diff --git "a/agentic_index/merged_2_to_17/docstore.json" "b/agentic_index/merged_2_to_17/docstore.json"
new file mode 100644--- /dev/null
+++ "b/agentic_index/merged_2_to_17/docstore.json"
@@ -0,0 +1 @@
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"\\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{Influence of processing parameters on the evolution of melt pool, porosity, and microstructures in Ti-6Al-4V alloy parts fabricated by selective laser melting }\n\n\n\\author{J. J. S. Dilip ${ }^{1,2}$ - Shanshan Zhang ${ }^{1}$ - Chong Teng ${ }^{3}$ - Kai Zeng ${ }^{3}$ - Chris Robinson ${ }^{3}$ -\\\\\nDeepankar Pal ${ }^{3} \\cdot$ Brent Stucker $^{3}$}\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 December 2016/Accepted: 2 August 2017/Published online: 9 August 2017\n\n(C) Springer International Publishing AG 2017\n\n\\begin{abstract}\nSelective laser melting involves melting and solidification of metal powder particles in a track-by-track and layer-by-layer method to fabricate 3D parts. The present investigation focuses on understanding the effect of laser power and scan speed on the evolution of melt pool, porosity and multiple thermal cycling effects on the microstructure in parts fabricated using selective laser melting. In this study, Ti-6Al-4V pre-alloyed powder was used to produce single-track deposits and bulk parts. Using different combinations of laser power and scan speeds, single-track deposits and bulk parts were produced. The cross-sections of the single-track deposits and bulk samples were prepared for metallographic observations and the melt pool shape and size and porosity were evaluated. When a low energy density was applied the un-melted powder particles produced irregularly shaped porosity, and a high energy density resulted in rounded porosity, which was due to keyhole effects. The samples produced with a proper combination of power and speeds were fully dense. Further, microstructural development under the influence of process condition was highlighted. Overall, the study demonstrates a good correlation between the single-track melt pool geometries, porosity in bulk parts and also demonstrates the microstructural inhomogeneity during deposition.", "start_char_idx": 0, "end_char_idx": 2921, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "4e26a95c-ea9e-4ece-b4e6-db3b8771eb74": {"__data__": {"id_": "4e26a95c-ea9e-4ece-b4e6-db3b8771eb74", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "157c7b21-42c7-43e5-9e9e-366b6ec34ec5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e2348540ef51fa07d2cf0971aacaeb8add0825bfd32747086356a5c177a7f0eb", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "14336fa2-579e-4668-9616-4a016e5c6b0c", "node_type": "1", "metadata": {}, "hash": "5e581960f4e52647b354f9f4cf0665adee3efb0eac823eeb48dbc52345132a18", "class_name": "RelatedNodeInfo"}}, "text": "In this study, Ti-6Al-4V pre-alloyed powder was used to produce single-track deposits and bulk parts. Using different combinations of laser power and scan speeds, single-track deposits and bulk parts were produced. The cross-sections of the single-track deposits and bulk samples were prepared for metallographic observations and the melt pool shape and size and porosity were evaluated. When a low energy density was applied the un-melted powder particles produced irregularly shaped porosity, and a high energy density resulted in rounded porosity, which was due to keyhole effects. The samples produced with a proper combination of power and speeds were fully dense. Further, microstructural development under the influence of process condition was highlighted. Overall, the study demonstrates a good correlation between the single-track melt pool geometries, porosity in bulk parts and also demonstrates the microstructural inhomogeneity during deposition.\n\\end{abstract}\n\n\\footnotetext{$\\boxtimes$ J. J. S. Dilip\n\n\\href{mailto:samueldilip@gmail.com}{samueldilip@gmail.com}\n\n1 Department of Industrial Engineering, Rapid Prototyping Center, University of Louisville, Louisville, KY 20292, USA\n\n2 HP Labs, 1501 Page Mill Road, Palo Alto, CA 94304, USA\n\n3 3DSIM, 1794 Olympic Parkway, Suite 110, Park City, UT 84098, USA\n}Keywords Additive manufacturing $\\cdot$ Selective laser melting $\\cdot$ Ti-6Al-4V alloy $\\cdot$ Single-track deposits\n\n\\section*{1 Introduction}\nAdditive manufacturing belongs to the group of manufacturing technologies where 3D parts are fabricated by material addition in a layer-by-layer fashion, usually from a computer-aided design model [1]. Additive manufacturing technologies offer enhanced design capabilities for geometric freedom that allows producing parts which are otherwise not possible to fabricate with traditional manufacturing processes. There are various additive manufacturing processes such as selective laser melting, direct laser deposition, electron beam melting, wire-feed additive manufacturing, shape deposition modeling, ultrasonic consolidation, binder jetting, and friction freeform fabrication for producing metallic components [1-8]. Titanium alloys are used in several structural applications due to their lower density, high strength to weight ratio, corrosion resistance, and elevated temperature properties [9]. Traditionally, titanium alloys are made by vacuum induction re-melting and carefully controlled thermo-mechanical processing to tune the microstructure that will demonstrate satisfactory mechanical properties. Although manufacturing methods are well established for titanium alloys, the high production cost limits the use of these alloys. Additive manufacturing could provide a means to fabricate parts in titanium alloys at a lower cost. Among the various grades of titanium alloys, Ti-6Al-4V $(\\alpha+\\beta$ alloy) is the most popular and finds its applications in aerospace, automotive, biomedical, defence and industrial sectors $[9,10]$. The alloy has good weldability characteristics, making it amenable for SLM.\n\nOf the commercially available additive manufacturing technologies, selective laser melting (SLM) is one of the most popular and successful powder-bed fusion based additive manufacturing processes. In SLM, consolidation of metal powder is achieved by melting and solidifying a small volume of material in a track-by-track and layer-bylayer fashion using a high-intensity laser. In other words, the laser beam scans over a layer of powder in a straight line and melts the powder particles under the beam and creates a small molten pool of metal. As the laser beam traverses, it leaves a thin track of solidified metal behind. On repeating the single track deposit with a well-defined overlap (hatch spacing), a layer of cross-section is produced. Upon repeating this layer-by-layer deposition, an entire part is constructed [1]. A simple schematic of the SLM process showing track-by-track and layer-by-layer deposition is presented in Fig. 1 [11]. SLM is controlled by various processing parameters such as laser power $(P)$, scanning speed $(v)$, layer thickness $(t)$ and hatch spacing (h). These parameters define energy density of the process as [12]:\n\n$E=\\frac{P}{v \\times h \\times t}$.\n\nAlthough energy density is a measure of the energy input to the process, there are other factors such as the composition of the metal, atmosphere used, scan pattern, and powder-bed temperature, which also play a significant role [13]. All the parameters mentioned above mutually influence each other, but the degree of effect by each parameter is not well understood.", "start_char_idx": 1961, "end_char_idx": 6613, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "14336fa2-579e-4668-9616-4a016e5c6b0c": {"__data__": {"id_": "14336fa2-579e-4668-9616-4a016e5c6b0c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "4e26a95c-ea9e-4ece-b4e6-db3b8771eb74", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9f41d2eb27d0ee2e4b42f6e287b3d48141c2622a5be34d80b840d80d3e43bfc2", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3b2cdb78-d366-4a62-ad12-9647c2bcf4cd", "node_type": "1", "metadata": {}, "hash": "74bcecde2ddc154248b60af483dd4630e82b28d4e6f0e4dcbc7a37ff8da789d4", "class_name": "RelatedNodeInfo"}}, "text": "Upon repeating this layer-by-layer deposition, an entire part is constructed [1]. A simple schematic of the SLM process showing track-by-track and layer-by-layer deposition is presented in Fig. 1 [11]. SLM is controlled by various processing parameters such as laser power $(P)$, scanning speed $(v)$, layer thickness $(t)$ and hatch spacing (h). These parameters define energy density of the process as [12]:\n\n$E=\\frac{P}{v \\times h \\times t}$.\n\nAlthough energy density is a measure of the energy input to the process, there are other factors such as the composition of the metal, atmosphere used, scan pattern, and powder-bed temperature, which also play a significant role [13]. All the parameters mentioned above mutually influence each other, but the degree of effect by each parameter is not well understood. Therefore, studying the basic element of SLM, i.e., the single-track deposits, will provide a deeper understanding of the process and could assist in identifying a process window for optimizing parameters, particularly when dealing with new alloy systems [11].\n\nIn recent times, a great deal of work has been carried out on the Ti-6Al-4V alloy for optimization of parameters, microstructural characterization, and mechanical property evaluation using SLM [12-15]. Gong et al. [11] reported a strategic method to arrive at optimum parameters through producing single beads on the base plate and extended their work to characterize a test pad $(10 \\mathrm{~mm} \\times 10 \\mathrm{~mm} \\times 1 \\mathrm{~mm})$ with multiple layers. Gong et al. described the effect of power and scan speed on the melt pool geometry, and also showed surface topology of multi-layer pads, which were evaluated for porosity and quality evaluation. However, a detailed study on porosity and microstructures was not reported. Also, in their study, the single-track deposits were made on a base plate made on a Ti plate. Very recently, Yang et al. [16] investigated the role of melt pool on microstructure and mechanical properties of Ti-Al-4V. The study explores the use of a keyhole mode over a conduction mode for SLM deposits, and it was noticed that the conduction mode provided denser parts with better mechanical properties. In their experiments, the single-track deposits were made on a pure Ti plate. In both the case studies, single-track deposits resulted in a significant amount of dilution with the base plate alloy. It is well known that dilution contributes to a change in the local composition of the melt pool, thus changing the melting temperature of the Ti-6Al-4V alloy powder in the local single-track vicinity. In other words, the volume of the melt pool created will be different from the actual volume when the melting temperature is changed. Hence, the estimate of melt pool size will probably be close to the actual one but not a true representation of the melt pool size. Therefore, a study on single tracks made of the same alloy (Ti-6Al-4V plate) is necessary to have an accurate measure of melt pool geometry. Thijis et al. [15] studied the influence of process parameters on porosity and the development of microstructures. In their study, they varied the energy density of the process (by altering the scan speed and hatch spacing) and presented its effects on porosity. They described the evolution of grain (elongated) structure in the deposits due to epitaxial growth, and the fast cooling in SLM resulting in a fully martensitic phase. The martensite phase formed will experience multiple thermal cycling effects during track-by-track and layer-by-layer material deposition and therefore, finally result in a microstructure containing a hierarchical structure of martensite [17].\n\nThe quality and the properties of parts produced by SLM primarily rely on the nature of single-track deposits, overlap between the layers, and thermal history. It is\\\\\nFig. 1 A schematic the SLM process showing track-by-track and layer-by-layer deposition of material [9]\n\n\\includegraphics[max width=\\textwidth, center]{2024_02_28_5b6806184856c64a957ag-02}\\\\\nessential to study and understand the mechanism of formation of single-track deposits based upon processing parameters such as scanning speed, laser power, and powder layer thickness. In the present work, we attempt to produce single-track deposits on Ti-6Al-4V alloy plate.", "start_char_idx": 5799, "end_char_idx": 10136, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3b2cdb78-d366-4a62-ad12-9647c2bcf4cd": {"__data__": {"id_": "3b2cdb78-d366-4a62-ad12-9647c2bcf4cd", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "14336fa2-579e-4668-9616-4a016e5c6b0c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b75ca6bba8bb83c1eb5a2e419e5e53bd0a3d3af0387c433d75e6d9e752190585", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "883f0d7a-64c9-4efb-a8b9-ff0bafbe571a", "node_type": "1", "metadata": {}, "hash": "deea7f74372a33969b38f6a78deb3eb0f2e61d5ae54fd25c7d6c6e9e9d97f354", "class_name": "RelatedNodeInfo"}}, "text": "The martensite phase formed will experience multiple thermal cycling effects during track-by-track and layer-by-layer material deposition and therefore, finally result in a microstructure containing a hierarchical structure of martensite [17].\n\nThe quality and the properties of parts produced by SLM primarily rely on the nature of single-track deposits, overlap between the layers, and thermal history. It is\\\\\nFig. 1 A schematic the SLM process showing track-by-track and layer-by-layer deposition of material [9]\n\n\\includegraphics[max width=\\textwidth, center]{2024_02_28_5b6806184856c64a957ag-02}\\\\\nessential to study and understand the mechanism of formation of single-track deposits based upon processing parameters such as scanning speed, laser power, and powder layer thickness. In the present work, we attempt to produce single-track deposits on Ti-6Al-4V alloy plate. The objectives of the present work are (i) to study the influence of process parameters on single-track deposits on the evolution of the melt pool and (ii) to understand the effect of process parameters on porosity and microstructures in bulk parts. We believe that this work will provide further insights into understanding the SLM process and could assist in developing a process window for faster identification of optimum process parameters.\n\n\\section*{2 Experimental work}\nTi-6Al-4V pre-alloyed powder $(15-45 \\mu \\mathrm{m})$ supplied by LPW Technology Inc., Pittsburg, PA, USA, was used in the present study. The powder was characterized using SEM for examining the particle size, shape and distribution. An EOS M270 direct metal laser sintering (DMLS) system with $\\mathrm{Yb}$-fiber laser (nominal maximum power $200 \\mathrm{~W}$ ) was used to fabricate the single-track deposits and bulk sample parts. Experiments were performed with multiple combinations of laser power and scan speeds to produce singletrack deposits and bulk samples (Table 1). A layer thickness of $30 \\mu \\mathrm{m}$ was maintained for all the test samples.\n\nWhen a thin wall equivalent to the beam diameter is made, the laser will scan as one single line, and thus make a single line of deposit. It is known that support structures in an EOS system have a minimum smallest dimension of $100 \\mu \\mathrm{m}$ [18]. Therefore, single-track deposits can be produced utilizing line support structure settings. To achieve a single line deposit, thin wall sections with the dimension of $0.1 \\mathrm{~mm} \\times 0.1 \\mathrm{~mm} \\times 100 \\mathrm{~mm}$ were made using Materialise Magics software and placed at a height of $5 \\mathrm{~mm}$. Then support structures were generated under these thin wall sections/parts. It is to be noted that these thin walls are sacrificial parts and will be deleted once supports are generated. Then parameters (listed in Table 1) with various laser powers and scan speeds were applied to each of the single line supports. A Ti-6Al-4V alloy plate of $3.3 \\mathrm{~mm}$ was placed on the build platform, and then a layer of $30 \\mu \\mathrm{m}$ thick powder was spread. A single exposure laser scan was applied to scan one single layer. In this method, single-\n\nTable 1 Single-track deposits and bulk samples made with various powers and scan speeds\n\nLaser power (W)\n\n$50,100,150,195$\n\nScan speed $(\\mathrm{mm} / \\mathrm{s})$\n\n$500,750,1000,1200$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_02_28_5b6806184856c64a957ag-03}\n\\end{center}\n\nFig. 2 Photograph of the Ti-6Al-4V plate showing single-track deposits (note: single tracks appear as thin vertical lines)\n\ntrack deposits on a Ti-6Al-4V alloy plate (thickness $3.3 \\mathrm{~mm}$ ) were made. The single-track deposits were pre-set at $5 \\mathrm{~mm}$ distance apart. Single-track deposits of a length of $100 \\mathrm{~mm}$ were made on the Ti-6Al-4V plate. A photograph of the plate containing the single-track deposits is shown in Fig. 2. The single-track deposits were cut at $1 / 3,1 / 2$ and $2 / 3$ lengths (sections A, B, and C) for microscopy studies.", "start_char_idx": 9258, "end_char_idx": 13273, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "883f0d7a-64c9-4efb-a8b9-ff0bafbe571a": {"__data__": {"id_": "883f0d7a-64c9-4efb-a8b9-ff0bafbe571a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3b2cdb78-d366-4a62-ad12-9647c2bcf4cd", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d4944485a48c8a6daf872a0ed05d768309c6ab9dc04d4ba2a3b6c33eabb885af", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "851576e5-fc5f-43e1-a6d8-5356025f3038", "node_type": "1", "metadata": {}, "hash": "dd28ab4171357a00499afaff06161636b9dabf736cef3381967cfd344b25f1e3", "class_name": "RelatedNodeInfo"}}, "text": "2 Photograph of the Ti-6Al-4V plate showing single-track deposits (note: single tracks appear as thin vertical lines)\n\ntrack deposits on a Ti-6Al-4V alloy plate (thickness $3.3 \\mathrm{~mm}$ ) were made. The single-track deposits were pre-set at $5 \\mathrm{~mm}$ distance apart. Single-track deposits of a length of $100 \\mathrm{~mm}$ were made on the Ti-6Al-4V plate. A photograph of the plate containing the single-track deposits is shown in Fig. 2. The single-track deposits were cut at $1 / 3,1 / 2$ and $2 / 3$ lengths (sections A, B, and C) for microscopy studies. The top surface of the single line deposit was examined under a scanning electron microscope. Later, bulk samples $(10 \\mathrm{~mm} \\times 10 \\mathrm{~mm} \\times 5 \\mathrm{~mm})$ were built using the same set of parameters. The bulk samples were sectioned, polished, and etched with Keller's reagent. The bulk samples were characterized using optical microscopy for examining the porosity and microstructures. The amount of porosity in the samples was estimated as per ASTM E-562.\n\n\\section*{3 Results and discussion}\nTi-6Al-4V pre-alloyed powder was characterized using SEM. Figure 3a shows morphology and distribution of the powder particles. Particle size and distribution were determined by measuring the diameters of individual particles from several different micrographs. The particles have a particle size distribution between 15 and $45 \\mu \\mathrm{m}$. The powders showed spherical morphology with bi-modal size distribution. Figure $3 b$ shows a SEM micrograph revealing characteristic micro-dendritic features on the surface of powder particles. This phenomenon occurs due to nucleation and growth of dendrites in the powder particle during slow cooling occurring in atomization process [8].\n\nFig. 3 a A low magnification SEM micrograph of Ti-6Al-4V powder. b A high magnification SEM micrograph of powder particles\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_02_28_5b6806184856c64a957ag-04(1)}\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_02_28_5b6806184856c64a957ag-04}\n\n$1200 \\mathrm{~mm} / \\mathrm{s}$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_02_28_5b6806184856c64a957ag-04(2)}\n\nFig. 4 SEM images showing the top surface morphology of the single-track deposits\n\nThe top surface of the single line deposits was observed under SEM, and the results are presented in Fig. 4. The single-track deposit scanned with low laser power, and slow scan speed ( $50 \\mathrm{~W}$ and $500 \\mathrm{~mm} / \\mathrm{s}$ ) shows a continuous, and a uniform weld bead. Keeping the laser power constant $(50 \\mathrm{~W})$, with an increase in the scan speed the single-track deposit was noticed to become inconsistent and discontinuous $(1000 \\mathrm{~mm} / \\mathrm{s})$, and eventually resulting in fragmentation of tracks $(1200 \\mathrm{~mm} / \\mathrm{s})$, commonly referred to as balling [11]. Balling appears spherical in shape (as shown in Fig. 5, $50 \\mathrm{~W}, 1200 \\mathrm{~mm} / \\mathrm{s}$ ) and bulging upwards which is a result of the dominant surface tension forces of the molten alloy. When such a sets of parameters are applied to fabricate the bulk parts, they may result in a significant amount of porosity $[9,11]$. Keeping scan speed constant, and with an increase in the laser power, the single bead deposit shows an increase in width. This increase in the width is due to the higher intensity of the laser beam, which causes a higher volume of melting and results in a wider and deeper melt pool [11] (Fig. 6). In the case of single tracks deposited with a laser power of 100,150 , and $195 \\mathrm{~W}$, the bead width was observed to decrease with an increase in scan speed; however, balling phenomenon was not observed at these higher laser power settings.", "start_char_idx": 12703, "end_char_idx": 16483, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "851576e5-fc5f-43e1-a6d8-5356025f3038": {"__data__": {"id_": "851576e5-fc5f-43e1-a6d8-5356025f3038", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "883f0d7a-64c9-4efb-a8b9-ff0bafbe571a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "de1068c4f370dbef1b6808fb7ed1ef0601ab8b91138a1215dd5c2e58dc092226", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "91d78ea1-2e7b-4a9e-a719-2f0ce2084c26", "node_type": "1", "metadata": {}, "hash": "cdcd6d64f28704210176ad335cceb6b9b32a2799f17de22eb4c7dc31276ee169", "class_name": "RelatedNodeInfo"}}, "text": "When such a sets of parameters are applied to fabricate the bulk parts, they may result in a significant amount of porosity $[9,11]$. Keeping scan speed constant, and with an increase in the laser power, the single bead deposit shows an increase in width. This increase in the width is due to the higher intensity of the laser beam, which causes a higher volume of melting and results in a wider and deeper melt pool [11] (Fig. 6). In the case of single tracks deposited with a laser power of 100,150 , and $195 \\mathrm{~W}$, the bead width was observed to decrease with an increase in scan speed; however, balling phenomenon was not observed at these higher laser power settings.