reach full densities [15,16].\n\n\\subsection*{2.3. Simulations}\nDetails of the ALE3D code and the 316L material properties used in the simulations are published elsewhere [9,17]. Briefly, the simulation used the actual particle size distribution, and random particle packing ( $40 \\%$ density) was modeled using the ALE3D utility code, ParticlePack [18]. A laser ray tracing algorithm was used to simulate laser interaction with the powder bed. The threedimensional model was addressed using a hybrid finite element and finite volume formulation on an unstructured grid. Simulations were run using each beam shape at Size $S$ for $P=550 \\mathrm{~W}$. To conserve computational time, the scan velocity was set at $1800 \\mathrm{~mm} / \\mathrm{s}$, resulting in an energy density of $61 \\mathrm{~J} / \\mathrm{mm}^{3}$. This energy density is slightly lower than the minimum value used in the experiments $\\left(80 \\mathrm{~J} / \\mathrm{mm}^{3}\\right)$.\n\n\\section*{3. Results}\n\\subsection*{3.1. Macrostructure}\nThe morphological characteristics of the melt tracks (i.e., track continuity, bead height, substrate penetration depth, contact angle, and centerline roughness) were mapped on plots of energy density vs. laser power for the different laser intensity profiles, and are presented in the Supporting Information (Figs. S1-S5). Height maps of selected tracks demonstrating trends in intensity profile and beam size are presented in Fig. 3.\n\nThe least suitable conditions for LPBF are discussed first in order to limit the practical process window. Circular intensity profiles at the largest beam size ( $\\mathrm{C}-\\mathrm{L}$ ) resulted in bead heights up to 4.8 times the powder layer thickness $(t, 50 \\mu \\mathrm{m})$ with high surface roughness $\\left(R_{a}=49.2 \\pm 16.7 \\mu \\mathrm{m}\\right)$. At $80-140 \\mathrm{~J} / \\mathrm{mm}^{3}$, the melt tracks adhered to the substrate only by a narrow neck (Fig. 4a, profile Type 1), or by wetting the surface and forming a semicircular melt bead cross-section (profile Type 2). On average, relatively high contact angles $\\left(92.4 \\pm 30.5^{\\circ}\\right)$ were formed, indicating poor substrate wetting. The C-L profile only produced discontinuous tracks (Fig. 3, Fig. S1).\n\nUsing the smallest beam size, the longitudinal and transverse elliptical beams produced single tracks with undesirable topographies. Track heights were $2.8 t$ for LE-S and $3.3 t$ for TE-S, with comparable centerline surface roughnesses of $50.3 \\pm 15.4 \\mu \\mathrm{m}$ and $51.6 \\pm 13.4 \\mu \\mathrm{m}$, respectively. In addition to significant balling, at $50-150 \\mathrm{~W}$ and $80-260 \\mathrm{~J} / \\mathrm{mm}^{3}$, the tracks demonstrated poor surface adhesion. At 350-550 W, however, keyhole-mode laser heating can be observed as evidenced by a deep \"margarita glass\"-shaped melt pool and $d / w>0.8$ (Fig. 4, profile Type 5). Since conduction-mode laser heating was only observed using a few $Q$ and $P$ combinations, the stark transition from poor adhesion (i.e., profile Types $0-2$ ) to keyhole formation (i.e., profile Type 5) with increasing power makes the LE-S and TE-S profiles unamenable to processing optimization in a manufacturing environment.\n\nIn contrast, the smallest circular intensity profiles (C-S) generally produced melt tracks appropriate for full builds as judged by track continuity and roughness (Figs. S1-S5). The C-S profile most resembles those used in commercial LPBF systems, and produced melt beads of moderate height (2.1t).", "start_char_idx": 825906, "end_char_idx": 829693, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "25808e49-2398-4c6f-823a-c68dc760c0ae": {"__data__": {"id_": "25808e49-2398-4c6f-823a-c68dc760c0ae", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "4396db22-3d8d-4335-bb8f-d7d387cac6f2", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "77c28f0bc9f0e498d6c0c2d1f0b7123383cd8b32af202bebc10e161288b9eb39", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0c22b5c8-bd66-455d-afa3-b94803e441fa", "node_type": "1", "metadata": {}, "hash": "1ca115ba14a30f607da61e45dff438860168039c01227fe2738345ab2c00fa44", "class_name": "RelatedNodeInfo"}}, "text": "At 350-550 W, however, keyhole-mode laser heating can be observed as evidenced by a deep \"margarita glass\"-shaped melt pool and $d / w>0.8$ (Fig. 4, profile Type 5). Since conduction-mode laser heating was only observed using a few $Q$ and $P$ combinations, the stark transition from poor adhesion (i.e., profile Types $0-2$ ) to keyhole formation (i.e., profile Type 5) with increasing power makes the LE-S and TE-S profiles unamenable to processing optimization in a manufacturing environment.\n\nIn contrast, the smallest circular intensity profiles (C-S) generally produced melt tracks appropriate for full builds as judged by track continuity and roughness (Figs. S1-S5). The C-S profile most resembles those used in commercial LPBF systems, and produced melt beads of moderate height (2.1t). Centerline surface roughness was generally low $\\left(R_{a}=20.1 \\pm 7.5 \\mu \\mathrm{m}\\right)$, and continuous tracks could be produced at $P=150-550 \\mathrm{~W}$ and $Q \\geq 140 \\mathrm{~J} / \\mathrm{mm}^{3}$. Contact angles between the bead and substrate were moderate $\\left(86.2 \\pm 21.5^{\\circ}\\right)$. Evidence of a transition to keyhole-mode laser heating can be observed circa $350-550 \\mathrm{~W}$ and $80-260 \\mathrm{~J} / \\mathrm{mm}^{3}$ (Fig. 4a). The depths\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c67706ca9b766b63e498g-03}\n\\end{center}\n\nFig. 2. Typical transverse melt track cross-section dimensions labeled. Here, $\\mathrm{h}=$ bead height, $\\mathrm{d}=$ substrate penetration depth, $\\mathrm{w}=$ maximum width of track root, $\\theta=$ contact angle.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c67706ca9b766b63e498g-04(1)}\n\\end{center}\n\nFig. 3. Height maps of single melt tracks produced at $P=250 \\mathrm{~W}$ and $Q=260 \\mathrm{~J} / \\mathrm{mm}^{3}$. Continuous tracks were formed using the C-S, C-M, LE-M, LE-L, TE-M, and TE-L profiles. A discontinuous, irregularly broken track was formed using the C-L profile. Discontinuous, balled tracks were formed using the LE-S and TE-S profiles. Each segment shown is $0.4-\\mathrm{cm}$ long, sampled from the middle of the $1.0-\\mathrm{cm}$ melt track.