\n\nThe single-track deposits produced on a Ti-6Al-4V alloy plate were sectioned and prepared for microstructural\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_02_28_5b6806184856c64a957ag-05}\n\n\\section*{$1200 \\mathrm{~mm} / \\mathrm{s}$}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_02_28_5b6806184856c64a957ag-05(1)}\n\\end{center}\n\nFig. 5 Cross-section optical micrographs of the single-track deposits produced on a Ti-6Al-4V alloy plate using various parameter combinations\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_02_28_5b6806184856c64a957ag-06}\n\nFig. 6 Variation of melt pool geometry on process parameters a bead width, $\\mathbf{b}$ depth of penetration and $\\mathbf{c}$ depth-to-width ratio observations. The etched cross-sections were examined under an optical microscope, and the micrographs are presented in Fig. 5. The morphology, width, and depth of the single-track deposits can be clearly observed from the optical micrographs. At a power level of $50 \\mathrm{~W}$ and scan speed of $500 \\mathrm{~mm} / \\mathrm{s}$, the energy was sufficient to melt the powder and a small portion of the base plate $(10 \\mu \\mathrm{m})$. When the scan speed was increased, the depth of the melted region was observed to decrease and eventually resulted in balling, which can be observed for the single track made with $50 \\mathrm{~W}, 1200 \\mathrm{~mm} / \\mathrm{s}$. This phenomenon occurs due to the reduction in the energy density as the scan speed was increased according to Eq. 1 [10]. The melt pool depth was observed to increase significantly at lower scan speeds $(500 \\mathrm{~mm} / \\mathrm{s})$ and higher power levels particularly from $100 \\mathrm{~W}$ (depth: $45 \\mu \\mathrm{m}$ ) to $195 \\mathrm{~W}$ (depth: $176 \\mu \\mathrm{m}$ ). The melt pool geometry was observed to have a keyhole shape for the laser power of $195 \\mathrm{~W}$, whereas for $100 \\mathrm{~W}$ it was bowl shape. This remarkable change in melt pool shape with laser irradiation can be attributed to keyhole versus conduction modes of melting. For lower laser power, melting occurs by locally melting the alloy with heat transfer by conduction and convection inside the melt pool. In the later case, with a laser power of $195 \\mathrm{~W}$, melting of the alloy occurs by keyhole mode, giving rise to deeper penetration. Keyhole is always associated with vaporization of the alloy and in many cases results in entrapped pores in the melt pool [16]. The single tracks with the parameter combinations of: $100 \\mathrm{~W}-500 \\mathrm{~mm} / \\mathrm{s}$, $150 \\mathrm{~W}-500 \\mathrm{~mm} / \\mathrm{s}, 150 \\mathrm{~W}-750 \\mathrm{~mm} / \\mathrm{s}, 150 \\mathrm{~W}-$ $1000 \\mathrm{~mm} / \\mathrm{s}, 195 \\mathrm{~W}-1000 \\mathrm{~mm} / \\mathrm{s}$, and $195 \\mathrm{~W}-1200 \\mathrm{~mm} / \\mathrm{s}$, have moderate energy input and provide consistent melt pool shape with sufficient depth of penetration (two to three layers deep).", "start_char_idx": 15803, "end_char_idx": 19427, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "91d78ea1-2e7b-4a9e-a719-2f0ce2084c26": {"__data__": {"id_": "91d78ea1-2e7b-4a9e-a719-2f0ce2084c26", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "851576e5-fc5f-43e1-a6d8-5356025f3038", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "03ddb254521511cd7da37b37ebe194381cc2de49a509025e90498ebfa0c6dbfb", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b35de2b5-8b99-49fb-9dd2-b580390a6a2e", "node_type": "1", "metadata": {}, "hash": "1b01ee1b8820a3bfda2e3a443be2f248bd856de27294e6ce5fbee0e09def5884", "class_name": "RelatedNodeInfo"}}, "text": "Keyhole is always associated with vaporization of the alloy and in many cases results in entrapped pores in the melt pool [16]. The single tracks with the parameter combinations of: $100 \\mathrm{~W}-500 \\mathrm{~mm} / \\mathrm{s}$, $150 \\mathrm{~W}-500 \\mathrm{~mm} / \\mathrm{s}, 150 \\mathrm{~W}-750 \\mathrm{~mm} / \\mathrm{s}, 150 \\mathrm{~W}-$ $1000 \\mathrm{~mm} / \\mathrm{s}, 195 \\mathrm{~W}-1000 \\mathrm{~mm} / \\mathrm{s}$, and $195 \\mathrm{~W}-1200 \\mathrm{~mm} / \\mathrm{s}$, have moderate energy input and provide consistent melt pool shape with sufficient depth of penetration (two to three layers deep). These parameters above when used with a well-defined melt pool overlap could provide a window of optimum processing conditions to produce fully dense parts. It is worth noting that the heat affected zone size close to the melt pool also varies with the energy density applied.\n\nThe overall effect of process parameters on the width and depth of the single-track deposits is presented in Fig. 6. Laser power and scan speed have a significant effect on the single-track melt pool geometry. The results in Fig. 6a indicate for all power levels, an increase in scan speed shows a decrease in bead width. An increase in laser power results in an increase in the width, due to the increase in the energy density. The effect of process parameters on the depth of penetration can be observed from Fig. 6b. The results indicate that both laser power and scan speed significantly affect the amount of melting and the depth penetration. When the energy density is high (high power -low speed), the result shows a higher depth of penetration and melting up to $175 \\mu \\mathrm{m}$ (equivalent to six layers melted\\\\\nbeneath). The effect of process parameters on the depth-towidth ratio is presented in Fig. 6c. For depth-to-width ratios around 0.37 to 0.6 , it has at least $2-3$ layers melted below and can ensure proper welding with the substrate. SLM can be considered very similar to laser welding, with high power levels and slow scan speeds, and a conduction mode similar to welding/deposition occurs, resulting in a deeper melt pool $[11,16,19,20]$.\n\nBulk sample parts of dimensions $10 \\mathrm{~mm} \\quad \\times$ $10 \\mathrm{~mm} \\times 5 \\mathrm{~mm}$ were fabricated using the parameters listed in Table 1. The SLM-built sample parts were cut and prepared for microstructural studies. The polished and etched cross-section surfaces of the as-built bulk samples are presented in Fig. 7. The effect of process parameters on the porosity/density of the sample can be clearly observed in Fig. 7. The samples made with parameters $50 \\mathrm{~W}$ laser power and different scan speeds reveal irregular shape pores (dark) with sharp edges and also some unmelted powder particles in the micrographs. The porosity was observed to increase as the scan speed was increased. These results have a good match with the single-track melt pool observations. The sample with $100 \\mathrm{~W}$ laser power and $500 \\mathrm{~mm} / \\mathrm{s}$ scan speed resulted in full density, and as the scan speed was increased the porosity in the parts showed a rise due to insufficient melting of the powder. With the higher laser power levels, 150 and $195 \\mathrm{~W}$, a scan speed of $500 \\mathrm{~mm} / \\mathrm{s}$ showed round voids. The sample with $195 \\mathrm{~W}$ laser power showed larger pore sizes in the cross-section. The formation of porosity in the deposits could be derived from the keyhole-shaped melt pool that developed while high power parameters were used. High energy density causes the alloy to melt and vaporize in some local regions; since the process is dynamic and quick, the vapors cannot escape fully and become entrapped in the melt pool, resulting in pores (which appear round) in the deposit [16, 19-22].", "start_char_idx": 18817, "end_char_idx": 22635, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b35de2b5-8b99-49fb-9dd2-b580390a6a2e": {"__data__": {"id_": "b35de2b5-8b99-49fb-9dd2-b580390a6a2e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "91d78ea1-2e7b-4a9e-a719-2f0ce2084c26", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c1bd783691e534b8e6e891428f4b7900092b35a8f5a2cc4c7274288f9aa3e5e8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c00f226d-8c93-42f1-a25f-1ea88381fa36", "node_type": "1", "metadata": {}, "hash": "f8e870c6f566de3598a4cd11505d683d837333b84a3480d7bb10698f8152ad3f", "class_name": "RelatedNodeInfo"}}, "text": "With the higher laser power levels, 150 and $195 \\mathrm{~W}$, a scan speed of $500 \\mathrm{~mm} / \\mathrm{s}$ showed round voids. The sample with $195 \\mathrm{~W}$ laser power showed larger pore sizes in the cross-section. The formation of porosity in the deposits could be derived from the keyhole-shaped melt pool that developed while high power parameters were used. High energy density causes the alloy to melt and vaporize in some local regions; since the process is dynamic and quick, the vapors cannot escape fully and become entrapped in the melt pool, resulting in pores (which appear round) in the deposit [16, 19-22]. However, the pores when formed towards the top of the melt pool are not detrimental because re-melting causes gas to escape out of that layer during subsequent\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_02_28_5b6806184856c64a957ag-07}\n\nFig. 7 Cross-section optical micrographs of the bulk samples showing variation in porosity based upon process parameters\n\nTable 2 Calculated energy densities $\\left(\\mathrm{J} / \\mathrm{mm}^{3}\\right)$ for various parameters applied for producing bulk samples\n\n\\begin{center}\n\\begin{tabular}{lcccc}\n\\hline\nLaser power $(\\mathrm{W})$ & \\multicolumn{2}{l}{Scan speed $(\\mathrm{mm} / \\mathrm{s})$} &  & 1200 \\\\\n\\cline { 2 - 5 }\n & 500 & 750 & 1000 & 13 \\\\\n\\hline\n50 & 33 & 22 & 33 & 27 \\\\\n100 & 66 & 44 & 50 & 41 \\\\\n150 & 100 & 66 & 65 & 54 \\\\\n195 & 130 & 86 & 33 &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nlayer deposition. The pores formed deep inside, and in the lower end of the melt pool, are more detrimental $[9,11,15,19,22]$. Therefore, higher power and lower speed should be avoided for overcoming such adverse defects. The samples made with parameters: (i) $150 \\mathrm{~W}$ and scan speeds 750 and $1000 \\mathrm{~mm} / \\mathrm{s}$, and (ii) $195 \\mathrm{~W}$ and scan speeds 1000 and $1200 \\mathrm{~mm} / \\mathrm{s}$ were fully dense.\n\nThe energy density gives an estimate of the energy input to the SLM process. Energy density estimation applied in SLM is calculated by using Eq. 1 and the values are presented in Table 2. The effect of energy density on the porosity of the samples produced by SLM of Ti-6Al-4V is shown in Fig. 8. The energy densities applied below $50 \\mathrm{~J} /$ $\\mathrm{mm}^{3}$ show a significant amount of porosity due to insufficient melting of the powder particles, which could be conceived from the shape of the porosity and presence of sintered un-melted powder particles. The energy densities applied higher than $66 \\mathrm{~J} / \\mathrm{mm}^{3}$ also show some amount of porosity due to higher energy resulting in keyhole effects confirmed by the rounded shape of pores $[9,11,19,20,22]$. The red dotted region in the Fig. 8 with the energy density values between 50 and $66 \\mathrm{~J} / \\mathrm{mm}^{3}$ produced samples near to full density.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_02_28_5b6806184856c64a957ag-08}\n\\end{center}\n\nFig. 8 Plot showing variation of porosity with respect to energy density\\\\\nAs described earlier, in SLM material addition takes place due to layer-by-layer melting and solidification of a thin layer of spread powder. In this process, the laser beam also re-melts some portion of the layers beneath to ensure good bonding between the layers. The solidification of the alloy begins with the formation of a $\\beta$ nucleus, and the preexisting $\\beta$ grains partially undergo melting and serve as heterogeneous sites for nucleation. Thus, newly formed $\\beta$ will grow epitaxially in the build direction or opposite to the heat extraction $[15,23]$.", "start_char_idx": 22006, "end_char_idx": 25623, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c00f226d-8c93-42f1-a25f-1ea88381fa36": {"__data__": {"id_": "c00f226d-8c93-42f1-a25f-1ea88381fa36", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b35de2b5-8b99-49fb-9dd2-b580390a6a2e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7e77d72bc3b41a3c261929c328a8d5c8c132f5104e9c43205cc57653643e6f61", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "09115403-187e-4e31-b26b-7b43c554ec60", "node_type": "1", "metadata": {}, "hash": "4bcb7f831ee256aa782b78ebaa6148fe50350e6dfb22fdd8f3bc0a7357d31e64", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_02_28_5b6806184856c64a957ag-08}\n\\end{center}\n\nFig. 8 Plot showing variation of porosity with respect to energy density\\\\\nAs described earlier, in SLM material addition takes place due to layer-by-layer melting and solidification of a thin layer of spread powder. In this process, the laser beam also re-melts some portion of the layers beneath to ensure good bonding between the layers. The solidification of the alloy begins with the formation of a $\\beta$ nucleus, and the preexisting $\\beta$ grains partially undergo melting and serve as heterogeneous sites for nucleation. Thus, newly formed $\\beta$ will grow epitaxially in the build direction or opposite to the heat extraction $[15,23]$. In close similarity to the weld solidification, the solidifying $\\beta$ grains tend to orient towards the moving heat source (laser beam), resulting in a slightly tilted grain structure. Further, the $\\beta$ grain orientation in the deposit highly depends on the laser power, scanning strategy and scan speed applied. They define the amount of time available for the melt to solidify at any particular instance of time [24]. The solidified high-temperature $\\beta$ (bcc) phase is unstable at lower temperatures and will transform (below $M_{\\mathrm{s}}$ ) to a metastable phase, martensitic $\\alpha^{\\prime}$ (hcp) phase by a shear-diffusion less reaction since the cooling rates in SLM are high $\\left(10^{8}-10^{5} \\mathrm{~K} / \\mathrm{s}\\right)$ [17]. Hence, the final resultant microstructure will have coarse columnar grains, which are highly oriented towards the build direction with martensite $\\alpha^{\\prime}$ inside the grains $[10,17,25]$. Due to the inherent layerby-layer deposition method, as a new layer is being deposited a narrow region (heat affected zone) close to the melt pool boundary will reach temperatures above the transformation temperature $\\left(990^{\\circ} \\mathrm{C}\\right)$, and martensite $\\left(\\alpha^{\\prime}\\right)$ transforms back to the high-temperature $\\beta$ phase $[12,17,25]$. As the laser beam traverses away, the high-temperature $\\beta$ phase, under faster cooling conditions will transform to martensite $\\left(\\alpha^{\\prime}\\right)$. The martensite formed from re-heating of primary martensite $\\left(\\alpha^{\\prime}\\right)$ to $\\beta$ phase and transformed back to martensite will be from here on referred to as $\\alpha^{\\prime}{ }_{\\text {(secondary) }}$ and the heat affected regions (areas colored in blue Fig. 10) result in $\\alpha^{\\prime}$ (tertiary). In other words, as the build progresses, the layers will experience multiple thermal cycling effects which lead to the formation of alternate areas of martensite $\\alpha^{\\prime}$ (primary), $\\alpha^{\\prime}$ (secondary) and $\\alpha_{\\text {(tertiary) }}^{\\prime}$ in the entire part [17]. A schematic presented in Fig. 9 illustrates the evolution of microstructure in the selective laser melted Ti-6Al-4V alloy. Although it is difficult to draw a clear line between the three martensites $\\left(\\alpha_{\\text {(primary) }}^{\\prime}, \\alpha_{\\text {(secondary) }}^{\\prime}\\right.$ and $\\left.\\alpha_{\\text {(tertiary) }}^{\\prime}\\right)$ in the as-built part\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_02_28_5b6806184856c64a957ag-09}\n\\end{center}\n\n\\section*{Single-track}\n\\section*{Multi-layer}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_02_28_5b6806184856c64a957ag-09(1)}\n\\end{center}\n\n\\section*{Multi -track and multi-layer}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_02_28_5b6806184856c64a957ag-09(3)}\n\\end{center}\n\nFig.", "start_char_idx": 24870, "end_char_idx": 28506, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "09115403-187e-4e31-b26b-7b43c554ec60": {"__data__": {"id_": "09115403-187e-4e31-b26b-7b43c554ec60", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c00f226d-8c93-42f1-a25f-1ea88381fa36", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2f49d51ba76a06a26875f0a4e589313693ea48ad11b716540c44ffa8c18eed2d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7046d513-3823-4155-9577-8d56af239672", "node_type": "1", "metadata": {}, "hash": "e7970c05354867880151fc225c52cf2e3e5a66f60972bb722f00107eca3e500b", "class_name": "RelatedNodeInfo"}}, "text": "9 A schematic illustration of microstructural evolution in a single-track, multi-layer, and multi-track, multi-layer Ti-6Al-4V SLM deposit\n\nmicrostructures it is important to understand the microstructural evolution of the alloy during the SLM process. In summary, the part will have preferentially-oriented epitaxial grains with high aspect ratio, with martensite.\n\nA thermal simulation was also carried out for the parameter $195 \\mathrm{~W}$ and $1200 \\mathrm{~mm} / \\mathrm{s}$ to estimate the temperature distribution from the melt pool boundary into the deposit. The temperature distribution plot defines the peak temperatures experienced by the regions while a track of material is being deposited. Therefore, the regions exposed to a temperature above the $\\beta$ transus $\\left(990{ }^{\\circ} \\mathrm{C}\\right)$ represent the\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_02_28_5b6806184856c64a957ag-09(2)}\n\\end{center}\n\nFig. 10 Plot from simulated thermal cycle of the melt pool boundary during deposition of a single track of Ti-6Al-4V alloy in SLM extent of heat affected zone converting to $\\beta$. The theoretically calculated temperature profiles through simulations closely matched the experimentally observed values (20$25 \\mu \\mathrm{m}$ ). To obtain the temperature distribution within the heat affected zone, the equation of heat transfer has been used as shown below [26, 27].\n\n$\\rho C_{\\mathrm{v}} \\frac{\\partial T}{\\partial t}=K\\left(\\frac{\\partial T}{\\partial x}+\\frac{\\partial T}{\\partial y}+\\frac{\\partial T}{\\partial z}\\right)+Q$\n\nwhere $\\rho$ is the density, $C_{\\mathrm{v}}$ is heat capacity, $K$ is the heat conductivity, $T$ is the temperature, and $Q$ is the internal heat generation per unit volume which can be calculated by:\n\n$Q=\\int_{v} q \\mathrm{~d} v$.\n\nThe heat flux $q$ can be approximated by a Gaussian function of laser energy:\n\n$q(x, y)=\\frac{2 A P}{\\pi \\omega^{2}} e^{-\\frac{2\\left(\\omega_{x}^{2}+\\omega_{y}^{2}\\right)}{\\omega^{2}}}$\n\nwhere $A$ is the absorptivity of laser energy, $P$ is the laser power, $\\omega$ is the radius of the laser beam, and $\\omega_{x}$ and $\\omega_{y}$ are the distance between a point and the center of the laser beam in $x$ and $y$ directions. The temperature ' $T$ ' is solved along each time step of the single bead scan with the consideration of nonlinear temperature dependent Ti-6Al$4 \\mathrm{~V}$ thermo-physical properties. The solidus temperature of the alloy Ti-6Al-4V corresponding to the melt pool boundary is taken as $1873 \\mathrm{~K}\\left(1600{ }^{\\circ} \\mathrm{C}\\right)$ [12, 27]. The melt\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_02_28_5b6806184856c64a957ag-10}\n\nFig. 11 Typical optical micrographs of a vertical cross-section of the near full dense samples a $100 \\mathrm{~W}, 500 \\mathrm{~mm} / \\mathrm{s}, \\mathbf{b} 150 \\mathrm{~W}, 750 \\mathrm{~mm} / \\mathrm{s}, \\mathbf{c} 150 \\mathrm{~W}$, $1000 \\mathrm{~mm} / \\mathrm{s}, \\mathbf{d} 195 \\mathrm{~W}, 1000 \\mathrm{~mm} / \\mathrm{s}$ and e $195 \\mathrm{~W}, 1200 \\mathrm{~mm} / \\mathrm{s}$\n\npool shape is obtained by tracking the material state using 3DSIM FLEX simulation software which solves the thermal diffusion problem for a moving laser source step by step. The temperature is recorded and outputted from the center of a melt pool towards the transverse direction with respect to the laser scanning direction. The temperature distribution away from the melt pool is plotted as a function of distance from the melt pool, the plotted region is indicated in Fig. 11.\n\nThe optical micrographs of the samples close to full density are presented in Fig. 11.", "start_char_idx": 28507, "end_char_idx": 32141, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7046d513-3823-4155-9577-8d56af239672": {"__data__": {"id_": "7046d513-3823-4155-9577-8d56af239672", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "09115403-187e-4e31-b26b-7b43c554ec60", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6be7d8efe7ec3b4bad1815b546451bd42a2c5af3fdc35005981fee222f1ae20e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "78b68bfe-c119-454e-89c8-20a68953e260", "node_type": "1", "metadata": {}, "hash": "579121623d3b7ca593b5a6451bf6d0b4fe6aad45afd135b42236907111930bc7", "class_name": "RelatedNodeInfo"}}, "text": "The temperature is recorded and outputted from the center of a melt pool towards the transverse direction with respect to the laser scanning direction. The temperature distribution away from the melt pool is plotted as a function of distance from the melt pool, the plotted region is indicated in Fig. 11.\n\nThe optical micrographs of the samples close to full density are presented in Fig. 11. The microstructural features show coarse columnar grains with martensite $\\alpha^{\\prime}$. The prior $\\beta$ grains have their lengths running several millimeters, and the width of the grains was in the range of 80$200 \\mu \\mathrm{m}$. The cross-section micrograph of the sample built using $100 \\mathrm{~W}, 500 \\mathrm{~mm} / \\mathrm{s}$ showed minor amounts of rounded porosity $(0.4 \\%)$. The samples built using 150 and $195 \\mathrm{~W}$ produced fully dense parts. The width of the grains was observed to be wider in the case of slower scan speeds, i.e., the samples at the same $150 \\mathrm{~W}$ laser power with $750 \\mathrm{~mm} / \\mathrm{s}$ showed higher grain width when compared to $1000 \\mathrm{~mm} / \\mathrm{s}$ ones. A similar trend was observed for the samples built using $195 \\mathrm{~W}$ with the scan speeds of 1000 and $1200 \\mathrm{~mm} / \\mathrm{s}$.\n\n\\section*{4 Summary}\nThe present work focuses on the evolution of single-track melt pools and porosity in parts made using SLM of alloy Ti-Al6-4V. The single-track deposits were made using\\\\\nvarying laser power and scan speeds, and their effects on the melt pool morphology were studied. Microstructural studies on the melt pool cross-section show that at a low power level and high scan speed the width of the track reduces, gradually becomes discontinuous, and eventually results in balling. The depth of penetration of the melt pool was observed to increase with the lower scan speed. At higher power levels, in some cases a keyhole effect was observed.\n\nThe bulk parts produced using parameters similar to single-track deposits showed a direct correlation to the energy density applied and the porosity evolution in the process. Characterization of the cross-sections of the bulk parts demonstrates a good correlation between the singletrack melt pool geometry and porosity in the bulk parts. It was learned from this investigation that the process parameters with low energy density and high energy density both result in porosity in the parts, however, due to different reasons. The melt pool information of single-track deposits could be an aid to select a process window determining an optimum set of process parameters. SLM processing parameters with $150 \\mathrm{~W}, 750 \\mathrm{~mm} / \\mathrm{s}$ and $195 \\mathrm{~W}$, $1000 \\mathrm{~mm} / \\mathrm{s}$ and $1200 \\mathrm{~mm} / \\mathrm{s}$ result in well-defined bowlshaped melt pools and contribute to near fully dense parts. Therefore, these sets of parameters could be recommended to produce denser parts in the Ti-6Al-4V alloy using selective laser melting.\n\n\\section*{References}\n\\begin{enumerate}\n  \\item Gibson I, Rosen D, Stucker B (2010) Additive manufacturing technologies: rapid prototyping to direct digital manufacturing. Springer\n\n  \\item Rafi HK, Karthik NV, Gong H, Starr TL, Stucker BE (2013) Microstructures and mechanical properties of Ti6Al4V parts fabricated by selective laser melting and electron beam melting. J Mater Eng Perform 22(12):3872-3883\n\n  \\item Thompson SM, Bian L, Shamsaei N, Yadollahi A (2015) An overview of direct laser deposition for additive manufacturing; part i: transport phenomena, modeling and diagnostics. Addit Manuf 8:36-62\n\n  \\item Baufeld B, Van der Biest O, Dillien S (2010) Texture and crystal orientation in Ti-6Al-4V builds fabricated by shaped metal deposition. Metall Mater Trans A 41(8):1917-1927\n\n  \\item Wang F, Williams S, Colegrove P, Antonysamy AA (2013) Microstructure and mechanical properties of wire and arc additive manufactured Ti-6Al-4V.", "start_char_idx": 31748, "end_char_idx": 35690, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "78b68bfe-c119-454e-89c8-20a68953e260": {"__data__": {"id_": "78b68bfe-c119-454e-89c8-20a68953e260", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7046d513-3823-4155-9577-8d56af239672", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3f70f70ecea99ba98103fac33af1e444bef87fec14c20a637910aa277021f51a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "dd529538-3f8a-420f-8aa8-1ef2c890e87e", "node_type": "1", "metadata": {}, "hash": "e5a44d9c5bce1270556e72026e0dc7da2b7544f005f25504f139757181883831", "class_name": "RelatedNodeInfo"}}, "text": "J Mater Eng Perform 22(12):3872-3883\n\n  \\item Thompson SM, Bian L, Shamsaei N, Yadollahi A (2015) An overview of direct laser deposition for additive manufacturing; part i: transport phenomena, modeling and diagnostics. Addit Manuf 8:36-62\n\n  \\item Baufeld B, Van der Biest O, Dillien S (2010) Texture and crystal orientation in Ti-6Al-4V builds fabricated by shaped metal deposition. Metall Mater Trans A 41(8):1917-1927\n\n  \\item Wang F, Williams S, Colegrove P, Antonysamy AA (2013) Microstructure and mechanical properties of wire and arc additive manufactured Ti-6Al-4V. Metall Mater Trans A 44(2):968977\n\n  \\item Dilip JJS, Miyanaji H, Lassell A, Starr TL, Stucker B (2017) A novel method to fabricate TiAl intermetallic alloy 3D parts using additive manufacturing. Def Technol 13(2):72-76\n\n  \\item Dilip JJS, Janaki Ram GD (2014) Friction freeform fabrication of superalloy Inconel 718: prospects and problems. Metall Mater Trans A 45(1):182-192\n\n  \\item Elahinia M et al (2016) Fabrication of NiTi through additive manufacturing: a review. Prog Mater Sci 83:630-663\n\n  \\item Collings EW (1984) The physical metallurgy of titanium alloys. American Society for Metals, Technology \\& Engineering, Ohio\n\n  \\item Al-Bermani SS, Blackmore ML, Zhang W, Todd I (2010) The origin of microstructural diversity, texture, and mechanical properties in electron beam melted Ti-6A1-4V. Metall Mater Trans A 41(13):3422-3434\n\n  \\item Anam M, Dilip JJS, Pal D, Stucker B (2016) A short study on the fabrication of single track deposits in SLM and characterization. In: 27th Solid freeform fabrication symposium, Austin, Texas\n\n  \\item Gong H, Rafi K, Gu H, Starr T, Stucker B (2014) Analysis of defect generation in Ti-6Al- $\\mathrm{V}$ parts made using powder bed fusion additive manufacturing processes. Addit Manuf 1-4:87-98\n\n  \\item Gong H, Zeng K, Dilip JJS, Pal D, Stucker B (2014) Melt pool characterization for selective laser melting of Ti-6Al-4V pre-alloyed powder. In: Solid freeform fabrication symposium, University of Texas, Austin, pp 256-267\n\n  \\item Xu W, Sun S, Elambasseril J, Liu Q, Brandt M, Qian M (2015) Ti-6Al-4V additively manufactured by selective laser melting with superior mechanical properties. JOM 67(3):668-673\n\n  \\item Thijs L, Verhaeghe F, Craeghs T, Humbeeck JV, Kruth J-P (2010) A study of the microstructural evolution during selective laser melting of Ti-6Al-4V. Acta Mater 58(9):3303-3312\n\n  \\item Yang J, Han J, Yu H, Yin J, Gao M, Wang Z, Zeng X (2016) Role of molten pool mode on formability, microstructure and mechanical properties of selective laser melted Ti-6Al-4V alloy. Mater Des 110:558-570\n\n  \\item Yang J, Yu H, Yin J, Gao M, Wang Z, Zeng X (2016) Formation and control of martensite in Ti-6Al-4V alloy produced by selective laser melting. Mater Des 108:308-318\n\n  \\item Yang L, Gong H, Dilip JJS, Stucker B (2014) Solid freeform fabrication symposium, University of Texas, Austin, pp 714-731\n\n  \\item Svenungsson J, Choquet I, Kaplan AFH (2015) Laser welding process-a review of Keyhole welding modelling. Phys Proc 78:182-191\n\n  \\item Verhaeghe F, Craeghs T, Heulens J, Pandelaers L (2009) A pragmatic model for selective laser melting with evaporation.", "start_char_idx": 35116, "end_char_idx": 38313, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "dd529538-3f8a-420f-8aa8-1ef2c890e87e": {"__data__": {"id_": "dd529538-3f8a-420f-8aa8-1ef2c890e87e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "78b68bfe-c119-454e-89c8-20a68953e260", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0e4dac2f2f48bfc41010f5ed59a07f32cc60ca3bcd0bd148b6f3570bf96a8c61", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6dca1284-3721-4743-bd5e-1c2fc4d00ccd", "node_type": "1", "metadata": {}, "hash": "4904b87176bf8fa54a6668387f07700f162ce04326ddf4a476a099157032bd6c", "class_name": "RelatedNodeInfo"}}, "text": "Mater Des 110:558-570\n\n  \\item Yang J, Yu H, Yin J, Gao M, Wang Z, Zeng X (2016) Formation and control of martensite in Ti-6Al-4V alloy produced by selective laser melting. Mater Des 108:308-318\n\n  \\item Yang L, Gong H, Dilip JJS, Stucker B (2014) Solid freeform fabrication symposium, University of Texas, Austin, pp 714-731\n\n  \\item Svenungsson J, Choquet I, Kaplan AFH (2015) Laser welding process-a review of Keyhole welding modelling. Phys Proc 78:182-191\n\n  \\item Verhaeghe F, Craeghs T, Heulens J, Pandelaers L (2009) A pragmatic model for selective laser melting with evaporation. Acta Mater 57(20):6006-6012\n\n  \\item Akman E, Demir A, Canel T, Sinmaz\u00e7elik T (2009) Laser welding of Ti6Al4V titanium alloys. J Mater Process Technol 209(8):3705-3713\n\n  \\item Gao X-L, Zhang L-J, Liu J, Zhang J-X (2014) Porosity and microstructure in pulsed Nd:YAG laser welded Ti6Al4V sheet. J Mater Process Technol 214(7):1316-1325\n\n  \\item Kou S (2003) Welding metallurgy. Wiley, New Jersey\n\n  \\item Zhao X, Li S, Zhang M, Liu Y, Sercombe TB, Wang S, Hao Y, Yang R, Murr LE (2016) Comparison of the microstructures and mechanical properties of $\\mathrm{Ti}-6 \\mathrm{Al}-4 \\mathrm{~V}$ fabricated by selective laser melting and electron beam melting. Mater Des 95:21-31\n\n  \\item Kelly SM, Kampe SL (2004) Microstructural evolution in laserdeposited multilayer Ti-6Al-4V builds: part I. Microstructural characterization. Metall Mater Trans A 35(6):1861-1867\n\n  \\item Krieth F, Bohn MS (1986) Principles of heat transfer, 4th edn. Harper and row publishers, New York\n\n  \\item Teng C, Gong H, Szabo A, Dilip JJS, Ashby K, Zhang S, Patil N, Pal D, Stucker B (2016) Simulating melt pool shape and lack of fusion porosity for selective laser melting of cobalt chromium components. J Manuf Sci Eng 139(1):011009\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\\usepackage{multirow}\n\n\\title{Laser powder bed fusion of nickel alloy 625: Experimental investigations of effects of process parameters on melt pool size and shape with spatter analysis $^{\\text {\u06af\u0930}}$ }\n\n\n\\author{Luis E. Criales ${ }^{\\mathrm{a}}$, Yi\u011fit M. Ar\u0131soy ${ }^{\\mathrm{a}}$, Brandon Lane ${ }^{\\mathrm{b}}$, Shawn Moylan ${ }^{\\mathrm{b}}$, Alkan Donmez ${ }^{\\mathrm{b}}$,\\\\\nTu\u011frul \u00d6zel ${ }^{\\mathrm{a}, *}$}\n\\date{}", "start_char_idx": 37725, "end_char_idx": 40387, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "6dca1284-3721-4743-bd5e-1c2fc4d00ccd": {"__data__": {"id_": "6dca1284-3721-4743-bd5e-1c2fc4d00ccd", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "dd529538-3f8a-420f-8aa8-1ef2c890e87e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7079336dbc41c2e5d0fda4b0135d02f0080c06d0a216e01bda409ad9e4810153", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "48fab9dd-6557-4108-916d-7128d39297c1", "node_type": "1", "metadata": {}, "hash": "93a8d1fecd8e3c920618913e16d0b0525d1d59228b125d5808d544d7ec42a50e", "class_name": "RelatedNodeInfo"}}, "text": "\\author{Luis E. Criales ${ }^{\\mathrm{a}}$, Yi\u011fit M. Ar\u0131soy ${ }^{\\mathrm{a}}$, Brandon Lane ${ }^{\\mathrm{b}}$, Shawn Moylan ${ }^{\\mathrm{b}}$, Alkan Donmez ${ }^{\\mathrm{b}}$,\\\\\nTu\u011frul \u00d6zel ${ }^{\\mathrm{a}, *}$}\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\\DeclareUnicodeCharacter{0131}{$\\imath$}\n\n\\begin{document}\n\\maketitle\na Rutgers, The State University of New Jersey, Department of Industrial \\& Systems Engineering, NJ, USA\n\nb National Institute of Standards and Technology, Engineering Laboratory, Gaithersburg, MD, USA\n\n\\section*{A R T I C L E I N F O}\n\\section*{Keywords:}\nSelective laser melting\n\nPowder bed fusion\n\nNickel alloy\n\nMelt pool\n\nSpatter\n\n\\begin{abstract}\nA B S T R A C T Laser powder bed fusion (L-PBF) as an metal additive manufacturing process that can produce fully dense 3D structures with complex geometry using difficult-to-process metal powders such as nickel-based alloy 625 which is one of the choice of metal materials for fabricating components in jet engines and gas turbines due to its high strength at elevated temperatures. L-PBF process parameters and scan strategy affect the resultant built quality and structural integrity. This study presents experimental investigations of the effects of process parameters and scan strategy on the relative density, melt pool size and shape. Fabricated test coupons were analyzed with two objectives in mind: i) to determine how close each coupon was to fully dense and ii) to determine melt pool dimensions (width and depth) and shape for each coupon. The identification and definition of a dynamic melt pool has been performed, a condition which indicates that melt pool geometry is constantly changing as the laser scans and moves along a single track. In order to gain in-depth understanding of the laser fusion processing of powder material, an in-situ thermal camera video recording is performed and analyzed for meltpool size, spattering particles, and heating and cooling rates during processing of powder material nickel alloy 625. The results reveal in-depth process information that can be used for further validation of modeling studies and adopted for the industrial practice.\n\\end{abstract}\n\n\\section*{1. Introduction}\nMetal additive manufacturing technology is attractive with unique applications in various industries for replacement or customized parts with complex geometries and structures [11,12,27]. As a metal additive manufacturing process, laser powder bed fusion (L-PBF) or traditionally known as selective laser melting process is favorable in obtaining fully dense structures without a need for post processing [9,21]. Many research studies have been reported on its applications, process improvement and parameter optimization $[35,36,38,43]$ and numerical modeling to predict the temperature field, melting and evaporation $([13,14,29,30,37,40])$ and microstructure analysis and prediction $[2,41,42]$. However, L-PBF process requires relatively high energy density levels and lower scan velocities to successfully melt and fuse the powder metal material when compared to laser sintering processes $[15,25]$. Due to high energy intensities applied with the high power laser beam, there may be meltpool instabilities, issues related to material spattering and balling, rapid material evaporation and keyhole effects [34,38].", "start_char_idx": 40164, "end_char_idx": 44081, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "48fab9dd-6557-4108-916d-7128d39297c1": {"__data__": {"id_": "48fab9dd-6557-4108-916d-7128d39297c1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "6dca1284-3721-4743-bd5e-1c2fc4d00ccd", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "01c3feefa7586e036f2cc172e97ded513dbd95c457bb82613bdca19b3170fd98", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "13a2db25-269d-40f2-b01d-de9a94c169f6", "node_type": "1", "metadata": {}, "hash": "651e2a83f873232d9ee4058b4304c0d7da7ce12842797c459441b1c15646be6b", "class_name": "RelatedNodeInfo"}}, "text": "As a metal additive manufacturing process, laser powder bed fusion (L-PBF) or traditionally known as selective laser melting process is favorable in obtaining fully dense structures without a need for post processing [9,21]. Many research studies have been reported on its applications, process improvement and parameter optimization $[35,36,38,43]$ and numerical modeling to predict the temperature field, melting and evaporation $([13,14,29,30,37,40])$ and microstructure analysis and prediction $[2,41,42]$. However, L-PBF process requires relatively high energy density levels and lower scan velocities to successfully melt and fuse the powder metal material when compared to laser sintering processes $[15,25]$. Due to high energy intensities applied with the high power laser beam, there may be meltpool instabilities, issues related to material spattering and balling, rapid material evaporation and keyhole effects [34,38]. Resultant built part quality, structural integrity and residual stresses $[6,24]$ is also a major concern especially for additively manufactured parts in nickel alloy 718 or nickel alloy 625 that are considered for deployment in mission critical components in aerospace applications. After all these research studies, the influence of L-PBF process parameters on the quality measures such as density and process signatures such as meltpool shape and size is still not fully understood.\n\nIn literature, the overwhelmingly exploited quality measure is the density of the final part in addition to surface roughness and dimensional tolerances $[16-18,24]$. Meltpool geometry is also widely studied due to being a determinant of density and surface roughness [18,23].\n\\footnotetext{\\$5 Official contribution of the National Institute of Standards and Technology (NIST); not subject to copyright in the United States. The full descriptions of the procedures used in this paper require the identification of certain commercial products. The inclusion of such information should in no way be construed as indicating that such products are endorsed by NIST or are recommended by NIST or that they are necessarily the best materials, instruments, software or suppliers for the purposes described.\n\n\\begin{itemize}\n  \\item Correspondence to: Rutgers, The State University of New Jersey, 96 Frelinghuysen Road, Piscataway, NJ 08854, USA.\n\\end{itemize}\n\nE-mail address: \\href{mailto:ozel@rutgers.edu}{ozel@rutgers.edu} (T. \u00d6zel).\n}\n\nKamath [17] claim that small meltpool depths make the system inefficient by increasing the processing time. On the other hand, large meltpools may yield vaporization of the substrate and causes pores in the structure that increase porosity [26]. To assure a stable meltpool, the meltpool dimensions are not allowed be too small or too large in order to avoid irregularities or droplets [24]. O\u2019Regan et al. [28] classifies the parameters affecting such measures under four groups: feedstock, build environment, laser, and meltpool. Most of these parameters are predefined, that is, their values have to be adjusted before processing and some are controllable, that is, their values can be changed during processing. Lastly, some criteria are classified as undefined, that is, their values depend on other parameter adjustments. Control and optimization over L-PBF systems are achieved by changing predefined and controllable parameters. Even though laser power, scan velocity, hatch distance, and layer thickness have been known to be the most important parameters through experimentations, their relative importance are statistically analyzed in the recent study of Kamath [17]. According to this study, scan velocity is the most important parameters. A higher scan velocity causes the interaction between material and the laser beam to be short, which results in a narrow meltpool which also leads to rough surfaces, whereas decreasing the scan velocity causes excessive heating and vaporization. A very high scan velocity causes instability and droplet formation due to free cylindrical meltpool geometry. A very low scan velocity yields distortion and irregularities due to balling effect [18]. A low scan velocity is known to ensure a dense structure with the cost of rough surface. Hence, the optimal scan velocity is a trade-off between resultant density and surface quality [24].\n\nCriales et al. [7] analyzed the effects of varying laser power, scan velocity, and the packing density of the powder material for selective laser melting of nickel alloy Inconel 625 using finite element simulations. A sensitivity analysis has been conducted to investigate the influence of material properties and process parameters on the predicted temperature profile along the center of the laser beam path.", "start_char_idx": 43150, "end_char_idx": 47902, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "13a2db25-269d-40f2-b01d-de9a94c169f6": {"__data__": {"id_": "13a2db25-269d-40f2-b01d-de9a94c169f6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "48fab9dd-6557-4108-916d-7128d39297c1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "72af8b5892d8f4376d4055650f7d0f5d29be45ac7b0438b412c1bfee2f5f89f4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1eefff8f-1460-4694-bf1e-76c9852d2874", "node_type": "1", "metadata": {}, "hash": "739cb2982fc27edfe80c015e24e823536f5075beb904235ff9c026a5639e6610", "class_name": "RelatedNodeInfo"}}, "text": "A very high scan velocity causes instability and droplet formation due to free cylindrical meltpool geometry. A very low scan velocity yields distortion and irregularities due to balling effect [18]. A low scan velocity is known to ensure a dense structure with the cost of rough surface. Hence, the optimal scan velocity is a trade-off between resultant density and surface quality [24].\n\nCriales et al. [7] analyzed the effects of varying laser power, scan velocity, and the packing density of the powder material for selective laser melting of nickel alloy Inconel 625 using finite element simulations. A sensitivity analysis has been conducted to investigate the influence of material properties and process parameters on the predicted temperature profile along the center of the laser beam path. They found that the packing density (or porosity) significantly affects the temperature profile. The powder reflectivity has the greatest effect on the predicted peak temperature and melts pool geometry, followed by laser power and scanning speed. In a recent study, Arisoy et al. [5] investigated L-PBF of nearly fully dense nickel alloy 625 . They observed that L-PBF generates a microstructure through directional solidification that can be controlled by scan strategies and selection of process parameters. They provided experimental investigations on microstructure formation including sizes of cellular grains and growth directions of columnar grains on the test coupons. They analyzed the main effects of process parameters including laser power, scan velocity, hatch distance, and scan strategy that produce various solidification cooling rates and thermal gradients during the process, which also contributed to understanding of the resultant microstructure.\n\n\\section*{2. Laser powder bed fusion of nickel alloy 625}\nLaser powder bed fusion (L-PBF) is an additive manufacturing process that enables direct fabrication of three-dimensional (3D) parts from computer models by scanning regions of a powder bed using a high energy laser beam that selectively melts and fuses cross-sectional geometry on each layer followed by subsequent solidification according to active ASTM terminology [1]. In L-PBF, the powder material is completely melted and solidified with an aim to achieve fully dense parts. A traditional L-PBF set-up typically requires a high power laser source (Fig. 1). Some of the key advantages of L-PBF over other manufacturing techniques include: (i) high flexibility in manufacturing complex shapes, (ii) quick process setup avoiding the need for tooling, and (iii) broad choice of materials including high strength superalloys. These advantages allow for quick transition between manufacturing products of different geometries within the same station.\n\nThe most attractive feature of L-PBF is the ability to use this process to produce highly complex geometries and structures that would normally not even be feasible using conventional production techniques. However, L-PBF has several major disadvantages: the laser heating process is known for its rapid heating times and unpredictable cooling times, which result in high localized residual stress, nonhomogeneous and anisotropic microstructure and material properties, as well as the formation of gas pores and voids in the microstructure, which often lead to reduced material density and mechanical properties such as strength, hardness, toughness, and fatigue resistance. Other than common concern of lack of fusion or gas induced porosity, dealing with structural defects such as residual stress, delamination, cracking are major challenges in L-PBF. The scan strategy, process temperature, powder mixture, build chamber atmosphere and many other inputs determine the occurrence and quantity of such defects [33].\n\nIn L-PBF, laser characteristics, process parameters, and material properties must be studied jointly to obtain a better understanding of the laser processing of powder metal materials. Laser characteristics are unique to the laser equipment such as maximum power, wavelength, beam spot diameter (or size), and beam energy distribution and usually cannot be modified by the end user. However, L-PBF involves a set of processing parameters that can be modified such as laser power $(P)$, scan velocity $\\left(v_{s}\\right)$, hatch distance $(h)$, stripe width $(w)$, and layer thickness (s) as shown in Fig. 2 and scan strategy rotation (SSR) as shown in Fig. 3.\n\nIn the L-PBF process, consecutive layers are built by processing powder material with a pre-specified powder layer thickness. These consecutive layers are processed slightly differently to ensure a robust build. More specifically, stripe orientation changes from layer to layer by a set margin. Two scan strategies available are a) $90^{\\circ}$ counter clockwise rotation, and b) $67^{\\circ}$ counter clockwise rotation between consecutive layers. Fig. 3 illustrates this concept for both of these laser scan strategies.", "start_char_idx": 47102, "end_char_idx": 52082, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1eefff8f-1460-4694-bf1e-76c9852d2874": {"__data__": {"id_": "1eefff8f-1460-4694-bf1e-76c9852d2874", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "13a2db25-269d-40f2-b01d-de9a94c169f6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4f1c8c3e839cfd84b6c2446505b313c58b657be0cff6602052675c44c00c5c46", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "4e0bc1b2-21c9-45f0-b2d3-8701ab6eb950", "node_type": "1", "metadata": {}, "hash": "922005553f506ca50efc37dea54944a82dd675b828b7d8a2fcaeafc5136ab35d", "class_name": "RelatedNodeInfo"}}, "text": "However, L-PBF involves a set of processing parameters that can be modified such as laser power $(P)$, scan velocity $\\left(v_{s}\\right)$, hatch distance $(h)$, stripe width $(w)$, and layer thickness (s) as shown in Fig. 2 and scan strategy rotation (SSR) as shown in Fig. 3.\n\nIn the L-PBF process, consecutive layers are built by processing powder material with a pre-specified powder layer thickness. These consecutive layers are processed slightly differently to ensure a robust build. More specifically, stripe orientation changes from layer to layer by a set margin. Two scan strategies available are a) $90^{\\circ}$ counter clockwise rotation, and b) $67^{\\circ}$ counter clockwise rotation between consecutive layers. Fig. 3 illustrates this concept for both of these laser scan strategies.