\n\nof the melt pools increased with increasing $Q$ and $P$ up to $278 \\mu \\mathrm{m}(d /$ $w=1.9)$ for $P=550 \\mathrm{~W}$ and $Q=260 \\mathrm{~J} / \\mathrm{mm}^{3}$.\n\nContinuous tracks with low roughness were also formed by the LE and TE profiles at Size M and L. These profiles produced bead heights closest to the powder layer thickness (i.e., 1.1-1.6t, Fig. S2) with low surface roughness $\\left(R_{a}<20 \\mu \\mathrm{m}\\right)$ in most cases (Fig. S5). At $P \\geq 150 \\mathrm{~W}$, continuous or nearly continuous tracks formed at all power densities with few exceptions (Fig. S1). The melt penetrated the substrate by approximately $1 t$ at $150-550 \\mathrm{~W}$, demonstrating conduction-mode laser heating as evidenced by a bowl-shaped melt pool and $d / w<0.8$ (i.e., profile Type 3 in Fig. $4 \\mathrm{a}$ ). The TE-M and TE-L profiles produced flatter bead profiles than the LE-M and LE-L profiles, as shown by lower contact angles (Fig. S4).\n\n\\subsection*{3.2. Microstructure}\nThe microstructure was examined at two different scales: (1) at the grain morphology level, and (2) at the solidification substructure level, which is also referred to as the solidification pattern.", "start_char_idx": 828898, "end_char_idx": 832243, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0c22b5c8-bd66-455d-afa3-b94803e441fa": {"__data__": {"id_": "0c22b5c8-bd66-455d-afa3-b94803e441fa", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "25808e49-2398-4c6f-823a-c68dc760c0ae", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2793f0a88cc547554b998b570c86140e306355f4ddea354a2699b7e5e9529d4a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6d0da013-9d4f-4b9f-904e-4fa160fb2e94", "node_type": "1", "metadata": {}, "hash": "6f4a260522f608fc59e66cf81f9a4b2fff721694ff865f33d5e72f1f55dddeba", "class_name": "RelatedNodeInfo"}}, "text": "S5). At $P \\geq 150 \\mathrm{~W}$, continuous or nearly continuous tracks formed at all power densities with few exceptions (Fig. S1). The melt penetrated the substrate by approximately $1 t$ at $150-550 \\mathrm{~W}$, demonstrating conduction-mode laser heating as evidenced by a bowl-shaped melt pool and $d / w<0.8$ (i.e., profile Type 3 in Fig. $4 \\mathrm{a}$ ). The TE-M and TE-L profiles produced flatter bead profiles than the LE-M and LE-L profiles, as shown by lower contact angles (Fig. S4).\n\n\\subsection*{3.2. Microstructure}\nThe microstructure was examined at two different scales: (1) at the grain morphology level, and (2) at the solidification substructure level, which is also referred to as the solidification pattern. The grain morphology can vary from equiaxed to columnar, while the solidification substructure can vary from planar to cellular to dendritic. While columnar grains are elongated and often nucleate epitaxially at the fusion boundary, equiaxed grains can develop anywhere in the melt.\n\nDistinguishing between cells and dendrites can be challenging in single melt tracks. Solidification cells grow antiparallel to the direction of heat extraction in a melt, while dendrites grow in the\\\\\nCircular\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c67706ca9b766b63e498g-04}\n\\end{center}\n\nLongitudinal Elliptical\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c67706ca9b766b63e498g-04(2)}\n\nTransverse Elliptical\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c67706ca9b766b63e498g-04(3)}\n\nFig. 4. Processing maps of energy density $\\left(\\mathrm{J} / \\mathrm{mm}^{3}\\right.$ ) versus laser power (W) for the circular (left), longitudinal elliptical (middle), and transverse elliptical (right) laser intensity profiles. (a) Melt zone profile type is shown (top row) with a schematic legend. The melt zone profile types were designated as follows: $0=$ no deposition; $1=$ low substrate wetting with necking between a nearly-spherical melt bead and the substrate; $2=$ good substrate wetting by a semicircular melt bead with no substrate penetration $(d / w \\approx 0) ; 3=$ shallow substrate penetration $(0<d / w \\leq 0.5)$ with conduction-mode laser melting; $4=$ intermediate substrate penetration $(0.5<d / w \\leq 0.8) ; 5=$ deep substrate penetration $(0.8<d / w)$ with keyhole-mode laser melting. (b) Solidification microstructure is shown (bottom row) with a schematic legend, where color level $0=$ no fusion, $1=$ equiaxed, $2=$ mixed equiaxedcolumnar, and 3 = columnar.\\\\\npreferred crystallographic direction closest to antiparallel to the direction of heat extraction [19]. This is to say that cells grow normal to the $s / 1$ interface, but with increasing growth rates $(R)$, crystallography effects can cause growth to adopt a favorable crystallographic direction. In the absence of secondary dendrite arms, cells and dendrites can be nearly indistinguishable, as was the case in most track cross-sections. Longitudinal sections (Fig. 5a) were necessary to uncover the tell-tale curvature of cellular grains [19-21], as cells have been observed to grow away from the fusion boundary and curve in the direction of laser scanning towards the surface of melt tracks [22]. Considering the high laser scan rates, the strong orientation preference of the large columnar grains indicate dendritic solidification. The equiaxed grains could be either cellular or dendritic. Note that homogeneously or stochastically nucleated equiaxed grains (i.e., those nucleated by random atomic fluctuations) are typically dendritic, not cellular [23].