\n\nIn L-PBF, the laser beam spot diameter is considered fixed (e.g., $d=100 \\mu \\mathrm{m}$ ) with uniform or near Gaussian beam energy distribution, but laser power, scan velocity, hatch distance, and layer thickness can be altered to a desired energy density setting, which affect the resultant melt pool geometry, heat affected area, quality of fusion, cooling rate, formation of solidification microstructure on the powder bed. The effects of these process parameter settings together with powder material characteristics on the variations of the resultant part quality in terms of density, material properties, dimensional quality, surface roughness, and defects are not well understood.\n\n\\section*{3. Experimental design}\nAn EOS M270 ${ }^{1}$ Direct Metal Laser Sintering (DMLS) machine was utilized for processing of experimental test coupons. This machine has a single-mode, continuous wave (CW) ytterbium fiber laser with maximum power of $200 \\mathrm{~W}$. An adequate quantity of commercial additive manufacturing grade nickel alloy 625 powder produced by gas atomized process with the average particle size of $35 \\mu \\mathrm{m}$ was used and solid coupons in the shape of cubes $(16 \\mathrm{~mm} \\times 16 \\mathrm{~mm} \\times 15 \\mathrm{~mm}$ ) were manufactured using an EOS M270 DMLS machine under nitrogen gas ambience at the National Institute for Standards \\& Technology (NIST) facility located in Gaithersburg, Maryland, USA. The powder material with -325 mesh size (particles that measure less than $44 \\mu \\mathrm{m}$ ) and atomized spherical morphology has a particle distribution of D60\\% $=29.4 \\mu \\mathrm{m}, \\mathrm{D} 10 \\%=13.5 \\mu \\mathrm{m}$, and $\\mathrm{D} 90 \\%=43.0 \\mu \\mathrm{m}$. The chemical composition of the powder material in wt\\% was reported as follows: $\\mathrm{Cr}$ $21.01 \\%$, Fe $0.85 \\%$, Mo $8.77 \\%$, Nb $3.35 \\%$, C $0.02 \\%$, Mn $0.36 \\%$, Si\n\\footnotetext{${ }^{1}$ Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.\n}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-03(2)}\n\\end{center}\n\nFig. 1. The laser powder bed fusion system (Direct Metal Laser Sintering by EOS GmbH).\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-03}\n\\end{center}\n\nFig. 2. L-PBF terminology [7].\n\n$0.39 \\%$, P $0.005 \\%$, S $0.003 \\%$, Al $0.1 \\%$, Ti $0.1 \\%$, Co $0.1 \\%$ and Ni-balance.\n\nExperiments were designed to establish a relationship between process parameters and part quality. During the experimental design phase, sets of process parameters to create test coupons were selected from a family of response surface methodology (RSM) design.", "start_char_idx": 51284, "end_char_idx": 55090, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "4e0bc1b2-21c9-45f0-b2d3-8701ab6eb950": {"__data__": {"id_": "4e0bc1b2-21c9-45f0-b2d3-8701ab6eb950", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1eefff8f-1460-4694-bf1e-76c9852d2874", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c72e3d2f954bca52a1288ce180fa4f0b57fe5aca321c3e569a8915667d2384b2", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "baf26542-c9ae-4597-b200-1fcfcf5461fd", "node_type": "1", "metadata": {}, "hash": "fb2bf6cdb9e21e2d801d1a76ce16d2823a7a546fc74080ff610c4a56da477d79", "class_name": "RelatedNodeInfo"}}, "text": "1. The laser powder bed fusion system (Direct Metal Laser Sintering by EOS GmbH).\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-03}\n\\end{center}\n\nFig. 2. L-PBF terminology [7].\n\n$0.39 \\%$, P $0.005 \\%$, S $0.003 \\%$, Al $0.1 \\%$, Ti $0.1 \\%$, Co $0.1 \\%$ and Ni-balance.\n\nExperiments were designed to establish a relationship between process parameters and part quality. During the experimental design phase, sets of process parameters to create test coupons were selected from a family of response surface methodology (RSM) design. There were two limitations that restricted experimental design selection: i) a maximum of 36 test coupons could be fabricated due to size constraints in the build platform of the L-PBF machine, and ii) hatch distance could only be increased or decreased in intervals of $0.01 \\mathrm{~mm}$. The first limitation eliminated the possibility of a three-level factorial design for three factors and two scan strategies, which would require a minimum of 54 treatments. The second limitation greatly reduced the applicability of Box-Wilson central composite design types [32], which require high resolution in between levels. Therefore, machine rounding error while input of process settings would have significantly altered the outcome of Box-Wilson type designs. Another alternative, the BoxBehnken design, offered an advantage by requiring comparatively fewer number of runs while maintaining rotatability. The Box-\\\\\nBehnken design for three factors is based on considering process parameter combinations at the midpoints of the edges of the process space cube, as well as at the center. Therefore, three levels of each factor are considered. These low, medium, and high levels for each factor are defined as: $P=169 \\mathrm{~W}, 182 \\mathrm{~W}$, and $195 \\mathrm{~W}, v_{\\mathrm{s}}=725 \\mathrm{~mm} / \\mathrm{s}$, $800 \\mathrm{~mm} / \\mathrm{s}$, and $875 \\mathrm{~mm} / \\mathrm{s}$, and $h=0.09 \\mathrm{~mm}, 0.10 \\mathrm{~mm}$, and $0.11 \\mathrm{~mm}$. Additionally, we define energy density as the amount of energy applied to the powder bed per unit volume. Energy density is then a function of laser power $(P)$, scan velocity $\\left(v_{s}\\right)$, hatch distance $(h)$, and layer thickness (s), as given in Eq. (1).\n\n$E=\\frac{P}{v_{s} \\bullet h \\bullet s}$\n\nThe range for each factor was selected so that resulting energy density for all sets fell within the calculated limits [3] that showed acceptable builds. Three additional coupons were built at the \"default settings\" for control purposes. The powder layer thickness is kept constant at $s=20 \\mu \\mathrm{m}$.\n\nThe test coupons fabricated using these parameter settings are $16 \\mathrm{~mm} \\times 16 \\mathrm{~mm}$ at the base, and $15 \\mathrm{~mm}$ in height. The final height of the coupons is less than $15 \\mathrm{~mm}$, as wire electrical discharge machining (w-EDM) is used to separate the built coupons from the platform, and some of the coupon remains attached to the platform. $16 \\mathrm{~mm}$ was selected as the width and length of the coupons so that each processed layer of powder is composed of four 4-mm wide stripes. Stripe overlap, defined as the area of material in which laser scanning overlaps by consecutive stripes, is $0.1 \\mathrm{~mm}$. Therefore, total stripe width is $4.1 \\mathrm{~mm}$. At first, a set of 18 coupons were fabricated using $90^{\\circ}$ rotation in scanning direction (stripe orientation) between layers. A second set of coupons, following the same experimental design as the first set, was processed using the default scanning rotation (stripe orientation) setting of the L-PBF machine, which is estimated to be an approximately $67^{\\circ}$ rotation.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_52a85307004f6d652296g-03(1)}\n\nFig. 3.", "start_char_idx": 54516, "end_char_idx": 58346, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "baf26542-c9ae-4597-b200-1fcfcf5461fd": {"__data__": {"id_": "baf26542-c9ae-4597-b200-1fcfcf5461fd", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "4e0bc1b2-21c9-45f0-b2d3-8701ab6eb950", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2709ab0b1b581fdb84770411745a2f6cec2ebcdb85a1ff6485ed2f237ad5d22f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "66574bf7-1e4a-49eb-8cbd-d71a3ffaa035", "node_type": "1", "metadata": {}, "hash": "e1a2e5cd8cf2a50b4f0f22330731c3cf2687619a1112a3cf1803e019ce2726da", "class_name": "RelatedNodeInfo"}}, "text": "Stripe overlap, defined as the area of material in which laser scanning overlaps by consecutive stripes, is $0.1 \\mathrm{~mm}$. Therefore, total stripe width is $4.1 \\mathrm{~mm}$. At first, a set of 18 coupons were fabricated using $90^{\\circ}$ rotation in scanning direction (stripe orientation) between layers. A second set of coupons, following the same experimental design as the first set, was processed using the default scanning rotation (stripe orientation) setting of the L-PBF machine, which is estimated to be an approximately $67^{\\circ}$ rotation.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_52a85307004f6d652296g-03(1)}\n\nFig. 3. Schematic of a stripe scan pattern with $90^{\\circ}$ (left) and $67^{\\circ}$ (right) CCW rotation between consecutively built layers [4].\n\n\\section*{4. Measurement of relative density}\nBoth sets of coupons, built with $90^{\\circ}$ and $67^{\\circ}$ scanning rotation between layers, were measured for size and mass to determine the density of each coupon. The objective is to determine how close each coupon was to fully dense. For this purpose, relative density is defined as shown in Eq. (2).\n\n$\\rho_{\\text {rel }}=\\frac{\\rho_{\\text {coupon }}}{\\rho_{\\text {bulk }}} \\times 100 \\%=\\frac{m / V}{\\rho_{\\text {bulk }}} \\times 100 \\%$\n\nwhere $m$ and $V$ are the mass and the volume of the coupon, respectively, and $\\rho_{\\text {bulk }}$ is the density of solid nickel alloy 625 . The mass of the coupon was calculated using a weighing scale with an accuracy of $0.001 \\mathrm{gr}$. The mass was measured five times for each coupon, which provides an average (29.623-30.255 gr) and standard deviation (0.004-0.008 gr). The volume of the coupon was calculated by measuring the length, width, and height of the coupon using a Coordinate Measurement Machine (CMM) with accuracy of $5 \\mu \\mathrm{m}$, resolution of $0.25 \\mu \\mathrm{m}$, and uncertainty of $2.5 \\mu \\mathrm{m}$. Similarly, multiple measurements of each dimension were taken to find the average volume (3592.16-3643.65 mm\u00b3). The bulk density of nickel alloy 625 is $8.440 \\mathrm{~g} / \\mathrm{cm}^{3}$. Relative density values are summarized in Table 1 . It should be noted that he uncertainty of measured density is about $20 \\mathrm{mg} / \\mathrm{cm}^{3}$ and the uncertainty in calculated relative density is about $0.3 \\%$.\n\n\\section*{5. Measurement and analysis of melt pool marks}\nMelt pool marks can be analyzed to determine important information regarding melt pool geometry. Melt pool geometry data is classified into two types: melt pool dimensions (width/depth) and melt pool shape.\n\n\\subsection*{5.1. Measurement of melt pool width and depth}\nMelt pool width and depth can be measured via digital optical microscopy (DOM) of the planes that allow a cross-sectional view of the melt pool, i.e., XZ and YZ. However, it should be noted that there is difficulty in measuring melt pool marks using microscope images especially with the depth measurements on multi-layer parts. It is certain that the subsequent layer will re-melt some of the recently processed layer, likely obscuring some of the melt pool marks and\n\nTable 1\n\nProcess parameters, energy density, and measured relative density.", "start_char_idx": 57687, "end_char_idx": 60908, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "66574bf7-1e4a-49eb-8cbd-d71a3ffaa035": {"__data__": {"id_": "66574bf7-1e4a-49eb-8cbd-d71a3ffaa035", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "baf26542-c9ae-4597-b200-1fcfcf5461fd", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b782ce1fb73a61def436881b8d24de6afceb538734491748c0711260bae1b462", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a6c902f9-c6d5-4870-a3d5-c3d01832f8e4", "node_type": "1", "metadata": {}, "hash": "d12fe186b7c65a404cf54ef83960fd751b43b728f8eba9a6f5115a385f920b11", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{5. Measurement and analysis of melt pool marks}\nMelt pool marks can be analyzed to determine important information regarding melt pool geometry. Melt pool geometry data is classified into two types: melt pool dimensions (width/depth) and melt pool shape.\n\n\\subsection*{5.1. Measurement of melt pool width and depth}\nMelt pool width and depth can be measured via digital optical microscopy (DOM) of the planes that allow a cross-sectional view of the melt pool, i.e., XZ and YZ. However, it should be noted that there is difficulty in measuring melt pool marks using microscope images especially with the depth measurements on multi-layer parts. It is certain that the subsequent layer will re-melt some of the recently processed layer, likely obscuring some of the melt pool marks and\n\nTable 1\n\nProcess parameters, energy density, and measured relative density.\n\n\\begin{center}\n\\begin{tabular}{llllll}\n\\hline\n\\begin{tabular}{l}\nLaser \\\\\nPower, \\\\\n$\\boldsymbol{P}[\\mathbf{W}]$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nScan \\\\\nVelocity, \\\\\n$\\boldsymbol{v}_{\\mathbf{s}}[\\mathbf{m m} /$ \\\\\n$\\mathbf{s}$ ] \\\\\n\\end{tabular} & \\begin{tabular}{l}\nHatch \\\\\nDistance, \\\\\n$\\boldsymbol{h}[\\mathbf{m m}]$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nEnergy \\\\\nDensity, \\\\\n$\\boldsymbol{E}[\\mathbf{J} /$ \\\\\n$\\left.\\mathbf{m m}^{\\mathbf{3}}\\right]$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nRelative \\\\\nDensity \\\\\n$\\left(\\mathbf{S S R}=\\mathbf{6 7}^{\\circ}\\right)$, \\\\\n$\\boldsymbol{\\rho}_{\\mathbf{r e l}}[\\%]$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nRelative \\\\\nDensity \\\\\n$\\left(\\mathbf{S S R}=\\mathbf{9 0}{ }^{\\circ}\\right.$ ), \\\\\n$\\boldsymbol{\\rho}_{\\mathbf{r e l}}[\\%]$ \\\\\n\\end{tabular} \\\\\n\\hline\n$\\mathbf{1 6 9}$ & 875 & 0.10 & 96.57 & 95.23 & 96.00 \\\\\n$\\mathbf{1 9 5}$ & 875 & 0.10 & 111.43 & 98.30 & 98.70 \\\\\n$\\mathbf{1 8 2}$ & 875 & 0.09 & 115.56 & 97.03 & 97.40 \\\\\n$\\mathbf{1 8 2}$ & 725 & 0.11 & 114.11 & 95.97 & 96.17 \\\\\n$\\mathbf{1 9 5}$ & 800 & 0.11 & 110.80 & 98.47 & 98.52 \\\\\n$\\mathbf{1 8 2}$ & 725 & 0.09 & 139.46 & 97.14 & 97.29 \\\\\n$\\mathbf{1 8 2}$ & 800 & 0.10 & 113.75 & 98.10 & 98.21 \\\\\n$\\mathbf{1 8 2}$ & 800 & 0.10 & 113.75 & 98.05 & 98.19 \\\\\n$\\mathbf{1 9 5}$ & 725 & 0.10 & 134.48 & 97.50 & 97.74 \\\\\n$\\mathbf{1 8 2}$ & 800 & 0.10 & 113.75 & 98.13 & 98.30 \\\\\n$\\mathbf{1 8 2}$ & 875 & 0.11 & 94.55 & 96.50 & 96.75 \\\\\n$\\mathbf{1 6 9}$ & 725 & 0.10 & 116.55 & 96.38 & 96.52 \\\\\n$\\mathbf{1 6 9}$ & 800 & 0.09 & 117.36 & 97.50 & 97.91 \\\\\n$\\mathbf{1 6 9}$ & 800 & 0.11 & 96.02 & 96.60 & 96.78 \\\\\n$\\mathbf{1 9 5}$ & 800 & 0.09 & 135.42 & 99.01 & 99.23 \\\\\n$\\mathbf{1 9 5}$ & 800 & 0.10 & 121.88 & 98.64 & 98.86 \\\\\n$\\mathbf{1 9 5}$ & 800 & 0.10 & 121.88 & 98.53 & 98.75 \\\\\n$\\mathbf{1 9 5}$ & 800 & 0.10 & 121.88 & 98.69 & 98.81 \\\\\n &  &  &  &  &  \\\\\n\\end{tabular}\n\\end{center}\n\nincreasing uncertainty in these depth measurements.", "start_char_idx": 60037, "end_char_idx": 62855, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a6c902f9-c6d5-4870-a3d5-c3d01832f8e4": {"__data__": {"id_": "a6c902f9-c6d5-4870-a3d5-c3d01832f8e4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "66574bf7-1e4a-49eb-8cbd-d71a3ffaa035", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b71bedb2724e52ad085c4487b0e11ad22686736a16f363b2ed7a081b0e3c8cbf", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "93e246be-0065-4e0d-97e7-704ec9c02bcb", "node_type": "1", "metadata": {}, "hash": "909065dc439b435ad4a8f9327098553fb6d21da949dfb183c7d6580d723d413c", "class_name": "RelatedNodeInfo"}}, "text": "Nevertheless, images were taken using a progressive scan digital microscope equipped with CMOS image sensor. Image size is $1600(\\mathrm{H})$ pixels $\\times 1200(\\mathrm{~V})$ pixels. The length of the melt pool at any specific time cannot be measured due to the continuous nature of the laser scanning process. Therefore, one single continuous track can be observed in the $x$-direction, as shown in Fig. 4a. Due to the $90^{\\circ}$ scanning strategy between layers, $\\mathrm{XZ}$ and $\\mathrm{YZ}$ become interchangeable when analyzing melt pool dimension. Melt pool width and depth can be measured every other layer due to the change in orientation of the scanning direction, which allows a view of the cross-section of the melt pool every other layer (Fig. 4b). It should be noted that the images given in Fig. 4 are used in explaining the processing of tracks and layers in L-PBF and they are not used in taking measurements of melt pool dimensions.\n\nIn order to obtain images where the melt pools could be measured, three of the coupon faces corresponding to XY-, XZ-, and YZ-plane, were electro-polished a total of $50 \\mu \\mathrm{m}$ deep. Therefore, melt pool measurements were taken at a cross-section very close to the edge of the coupon (see Fig. 5).\n\nNote that points A, B, and C will represent consecutive melt pools observed in an image taken of the YZ-plane. The distance between A-B and $\\mathrm{B}-\\mathrm{C}$ is the same, and equivalent to one hatch distance. However, there is a discrepancy between the time necessary for the laser to arrive at point $\\mathrm{B}$ from point $\\mathrm{A}$, and the time required to reach point $\\mathrm{C}$ from point B. Assuming that the laser off-time between hatches is $0.042 \\mathrm{~ms}$ measured during coupon building using a high speed camera at 24,000 frames/s, and the scan velocity is $800 \\mathrm{~mm} / \\mathrm{s}$ for a $4 \\mathrm{~mm}$ stripe width, it follows that:\n\n$t_{A B} \\approx \\frac{2 w}{v}=\\frac{2(4 \\mathrm{~mm})}{800 \\mathrm{~mm} / \\mathrm{s}}=10 \\mathrm{~ms}$\n\n$t_{B C} \\approx$ laser off time $=0.042 \\mathrm{~ms}$\n\nTherefore, it takes approximately $10 \\mathrm{~ms}$ longer for the laser to reach the same $x$-coordinate location on consecutive hatches, depending on whether this particular location of interest constitutes the beginning or the end of a scanned hatch. This difference in time is considerable, because it allows the local powder material to cool about $10 \\mathrm{~ms}$ and has an effect on the melt pool dimensions, as shown next.\n\nTwo different sizes of melt pools were observed due to the characteristics of the laser scanning process described previously: i) a Type I melt pool, where the area being processed (points A and C in Figs. 5 and 6) is still within the heat-affected zone of the previous hatch scanning, and ii) a type II melt pool, where the area currently being processed (location B in Figs. 5 and 6) is no longer affected by the heat from the laser scanning of the previous hatch or track.\n\nType I and Type II melt pools can be formally defined as follows: in an YZ-plane at a specific $x$-location ( $x$ is fixed), the time elapsed between two consecutive passes of the laser footprint through this plane will vary as a function of $x$. For locations very close to the stripe boundaries, the difference in time elapsed is the largest. This leads to different sized melt-pools along this particular YZ-plane. The size of the melt pool will depend on the scanning direction. Melt pools at a location at the beginning of the stripe will be larger (Type I) and melt pools at a location at the end of a processed stripe will be smaller (Type II). The difference in melt pool sizes can be attributed to the presence of a heat-affected zone (HAZ) and rapid cooling times. Digital optical microscopy imaging and thermal camera imaging were used to corroborate these results.\n\nA digital optical microscope was utilized to obtain images of the electro-polished surfaces from which the melt pool width and depth were measured.", "start_char_idx": 62856, "end_char_idx": 66889, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "93e246be-0065-4e0d-97e7-704ec9c02bcb": {"__data__": {"id_": "93e246be-0065-4e0d-97e7-704ec9c02bcb", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a6c902f9-c6d5-4870-a3d5-c3d01832f8e4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f2346e7ec6fa0eb0faf60ee63f5233aecf152de64486d3de42712c51463b0be4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c8ee89a4-df83-4c36-9ef5-2ae10eb395b4", "node_type": "1", "metadata": {}, "hash": "6b084a7ce02a1d96f4ff0367146432d3ae91f474c28f74c736b542f1d996b377", "class_name": "RelatedNodeInfo"}}, "text": "For locations very close to the stripe boundaries, the difference in time elapsed is the largest. This leads to different sized melt-pools along this particular YZ-plane. The size of the melt pool will depend on the scanning direction. Melt pools at a location at the beginning of the stripe will be larger (Type I) and melt pools at a location at the end of a processed stripe will be smaller (Type II). The difference in melt pool sizes can be attributed to the presence of a heat-affected zone (HAZ) and rapid cooling times. Digital optical microscopy imaging and thermal camera imaging were used to corroborate these results.\n\nA digital optical microscope was utilized to obtain images of the electro-polished surfaces from which the melt pool width and depth were measured. All the images utilized for analysis were captured in 1600 pixel $\\times 1200$ pixel resolution and $500 \\times$ magnification. The images were measured using a built-in scale provided by the optical microscope, as seen in the lower right corner of Fig. 7.\n\nFirst, the number of pixels that makes up the length of the scale\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-05}\n\\end{center}\n\n(a) $\\mathrm{XY}$ view\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-05(2)}\n\\end{center}\n\n(b) YZ view\n\nFig. 4. Views of Coupon 35 surfaces ( $P=195 \\mathrm{~W}, v_{s}=800 \\mathrm{~mm} / \\mathrm{s}, h=0.1 \\mathrm{~mm}$ ). (a) XY view (b) YZ view.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_52a85307004f6d652296g-05(1)}\n\nFig. 5. Location of electro-polished surface relative to XY-plane.\n\n$(100 \\mu \\mathrm{m})$ was counted to obtain a pixel-to- $\\mu \\mathrm{m}$ conversion ratio. Then, the width and depth of the melt pools were measured by drawing colorcoded lines on the images and counting the number of pixels spanned by each individual line. Then, the measurements were converted to micrometers using the conversion ratio $(0.4184 \\mu \\mathrm{m} /$ pixel $)$. The width of Type I and Type II melt pools were marked using red (RGB=255-00 ) and blue ( $\\mathrm{RGB}=0-0-255)$, respectively (see Fig. $7 \\mathrm{a}$ and b). A subjectivity error of a few pixels should be noted when selecting the melt pool boundary, which leads to a Type-B uncertainty of $u_{M P}=(0.4184 \\mu \\mathrm{m} / \\mathrm{pixel}) \\square$ (3 pixels $)=1.2552 \\mu \\mathrm{m}$ for each length measurement by assuming a $67 \\%$ probability that the melt pool boundaries exist within 3 pixel of the points selected (1.5 pixel per boundary) [31].