\n\nScanning electron microscopy of etched cross-sections revealed that, regardless of the beam shape used, all tracks possess a very narrow region of planar growth at the fusion boundary (Fig. 5b).", "start_char_idx": 831510, "end_char_idx": 835320, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "6d0da013-9d4f-4b9f-904e-4fa160fb2e94": {"__data__": {"id_": "6d0da013-9d4f-4b9f-904e-4fa160fb2e94", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0c22b5c8-bd66-455d-afa3-b94803e441fa", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "57160823e9f2e0ebc41dac21c79dcbea8a6b9fd4f32a777c145a2076254568c1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "09d153d3-e135-4b58-97d5-6db27e3dc5c7", "node_type": "1", "metadata": {}, "hash": "99a05ed8605dc1e8613ed1558e180447cb11a4e80748a899192fcc55555a317a", "class_name": "RelatedNodeInfo"}}, "text": "Longitudinal sections (Fig. 5a) were necessary to uncover the tell-tale curvature of cellular grains [19-21], as cells have been observed to grow away from the fusion boundary and curve in the direction of laser scanning towards the surface of melt tracks [22]. Considering the high laser scan rates, the strong orientation preference of the large columnar grains indicate dendritic solidification. The equiaxed grains could be either cellular or dendritic. Note that homogeneously or stochastically nucleated equiaxed grains (i.e., those nucleated by random atomic fluctuations) are typically dendritic, not cellular [23].\n\nScanning electron microscopy of etched cross-sections revealed that, regardless of the beam shape used, all tracks possess a very narrow region of planar growth at the fusion boundary (Fig. 5b). This region was typically less than $1.5-\\mu \\mathrm{m}$ thick, and quickly transitioned to cellular or dendritic growth towards the center of the melt pool. Since cellular and dendritic grains typically make up\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c67706ca9b766b63e498g-05}\n\\end{center}\n\nFig. 5. (a) Longitudinal cross-section of a melt track, where the laser scanning direction is right to left. Columnar dendritic and equiaxed grains are observable. This track was formed using a LE-L beam at $P=550 \\mathrm{~W}$ and $Q=140 \\mathrm{~J} / \\mathrm{mm}^{3}$. (b) Transverse crosssection of a melt track showing a transition from planar, to cellular, to mixed cellular and dendritic growth, where the laser scanning direction is out of the plane of the image. Microsegregation-related pitting corrosion is seen most clearly near the fusion boundary, where $\\mathrm{R}$ is lowest. This track was formed using a TE-L beam at $\\mathrm{P}=350 \\mathrm{~W}$ and $Q=260 \\mathrm{~J} / \\mathrm{mm}^{3}$. nearly the entire bulk of LPBF alloys, the discussion will not dwell on the planar regions. Adjacent to the planar growth region, solutepoor cell/dendrite cores etched deeply, indicating pitting corrosion (Fig. 5b). These pits were not present prior to etching.\n\nA solidification map of laser power $v s$. energy density for each laser intensity profile and size is shown in Fig. 4b. The tracks represented by off-white data markers ( color level $=0$ ) were absent at the cross-section due to lack of fusion or sampling at a balling trough, and will not be discussed here. Generally, regardless of beam ellipticity or size, equiaxed solidification was favored at lower laser powers, particularly when substrate penetration by the melt was absent or poor. With increasing power and scan speed, the concentration of columnar grains increases (Fig. 6). Tracks demonstrating keyhole-mode laser heating (i.e., profile Type 5, Fig. 4a) consist entirely of columnar grains.\n\nMost interestingly, the parameter space over which equiaxed or mixed equiaxed-columnar microstructures are produced is much larger for the elliptical beam profiles than for the circular beam profiles, with the TE profile being most encouraging for equiaxed solidification (Fig. 4b). For example, at $350 \\mathrm{~W}$ and $\\mathrm{Q}=80-260 \\mathrm{~J} /$ $\\mathrm{mm}^{3}$, the C-M profile will only result in columnar solidification (Fig. 7). However, without changing laser power, scan speed, or beam size, a greater area fraction of equiaxed grains can be achieved for LE profiles at $Q=260 \\mathrm{~J} / \\mathrm{mm}^{3}$ and TE profiles at $\\mathrm{Q}=200-260 \\mathrm{~J} / \\mathrm{mm}^{3}$. The tendency for elliptical profiles to increase the area fraction of equiaxed grains is generally observed at $d /$ $w \\approx 0.2-0.5$, when conduction-mode laser heating of the substrate occurs. These results confirm that site-specific microstructural control is achievable by varying beam ellipticity.\n\n\\section*{4.", "start_char_idx": 834501, "end_char_idx": 838328, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "09d153d3-e135-4b58-97d5-6db27e3dc5c7": {"__data__": {"id_": "09d153d3-e135-4b58-97d5-6db27e3dc5c7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "6d0da013-9d4f-4b9f-904e-4fa160fb2e94", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3b2b9d9c4a19d3bab9aa695ca0555599601018e84e3a425d40d9ddf5ecd4e910", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1bbd6a24-984f-4088-9948-a7f5e6dc27aa", "node_type": "1", "metadata": {}, "hash": "fbf2306f20ef8e2498afb5cd8d9ba0bea3703a52e125134b33c1ead135e328ae", "class_name": "RelatedNodeInfo"}}, "text": "7). However, without changing laser power, scan speed, or beam size, a greater area fraction of equiaxed grains can be achieved for LE profiles at $Q=260 \\mathrm{~J} / \\mathrm{mm}^{3}$ and TE profiles at $\\mathrm{Q}=200-260 \\mathrm{~J} / \\mathrm{mm}^{3}$. The tendency for elliptical profiles to increase the area fraction of equiaxed grains is generally observed at $d /$ $w \\approx 0.2-0.5$, when conduction-mode laser heating of the substrate occurs. These results confirm that site-specific microstructural control is achievable by varying beam ellipticity.\n\n\\section*{4. Simulations}\nBeam shape effects on track macro- and microstructures were further investigated by modeling laser-material interactions using the ALE3D code (Movies 1-3). During the track melting simulations, the role of surface tension and vapor recoil on track topography can be observed (Figs. 8 and 9). In order to reduce surface energy, capillary forces pull liquid metal towards the center of the melt track, smoothing the track surface and wetting the substrate [17]. However, surface tension effects can also cause PlateauRaleigh instability and track discontinuity. Using Fig. 8, the lateral temperature gradient can be judged by using the distance between the red and gray isothermal contours, where the red contour is approximately the melting temperature of 316L steel ( $1700 \\mathrm{~K}$ ) and gray is $500 \\mathrm{~K}$. For each beam intensity profile, a slight denudation zone (or bare zone) exists between the melt track and the surrounding heat-affected particles (Fig. 8). The physics of the more dominant contributions to denudation is discussed in detail for Gaussian beams elsewhere [11].