\\\\\nA Matlab code was then used to automatically detect the colored lines and obtain the width and depth of each individual marked melt pool using the scale as a reference. While each melt pool is measured only once for each image, multiple optical images of each coupon were analyzed following this methodology, and the results were compiled to obtain an average melt pool width and depth, with corresponding standard deviation. It was found that melt pool width changes considerably based on the type of melt pool. Melt pool depth also varies slightly between types, though there is significant overlap when accounting for standard deviation. Table 2 summarizes all melt pool width and depth by type for each coupon, with the respective standard deviation. The average values incorporated $>30$ individual measurements, resulting in a measurement uncertainty less than\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-05(3)}\n\\end{center}\n\nFig. 6. Definition of Type I and Type II melt pools.", "start_char_idx": 66111, "end_char_idx": 69727, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c8ee89a4-df83-4c36-9ef5-2ae10eb395b4": {"__data__": {"id_": "c8ee89a4-df83-4c36-9ef5-2ae10eb395b4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "93e246be-0065-4e0d-97e7-704ec9c02bcb", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3edc5d5c0a4df468a123a00d4af3f3f4107774ab58696c3dc076d2a78e9e25d0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "582adee3-8b94-457c-b7a8-09dfe2b90dd4", "node_type": "1", "metadata": {}, "hash": "dd0c3f20b7004d5e0337edb00aa16f6bea592919c2ea4d1a08d2e58a9a1a7b9f", "class_name": "RelatedNodeInfo"}}, "text": "While each melt pool is measured only once for each image, multiple optical images of each coupon were analyzed following this methodology, and the results were compiled to obtain an average melt pool width and depth, with corresponding standard deviation. It was found that melt pool width changes considerably based on the type of melt pool. Melt pool depth also varies slightly between types, though there is significant overlap when accounting for standard deviation. Table 2 summarizes all melt pool width and depth by type for each coupon, with the respective standard deviation. The average values incorporated $>30$ individual measurements, resulting in a measurement uncertainty less than\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-05(3)}\n\\end{center}\n\nFig. 6. Definition of Type I and Type II melt pools.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-06(1)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-06}\n\\end{center}\n\n(b)\n\nFig. 7. Marked melt pool (a) width and (b) depth of Coupon 29 (XZ-plane).\n\n$u_{M P_{\\_} \\text {ave }}=u_{M P} / \\sqrt{30}=1.2552 \\mu \\mathrm{m} / 5.477=0.229 \\mu \\mathrm{m}$ for each coupon. The standard deviation columns in table represent the square root of the variance.\n\n\\subsection*{5.2. Melt pool shape analysis}\nThe laser heating effect described in the previous section produces a notable effect on the geometrical shape of the melt pool as well. In particular, by analyzing the images obtained via digital optical microscopy, it was observed that the location along the $y$-axis at which the maximum melting depth occurs does not necessarily lie on the hatch (or track) centerline. To quantify this effect, a measure of the melt pool shape was developed and will be explained next.\n\nFor this analysis, we will consider once again the cross-sectional (YZ-plane) view of the melt pool. The melt pool width, $w$, and the distance from the edge of the melt pool farther away from the previous hatch to the location at which the maximum melted depth is observed, $a$, are measured using the same methodology as before (see Fig. 8a).\n\nThen, a measure for the melt pool shape is defined as follows:\n\n$\\varphi(a, w)=\\frac{a-w / 2}{w / 2}=\\frac{2 a-w}{w}$\n\nWith this definition, a way to determine how skewed the melt pool is has been established. If the melt pool is perfectly symmetrical about the $z$-axis, then $a=w / 2$ and $\\varphi=0$, or $0 \\%$. On the contrary, if the melt pool is completely skewed towards the previous processed hatch due to the heat-affected zone, then $a \\rightarrow w / 2$, in which case $\\varphi \\rightarrow 1$, or $100 \\%$. In summary, this measure gives a value between 0 and 1 (or $0 \\%$ and $100 \\%$ ) that quantifies how asymmetrical the melt pool geometry is. To further illustrate how this measure is employed, consider the following example taken from the digital optical image microscopy obtained of Coupon 29, previously shown in Fig. 6. In this example we consider only a single melt pool. Note that $w$ and $a$ have been measured in pixels and have not been converted to micrometers to avoid rounding error (see Fig. 8b).\n\nThe melt pool shape can then be determined using Eq. (4):\n\n$\\varphi(242,346)=\\frac{242-346 / 2}{346 / 2}=0.3988=39.88 \\%$\n\nThis value of $\\varphi$ close to $40 \\%$ indicates that the melt pool is considerably asymmetrical, indicating a strong effect of the alreadyprocessed scanned hatch (or track). By repeating this process for all melt pools previously measured, it is possible to obtain an average measure (and standard deviation) of the melt pool shape for a specific set of process parameters. Then, the melt pool shape measure for different process parameters can be tabulated and presented for comparison, as shown in Table 3.", "start_char_idx": 68868, "end_char_idx": 72752, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "582adee3-8b94-457c-b7a8-09dfe2b90dd4": {"__data__": {"id_": "582adee3-8b94-457c-b7a8-09dfe2b90dd4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c8ee89a4-df83-4c36-9ef5-2ae10eb395b4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "80c8985f6796fad18cfc4c0136a903e5487b4bbabf43e0da7d7da7a4c869dbee", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a90dba9a-f433-4a80-982a-4a0b379f28fc", "node_type": "1", "metadata": {}, "hash": "06ef77d5b7cf741de42e153fde0f66a63416ba77ff63bfe3491cf08fa44b174a", "class_name": "RelatedNodeInfo"}}, "text": "In this example we consider only a single melt pool. Note that $w$ and $a$ have been measured in pixels and have not been converted to micrometers to avoid rounding error (see Fig. 8b).\n\nThe melt pool shape can then be determined using Eq. (4):\n\n$\\varphi(242,346)=\\frac{242-346 / 2}{346 / 2}=0.3988=39.88 \\%$\n\nThis value of $\\varphi$ close to $40 \\%$ indicates that the melt pool is considerably asymmetrical, indicating a strong effect of the alreadyprocessed scanned hatch (or track). By repeating this process for all melt pools previously measured, it is possible to obtain an average measure (and standard deviation) of the melt pool shape for a specific set of process parameters. Then, the melt pool shape measure for different process parameters can be tabulated and presented for comparison, as shown in Table 3. It should be noted that at least 30 measurement samples for each melt pool type per coupon were collected. The main conclusion from this analysis is that beyond the variation in melt pool shape between processing conditions, Type I and\n\nTable 2\n\nSummary of melt pool dimensional measurements $\\left(S S R=90^{\\circ}\\right.$ ) by melt pool type.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n\\multirow[b]{2}{*}{Coupon \\#} & \\multirow[b]{2}{*}{$P[W]$} & \\multirow[b]{2}{*}{$v_{s}[\\mathbf{m m} / \\mathrm{s}]$} & \\multirow[b]{2}{*}{$h[\\mathrm{~mm}]$} & \\multicolumn{2}{|c|}{}\\begin{tabular}{l}\nMelt Pool Width - Avg. \\\\\n$[\\mu \\mathrm{m}]$ \\\\\n\\end{tabular} & \\multicolumn{2}{|c|}{}\\begin{tabular}{l}\nMelt Pool Width - Std Dev. \\\\\n$[\\mu \\mathrm{m}]$ \\\\\n\\end{tabular} & \\multicolumn{2}{|c|}{}\\begin{tabular}{l}\nMelt Pool Depth - Avg. \\\\\n$[\\mu \\mathrm{m}]$ \\\\\n\\end{tabular} & \\multicolumn{2}{|c|}{}\\begin{tabular}{l}\nMelt Pool Depth - Std Dev.", "start_char_idx": 71931, "end_char_idx": 73708, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a90dba9a-f433-4a80-982a-4a0b379f28fc": {"__data__": {"id_": "a90dba9a-f433-4a80-982a-4a0b379f28fc", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "582adee3-8b94-457c-b7a8-09dfe2b90dd4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0743df95cc7cbc9f9ba7ea5ebb720325a3400a3e88f6297c27cee26bafc809c8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bc8786ee-5b11-4495-9795-f0f6db35fc81", "node_type": "1", "metadata": {}, "hash": "b4c2c43f094b6bbcdd9e68d75c87e55a9e5e9229f67fa2c26f647ca61d9559d6", "class_name": "RelatedNodeInfo"}}, "text": "\\\\\n$[\\mu \\mathrm{m}]$ \\\\\n\\end{tabular} & \\multicolumn{2}{|c|}{}\\begin{tabular}{l}\nMelt Pool Width - Std Dev. \\\\\n$[\\mu \\mathrm{m}]$ \\\\\n\\end{tabular} & \\multicolumn{2}{|c|}{}\\begin{tabular}{l}\nMelt Pool Depth - Avg. \\\\\n$[\\mu \\mathrm{m}]$ \\\\\n\\end{tabular} & \\multicolumn{2}{|c|}{}\\begin{tabular}{l}\nMelt Pool Depth - Std Dev. \\\\\n$[\\mu \\mathrm{m}]$ \\\\\n\\end{tabular} \\\\\n\\hline\n &  &  &  & $\\mathbf{I}$ & II & $\\mathbf{I}$ & II & $\\mathbf{I}$ & II & $\\mathbf{I}$ & II \\\\\n\\hline\n01 & 169 & 875 & 0.10 & 134 & 92 & 12 & 9 & 35 & 31 & 6 & 5 \\\\\n\\hline\n04 & 195 & 875 & 0.10 & 170 & 111 & 25 & 7 & 49 & 46 & 7 & 8 \\\\\n\\hline\n06 & 182 & 875 & 0.09 & 149 & 101 & 17 & 16 & 45 & 38 & 7 & 5 \\\\\n\\hline\n08 & 182 & 725 & 0.11 & 153 & 107 & 25 & 12 & 48 & 39 & 8 & 9 \\\\\n\\hline\n09 & 195 & 800 & 0.11 & 143 & 109 & 13 & 9 & 44 & 42 & 7 & 7 \\\\\n\\hline\n12 & 182 & 725 & 0.09 & 134 & 113 & 18 & 11 & 45 & 36 & 7 & 10 \\\\\n\\hline\n14 & 182 & 800 & 0.10 & 132 & 109 & 11 & 10 & 44 & 38 & 7 & 6 \\\\\n\\hline\n15 & 182 & 800 & 0.10 & 128 & 105 & 12 & 11 & 40 & 33 & 9 & 6 \\\\\n\\hline\n16 & 195 & 725 & 0.10 & 152 & 114 & 13 & 11 & 52 & 42 & 18 & 10 \\\\\n\\hline\n17 & 182 & 800 & 0.10 & 143 & 112 & 10 & 7 & 48 & 38 & 6 & 7 \\\\\n\\hline\n18 & 182 & 875 & 0.11 & 134 & 110 & 13 & 15 & 47 & 32 & 7 & 7 \\\\\n\\hline\n20 & 169 & 725 & 0.10 & 159 & 106 & 13 & 8 & 51 & 42 & 8 & 6 \\\\\n\\hline\n21 & 169 & 800 & 0.09 & 154 & 107 & 14 & 9 & 47 & 45 & 8 & 9 \\\\\n\\hline\n23 & 169 & 800 & 0.11 & 150 & 96 & 28 & 11 & 43 & 33 & 6 & 6 \\\\\n\\hline\n29 & 195 & 800 & 0.09 & 149 & 103 & 15 & 16 & 49 & 39 & 7 & 12 \\\\\n\\hline\n35 & 195 & 800 & 0.10 & 155 & 112 & 11 & 15 & 50 & 41 & 6 & 7 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-07(3)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-07}\n\\end{center}\n\n(b)\n\nFig. 8.", "start_char_idx": 73386, "end_char_idx": 75264, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bc8786ee-5b11-4495-9795-f0f6db35fc81": {"__data__": {"id_": "bc8786ee-5b11-4495-9795-f0f6db35fc81", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a90dba9a-f433-4a80-982a-4a0b379f28fc", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "59048ff145ef11eeab9abf4a290071e7e67079f48cdc5be85206419ceb213079", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a4e47644-8338-4de6-868e-2f8c574232d6", "node_type": "1", "metadata": {}, "hash": "95cc2794553a046978b627a703140ac7a216459ad552699280f75d22065f95fd", "class_name": "RelatedNodeInfo"}}, "text": "8. (a) Location of maximum depth of melted material, (b) measurements for calculation of melt pool shape.\n\nTable 3\n\nSummary of melt pool shape measurements $\\left(S S R=90^{\\circ}\\right)$ by melt pool type.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline\n\\multirow[b]{2}{*}{Coupon \\#} & \\multirow[b]{2}{*}{$P[W]$} & \\multirow[b]{2}{*}{}\\begin{tabular}{l}\n$v_{s}$ \\\\\n$[\\mathbf{m m} /$ \\\\\n$s]$ \\\\\n\\end{tabular} & \\multirow[b]{2}{*}{$h[\\mathrm{~mm}]$} & \\multicolumn{2}{|c|}{}\\begin{tabular}{l}\nMelt Pool \\\\\nShape - Avg. \\\\\n$[\\%]$ \\\\\n\\end{tabular} & \\multicolumn{2}{|c|}{}\\begin{tabular}{l}\nMelt Pool \\\\\nShape - Std \\\\\nDev. [\\%] \\\\\n\\end{tabular} \\\\\n\\hline\n &  &  &  & I & II & I & II \\\\\n\\hline\n01 & 169 & 875 & 0.10 & 10.0 & 2.2 & 3.1 & 2.9 \\\\\n\\hline\n04 & 195 & 875 & 0.10 & 16.1 & 13.4 & 2.5 & 2.4 \\\\\n\\hline\n06 & 182 & 875 & 0.09 & 19.4 & 15.3 & 3.1 & 2.7 \\\\\n\\hline\n08 & 182 & 725 & 0.11 & 12.6 & 12.7 & 4.3 & 4.7 \\\\\n\\hline\n09 & 195 & 800 & 0.11 & 11.8 & 10.5 & 4.2 & 4.0 \\\\\n\\hline\n12 & 182 & 725 & 0.09 & 15.0 & 2.7 & 3.2 & 4.7 \\\\\n\\hline\n14 & 182 & 800 & 0.10 & 10.9 & 1.0 & 4.0 & 4.1 \\\\\n\\hline\n15 & 182 & 800 & 0.10 & 16.3 & 6.7 & 3.7 & 4.5 \\\\\n\\hline\n16 & 195 & 725 & 0.10 & 9.5 & 11.5 & 3.6 & 4.1 \\\\\n\\hline\n17 & 182 & 800 & 0.10 & 8.6 & 0.4 & 2.7 & 4.5 \\\\\n\\hline\n18 & 182 & 875 & 0.11 & 7.1 & 0.1 & 2.4 & 3.1 \\\\\n\\hline\n20 & 169 & 725 & 0.10 & 11.0 & 2.6 & 3.6 & 6.1 \\\\\n\\hline\n21 & 169 & 800 & 0.09 & 23.4 & 11.5 & 5.1 & 6.4 \\\\\n\\hline\n23 & 169 & 800 & 0.11 & 9.1 & 0.2 & 2.8 & 6.4 \\\\\n\\hline\n29 & 195 & 800 & 0.09 & 21.0 & 6.0 & 5.2 & 5.5 \\\\\n\\hline\n35 & 195 & 800 & 0.10 & 5.4 & 3.5 & 2.5 & 3.3 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nType II melt pools obtained via the same processing conditions often have considerably different shapes.\n\n\\section*{6. Effect of process parameters on melt pool size and shape}\nThe effects of L-PBF process parameters such as laser power, scan velocity, and hatch distance on the melt pool geometry has been investigated.\n\n\\subsection*{6.1.", "start_char_idx": 75262, "end_char_idx": 77243, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a4e47644-8338-4de6-868e-2f8c574232d6": {"__data__": {"id_": "a4e47644-8338-4de6-868e-2f8c574232d6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bc8786ee-5b11-4495-9795-f0f6db35fc81", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b2681e89d324c75ca62d8466a5947f86a9212455a71ff4c43a1511bce0f2359d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b7494e39-fa55-4ea1-97dc-94f5b2f11e89", "node_type": "1", "metadata": {}, "hash": "49fe6c8114730ce3d180429ccca8b120112075748101f64b4be7873cc60dd717", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{6. Effect of process parameters on melt pool size and shape}\nThe effects of L-PBF process parameters such as laser power, scan velocity, and hatch distance on the melt pool geometry has been investigated.\n\n\\subsection*{6.1. Effect of process parameters on melt pool width and depth}\nThe effect of process parameters on melt pool dimensions (width and depth) can be analyzed via main effect plots, as shown in Figs. 911. Melt pool size increases with increasing laser power and decreasing scan velocity. However, the behavior is clearly non-linear. Additionally,\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-07(1)}\n\\end{center}\n\n(a) the melt pool width and depth measurements taken indicate that there is a large difference between Type I and Type II melt pool width (approx. $50 \\mu \\mathrm{m}$ ). This is in contrast with the difference between Type I and Type II melt pool depth, which does not appear to vary significantly (approx. $10 \\mu \\mathrm{m}$ ). Melt pool width and depth decrease with increasing hatch distance, especially for Type I melt pools. This is in agreement with what is intuitively expected, since a larger hatch distance causes the heat affected zone from a previously scanned track to be further away from the following track. Additionally, the difference in depth between Type I and Type II melt pools is greatly reduced with increasing hatch distance.\n\nAnother way to analyze these results is to consider the behavior of melt pool depth and width as a function of laser energy density, as shown in Figs. 12 and 13. The trend lines show that melt pool size increases slightly as energy density increases. This behavior is more noticeable in melt pool depth than in melt pool width. Furthermore, there is no appreciable difference in behavior between Type I and Type II melt pool size when considering energy density as an all-inclusive factor. In summary, the measurements taken for melt pool width and depth give very significant insight into the dynamic nature of melt pool size. Furthermore, the change in melt pool size is non-linear.\n\n\\subsection*{6.2. Effect of process parameters on melt pool shape}\nThe effect of processing parameters on melt pool shape can be represented via main effect plots, as seen in Figs. 14-16. Notice the considerable effect of low hatch distance in Type I melt pools and of high laser power in Type II melt pools. Melt pool shape tends to be more asymmetric with increasing laser power and increasing scan velocity, especially for Type II melt pools. However, the behavior is clearly non-linear. Melt pool shape measurements taken indicate that there is a considerable difference between Type I and Type II melt pool shapes. Type I melt pools are considerably more asymmetric than Type II melt pools. This behavior is more easily observable at lower scan velocities. Notice that Type I melt pools tend to be more symmetric when the highest level of hatch distance is utilized. This is intuitive from the fact that a higher hatch distance, the distance between consecutive scanned tracks, results in the melt pool being further removed from the heat affected zone due to melting of the previous\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-07(2)}\n\\end{center}\n\n(b)\n\nFig. 9. Effect of laser power on melt pool (a) width, (b) depth.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-08(2)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-08(1)}\n\\end{center}\n\n(b)\n\nFig. 10. Effect of scan velocity on melt pool (a) width, (b) depth.\n\ntrack.\n\nIt is possible to consider how melt pool shape changes as a function of laser energy density, using the definition introduced earlier. Recall that energy density is a function of laser power, scan velocity, layer thickness, and hatch distance. Fig. 17 shows a plot of melt pool shape, by type, as a function of energy density.\n\nThe trend line on Fig. 17 shows that melt pool shape is more asymmetrical as energy density increases. This behavior is more noticeable in Type I melt pool than in Type II melt pools.", "start_char_idx": 77010, "end_char_idx": 81212, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b7494e39-fa55-4ea1-97dc-94f5b2f11e89": {"__data__": {"id_": "b7494e39-fa55-4ea1-97dc-94f5b2f11e89", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a4e47644-8338-4de6-868e-2f8c574232d6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3e511a3a88b45413e7bd51bba7f9d216ea3c7eb569dc9976fc5d719615aafe29", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "953375ed-ad35-4b7d-a74c-cf3d1f0c4842", "node_type": "1", "metadata": {}, "hash": "031d3ac3106049f5e0d1cdd4a2188cdc9f8c456ea35fe8261385faf10529c514", "class_name": "RelatedNodeInfo"}}, "text": "10. Effect of scan velocity on melt pool (a) width, (b) depth.\n\ntrack.\n\nIt is possible to consider how melt pool shape changes as a function of laser energy density, using the definition introduced earlier. Recall that energy density is a function of laser power, scan velocity, layer thickness, and hatch distance. Fig. 17 shows a plot of melt pool shape, by type, as a function of energy density.\n\nThe trend line on Fig. 17 shows that melt pool shape is more asymmetrical as energy density increases. This behavior is more noticeable in Type I melt pool than in Type II melt pools. In summary, the difference in melt pool shape for Type I and Type II melt pools can be mostly attributed to the effect of the heat-affected zone from the previous scanned track. Therefore, hatch distance is the most relevant factor, as hypothesized initially.\n\n\\section*{7. In-situ thermal monitoring}\nIn-situ monitoring of the process using two-color pyrometer thermal camera [10] and thermography ([20]) can be utilized to quantitatively analyze melt pool size and investigate spattering phenomenon [34]. Video recordings of the process can be utilized if a camera is placed in the L-PBF process chamber. Due to the nature of the process, i.e., a laser beam moving at very high speeds, a high frame rate (HFR) camera is required. An HFR infrared camera has been setup to observe a portion of the build area of an L-PBF machine at the National Institute of Standards and Technology (NIST) facility in Gaithersburg, MD, and the process has been recorded for a test coupon (Coupon 35) fabricated using $P=195 \\mathrm{~W}, \\quad v_{s}=800 \\mathrm{~mm} / \\mathrm{s}$, and $h=0.10 \\mathrm{~mm}$.\n\nThis section presents investigations on the melt pool size and spattering analyses of the process using the HFR thermal camera recording. There are some difficulties in processing of these images. The finite dynamic range of the camera means much of the data is at the noise floor outside the melt pool, or saturated due to the high temperatures within the melt pool. The spattering particles that occupy the same area as the melt pool in the image frame (e.g., particles that are immediately above the melt pool) are not all recoverable from the images as they may also saturate the camera and appear to coincide with the saturated melt pool. In addition, a visible lens glare (or ghosting) creates an erroneously increased temperature measurement which affects relative uncertainty at low temperature values. Furthermore, the speed, path, and frequency of spatter particles are not always captured since the spatter frequency is at or above the camera frame rate. Additionally, solidified and powder regions have locally variant emissivity values, which effectively cause spatially variant and 'noisy' temperature measurements. However, for simplicity, a single emissivity value is assumed, which is likely the largest contributor to temperature measurement uncertainty.\n\n\\subsection*{7.1. Experimental set-up for thermal camera}\nThe thermal camera properties are shown in Table 4. The camera has an integration time of $0.040 \\mathrm{~ms}$ and can record at 1800 frames per second, which translates to $0.5555 \\mathrm{~ms}$ per frame. In the instantaneous field of view (iFoV), each pixel represents $36 \\mu \\mathrm{m}$. Thermal video and process parameters are shown in Table 5. The video recording of the test coupon has 801 total frames. The processing occurs out of the view of the camera for 99 frames. Horizontal scanning is recorded for 602 frames with approximately 60 tracks, and a vertical scanning of the stripe boundary is recorded for 100 frames. Since each track is processed for $5.125 \\mathrm{~ms}$ (calculated from track length divided by scan velocity), the camera records approximately 9.23 frames per track. The non-integer number means that the frequency of the process is different than what the camera records, therefore the initial and final point of each track are not necessarily recorded with the camera. It is also important to note that some frames during processing are missing in the recording, i.e., skipping occurs.\n\nMoreover, as shown in Fig. 17, the camera is placed at a $43.7^{\\circ}$ angle with the powder bed. Recording at this angle causes the image of the build plane surface in the $y$ direction to appear smaller than the actual size.", "start_char_idx": 80629, "end_char_idx": 84986, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "953375ed-ad35-4b7d-a74c-cf3d1f0c4842": {"__data__": {"id_": "953375ed-ad35-4b7d-a74c-cf3d1f0c4842", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b7494e39-fa55-4ea1-97dc-94f5b2f11e89", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7e78c97e4c3eb9fa4966c299392f4c0937e8ea46c0aba9ed63ae84a9aa4f7589", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "01b12205-8747-4dc3-b044-791f1185efdf", "node_type": "1", "metadata": {}, "hash": "dda11dc7291381175719b7f9d818d4e9866f3f368afbbef121c956e2ed2a0c1a", "class_name": "RelatedNodeInfo"}}, "text": "Horizontal scanning is recorded for 602 frames with approximately 60 tracks, and a vertical scanning of the stripe boundary is recorded for 100 frames. Since each track is processed for $5.125 \\mathrm{~ms}$ (calculated from track length divided by scan velocity), the camera records approximately 9.23 frames per track. The non-integer number means that the frequency of the process is different than what the camera records, therefore the initial and final point of each track are not necessarily recorded with the camera. It is also important to note that some frames during processing are missing in the recording, i.e., skipping occurs.\n\nMoreover, as shown in Fig. 17, the camera is placed at a $43.7^{\\circ}$ angle with the powder bed. Recording at this angle causes the image of the build plane surface in the $y$ direction to appear smaller than the actual size. Each pixel represents a $36 \\mu \\mathrm{m}$ horizontal instantaneous field of view (iFoV), however, due to the recording angle, the $\\mathrm{iFoV}$ size, projected onto the build plane, is corrected in the $y$ direction with\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-08}\n\\end{center}\n\n(b)\n\n(a)\n\nFig. 11. Effect of hatch distance on melt pool (a) width, (b) depth.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-09(2)}\n\\end{center}\n\nFig. 12. Effect of process energy density on melt pool width.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-09(3)}\n\\end{center}\n\nFig. 13. Effect of process energy density on melt pool depth.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-09(1)}\n\\end{center}\n\nFig. 14. Effect of laser power on melt pool shape.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-09(4)}\n\\end{center}\n\nFig. 15. Effect of scan velocity on melt pool shape.\n\n$d y^{\\prime}=\\frac{d y}{\\sin (43.7)}=1.48 d y=52 \\mu \\mathrm{m}$. Calibrated temperature range for these settings is $450-1020^{\\circ} \\mathrm{C}$ based on blackbody temperature ( $\\varepsilon \\approx 1$ ). For the purpose of this study, an assumed emissivity value of 0.2 is uniformly applied for every pixel to calculate true temperature. It is important to note that for $\\varepsilon=0.2$, the measurement range based on the calibration shifts to $555-1380^{\\circ} \\mathrm{C}$. However, due to non-linearity of the camera, temperatures below $600{ }^{\\circ} \\mathrm{C}$ should be treated with caution.\n\n\\subsection*{7.2. Melt pool size analysis}\nIt is possible to infer changes in the sizes of melt pools from the thermal camera recording by observing the size of the measurable\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-09}\n\\end{center}\n\nFig. 16. Effect of hatch distance on melt pool shape.\n\nisotherms surrounding the actual liquid melt pool. Each frame can be processed individually such that pixels with temperatures exceeding the liquidus temperature $\\left(1350^{\\circ} \\mathrm{C}\\right.$ for nickel alloy 625$)$ are segmented from colder pixels. Fig. 18 shows the result of image segmentation using liquidus temperature as a threshold on single frame where the molten region is marked red, and colder region is marked blue. Using Matlab's built-in functions, a bounding box is created around the melt pool such that the height of the box gives the width of the melt pool in pixels. This process is repeated for 185 different frames that belong to 20 different tracks.", "start_char_idx": 84117, "end_char_idx": 87686, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "01b12205-8747-4dc3-b044-791f1185efdf": {"__data__": {"id_": "01b12205-8747-4dc3-b044-791f1185efdf", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "953375ed-ad35-4b7d-a74c-cf3d1f0c4842", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e5b1f205769523cf58aff3e19cfbecf9fb011d0607cdafbc5172ed4ae6ab2e94", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5e5f0271-32b9-4850-ab86-f86d34837fa9", "node_type": "1", "metadata": {}, "hash": "f1daccdec0d06ef68d516db2a9b5193706c873535742e18e93fdf86745b3ad6d", "class_name": "RelatedNodeInfo"}}, "text": "16. Effect of hatch distance on melt pool shape.\n\nisotherms surrounding the actual liquid melt pool. Each frame can be processed individually such that pixels with temperatures exceeding the liquidus temperature $\\left(1350^{\\circ} \\mathrm{C}\\right.$ for nickel alloy 625$)$ are segmented from colder pixels. Fig. 18 shows the result of image segmentation using liquidus temperature as a threshold on single frame where the molten region is marked red, and colder region is marked blue. Using Matlab's built-in functions, a bounding box is created around the melt pool such that the height of the box gives the width of the melt pool in pixels. This process is repeated for 185 different frames that belong to 20 different tracks. During the processing of melt pool size calculations, it is observed that some of the spattering particles that are in close proximity to the melt pool affect the melt pool size calculation algorithm. For simplicity, we refer to these particles as attached particles. Fig. 19 shows these attached particles and how they may affect the melt pool size calculation. Measurements coming from the melt pool size calculation algorithm are processed frame by frame to reduce or eliminate the errors caused by the attached spattering particles.\n\nFurthermore, the imaging system resolution is limited by inherent blur or focus, which tends to cause high temperature peaks to decrease, and neighboring lower temperature to apparently increase, effectively increasing the measured size of lower isotherm temperature bands. Combined with reflections from the surface of the processed area, attached spattering particles, uncertain true emissivity value, and potentially other optical phenomena, melt pool width measurements\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-10(1)}\n\\end{center}\n\nFig. 17. Effect of process energy density on melt pool shape.\n\nTable 4\n\nThermal camera parameters.\n\n\\begin{center}\n\\begin{tabular}{ll}\n\\hline\nWavelength (filter) & $1350-1600 \\mathrm{~nm}$ \\\\\nIntegration Time & $0.040 \\mathrm{~ms}$ \\\\\nFrame Rate & $1800 \\mathrm{frames} / \\mathrm{s}$ \\\\\niFoV & $36 \\mathrm{~mm} /$ pixel \\\\\nImaging window & 360 pixels $\\times 128$ pixels $(12.96 \\mathrm{~mm} \\times 4.61 \\mathrm{~mm})$ \\\\\n\\end{tabular}\n\\end{center}\n\nTable 5\n\nThermal video and process parameters.\n\n\\section*{Scan velocity: $800 \\mathrm{~mm} / \\mathrm{s}$}\nStripe width (track length) including overlap: $4.1 \\mathrm{~mm}$\n\nLaser scanning of a track : $4.1 \\mathrm{~mm} / 800 \\frac{\\mathrm{mm}}{\\mathrm{s}}=5.125 \\mathrm{~ms}$\n\nCamera frame rate: $1800 \\mathrm{fps}$ or $0.5555 \\mathrm{~ms}$ per frame\n\n$\\approx 9.23$ frames per track of laser scanning\n\nLaser $\\mathrm{ON}: \\approx 9$ frames\n\nLaser OFF (0.042 ms): 0-1 frame\n\nTotal frames: 801\n\nHatching: 602 frames\n\nVertical (track boundary): 100 frames\n\nOut-of-frame: 99 frames from thermal images resulted in values considerably larger than the measurements obtained via digital microscopy reported in earlier sections [22]. In addition, the quantization error, equal to one pixel or the vertical iFoV size of $52 \\mu \\mathrm{m}$, is significant compared to the melt pool widths measured via microscopy (approximately 30\\%). Due to these significant sources of uncertainty, only relative changes in melt pool size may be discerned from thermal images.\n\nMelt pool width measurements obtained via digital optical microscopy are utilized in order to calculate a linear correction factor for melt pool width measurements obtained from thermal images for more direct comparison. Correction factors are calculated for Type I (beginning of track, at $|x|=0 \\mathrm{~mm}$ ) and Type II (end of track, at $|x|=4 \\mathrm{~mm}$ ) melt pools by relating the microscopy-measured melt pool width to thermal image measurements. A linear correction function is applied on all melt pool measurements obtained via thermal imaging.\n\nA total of 185 frames from the camera recording are analyzed with this method to calculate the melt pool width. Fig.", "start_char_idx": 86956, "end_char_idx": 90990, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5e5f0271-32b9-4850-ab86-f86d34837fa9": {"__data__": {"id_": "5e5f0271-32b9-4850-ab86-f86d34837fa9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "01b12205-8747-4dc3-b044-791f1185efdf", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "97422ceab1b3a34cc95284d135f01ae67b044bfbbdf6386ed6d7c68246024b74", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "81d7a4ff-34c6-4c72-b1c0-69f4186abc81", "node_type": "1", "metadata": {}, "hash": "610534ac336a68a5e97d8e853133296054c4e4af8e3c9bb4d19267fef7d738c0", "class_name": "RelatedNodeInfo"}}, "text": "Due to these significant sources of uncertainty, only relative changes in melt pool size may be discerned from thermal images.\n\nMelt pool width measurements obtained via digital optical microscopy are utilized in order to calculate a linear correction factor for melt pool width measurements obtained from thermal images for more direct comparison. Correction factors are calculated for Type I (beginning of track, at $|x|=0 \\mathrm{~mm}$ ) and Type II (end of track, at $|x|=4 \\mathrm{~mm}$ ) melt pools by relating the microscopy-measured melt pool width to thermal image measurements. A linear correction function is applied on all melt pool measurements obtained via thermal imaging.\n\nA total of 185 frames from the camera recording are analyzed with this method to calculate the melt pool width. Fig. 20 shows the results of this analysis where the values are calculated across all 185 frames and the $x$ locations are calculated explicitly based on the number of frames recorded in that track and the scanning speed of the laser. The main conclusion that can be drawn from this analysis is that melt pool width tends to decrease from the beginning of each track towards the end of each track, which is in agreement with the results presented\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_52a85307004f6d652296g-10(2)}\n\n(b)\n\n$37.5^{\\circ}$ port angle $43.7^{\\circ}$ camera angle $\\sim 150 \\mathrm{~mm}$ distance Build Plate\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-10}\n\\end{center}\n\nFig. 18. Thermal camera set-up, (a) Side-view of the L-PBF machine, custom door, and thermal camera, (b) CAD solid model of L-PBF machine build chamber and custom viewport, (c) optical axis, plane of focus and vertical iFoV projected on the build plane.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-11(2)}\n\\end{center}\n\nFig. 19. Melt pool width measurements (calculated and actual) along with attached and detached spattering particles. Dimensions are in pixels.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-11(1)}\n\\end{center}\n\nFig. 20. Minimum, maximum and average melt pool width after attached particle and optical image comparison corrections. Error bars represent sample standard deviations.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-11}\n\\end{center}\n\nFig. 21. Processing steps for spattering particle detection.\n\nfrom optical imaging analysis. A non-linear correction factor could be employed if melt pool dimension measurements were available from optical imaging at other coupon cross-section locations.\n\n\\subsection*{7.3. Spattering analysis}\nSpattering is a common but potentially detrimental phenomenon that is observed during L-PBF. When the laser beam hits an area, local evaporation of the melt pool cause some of the molten metal to eject from the melt pool, or surrounding heated particles to be blown away by the strong local convective flow, and land on other areas [19]. These particles are often observed to move in opposite direction of the laser beam and they may affect the melt pool behavior during processing. It is possible to determine the sizes and temperatures of the spattering particles from the HFR thermal video recording.\n\nSpattering particles are originating from the vicinity of the melt pool; therefore they have high temperatures and thus appear as bright clusters of pixels. Each frame of the thermal video recording is preprocessed in order to improve the quality of the particle count and size measurements. One of the biggest problems is the existence of the lens glare around the melt pool region. This not only creates difficulties in particle detection, but also creates spurious temperature fields. In order to remedy this, a lens glare filter is implemented in the region close to the melt pool. Images obtained from the red channel are first converted to grayscale images. Afterwards, a threshold based on pixel color density is implemented to segregate the image into black and white areas such that the lens glare region as well as the melt pool inside it are grouped together, and are separated from the lower density regions.", "start_char_idx": 90185, "end_char_idx": 94443, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "81d7a4ff-34c6-4c72-b1c0-69f4186abc81": {"__data__": {"id_": "81d7a4ff-34c6-4c72-b1c0-69f4186abc81", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5e5f0271-32b9-4850-ab86-f86d34837fa9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b8570b1234573fdb34f2a5a0f0af4828c997023ae8c2d711b14ec1169a1d237f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9f81800a-4217-479b-aa1e-95164b0f009a", "node_type": "1", "metadata": {}, "hash": "61c24c95405ab61b01f70040bdafd3fb24d313f07e8e2baf8f2cc04a2421eb8b", "class_name": "RelatedNodeInfo"}}, "text": "It is possible to determine the sizes and temperatures of the spattering particles from the HFR thermal video recording.\n\nSpattering particles are originating from the vicinity of the melt pool; therefore they have high temperatures and thus appear as bright clusters of pixels. Each frame of the thermal video recording is preprocessed in order to improve the quality of the particle count and size measurements. One of the biggest problems is the existence of the lens glare around the melt pool region. This not only creates difficulties in particle detection, but also creates spurious temperature fields. In order to remedy this, a lens glare filter is implemented in the region close to the melt pool. Images obtained from the red channel are first converted to grayscale images. Afterwards, a threshold based on pixel color density is implemented to segregate the image into black and white areas such that the lens glare region as well as the melt pool inside it are grouped together, and are separated from the lower density regions. Then, pixels in this region are divided into multiple bins based on their intensities and the median density of all bins that belong to the lens glare - melt pool regions are calculated and subtracted from this region. It is important to note that a tradeoff is necessary between the complete removal of the lens glare and preserving particle information, and rather conservative values are used in this study. As the next step in particle detection, another density based thresholding is employed to reveal the pixels at a certain temperature range, followed by median filtering to reduce noise. The resulting image is then processed to count the number of pixels in each particle that represent the area of each particle. These areas, in units of pixels, are then converted to millimeters using the iFoV sizes calculated for the camera, disregarding\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_52a85307004f6d652296g-12}\n\nFig. 22. Frames from the thermal camera video showing the processing of a single track.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-13(5)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-13(4)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-13(2)}\n\\end{center}\n\n(c)\n\nFig. 23. Minimum, maximum and average temperature histories grouped by the $x$ coordinates: At the beginning of the track (a), middle of the track (b) and end of the track (c) across multiple tracks. Error bars represent sample standard deviations. Only the tracks with positive scanning direction $(+x)$ are shown.\n\nthe geometric perspective size changes caused by their motion towards the camera. Fig. 21 summarizes the processing steps for spattering calculation. This process is repeated for each frame in the thermal video, and detected particles are recorded. The ratio of total area of spattering particles to the total processing area $\\left(6 \\mathrm{~mm} \\times 4.1 \\mathrm{~mm}=24.6 \\mathrm{~mm}^{2}\\right)$, denoted by percentage spatter $(\\% \\mathrm{~S})$ is reported for each of the processed frames. It should be noted that some of the spattering particles that are much closer to the camera lens appear larger affecting the percentage spatter value.\n\nFig. 22 shows thermal images from a single track. Measured melt pool width $\\left(\\mathrm{MP}_{\\mathrm{w}}\\right)$, frame number $(\\mathrm{F})$, calculated relative track distance $\\left(\\mathrm{x}_{\\mathrm{r}}\\right)$ and spattering percentage $(\\% \\mathrm{~S})$ are shown in each frame. Here, $\\mathrm{x}_{\\mathrm{r}}$ is calculated by assuming the first frame of each track is at $\\mathrm{x}_{\\mathrm{r}}=0 \\mathrm{~mm}$, and each frame increases this distance with respect to the recording rate and laser speed $(0.5555 \\mathrm{~ms} /$ frame $\\times 800 \\mathrm{~mm} / \\mathrm{s}=0.4444 \\mathrm{~mm} /$ frame), rather than measuring the coordinates of the melt pool at each frame.", "start_char_idx": 93401, "end_char_idx": 97462, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9f81800a-4217-479b-aa1e-95164b0f009a": {"__data__": {"id_": "9f81800a-4217-479b-aa1e-95164b0f009a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "81d7a4ff-34c6-4c72-b1c0-69f4186abc81", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e5de2416aa9b5ccb116f32f005e236f59964859d6a4659d82bf3cf298f18f2d8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b1897a60-43e6-41da-a855-bf3efb34583e", "node_type": "1", "metadata": {}, "hash": "a28b3d0d46d85cff953e7b9b2603e64a3e15e66e2c4c641fba206dd3d5b43ba5", "class_name": "RelatedNodeInfo"}}, "text": "Fig. 22 shows thermal images from a single track. Measured melt pool width $\\left(\\mathrm{MP}_{\\mathrm{w}}\\right)$, frame number $(\\mathrm{F})$, calculated relative track distance $\\left(\\mathrm{x}_{\\mathrm{r}}\\right)$ and spattering percentage $(\\% \\mathrm{~S})$ are shown in each frame. Here, $\\mathrm{x}_{\\mathrm{r}}$ is calculated by assuming the first frame of each track is at $\\mathrm{x}_{\\mathrm{r}}=0 \\mathrm{~mm}$, and each frame increases this distance with respect to the recording rate and laser speed $(0.5555 \\mathrm{~ms} /$ frame $\\times 800 \\mathrm{~mm} / \\mathrm{s}=0.4444 \\mathrm{~mm} /$ frame), rather than measuring the coordinates of the melt pool at each frame.\n\nThis analysis reveals that material spattering during laser processing of powder material is significant that is the spattering percentage is $20 \\%$ or more and in some instances it becomes as high as $70 \\%$.\n\n\\subsection*{7.4. Heating and cooling rates}\nThe thermal camera images can be utilized to quantify the heating and cooling rates. By sampling the temperature data at certain points, the rate of cooling and heating can be estimated. Although absolute temperature measurements are affected by multiple potential sources of uncertainty previously mentioned, these create systematic bias errors, therefore differential measurements (like heating or cooling rate), may cancel a significant portion of this error. At this point, it is important to note that due to the asynchrony between the frequency of\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-13}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-13(1)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_52a85307004f6d652296g-13(3)}\n\\end{center}\n\n(c)\n\nFig. 24. Minimum, maximum and average temperature histories grouped by the $x$ coordinates: At the beginning of the track (a), middle of the track (b) and end of the track (c) across multiple tracks. Error bars represent sample standard deviations. Only the tracks with negative scanning direction $(-x)$ are shown.\n\ntrack processing and the recording rate of the camera, the $x$-coordinates of melt pools do not align across tracks. Theoretically, there can be up to $\\frac{4.1 \\mathrm{~mm}}{10}=410 \\mu \\mathrm{m}$ difference in melt pool $x$-coordinates between different tracks, considering that each track takes at most 10 frames to be processed. This causes an inconsistency in temperature measurements between tracks, when analyzed individually. In order to alleviate this, the temperature histories for certain tracks are shifted temporally ( $\\pm 1$ frame) as a post processing operation in an attempt to create an agreement with the rest of the tracks. Furthermore, multiple tracks are used in the analysis and an average temperature history is constructed. Out of the 20 tracks analyzed, 10 of them have a positive scanning direction (laser moves in the $+x$ direction) while the other 10 have a negative scanning direction. These two groups of tracks are analyzed separately.\n\nAt each frame from the thermal camera data, the centroid of the melt pool is calculated. Each track's center in $y$-coordinate is identified using the mean of melt pool centroids that are observed in that track. These $y$-coordinates are used in the following analysis. Temperature measurements at various $x$-coordinates (the beginning, middle, and end of the track) are recorded during the timeframe of the processing of each track (up to a maximum of 10 frames), at the respective track centers in $y$-coordinates. It is important to note that spattering particles, if positioned on top of the sampling points, can affect the result of this analysis.\n\nFig. 23 shows the minimum, maximum and mean temperatures observed at three different $x$ locations: the beginning, middle and the end of the track, for the tracks with positive scanning directions. It is seen that the temperatures are very high at the beginning of the track when the processing starts, because the meltpool is located in this region.", "start_char_idx": 96778, "end_char_idx": 100906, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b1897a60-43e6-41da-a855-bf3efb34583e": {"__data__": {"id_": "b1897a60-43e6-41da-a855-bf3efb34583e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9f81800a-4217-479b-aa1e-95164b0f009a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "de76745e2aaa70af35d1c18bf1f3356a6f656bab134af7920c2a3069ebf35515", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a6aaf17a-1c44-49b6-9ff5-c79db9f9860b", "node_type": "1", "metadata": {}, "hash": "55679cf51f5ccc2461d4ebdae9fc3363827bb652961b3f873e9b9462019811a0", "class_name": "RelatedNodeInfo"}}, "text": "Each track's center in $y$-coordinate is identified using the mean of melt pool centroids that are observed in that track. These $y$-coordinates are used in the following analysis. Temperature measurements at various $x$-coordinates (the beginning, middle, and end of the track) are recorded during the timeframe of the processing of each track (up to a maximum of 10 frames), at the respective track centers in $y$-coordinates. It is important to note that spattering particles, if positioned on top of the sampling points, can affect the result of this analysis.\n\nFig. 23 shows the minimum, maximum and mean temperatures observed at three different $x$ locations: the beginning, middle and the end of the track, for the tracks with positive scanning directions. It is seen that the temperatures are very high at the beginning of the track when the processing starts, because the meltpool is located in this region. As the time passes, this point cools down. In contrast, the end of the track starts off with a low temperature, and heats up when the\\\\\nlaser reaches and melts the region. As expected, the middle point of the track heats up as the laser approaches, and cools down as it departs.\n\nFig. 24 shows the temperatures for the tracks with negative scanning directions which indicate similar results. Figs. 23 and 24 reveal similar heating and cooling profiles due to the nature of the high energy density laser processing. The differences between them can be related to conductivity due to the layout of neighboring solid/powder regions, local differences in emissivity and powder geometry as well as spattering particles that overlap the sampling points. Furthermore, it is possible to obtain the rate of cooling and heating from these figures. The heating rates in Fig. 23 are roughly $600^{\\circ} \\mathrm{C} / \\mathrm{ms}$ and heating rates in Fig. 24 are roughly $1000^{\\circ} \\mathrm{C} / \\mathrm{ms}$. The cooling rates are approximately $150^{\\circ} \\mathrm{C} / \\mathrm{ms}$ in both figures. These observations are in agreement with the literature [39]. In comparison, welding process is said to have a much slower cooling rate of $0.550{ }^{\\circ} \\mathrm{C} / \\mathrm{ms}$ [8].