\n\nSupplementary video related to this article can be found at \\href{http://dx.doi.org/10.1016/j.actamat.2017.02.025}{http://dx.doi.org/10.1016/j.actamat.2017.02.025}.\n\nSince the simulations were performed for a short distance $(0.050 \\mathrm{~cm})$, undulations in the melt track surfaces cannot easily be tied to track discontinuities, which occur over similar or longer length scales (trough to trough) for the C-S, LE-S, and TE-S profiles at $P=550 \\mathrm{~W}$ and $Q=80 \\mathrm{~J} / \\mathrm{mm}^{3}$ (Fig. S6). Nevertheless, melt velocity vectors are shown on longitudinal cross-sectional views in Fig. 9. The shape of each topological depression mirrored the beam shape used. At $z=0 \\mathrm{~cm}$, considering the distance between the front of the topological depression and the $1700 \\mathrm{~K}$ (red) isothermal contour in the tail region, the temperature gradient is steepest in the scanning direction using the TES profile $\\left(68 \\times 10^{3} \\mathrm{~K} / \\mathrm{cm}\\right)$, followed by the $\\mathrm{C}-\\mathrm{S}\\left(50 \\times 10^{3} \\mathrm{~K} / \\mathrm{cm}\\right)$ and LE-S $\\left(47 \\times 10^{3} \\mathrm{~K} / \\mathrm{cm}\\right)$ profiles. This is related to the intensity distributions produced by the different beam profiles: the\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c67706ca9b766b63e498g-06(1)}\n\nFig. 6. Cross-sections of melt track roots produced using the C-M profile at constant energy density $\\left(260 \\mathrm{~J} / \\mathrm{mm}^{3}\\right.$ ) and varying power: (a) $P=50 \\mathrm{~W}$, (b) $P=250 \\mathrm{~W}$, and (c) $P=550 \\mathrm{~W}$. The percent area occupied by equiaxed grains (as opposed to columnar grains) increases with increasing laser power and scan speed.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c67706ca9b766b63e498g-06(2)}\n\nFig. 7.", "start_char_idx": 837753, "end_char_idx": 841263, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1bbd6a24-984f-4088-9948-a7f5e6dc27aa": {"__data__": {"id_": "1bbd6a24-984f-4088-9948-a7f5e6dc27aa", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "09d153d3-e135-4b58-97d5-6db27e3dc5c7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8f53e8ee03892785caff0eddb84aa9a709944c589cbecd9704f25760f4a81ca3", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "04b103cc-a466-4fda-90e6-b0bff096862a", "node_type": "1", "metadata": {}, "hash": "fca1ff12300b711f99c3ba676a402bc568de11806d0ea64a110f731d83a35a93", "class_name": "RelatedNodeInfo"}}, "text": "6. Cross-sections of melt track roots produced using the C-M profile at constant energy density $\\left(260 \\mathrm{~J} / \\mathrm{mm}^{3}\\right.$ ) and varying power: (a) $P=50 \\mathrm{~W}$, (b) $P=250 \\mathrm{~W}$, and (c) $P=550 \\mathrm{~W}$. The percent area occupied by equiaxed grains (as opposed to columnar grains) increases with increasing laser power and scan speed.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c67706ca9b766b63e498g-06(2)}\n\nFig. 7. Cross-sections of melt track roots produced at constant beam size, power, and energy density (Size M, $350 \\mathrm{~W}$, and $260 \\mathrm{~J} / \\mathrm{mm}^{3}$ ) as beam shape is varied. The percent area occupied by equiaxed grains (as opposed to columnar grains) is $2 \\%$ (a, C-M), $28 \\%$ (b, LE-M), and $77 \\%$ (c, TE-M). The substrate penetration depths were $71.9,73.3$, and $78.0 \\mu \\mathrm{m}$ for the C-M, LE-M, and TE-M profiles, respectively.\n\ncenterline of tracks melted by the LE-S profile experience heating longer than those melted by the TE-S profile.\n\nThe maximum melt flow velocity was lower in magnitude using the $C$-S profile $\\left(1.1 \\times 10^{-3} \\mathrm{~cm} / \\mathrm{s}\\right)$ than using the TE-S $\\left(1.3 \\times 10^{-3} \\mathrm{~cm} / \\mathrm{s}\\right)$ and LE-S $\\left(2.2 \\times 10^{-3} \\mathrm{~cm} / \\mathrm{s}\\right)$ profiles. Examining the topological depression caused by vapor recoil, the TE-S profile produced backward melt flow at the greatest velocity, with horizontal flow from the bottom of the topological depression and upward melt flow near the surface of the tailing wall of the depression. The LE-S profile produced backward melt flow at a lower velocity, although the flow was directed downward in the depression. Near the surface of the tailing wall of the depression, melt flow was in the forward direction, creating a breaking wave that resulted in a trail of trapped pores. (The existence of these pores could not be confirmed in the closest experiment (LE-S, $P=550 \\mathrm{~W}, Q=80 \\mathrm{~J} / \\mathrm{mm}^{3}$ ) since the discontinuous track separated from the substrate during sectioning.) The C-S profile produced the lowest velocity backward melt flow, which was met by\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c67706ca9b766b63e498g-06}\n\nFig. 8. Top-down view of melt-track formation by the (a) C-S, (b) LE-S, and (c) TE-S profiles, where laser scanning occurs in the positive x-direction. The pseudo-colors correspond to temperature linearly, where red is $3200 \\mathrm{~K}$ and blue is room temperature. The isothermal contours were assigned as follows: gray $=500 \\mathrm{~K}$, red $=1700 \\mathrm{~K}$, fuchsia $=2500 \\mathrm{~K}$, black $=3500 \\mathrm{~K}$. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c67706ca9b766b63e498g-07}\n\nFig. 9. Longitudinal cross-sectional view of melt-track formation by the (a) C-S, (b) LE-S, and (c) TE-S profiles, where laser scanning occurs in the positive $x$-direction. The pseudocolor range corresponds to temperature linearly, where red is $3200 \\mathrm{~K}$ and blue is room temperature $(298 \\mathrm{~K})$.", "start_char_idx": 840791, "end_char_idx": 844045, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "04b103cc-a466-4fda-90e6-b0bff096862a": {"__data__": {"id_": "04b103cc-a466-4fda-90e6-b0bff096862a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1bbd6a24-984f-4088-9948-a7f5e6dc27aa", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "468db5174b78fe070297687d21e5a82813c7912463f01e523087d862ec766d70", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "eccda2b7-cf24-4f07-8459-900643c18ae2", "node_type": "1", "metadata": {}, "hash": "9f36d82890bf13c51efe82dfc8dc8fb23f8ae762a222e1fb980a38e4963b74dc", "class_name": "RelatedNodeInfo"}}, "text": "(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c67706ca9b766b63e498g-07}\n\nFig. 9. Longitudinal cross-sectional view of melt-track formation by the (a) C-S, (b) LE-S, and (c) TE-S profiles, where laser scanning occurs in the positive $x$-direction. The pseudocolor range corresponds to temperature linearly, where red is $3200 \\mathrm{~K}$ and blue is room temperature $(298 \\mathrm{~K})$. Isothermal contours are shown, where gray $=500 \\mathrm{~K}$, red $=1700 \\mathrm{~K}$, magenta $=2500 \\mathrm{~K}$, and black $=3500 \\mathrm{~K}$. The sizes of the velocity vectors scale with magnitude. For subfigure b, trapped pores in the melt track are shown in white. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)\n\nforward and upward melt flow in the transition region. For all three beam shapes, in addition to backward melt flow in the tail region, some degree of melt mixing was observed in the transition region. The contribution of the melt vortex to cooling the molten metal has been reported [10].\n\nThe ALE3D simulations also model spatter, and a more in-depth study of spatter patterns can be found elsewhere [24]. Although spatter occurred for each intensity profile studied, the extent and nature of spatter was very different (Movies 1-3). For the LE-S profiles, relatively small spatter droplets ejected laterally and backward from the topological depression. For the TE-S profile, spatter can be described by the so-called \"snow plow\" effect, wherein liquid metal builds up ahead of the laser spot, eventually causing the forward ejection of a very large spatter droplet [24]. The C-S profile demonstrated spatter intermediate to that observed for the LE-S and TE-S profiles. In the experiments, very few spatter particles were observed for the tracks that most closely resembled the conditions simulated (Fig. S6).\n\n\\section*{5. Discussion}\n\\subsection*{5.1. Macrostructure}\nThe traditional approach to AM parameter selection places heavy emphasis on defect mitigation. To reduce lack-of-fusion defects, smooth, continuous tracks with bead heights close to the powder layer thickness are highly desirable. Tall melt beads can impede uniform powder spreading, while undulations in the build surface from balling or discontinuous tracks can be amplified in subsequent layers. In both cases, the likelihood of void formation is very high. The depth of melt penetration into the substrate also needs optimization. While poor surface adhesion can result in flat defects that act as crack nucleation sites, deep substrate penetration can be accompanied by keyhole voids [13].\n\nThe results show that circular and elliptical beam intensity profiles perform best at different sizes. Of the profiles sizes, laser powers, and scan rates studied, the C-L, LE-S, and TE-S profiles\\\\\nproduced melt tracks that were undesirable in terms of bead height ( $>3 t$ ), roughness $\\left(R_{a}>40 \\mu \\mathrm{m}\\right)$, and continuity (Fig. 3). Previous computational work has related track discontinuity to the PlateauRaleigh instability and showed that track stability increases with increasing laser power and spot size, which increase track width [17]. For the LE and TE profiles, track continuity increased with increasing spot size (Fig. 3) as roughness decreased (Fig. S4). However, an opposite trend was observed for the circular profile, which yielded high roughness, high bead heights, and low substrate penetration depths using C-L. The C-L profile delivers the same power as the C-S profile, but distributed over a larger area. The higher roughness produced by $\\mathrm{C}-\\mathrm{L}$ could be related to a decrease in surface flow driven by the Marangoni effect. For a specific subset of beam intensity profiles (i.e., the C-S, C-M, LE-M, LE-L, TE-M, and TE-L profiles), the tracks became more continuous and less rough with increasing power (Figs. S1 and S5) as described by earlier simulations [17].", "start_char_idx": 843513, "end_char_idx": 847642, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "eccda2b7-cf24-4f07-8459-900643c18ae2": {"__data__": {"id_": "eccda2b7-cf24-4f07-8459-900643c18ae2", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "04b103cc-a466-4fda-90e6-b0bff096862a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2c4ef79beaccc9444183850222c6371b163c30a23b737a495c91a679fc739920", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3105dac6-2f5c-4a9f-9ea4-06e34633f2b2", "node_type": "1", "metadata": {}, "hash": "faedfe3a8201de72e60f04f8a604d65cd02f45a66823bea0cc3c6a221e00fc37", "class_name": "RelatedNodeInfo"}}, "text": "For the LE and TE profiles, track continuity increased with increasing spot size (Fig. 3) as roughness decreased (Fig. S4). However, an opposite trend was observed for the circular profile, which yielded high roughness, high bead heights, and low substrate penetration depths using C-L. The C-L profile delivers the same power as the C-S profile, but distributed over a larger area. The higher roughness produced by $\\mathrm{C}-\\mathrm{L}$ could be related to a decrease in surface flow driven by the Marangoni effect. For a specific subset of beam intensity profiles (i.e., the C-S, C-M, LE-M, LE-L, TE-M, and TE-L profiles), the tracks became more continuous and less rough with increasing power (Figs. S1 and S5) as described by earlier simulations [17].