\n\n\\section*{8. Conclusions}\nIn this paper, a complete and thorough analysis of coupons additively fabricated using laser powder bed fusion (selective laser melting) of nickel alloy 625 powder has been presented. A methodology was defined and applied to analyze a set of test coupons, following a Box-Behnken experimental design. These coupons were analyzed with two objectives in mind: i) to determine how close each coupon was to fully dense and ii) to determine melt pool dimensions (width, and depth) and shape for each coupon. The main conclusion of this paper is the identification and definition of a dynamic melt pool, a condition which indicates that melt pool geometry is constantly changing as the laser scans a single track. Specifically, two different types of melt pools (i.e. Type I and Type II) have been identified from the process analysis. When the laser beam begins to process a new track that is still within the heat-affected zone of the previous scanning, the melt pool is named Type I and the width is the largest and the shape is highly skewed towards the heat-affected zone. As laser processing of the track reaches to the end of the track so called Type II melt pool becomes normal in shape and smallest in width. This is a unique observation that the melt pool size and shape changes dynamically leading to some new process knowledge in LPBF. The presence of melt pools of varying size may prove key in future research for microstructure characterization and the calculation of mechanical properties of additively manufactured parts.\n\nIn order to gain in-depth understanding of the laser fusion processing of powder material, an in-situ thermal camera video recording is performed and analyzed for meltpool size, spattering particles and heating and cooling rates during processing of nickel alloy 625 powder material. From in-situ thermal video imaging analysis, significant powder particle spatter has been observed with about $20-35 \\%$ of the total area being processed spattered along a single track leading to substantial powder material and heat loss.", "start_char_idx": 99990, "end_char_idx": 104271, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a6aaf17a-1c44-49b6-9ff5-c79db9f9860b": {"__data__": {"id_": "a6aaf17a-1c44-49b6-9ff5-c79db9f9860b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b1897a60-43e6-41da-a855-bf3efb34583e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4ca3eca083a0599636e1230144b7f464f725194703b9b97b2fd0d287c459a198", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "da412d5c-9811-4597-bf01-c479c174ba4a", "node_type": "1", "metadata": {}, "hash": "e3a68f5c2c79c38ae46aa5ad0b152148d2e5778cfd71143d175bf0d489ccd2c1", "class_name": "RelatedNodeInfo"}}, "text": "As laser processing of the track reaches to the end of the track so called Type II melt pool becomes normal in shape and smallest in width. This is a unique observation that the melt pool size and shape changes dynamically leading to some new process knowledge in LPBF. The presence of melt pools of varying size may prove key in future research for microstructure characterization and the calculation of mechanical properties of additively manufactured parts.\n\nIn order to gain in-depth understanding of the laser fusion processing of powder material, an in-situ thermal camera video recording is performed and analyzed for meltpool size, spattering particles and heating and cooling rates during processing of nickel alloy 625 powder material. From in-situ thermal video imaging analysis, significant powder particle spatter has been observed with about $20-35 \\%$ of the total area being processed spattered along a single track leading to substantial powder material and heat loss. During high energy density laser processing of nickel alloy 625 powder material, a rapid heating from about $600-800^{\\circ} \\mathrm{C}$ temperature to $1200-1400{ }^{\\circ} \\mathrm{C}$ with a heating rate of $600^{\\circ} \\mathrm{C} / \\mathrm{ms}$ towards the scanning direction and cooling from the peak process temperature to $600{ }^{\\circ} \\mathrm{C}$ with a rate of $150^{\\circ} \\mathrm{C} / \\mathrm{ms}$ have been measured. These measured heating and cooling rates provide new in-depth process understanding and can be used in validating LPBF simulation models for prediction of thermal field and solidification microstructure.\n\n\\section*{Acknowledgement}\nThis project was supported by the National Institute of Standards and Technology, United States Department of Commerce, under the financial assistance number 70NANB14H227.\n\n\\section*{References}\n[1] ASTM ISO / ASTM52900-15, Standard Terminology for Additive Manufacturing General Principles - Terminology, ASTM International, West Conshohocken, PA, 2015.\n\n[2] K.N. Amato, S.M. Gaytan, L.E. Murr, E. Martinez, P.W. Shindo, J. Hernandez, S. Collins, F. Medina, Microstructures and mechanical behavior of Inconel 718 fabricated by selective laser melting, Acta Mater. 60 (2012) 2229-2239.\n\n[3] M.A. Anam, J.J.S. Dilip, D. Pal, B. Stucker, Effect of scan pattern on the microstructural evolution of Inconel 625 during selective laser melting, in: Proceedings of 25th Annual International Solid Freeform Fabrication Symposium, Austin, Texas, 2014.\n\n[4] M.A. Anam, D. Pal, B. Stucker, Modeling and experimental validation of nickelbased super alloy (Inconel 625) made using selective laser melting, in: Proceeding of the 24th Annual International Solid Free form Fabrication Symposium-An Additive Manufacturing Conference, Austin, TX, USA, 2013, pp. 463-473.\n\n[5] Y.M. Arisoy, L.E. Criales, T. \u00d6zel, B. Lane, S. Moylan, A. Donmez, Influence of scan strategy and process parameters on microstructure and its optimization in additively manufactured nickel alloy 625 via laser powder bed fusion, Int. J. Adv. Manuf. Technol. (2016). \\href{http://dx.doi.org/10.1007/s00170-016-9429-z}{http://dx.doi.org/10.1007/s00170-016-9429-z}.\n\n[6] E. Brinksmeier, G. Levy, D. Meyer, A.B. Spierings, Surface integrity of selectivelaser-melted components, CIRP Ann.-Manuf. Technol. 59 (1) (2010) 601-606.\n\n[7] L. Criales, Y.M. Arisoy, T. \u00d6zel, Sensitivity analysis of material and process parameters in finite element modeling of selective laser melting of Inconel 625, Int. J. Adv. Manuf. Technol. 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Wang, K. Guan, M. Gao, X. Li, X. Chen, X. Zeng, The microstructure and mechanical properties of deposited-IN718 by selective laser melting, J. Alloy. Compd. 513 (2012) 518-523,\n\n[42] I. Yadroitsev, P. Krakhmalev, I. Yadroitsava, Selective laser melting of Ti6Al4V alloy for biomedical applications: Temperature monitoring and microstructural evolution, J. Alloy. Compd. 583 (2013) 404-409.\n\n[43] E. Yasa, J.-P. Kruth, J. Deckers, Manufacturing by combining Selective Laser Melting and Selective Laser Erosion/laser re-melting, CIRP Ann.-Manuf. Technol. 60 (1) (2011) 263-266.\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{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{Optimization of Laser Powder Bed Fusion Processing Using a Combination of Melt Pool Modeling and Design of Experiment Approaches: Density Control }\n\n\n\\author{Morgan Letenneur, Alena Kreitcberg and Vladimir Brailovski *\\\\\nDepartment of Mechanical Engineering, \u00c9cole de technologie sup\u00e9rieure, 1100 Notre-Dame Street West,\\\\\nMontreal, QC H3C 1K3, Canada; morgan.letenneur.1@etsmtl.net (M.L.); alena.kreitcberg.1@ens.etsmtl.ca (A.K.)\\\\\n* Correspondence: vladimir.brailovski@etsmtl.ca; Tel.: +1-514-396-8594}\n\\date{}\n\n\n\\begin{document}\n\\maketitle\nArticle\n\nReceived: 18 December 2018; Accepted: 12 February 2019; Published: 21 February 2019\n\n\\begin{abstract}\nA simplified analytical model of the laser powder bed fusion (LPBF) process was used to develop a novel density prediction approach that can be adapted for any given powder feedstock and LPBF system. First, calibration coupons were built using IN625, Ti64 and Fe powders and a specific LPBF system. These coupons were manufactured using the predetermined ranges of laser power, scanning speed, hatching space, and layer thickness, and their densities were measured using conventional material characterization techniques. Next, a simplified melt pool model was used to calculate the melt pool dimensions for the selected sets of printing parameters. Both sets of data were then combined to predict the density of printed parts. This approach was additionally validated using the literature data on AlSi10Mg and 316L alloys, thus demonstrating that it can reliably be used to optimize the laser powder bed metal fusion process.\n\\end{abstract}\n\nKeywords: additive manufacturing; laser powder bed fusion; process optimization; analytical model\n\n\\section*{1. Introduction}\nInterest in laser powder bed fusion (LPBF) additive manufacturing (AM) has spiked in many industries, creating a high demand for new AM-ready metallic materials [1]. However, the mechanical properties, surface finish, and precision of LPBF parts are dependent on more than 60 processing parameters [2], which all need to be optimized. There are currently two main ways to realize this process optimization for new alloys. Most often, this optimization is carried out by defining an experiment plan that covers different arrangements of laser power, scanning speed, hatching space, layer thickness, scanning strategy and part orientation for a given alloy [3-10]. Once the specimens are printed, their mechanical properties are evaluated and a conclusion is drawn on the influence of the different processing parameters on the final part geometric and service attributes. This approach yields satisfying results, but requires multiple printing jobs and time-consuming post-processing experiments.", "start_char_idx": 113518, "end_char_idx": 117308, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "cdc320db-06ff-4fe2-9606-5b2dbc36ceee": {"__data__": {"id_": "cdc320db-06ff-4fe2-9606-5b2dbc36ceee", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d04fe305-175b-452e-ae82-5e02d8606d03", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "129fa910bb37a6d48c01483da16673f30ac5f4d5a39f0660191a124ddf394131", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fdb2d17a-247c-4e57-a71e-94ab5bf2d82c", "node_type": "1", "metadata": {}, "hash": "80d94a4a170111d8c78d7c8d0686d993c114e9aa4c9252c6cb4f73e3eae53a54", "class_name": "RelatedNodeInfo"}}, "text": "Introduction}\nInterest in laser powder bed fusion (LPBF) additive manufacturing (AM) has spiked in many industries, creating a high demand for new AM-ready metallic materials [1]. However, the mechanical properties, surface finish, and precision of LPBF parts are dependent on more than 60 processing parameters [2], which all need to be optimized. There are currently two main ways to realize this process optimization for new alloys. Most often, this optimization is carried out by defining an experiment plan that covers different arrangements of laser power, scanning speed, hatching space, layer thickness, scanning strategy and part orientation for a given alloy [3-10]. Once the specimens are printed, their mechanical properties are evaluated and a conclusion is drawn on the influence of the different processing parameters on the final part geometric and service attributes. This approach yields satisfying results, but requires multiple printing jobs and time-consuming post-processing experiments. It could easily be realized for a single alloy, but becomes prohibitively expensive if multiple process optimization campaigns are required.\n\nAnother way a new AM material can be introduced is by applying a numerical modeling approach with the objective of finding the appropriate printing parameters, as shown in [11-15]. However, due to a large number of variables, these models require significant time and computer resources to model a single laser track, let alone a complex part. Moreover, the more complex the model, the more laborious the calibration procedure, which makes the process optimization more cumbersome and labor-intensive.\n\nIn this work, we investigate the possibility of using a combination of a simplified analytical model of the melt pool and of an experimental calibration routine to create a density control algorithm for the\\\\\nlaser powder bed fusion process. The main objective of this approach is to reduce the time, the number of printing jobs and the quantity of post-processing characterization work needed to optimize the process for any given powder feedstock and any given LPBF system.\n\n\\section*{2. Methodology}\nPrevious studies have demonstrated that the density of LPBF manufactured parts is mostly dependent on the following three dimensionless melt pool metrics (Figure 1): melt pool depth-to-layer thickness ratio $(D / t)$, melt pool width-to-hatching space ratio $(W / h)$, and melt pool length-to-melt pool width ratio $(L / W)$, and that the highest density is generally obtained for $1.5<D / t<2,1.5<W / h<2.5$ and $L / W<2 P i[16,17]$. Based on these observations, we investigated the possibility of using the $D / t$, $W / h$ and $L / W$ ratios to correlate a specific combination of LPBF processing parameters (laser power, scanning speed, layer thickness, and hatching space) with the density of a printed material.\n\nThis study was conducted in three phases: first, the analytical model of a thermal field generated by a moving heat source in a solid body is used to evaluate the melt pool dimensions for a given set of LPBF processing parameters. Then, a relationship between the melt pool dimensions and the density of the printed material was found experimentally for a given material and LPBF system. Finally, using the numerical model developed and the experimental relationship found, the LPBF processing parameters were linked to the density of the manufactured parts with the objective of developing a porosity prediction algorithm for different materials and different LPBF systems.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-02}\n\\end{center}\n\nFigure 1. Schematic representation of the melt pool and the corresponding geometric characteristics [18].\n\n\\subsection*{2.1. Melt Pool Calculations}\nFirst, calculations of the LPBF melt pool dimensions were carried out using the analytical model of a semi-infinite solid with a moving Gaussian heat source [19]. This model has been successfully used for the determination of the LPBF processing parameters for pure iron [18] and Ti-Zr-Nb alloy [20]. The Gaussian model involves a symmetrical distribution of laser irradiance across the beam. The energy from the laser is assumed to be applied on the powder bed surface for a time interval defined by the scanning speed and the laser spot size. In this case, for a Gaussian beam moving with a given velocity, the temperature distribution $T(x \\cdot y \\cdot z)$ in the powder bed is calculated by Equations (1)-(3):", "start_char_idx": 116299, "end_char_idx": 120820, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fdb2d17a-247c-4e57-a71e-94ab5bf2d82c": {"__data__": {"id_": "fdb2d17a-247c-4e57-a71e-94ab5bf2d82c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "cdc320db-06ff-4fe2-9606-5b2dbc36ceee", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ebbace840b81a78edf714645daf412b7a7e55869c1d46b07841fe52893f56299", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "decf5d68-9ce3-4701-b56e-7e48f3c2c568", "node_type": "1", "metadata": {}, "hash": "acf80396f93f6f191dd909d2709260aaed2797f1c1c03e9a98cf5ccf53788878", "class_name": "RelatedNodeInfo"}}, "text": "Schematic representation of the melt pool and the corresponding geometric characteristics [18].\n\n\\subsection*{2.1. Melt Pool Calculations}\nFirst, calculations of the LPBF melt pool dimensions were carried out using the analytical model of a semi-infinite solid with a moving Gaussian heat source [19]. This model has been successfully used for the determination of the LPBF processing parameters for pure iron [18] and Ti-Zr-Nb alloy [20]. The Gaussian model involves a symmetrical distribution of laser irradiance across the beam. The energy from the laser is assumed to be applied on the powder bed surface for a time interval defined by the scanning speed and the laser spot size. In this case, for a Gaussian beam moving with a given velocity, the temperature distribution $T(x \\cdot y \\cdot z)$ in the powder bed is calculated by Equations (1)-(3):\n\n\n\\begin{equation*}\nT(x \\cdot y \\cdot z)=T_{0}+\\frac{A P}{k r_{f} \\pi^{\\frac{3}{2}}} \\int_{\\infty}^{0} \\frac{1}{1+\\tau^{2}} \\exp (C) d \\tau \\tag{1}\n\\end{equation*}\n\n\n\n\\begin{gather*}\nC=-\\frac{\\tau^{2}}{1+\\tau^{2}}\\left[\\left(\\xi-\\frac{P_{e}}{2 \\tau^{2}}\\right)^{2}+\\eta^{2}\\right]-\\tau^{2} \\zeta^{2}  \\tag{2}\\\\\n\\xi=\\sqrt{2} \\frac{x}{r_{f}} \\cdot \\eta=\\sqrt{2} \\frac{y}{r_{f}} \\cdot \\zeta=\\sqrt{2} \\frac{z}{r_{f}} \\cdot P e=\\frac{r_{f} \\mathrm{v}}{2 \\sqrt{2} \\alpha} \\cdot \\tau=\\frac{r_{f}}{2 \\sqrt{2 \\alpha t}} \\tag{3}\n\\end{gather*}\n\n\nwhere $T_{0}$ is the powder bed temperature $\\left({ }^{\\circ} \\mathrm{C}\\right) ; A$, the absorptivity; $P$, the laser power $(\\mathrm{W}) ; k$, the thermal conductivity $(\\mathrm{W} /(\\mathrm{m} \\cdot \\mathrm{K})) ; r_{f}$, the laser beam radius $(\\mathrm{m}) ; P e$, the Peclet number; $v$, the scanning speed $(\\mathrm{m} / \\mathrm{s}) ; \\alpha$, the thermal diffusivity $\\left(\\mathrm{m}^{2} / \\mathrm{s}\\right) ; \\rho$, the material density $\\left(\\mathrm{kg} / \\mathrm{m}^{3}\\right) ; c_{p}$, the specific heat $(\\mathrm{J} /(\\mathrm{kg} \\cdot \\mathrm{K}))$, and $t$, time $(\\mathrm{s})$.\n\nThe laser energy absorptivity $A$ is estimated using Equation (4) from the Drude's theory [19,21]:\n\n\n\\begin{equation*}\nA \\approx 0.365\\left(\\lambda \\sigma_{0}\\right)^{-0.5}=0.365\\left(\\frac{\\rho_{0}}{\\lambda}\\right)^{0.5} \\tag{4}\n\\end{equation*}", "start_char_idx": 119967, "end_char_idx": 122198, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "decf5d68-9ce3-4701-b56e-7e48f3c2c568": {"__data__": {"id_": "decf5d68-9ce3-4701-b56e-7e48f3c2c568", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fdb2d17a-247c-4e57-a71e-94ab5bf2d82c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c0d136166f431a276753373af5a26e149f2538affaacece90c107a64b2f91741", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f2781302-03d7-4606-82e6-2c5e45fc8d8d", "node_type": "1", "metadata": {}, "hash": "d7bd7249ba7db8d388d8af2672642c0d5aff9cea1b7f6a88232c34c7d2cbfd80", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{equation*}\nA \\approx 0.365\\left(\\lambda \\sigma_{0}\\right)^{-0.5}=0.365\\left(\\frac{\\rho_{0}}{\\lambda}\\right)^{0.5} \\tag{4}\n\\end{equation*}\n\n\nwhere $\\lambda$ is the laser wavelength $(\\mu \\mathrm{m}), \\sigma_{0}$, the electrical conductivity $(\\mathrm{S} / \\mathrm{m})$, and $\\rho_{0}$, the electrical resistivity of the irradiated material $(\\mathrm{Ohm} \\cdot \\mathrm{m})$.\n\n\\subsection*{2.2. Experimental Calibration}\n\\subsection*{2.2.1. Materials, Equipment and Plan of Experiment}\nThe experimental part of this study was conducted using the EOS-supplied IN625 powder and an EOSINT M280 LPBF system (EOS GmbH, Munich, Germany) equipped with a $400 \\mathrm{~W}$ ytterbium fiber laser (beam radius $r_{f}=50 \\mu \\mathrm{m}$ ). The initial temperature of the substrate (build platform) $T_{0}=60^{\\circ} \\mathrm{C}$. To design the plan of experiments, the analytical model represented by Equations (1)-(4) was used first. To this end, the following physical properties of an irradiated body: thermal conductivity $k_{0}$ [22], specific heat $C_{p 0}$ [23], and electrical resistivity $\\rho_{0}$ [24] need to be calculated, taking into account the effective powder bed density $\\varphi$, the latter being the powder morphology and spreading mechanism-dependent:\n\n\n\\begin{equation*}\nk=k_{0} \\times \\frac{\\varphi}{0.5(3-\\varphi)} ; C_{p}=C_{p 0} \\times \\varphi ; \\rho=0.696 \\times \\frac{4}{\\varphi} \\times \\rho_{0} \\tag{5}\n\\end{equation*}\n\n\nIn this work, the density $\\phi$ of IN625 powder spread by a standard EOS metal doctor blade and measured using the encapsulated samples method [25] was found to be close to $60 \\%$. Given the preceding, the IN625 alloy properties used for calculations are shown in Table 1. They were taken at room temperature, and it is considered that the preceding layer cools down to $60{ }^{\\circ} \\mathrm{C}$ between two scanning runs.\n\nTable 1. Physical properties of IN625 powder [26,27].\n\n\\begin{center}\n\\begin{tabular}{ccc}\n\\hline\n & Bulk & Powder $(\\boldsymbol{\\varphi} \\mathbf{6 0 \\%})$ \\\\\n\\hline\nMelting temperature, ${ }^{\\circ} \\mathrm{C}$ & 1350 & 1350 \\\\\nDensity, $\\mathrm{kg} / \\mathrm{m}^{3}$ & 8440 & 5072 \\\\\nThermal conductivity, $\\mathrm{W} /(\\mathrm{m} \\cdot \\mathrm{K})$ & 25.2 & 15.1 \\\\\nSpecific heat capacity, $\\mathrm{J} /(\\mathrm{kg} \\cdot \\mathrm{K})$ & 670 & 403 \\\\\nElectrical resistivity, $10^{-8} \\Omega \\cdot \\mathrm{m}$ & 134 & 223 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nThe temperature distribution map shown in Figure 2 represents an example of calculations using Equations (1)-(5). It corresponds to the following set of LPBF processing parameters: $P=270 \\mathrm{~W}$, $v=1000 \\mathrm{~mm} / \\mathrm{s}$, and $t=40 \\mu \\mathrm{m}$ applied to IN625 powder (Table 1). From this temperature map, the melt pool width, depth and length are delimited by the alloy melting temperature of $1350{ }^{\\circ} \\mathrm{C}: \\mathrm{W}=173 \\mu \\mathrm{m}$, $D=89 \\mu \\mathrm{m}$, and $L=806 \\mu \\mathrm{m}$, which correspond to the following dimensionless metrics: $D / t=2.2$ and\\\\\n$L / W=4.7$ (since only a single track is modeled, the hatching space $h$ is not considered at this stage). This calculation procedure can be repeated for any material and any given set of processing parameters.", "start_char_idx": 122054, "end_char_idx": 125298, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f2781302-03d7-4606-82e6-2c5e45fc8d8d": {"__data__": {"id_": "f2781302-03d7-4606-82e6-2c5e45fc8d8d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "decf5d68-9ce3-4701-b56e-7e48f3c2c568", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ac15aab4eca145a12675000ef0c1d8477104c5e5054653769af8f3c75b28113e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "52f1f864-f20d-4c9d-9e5d-f41bb0192f88", "node_type": "1", "metadata": {}, "hash": "f42c0c9406faceb11b256572852e4d4756e71b1ae8a740116c6f923ceed0900e", "class_name": "RelatedNodeInfo"}}, "text": "From this temperature map, the melt pool width, depth and length are delimited by the alloy melting temperature of $1350{ }^{\\circ} \\mathrm{C}: \\mathrm{W}=173 \\mu \\mathrm{m}$, $D=89 \\mu \\mathrm{m}$, and $L=806 \\mu \\mathrm{m}$, which correspond to the following dimensionless metrics: $D / t=2.2$ and\\\\\n$L / W=4.7$ (since only a single track is modeled, the hatching space $h$ is not considered at this stage). This calculation procedure can be repeated for any material and any given set of processing parameters.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-04}\n\\end{center}\n\nFigure 2. Melt pool dimensions for IN625 powder when $P=270 \\mathrm{~W}, v=1000 \\mathrm{~mm} / \\mathrm{s}$, and $t=40 \\mu \\mathrm{m}$; the melt pool width and depth are delimited by the alloy melting temperature.\n\n\\subsection*{2.2.2. Melt Pool Dimensions-Density Relationship}\nTo establish the relationship between the previously defined dimensionless melt pool metrics and the density of manufactured parts, $10 \\mathrm{~mm}$-diameter $15 \\mathrm{~mm}$-height cylindrical coupons of IN625 alloy were printed to cover a $D / t$ ratio ranging from 1 to $3.5, W / h$, from 0.5 to 3 and $L / W$, from 3 to 6 . To find the LPBF parameters resulting in these melt pool dimensions, the following ranges of printing parameters were reversely computed using the melt pool model presented in Section 2.1: the laser power varying from 160 to $350 \\mathrm{~W}$, the scanning speed, from 560 to $2800 \\mathrm{~mm} / \\mathrm{s}$, and the hatching space, from 30 to $550 \\mu \\mathrm{m}$; the layer thickness $t$ was kept constant at $40 \\mu \\mathrm{m}$ (see Table 2 for the selected values of the LPBF processing parameters). Two specimens were printed for each set of printing parameters.