\n\nAlthough some evidence of keyhole-mode laser heating can be observed for the LE-S and TE-S profiles at high power (Fig. 4b), keyhole-mode melting occurred over the widest parameter space for the C-S profile ( $P=250-550 \\mathrm{~W}, Q=140-260 \\mathrm{~J} / \\mathrm{mm}^{3}$ ) which, without performing metallographic cross-sections, produced tracks that met macroscopic expectations. In conventional laser welding, keyhole-mode laser heating is generally described in terms of power or energy densities. SEM of track cross-sections showed that the laser-heating mode is also a function of laser intensity profile (i.e., ellipticity). For example, at $350 \\mathrm{~W}$ and $260 \\mathrm{~J} /$ $\\mathrm{mm}^{3}$, the $\\mathrm{C}-\\mathrm{S}$ profile produced a melt track that demonstrates keyhole-mode laser heating, while the LE-S and TE-S profiles did not (Fig. 4a, Fig. S7).\n\nThis investigation was initially motivated by the possibility of producing favorable track morphologies in designated locations by varying laser beam ellipticity. For example, at Size M, bead height, track continuity, and substrate wetting are improved using elliptical intensity profiles compared to circular ones. However, this trend is not observed at all beam sizes. The extreme case occurs at Size S, for which the circular profile far out-performs the LE-S and TE-S profiles. At Size L, the LE-L and TE-L profiles dramatically improve track macrostructure; but, the C-L profile would be inappropriate for most AM applications since it results in discontinuous, balled tracks in the first place. However, instead of being used for adding material, elliptical beams could be used to reprocess regions deposited by circular profiles to reduce surface roughness.\n\n\\subsection*{5.2. Microstructure}\nThe current understanding of how temperature gradients (G) and solidification rates $(\\mathrm{R})$ affect solidification microstructures and patterns is heavily based on conventional metastable and rapid solidification studies [19]. Measuring G and R during LPBF remains experimentally challenging due to the localized nature of melting and the extreme rate of solidification. Myriad numerical efforts have been dedicated to modeling the microstructures formed under certain $G$ and $R$, but most efforts are not yet fully predictive [25-34]. Real-time observations of laser-melted alloy solidification have been made using several techniques [35,36], but simple binary systems are generally used as case studies. Popular AM candidates, however, are multicomponent, polymorphic, and/or multiphase (e.g., stainless steels, Inconels, Ti-6Al-4V, AlSi10 Mg, etc.). To shed light on the mechanisms that give rise to the unique microstructures of LPBF materials, ALE3D simulations of temperature gradients and flow patterns provide useful information. For example, the velocity vectors modeled demonstrate the dynamic nature of LPBF, and the inapplicability of solidification analyses developed for casting.\\\\\nDuring solidification, the propagation rate of the $s / 1$ interface $(R)$ scales with laser scan speed $(v)$ according to:\n\n$R=v \\cos \\alpha$\n\nwhere $\\alpha$ is the angle between the laser scanning direction and the solidification direction. Since solidification occurs normal to the fusion boundary, $\\mathrm{R}$ is zero at the fusion boundary and maximum along the track centerline [20]. The presence of a narrow planar growth regime at the fusion boundary supports this analysis, since planar growth is favored at very high G/R.", "start_char_idx": 846885, "end_char_idx": 851157, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3105dac6-2f5c-4a9f-9ea4-06e34633f2b2": {"__data__": {"id_": "3105dac6-2f5c-4a9f-9ea4-06e34633f2b2", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "eccda2b7-cf24-4f07-8459-900643c18ae2", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9d1e412bf92e1875a8994bc8444c261d0500059e3a5d63a4fb54a44deb17417c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "722cb401-2315-478a-be4d-7839ef984f42", "node_type": "1", "metadata": {}, "hash": "4162ead5b3d6dcf0088650de8167f46d6b8f7e9138730552d095806ad74ced3e", "class_name": "RelatedNodeInfo"}}, "text": "To shed light on the mechanisms that give rise to the unique microstructures of LPBF materials, ALE3D simulations of temperature gradients and flow patterns provide useful information. For example, the velocity vectors modeled demonstrate the dynamic nature of LPBF, and the inapplicability of solidification analyses developed for casting.\\\\\nDuring solidification, the propagation rate of the $s / 1$ interface $(R)$ scales with laser scan speed $(v)$ according to:\n\n$R=v \\cos \\alpha$\n\nwhere $\\alpha$ is the angle between the laser scanning direction and the solidification direction. Since solidification occurs normal to the fusion boundary, $\\mathrm{R}$ is zero at the fusion boundary and maximum along the track centerline [20]. The presence of a narrow planar growth regime at the fusion boundary supports this analysis, since planar growth is favored at very high G/R. As G/R decreases and the degree of constitutional undercooling increases, perturbations in the planar $s / 1$ interface develop and grow as cells or dendrites, rejecting solute atoms into the surrounding liquid phase by microsegregation. After complete solidification, soluteaccommodating dislocation walls can be found in the interdendritic/intercellular regions [37]. In this study, pitting corrosion occurred preferentially in cell/dendrite cores during etching, most aggressively near the fusion boundary (Fig. 5b). This has previously been ascribed to Mo and $\\mathrm{Cr}$ microsegregation [38-41], the degree of which increases with decreasing R [42]. It can be inferred that solidification proceeds relatively slowly for some distance (up to $\\sim 40 \\mu \\mathrm{m}$, in Fig. 5b) past the instability of planar growth. Slowly solidifying directional grains are terminated (or \"pinched-off\") in the melt zone by more rapidly propagating, advantageously oriented grains in the vicinity. In a full LPBF part build, these favorably oriented grains can propagate through multiple additive layers, producing a problematically coarse microstructure.\n\nBecause of their origins in discrete perturbations, cells and dendrites are also associated with low-angle boundaries and small intragranular misorientations. Several studies have been dedicated to understanding how and to what extent these solidification defects affect the mechanical properties of AM materials [37,43]. From a practical standpoint, it should be considered that the features of cells and dendrites are greatly diminished by post-process annealing [44] while grain boundaries continue to persist and evolve, playing a larger role in boundary strengthening and texture effects. A close examination of LPBF grain morphologies is therefore warranted.\n\nA majority of the columnar grains observed were resolutely dendritic. The primary dendrites seen in the columnar grains impinged upon one another prior to the formation of secondary dendrite arms in all cases, indicating rapid solidification, close dendrite spacing, and interdendritic solute trapping. Furthermore, columnar dendritic solidification was observed at high powers and scan speeds for all of the intensity profiles studied (Figs. 4b and 6). This was expected since columnar dendritic solidification occurs at low G/R [45] and R scales with scan speed. However, keeping scan speed constant, mixed equiaxed-columnar microstructures could be produced using elliptical profiles at moderate powers (250-350 W), but not using circular profiles, highlighting the need for important physical considerations (e.g., temperature gradient and melt dynamics) as they relate to beam shape.\n\nFor each of the beam intensity profiles studied, columnar dendritic grains were exclusively observed for tracks with $d / w>0.5$. With increasing power, scan speed, and substrate penetration, columnar dendritic solidification becomes more prominent for several possible reasons (Fig. 6). Since $Q$ is held constant, $v$ and $\\mathrm{R}$ increase with $P$, such that $\\mathrm{G} / \\mathrm{R}$ decreases. Also, as the contact area between the melt and the high-thermal conductivity substrate increases, the melt cooling rate increases. While the latter observation seems to indicate that microstructures can be tailored by way of cooling rate control, this approach ignores solute interactions, undercooling effects, and transformation enthalpies. Purely thermal models have failed to predict the columnar-to-\\\\\nequiaxed transition even for conventional processes, while phasefield models are making progress at AM-relevant solidification rates by using more complete thermodynamic and kinetic approaches [46-49].", "start_char_idx": 850282, "end_char_idx": 854876, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "722cb401-2315-478a-be4d-7839ef984f42": {"__data__": {"id_": "722cb401-2315-478a-be4d-7839ef984f42", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3105dac6-2f5c-4a9f-9ea4-06e34633f2b2", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "61c00ebc893a0f243f6ec60debefd68a897f15404562a21b517b373145b8d050", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0a91fa42-0cc7-414e-a5bd-e6f4f91e2e45", "node_type": "1", "metadata": {}, "hash": "263a9b62361b9e957700faaca74a2fce24dc5866e5505c4ae2aa126649efded1", "class_name": "RelatedNodeInfo"}}, "text": "With increasing power, scan speed, and substrate penetration, columnar dendritic solidification becomes more prominent for several possible reasons (Fig. 6). Since $Q$ is held constant, $v$ and $\\mathrm{R}$ increase with $P$, such that $\\mathrm{G} / \\mathrm{R}$ decreases. Also, as the contact area between the melt and the high-thermal conductivity substrate increases, the melt cooling rate increases. While the latter observation seems to indicate that microstructures can be tailored by way of cooling rate control, this approach ignores solute interactions, undercooling effects, and transformation enthalpies. Purely thermal models have failed to predict the columnar-to-\\\\\nequiaxed transition even for conventional processes, while phasefield models are making progress at AM-relevant solidification rates by using more complete thermodynamic and kinetic approaches [46-49].\n\nA novel and significant finding was that, even when substrate penetration depths are comparable and all other processing parameters are equal (i.e., $P, v, Q w_{b}, t$ ), varying the beam intensity profile alters the ratio of equiaxed to columnar grains (Fig. 7). Due to the presence of very high temperature gradients, the homogeneous nucleation of equiaxed grains is not expected [23]. However, equiaxed solidification can be achieved by non-stochastic or athermal nucleation mechanisms under the influence of melt mixing. By accounting for Marangoni convection and recoil pressure effects, the simulations show the presence of a melt vortex following the topological depression of a melt track, wherein hot molten metal is stirred from the depression towards the much cooler transition region at high velocity. Notably, higher melt flow velocities were found using the LE and TE intensity profiles than the C profiles (Fig. 9). The high-velocity flow can cause dendrite tip fragmentation and redistribution, allowing the solid fragments to act as intrinsic nucleation sites for equiaxed grains ahead of the growth front in the melt zone [50,51]. (Note that dendrite fragmentation is not caused by pure mechanical deformation [52], but by constitutional remelting at dendrite roots. The remelting can be caused by locally high interdendritic solute contents [53-55] or by elastic energy changes that cause a shift in the thermodynamic equilibrium at the $s / 1$ interface [56].) The possibility of dendrite fragmentation for equiaxed grain nucleation is supported by the experimental results, which show that the LE and TE profiles each produce equiaxed microstructures over a larger parameter space than the $C$ profiles (Figs. $4 \\mathrm{~b}$ and 7). This type of spurious nucleation is undesirable during single crystal repair by epitaxial laser metal forming [57,58], but is highly desirable in the additive manufacturing of alloys with isotropic properties. Though less likely than dendrite fragmentation, the athermal nucleation of equiaxed grains could occur if near-critical embryos are suddenly undercooled by being quickly stirred into cooler molten metal [45]. The temperature decrease reduces the requisite critical nucleus size to activate stable and continuous growth. While the exact underlying mechanisms of equiaxed solidification are not confirmed, this study demonstrates the efficacy of laser intensity spatial profile modulation for site-specific microstructural control.\n\nIn laser powder-bed fusion, the ability to tailor microstructures in specific locations gives rise to major implications. Beyond HallPetch strengthening, equiaxed grains can be used to limit hot cracking in susceptible materials, to introduce a more treacherous path for intergranular crack propagation, or to improve fatigue life near surfaces and stress-concentrating geometric features. Large columnar grains can improve creep resistance or result in strong textures and anisotropic properties for specific applications. With the advent of microstructural control, LPBF is transformed from a convenient net-shape manufacturing tool to a powerful processing technique for the production of designer materials with enhanced properties and performance.\n\n\\section*{6. Conclusions}\nThe effects of circular, longitudinal elliptical, and transverse elliptical laser intensity profiles on single-track macrostructures and microstructures were investigated. At Size S (the $100 \\mu \\mathrm{m}-$ equivalent beam size), the circular profile produced smooth, continuous tracks, while the elliptical profiles both resulted in rough, discontinuous tracks with poor substrate wetting at the energy densities and laser powers studied. Keyhole-mode laser heating was only observed at Size S, and most prominently using the circular beam profile. Moreover, the laser heating mode was determined by beam shape as well as laser power and energy density.", "start_char_idx": 853995, "end_char_idx": 858810, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0a91fa42-0cc7-414e-a5bd-e6f4f91e2e45": {"__data__": {"id_": "0a91fa42-0cc7-414e-a5bd-e6f4f91e2e45", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "9c6fca6e-d2f6-4e3f-ad6f-c9b1cf8e5ec4", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "232ff552ab671eacd59bc33a823e2eced64593e56e3d355e6068b60f57480aed", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "722cb401-2315-478a-be4d-7839ef984f42", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_56_to_69.txt", "file_name": "merged_56_to_69.txt", "file_type": "text/plain", "file_size": 875601, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c4ddb8a948ace7fd64ce1f38354844e1f03db583ddc893783f001e62c0c5e60c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "59e9e329-e193-4e07-ab19-0ea7382e4c8e", "node_type": "1", "metadata": {}, "hash": "c21b627c10523dfcfa6e5737737a83f96b9f0f19183e3a1d770ad3d4de93c735", "class_name": "RelatedNodeInfo"}}, "text": "Large columnar grains can improve creep resistance or result in strong textures and anisotropic properties for specific applications. With the advent of microstructural control, LPBF is transformed from a convenient net-shape manufacturing tool to a powerful processing technique for the production of designer materials with enhanced properties and performance.\n\n\\section*{6. Conclusions}\nThe effects of circular, longitudinal elliptical, and transverse elliptical laser intensity profiles on single-track macrostructures and microstructures were investigated. At Size S (the $100 \\mu \\mathrm{m}-$ equivalent beam size), the circular profile produced smooth, continuous tracks, while the elliptical profiles both resulted in rough, discontinuous tracks with poor substrate wetting at the energy densities and laser powers studied. Keyhole-mode laser heating was only observed at Size S, and most prominently using the circular beam profile. Moreover, the laser heating mode was determined by beam shape as well as laser power and energy density. At Size M and L (the 175 and $250 \\mu$ m-equivalent beam sizes), track continuity, smoothness, and substrate adhesion are improved with the use of elliptical intensity profiles while melt bead heights are reduced.\n\nMore importantly, beam ellipticity demonstrated a strong effect on solidification microstructure. The elliptical intensity profiles produced equiaxed or mixed equiaxed-columnar grains over a much larger parameter space than the circular profiles when conduction-mode laser heating occurred. This indicates that at moderate powers ( $150-450 \\mathrm{~W}$ ), grain morphology can be tailored by varying beam intensity spatial profile while maintaining constant laser power and scan speed. With the ability to control microstructures locally and on the fly, site-specific properties can be directly engineered into additively manufactured parts.\n\n\\section*{Acknowledgements}\nThis work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, supported by the Office of Laboratory Directed Research and Development (LDRD), tracking numbers 15-ERD-037 and LDRD 15-ERD-006. TTR was supported in part by the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists (WDTS) under the Visiting Faculty Program (VFP). The authors acknowledge useful discussions with Joseph T. McKeown and Wayne E. King. The LLNL document review and release number is LLNL-JRNL-713205.\n\n\\section*{Appendix A. Supplementary data}\nSupplementary data related to this article can be found at http:// \\href{http://dx.doi.org/10.1016/j.actamat.2017.02.025}{dx.doi.org/10.1016/j.actamat.2017.02.025}.\n\n\\section*{References}\n[1] C. K\u00f6rner, H. Helmer, A. Bauerei\u00df, R.F. Singer, Tailoring the grain structure of IN718 during selective electron beam melting, MATEC Web Conf. 14 (2014) 8001, \\href{http://dx.doi.org/10.1051/matecconf/20141408001}{http://dx.doi.org/10.1051/matecconf/20141408001}.\n\n[2] R.R. Dehoff, M.M. Kirka, W.J. Sames, H. Bilheux, A.S. Tremsin, L.E. Lowe, S.S. Babu, Site specific control of crystallographic grain orientation through electron beam additive manufacturing, Mater. Sci. Technol.. 31 (n.d.) 931-938.\n\n[3] T. Niendorf, S. Leuders, A. Riemer, H.A. Richard, T. Tr\u00f6ster, D. Schwarze, Highly anisotropic steel processed by selective laser melting, Metall. Mater. Trans. 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