\n\nTable 2. Imposed melt pool metrics and calculated processing parameters (plan of experiments).\n\n\\begin{center}\n\\begin{tabular}{ccc}\n\\hline\n & Melt Pool Dimensionless Metrics &  \\\\\n\\hline\n\\multirow{3}{*}{Imposed} & $D / t$ & $1,1.5,2,2.5,3,3.5$ \\\\\n & $W / h$ & $0.5,1,1.5,2,2.5,3$ \\\\\n & $L / W$ & $3.2,3.9,4.5,5$ \\\\\n\\hline\n & LPBF Processing Parameters &  \\\\\n\\hline\n\\multirow{3}{*}{Calculated} & $160,225,340,345,350$ &  \\\\\n & Laser power $P, \\mathrm{~W}$ & $560,800,1060,1180,1680,1940,2800$ \\\\\n & Scanning speed $v, \\mathrm{~mm} / \\mathrm{s}$ & 40 \\\\\n & Layer thickness $t, \\mu \\mathrm{m}$ & $30,40, \\ldots, 180,190,210,230,270,280,350,390,430,470,550$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nAfter processing, the printed coupons were cut off the build plate and their densities measured using the Archimedes' technique (ASTM B962-15). Each density measurement using a SARTORIUS Secura 324-1s scale (Sartorius, Goettingen, Germany), having a precision of $\\sim 0.001 \\mathrm{~g}$, was repeated at least 3 times.\n\nThe results of this experiment are collected in Table 3 (Appendix A) and plotted in Figure 3 in the $D / t-W / h$-density coordinates.", "start_char_idx": 124785, "end_char_idx": 127729, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "52f1f864-f20d-4c9d-9e5d-f41bb0192f88": {"__data__": {"id_": "52f1f864-f20d-4c9d-9e5d-f41bb0192f88", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f2781302-03d7-4606-82e6-2c5e45fc8d8d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0217d8297bd70f95efa72bc426ec1792ae25fa45af9f950cc7d5b4240d63a2f3", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "dd16b88c-c45d-42ce-ba48-b36b6881b820", "node_type": "1", "metadata": {}, "hash": "40b54e84e4a803260d5c478137ead5853849bda9d753b668c482ca3e037fe65a", "class_name": "RelatedNodeInfo"}}, "text": "Each density measurement using a SARTORIUS Secura 324-1s scale (Sartorius, Goettingen, Germany), having a precision of $\\sim 0.001 \\mathrm{~g}$, was repeated at least 3 times.\n\nThe results of this experiment are collected in Table 3 (Appendix A) and plotted in Figure 3 in the $D / t-W / h$-density coordinates. It can be seen from this figure that the density of IN625 coupons exceeding $99.5 \\%$ (this value was selected arbitrarily to limit the amount of experimental data, while leaving enough space for optimization) was obtained for a $D / t$ ratio ranging from 1.5 to 2.75 and a $W / h$\\\\\nratio ranging from 1.8 to 2.8 . The corresponding $L / W$ ratio ranged from 3.8 to 4.6 (not shown on this diagram). Note that the calculated values fall close to the ranges recommended in the literature, which are $1.5<D / t<2,1.5<W / h<2.5$ and $L / W<2 \\operatorname{Pi}[28]$.\n\nFrom Figure 3 , assuming that the calculated $D / t, W / h$ ratios correspond to the effectively obtained melt pool dimensions, the materials density can be expressed as their function as follows:\n\n\n\\begin{equation*}\n\\rho=a 0+a 1 \\cdot\\left(\\frac{D}{t}\\right)+a 2 \\cdot\\left(\\frac{W}{h}\\right)+a 3 \\cdot\\left(\\frac{D}{t}\\right)^{2}+a 4 \\cdot\\left(\\frac{D}{t}\\right) \\cdot\\left(\\frac{W}{h}\\right)+a 5 \\cdot\\left(\\frac{W}{h}\\right)^{2} \\tag{6}\n\\end{equation*}\n\n\nwhere $a 0=0.512, a 1=0.212, a 2=0.225, a 3=-0.027, a 4=-0.384$, and $a 5=-0.031$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-05}\n\\end{center}\n\nFigure 3. Density of the printed coupons as a function of the $D / t$ and $W / h$ ratios; the calculated $D / t-W / h$ area corresponds to the measured density of the printed material exceeding $99.5 \\pm 0.1 \\%$.\n\n\\subsection*{2.3. Energy Density-Build Rate Processing Map}\nIn this work, the LPBF processing conditions were expressed by a combination of two metrics: the volumetric laser energy density $E\\left(\\mathrm{~J} / \\mathrm{mm}^{3}\\right)(7)$ and the material build rate $B R\\left(\\mathrm{~cm}^{3} / \\mathrm{h}\\right)(8)$; the product of both corresponds to the laser power $P$ (Watts).\n\n\n\\begin{align*}\n& E\\left(J / \\mathrm{mm}^{3}\\right)=\\frac{P}{v \\cdot h \\cdot t}  \\tag{7}\\\\\n& B R\\left(\\mathrm{~cm}^{3} / h\\right)=v \\cdot h \\cdot t \\tag{8}\n\\end{align*}\n\n\nNext, the analytical model (1-5) and Table 1 were used to map three $E-B R$ areas corresponding to the experimentally obtained optimal ranges of the melt pool metrics (Figure 4a): $D / t=1.5-2.75$, $W / h=1.8-2.8$, and $L / W=3.8-4.6$. These maps are calculated by varying the laser power from 20 to $380 \\mathrm{~W}$; the scanning speed, from 100 to $4000 \\mathrm{~mm} / \\mathrm{s}$; the hatching space, from 30 to $200 \\mu \\mathrm{m}$, and the layer thickness, from 20 to $80 \\mu \\mathrm{m}$.\n\nThree $E-B R$ areas of Figure 4a were then superposed in Figure $4 \\mathrm{~b}$ to schematically delimit a common processing window, which must guarantee the maximum density of printed IN625 parts.", "start_char_idx": 127418, "end_char_idx": 130404, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "dd16b88c-c45d-42ce-ba48-b36b6881b820": {"__data__": {"id_": "dd16b88c-c45d-42ce-ba48-b36b6881b820", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "52f1f864-f20d-4c9d-9e5d-f41bb0192f88", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ac2fdcae4c67e854ac6336e6efac57815a15db40bc3fafa52239ae198f88667e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5d652c49-d6d7-448c-89d4-0f92dce2e869", "node_type": "1", "metadata": {}, "hash": "b375fe962834fce9f7cb869d06801d5124280c3f7680db550164c43ac46e7b0c", "class_name": "RelatedNodeInfo"}}, "text": "These maps are calculated by varying the laser power from 20 to $380 \\mathrm{~W}$; the scanning speed, from 100 to $4000 \\mathrm{~mm} / \\mathrm{s}$; the hatching space, from 30 to $200 \\mu \\mathrm{m}$, and the layer thickness, from 20 to $80 \\mu \\mathrm{m}$.\n\nThree $E-B R$ areas of Figure 4a were then superposed in Figure $4 \\mathrm{~b}$ to schematically delimit a common processing window, which must guarantee the maximum density of printed IN625 parts. Next, the densities of the printed coupons (Figure 3 and Table 1 in the Annex) were superposed on this\\\\\nprocessing window, and it can be seen that the coupons with a density $\\geq 99.5 \\%$ are indeed located, within a certain margin of error, in the numerically predicted optimal processing window. By refining the scanning steps and using calibration Equation (6), the described approach can then be used to build a more detailed processing map for IN625 powder (Figure 4c).\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-06(4)}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-06(2)}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-06(3)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-06(1)}\n\\end{center}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-06}\n\\end{center}\n\nFigure 4. (a) Optimal areas for the $D / t, W / h$, and $L / W$ ratios; (b) superposition of the numerically optimized processing window; (c) experimentally calibrated processing map.\n\n\\subsection*{2.4. Validation Strategy for the Proposed Processing Optimization Approach}\nWe hypothesize that such a combined processing optimization approach is valid for any material processed by a given LPBF system. In our case it is the EOS M280 LPBF system. To verify this hypothesis, the results of such an optimization were compared with the numerical and experimental data found in the literature. This comparison was carried out in two phases: first, the melt pool dimensions were calculated for AlSi10Mg and 316L powders using a simplified analytical model of this work (Equations (1)-(5)), and then compared against those obtained for the same feedstock material, but using more powerful finite element models (FEM). These FEM models take into account the optical penetration depth, the mass transfer-related phenomena, such as the Marangoni convection and the Rayleigh capillary flow, and the heat losses to the environment [11,29]. Secondly, the numerically predicted densities for pure iron and Ti-6Al-4V alloy powders are compared with their experimentally measured equivalents from [6] and [18]. The optimal processing windows for all these validation studies were obtained using the algorithm previously presented. The data used for these calculations were taken from the corresponding literature sources.\n\n\\section*{3. Validation}\n\\subsection*{3.1. Melt Pool Dimensions (Single Track)}\nAs experimental validation of the melt pool model used in this study (Equations (1)-(5)) has already been carried out in our previous work [20], a decision was made to extend the validation experiments to literature data. With this objective in mind, the single track melt pool dimensions calculated by the said analytical model were compared with those calculated by two different finite\\\\\nelement models. Note that each of these models was experimentally validated by their authors for two different alloys: 316L [11] and AlSi10Mg [14]. For ease of understanding and because the width and the depth of the melt pool are the most important characteristics impacting the density of the printed material, the geometric validation was limited to these two characteristics.", "start_char_idx": 129947, "end_char_idx": 133793, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5d652c49-d6d7-448c-89d4-0f92dce2e869": {"__data__": {"id_": "5d652c49-d6d7-448c-89d4-0f92dce2e869", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "dd16b88c-c45d-42ce-ba48-b36b6881b820", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "771a4ec197dc191137634c6f7717d44684c044692f7cdb3756b60d85fe673ebe", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "e01f7288-5660-47b3-a85f-5f9cef8b7a74", "node_type": "1", "metadata": {}, "hash": "f98435238f48d55b9b4831f91b60fd9e9a09c561e3b83a635697fefc4e094588", "class_name": "RelatedNodeInfo"}}, "text": "The data used for these calculations were taken from the corresponding literature sources.\n\n\\section*{3. Validation}\n\\subsection*{3.1. Melt Pool Dimensions (Single Track)}\nAs experimental validation of the melt pool model used in this study (Equations (1)-(5)) has already been carried out in our previous work [20], a decision was made to extend the validation experiments to literature data. With this objective in mind, the single track melt pool dimensions calculated by the said analytical model were compared with those calculated by two different finite\\\\\nelement models. Note that each of these models was experimentally validated by their authors for two different alloys: 316L [11] and AlSi10Mg [14]. For ease of understanding and because the width and the depth of the melt pool are the most important characteristics impacting the density of the printed material, the geometric validation was limited to these two characteristics.\n\nRegarding 316L, the simulations were carried out with an initial powder bed temperature of $296 \\mathrm{~K}$ (first track in [11]), a fixed laser power of $110 \\mathrm{~W}$ and a scanning speed ranging from 80 to $150 \\mathrm{~mm} / \\mathrm{s}$. For AlSi10Mg, the simulations were realized for a laser power ranging from 150 to $300 \\mathrm{~W}$ and a fixed scanning speed of $200 \\mathrm{~mm} / \\mathrm{s}$ [14]. In both cases, computations using (Equations (1)-(5)) were carried out using the physical properties taken from the corresponding literature sources (Table 3). In other words, the electrical resistivity, the thermal conductivity and the specific heat capacity values used in our calculations were set identical to those used in [11] and [14] and recalculated for a $60 \\%$ powder bed density. This last value was selected on the basis of our previous results because no such information was provided in the literature sources.\n\nTable 3. Physical properties of the AlSi10Mg [13] and 316L [15] powders used for melt pool modeling.\n\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\n & \\multicolumn{2}{c}{AlSi10Mg} & \\multicolumn{2}{c}{316L} \\\\\n\\cline { 2 - 5 }\n & Bulk & Powder $(\\boldsymbol{\\varphi = 6 0 \\%})$ & Bulk & Powder $(\\boldsymbol{\\varphi} \\mathbf{6 0 \\%})$ \\\\\n\\hline\nMelting temperature, ${ }^{\\circ} \\mathrm{C}$ & 600 & 600 & 1400 & 1400 \\\\\nDensity, $\\mathrm{kg} / \\mathrm{m}^{3}$ & 2650 & 1590 & 8000 & 4800 \\\\\nThermal conductivity, $\\mathrm{W} /(\\mathrm{m} \\cdot \\mathrm{K})$ & 147 & 88.2 & 16.2 & 9.7 \\\\\nSpecific heat capacity, $\\mathrm{J} /(\\mathrm{kg} \\cdot \\mathrm{K})$ & 739 & 443.4 & 530 & 318 \\\\\nElectrical resistivity, $10^{-8} \\Omega \\cdot \\mathrm{m}$ & $7.8[30]$ & 4.7 & 74 & 123 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nThe melt pool profiles calculated by the model of this study and those found in the literature are plotted in Figure 5 for different sets of printing parameters. The mean deviations between the results of the analytical and the finite element models are $4.3 \\pm 1.2 \\%$ for $316 \\mathrm{~L}$ and $10.5 \\pm 5.8 \\%$ for AlSi10Mg. (Note that the numerically estimated impact of a $5.8 \\%$ deviation in the AlSi10Mg melt pool dimensions would have introduced only $\\sim 0.2 \\%$ variation in the predicted density values; the last number being calculated by introducing a value of $5.8 \\%$ in the density Equation (6)).", "start_char_idx": 132851, "end_char_idx": 136160, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "e01f7288-5660-47b3-a85f-5f9cef8b7a74": {"__data__": {"id_": "e01f7288-5660-47b3-a85f-5f9cef8b7a74", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5d652c49-d6d7-448c-89d4-0f92dce2e869", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c21ff96d212c20d973584c08e122019077a591b40e32c03e9e05d58759f7d904", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1dee1abc-84dc-4cbe-8d39-c3de4a062fe2", "node_type": "1", "metadata": {}, "hash": "9d612d2bd288f4ca915a50b8839aecc85fa54e2ec0fc018addd12b13a0aef895", "class_name": "RelatedNodeInfo"}}, "text": "The mean deviations between the results of the analytical and the finite element models are $4.3 \\pm 1.2 \\%$ for $316 \\mathrm{~L}$ and $10.5 \\pm 5.8 \\%$ for AlSi10Mg. (Note that the numerically estimated impact of a $5.8 \\%$ deviation in the AlSi10Mg melt pool dimensions would have introduced only $\\sim 0.2 \\%$ variation in the predicted density values; the last number being calculated by introducing a value of $5.8 \\%$ in the density Equation (6)).\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-07}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-07(2)}\n\\end{center}\n\nAlSi10Mg\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_fc09789349ca6c152437g-07(1)}\n\nFigure 5. Comparison of the melt pools profiles for (a) 316L [11] and (b) AlSi10Mg [14] alloys.\n\n\\subsection*{3.2. Density of the Same Alloy Printed with Two Different Layer Thicknesses}\nUsing a combination of the analytical modeling of melt pool dimensions (Equations (1)-(5)) and Equation (6), representing the correspondence between the melt pool dimensions and the density of the printed parts, processing windows can be calculated for multi-track LPBF. To validate this approach, processing maps for Ti64 alloy printed with two layer thicknesses (30 and $60 \\mathrm{um}$ ) are plotted in Figure 6. The physical properties used for these calculations are collected in Table 4.\n\nNote that the powder bed densities (evaluated using the method of encapsulated samples [25]) in these two cases are not identical: it is higher in the former than in the latter case, with $\\varphi=70 \\%$ for $t=30 \\mu \\mathrm{m}$ and $\\varphi=60 \\%$ for $t=60 \\mu \\mathrm{m}$. These changes in the powder bed density are due to the\\\\\ndifferences in the powder spreading conditions for different layer thicknesses as demonstrated in [31]. If a layer thickness is smaller than the D90 value of the powder particle distribution [32], the density increases because the biggest particles are kept at the top of the layer and finally swept out by the recoater [33], which increases the powder bed density. It can be seen from Figure 6 that the higher the powder bed density $(70 \\%$, Figure $6 \\mathrm{~b}$, instead of $60 \\%$, Figure $6 \\mathrm{a})$, the higher the optimal laser power density, while the lower the build rate of the process. Similar results were reported in [31].\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-08(1)}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-08}\n\\end{center}\n\nFigure 6. Processing maps for Ti64 alloy for layer thicknesses of (a) $60 \\mu \\mathrm{m}$ and (b) $30 \\mu \\mathrm{m}$ (EOS M 280).\n\nTable 4. Physical properties of Ti64 powders used for melt pool modeling [26,34].", "start_char_idx": 135707, "end_char_idx": 138574, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1dee1abc-84dc-4cbe-8d39-c3de4a062fe2": {"__data__": {"id_": "1dee1abc-84dc-4cbe-8d39-c3de4a062fe2", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e01f7288-5660-47b3-a85f-5f9cef8b7a74", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3c731fc358434585977cc62adee908d17b40901badfd416658a3640d78b4528f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7e8fc634-6cc5-4310-b610-1d5745453ad4", "node_type": "1", "metadata": {}, "hash": "14b3d0c8eea6a350007d5ec5d56da1c21dbec8c90fee385480872e587f5be148", "class_name": "RelatedNodeInfo"}}, "text": "Similar results were reported in [31].\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-08(1)}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-08}\n\\end{center}\n\nFigure 6. Processing maps for Ti64 alloy for layer thicknesses of (a) $60 \\mu \\mathrm{m}$ and (b) $30 \\mu \\mathrm{m}$ (EOS M 280).\n\nTable 4. Physical properties of Ti64 powders used for melt pool modeling [26,34].\n\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\n & \\multicolumn{2}{c}{Ti64 $(t=\\mathbf{6 0} \\boldsymbol{\\mu \\mathrm { m }})$} & Ti64 $(t=\\mathbf{3 0} \\boldsymbol{\\mu \\mathrm { m }})$ \\\\\n\\cline { 2 - 4 }\n & Bulk & Powder $(\\boldsymbol{\\varphi} \\mathbf{6 0 \\%})$ & Powder $(\\boldsymbol{\\varphi}=\\mathbf{7 0} \\mathbf{)} \\mathbf{c}$ \\\\\n\\hline\nMelting temperature, ${ }^{\\circ} \\mathrm{C}$ & 1660 & 1660 & 1660 \\\\\nDensity, $\\mathrm{kg} / \\mathrm{m}^{3}$ & 4410 & 2630 & 3150 \\\\\nThermal conductivity, $\\mathrm{W} /(\\mathrm{m} \\cdot \\mathrm{K})$ & 7.3 & 4.27 & 5.18 \\\\\nSpecific heat capacity, $\\mathrm{J} /(\\mathrm{kg} \\cdot \\mathrm{K})$ & 570 & 342 & 405 \\\\\nElectrical resistivity, $10^{-8} \\Omega \\cdot \\mathrm{m}$ & 170 & 283 & 239 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nThe experimentally measured densities of Ti64 coupons printed with the layer thicknesses of $t=60 \\mu \\mathrm{m}$ (Figure 6a) and $30 \\mu \\mathrm{m}$ (Figure 6b) were then superposed on the calculated processing maps (these coupons were printed using EOS Ti64 powder and the EOS M280 system of this study). The mean porosity deviations for $t=60 \\mu \\mathrm{m}$ corresponded to $0.8 \\%$, while for $t=30 \\mu \\mathrm{m}$, it was $0.4 \\%$.\n\n\\subsection*{3.3. Density of Two Different Alloys}\nThe reliability of the proposed processing optimization approach was then studied for Fe [18] and AlSi10Mg [35] powders. The density predictions were made using the physical properties of Table 5 and the processing maps are plotted in Figure 7a,b. The experimentally measured density values were superposed, and the deviations between the model and the experiment corresponded to $0.8 \\%$ for $\\mathrm{Fe}$ and $0.7 \\%$ for AlSi10Mg powders.\n\nTable 5. Physical properties of Fe [3] and AlSi10Mg [20] powders used for melt pool modeling.", "start_char_idx": 138103, "end_char_idx": 140364, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7e8fc634-6cc5-4310-b610-1d5745453ad4": {"__data__": {"id_": "7e8fc634-6cc5-4310-b610-1d5745453ad4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1dee1abc-84dc-4cbe-8d39-c3de4a062fe2", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d8cad6b86b8335d8dd86f46d503be80e3c58eb255cef29c2fca46808982ab989", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a2a0c635-e82d-414a-a1db-68b43852e588", "node_type": "1", "metadata": {}, "hash": "49bb63fa8c2869cf782dfb2b0faf13711c7dae6b5eb7ce5aabeac2108a2e768c", "class_name": "RelatedNodeInfo"}}, "text": "The mean porosity deviations for $t=60 \\mu \\mathrm{m}$ corresponded to $0.8 \\%$, while for $t=30 \\mu \\mathrm{m}$, it was $0.4 \\%$.\n\n\\subsection*{3.3. Density of Two Different Alloys}\nThe reliability of the proposed processing optimization approach was then studied for Fe [18] and AlSi10Mg [35] powders. The density predictions were made using the physical properties of Table 5 and the processing maps are plotted in Figure 7a,b. The experimentally measured density values were superposed, and the deviations between the model and the experiment corresponded to $0.8 \\%$ for $\\mathrm{Fe}$ and $0.7 \\%$ for AlSi10Mg powders.\n\nTable 5. Physical properties of Fe [3] and AlSi10Mg [20] powders used for melt pool modeling.\n\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\n & Fe & AlSi10Mg &  &  \\\\\n\\hline\n & Bulk & \\begin{tabular}{c}\nPowder $(t=\\mathbf{6 0} \\boldsymbol{\\mu m} ;$ \\\\\n$\\boldsymbol{\\varphi}=\\mathbf{6 0} \\%)$ \\\\\n\\end{tabular} & Bulk & \\begin{tabular}{c}\nPowder $(t=\\mathbf{3 0} \\boldsymbol{\\mu m} ;$ \\\\\n$\\boldsymbol{\\varphi}=\\mathbf{4 5 \\%})$ \\\\\n\\end{tabular} \\\\\n\\hline\nMelting temperature, ${ }^{\\circ} \\mathrm{C}$ & 1660 & 1660 & 600 & 600 \\\\\nDensity, $\\mathrm{kg} / \\mathrm{m}^{3}$ & 8000 & 4800 & 2650 & 1200 \\\\\nThermal conductivity, $\\mathrm{W} /(\\mathrm{m} \\cdot \\mathrm{K})$ & 16.2 & 9.7 & 147 & 66.6 \\\\\nSpecific heat capacity, $\\mathrm{J} /(\\mathrm{kg} \\cdot \\mathrm{K})$ & 530 & 318 & 739 & 335 \\\\\nElectrical resistivity, $10^{-8} \\Omega \\cdot \\mathrm{m}$ & 74 & 123 & 7.8 & 17.2 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-09(3)}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-09(2)}\n\\end{center}\n\nFigure 7. Processing maps for (a) Fe and (b) AlSi10Mg.\n\n\\section*{4. Discussion and Application Example}\nNotwithstanding that the simplified analytical model used in this study does not take into account the specificities of a given printing system in terms of heat exchange and powder spreading conditions, which both influence the density of the manufactured parts, it was demonstrated that such a model could provide useful information in terms of the energy density and the build rate values, which are potentially suitable for the printing of dense parts. However, to determine the exact set of processing parameters, such as the laser power, speed, hatching space, and layer thickness, an additional condition must be respected, and this condition corresponds to the ratio between the hatching space and the layer thickness, $h / t$.\n\nTo establish such a condition, the previously developed model was used to plot the density of IN625 components as a function of the $h / t$ ratio for different layer thicknesses (Figure 8a). From this plot, it is clear that to maximize the material density, the selection of a hatching space must be related to the selection of a layer thickness (Figure 8b). For example, to guarantee the maximum material density $\\geq 99.8 \\%$, with a layer thickness of $t=30 \\mu \\mathrm{m}$, the hatching space variations must be limited to the 50 to $80 \\mu \\mathrm{m}$ range, while for a layer thickness of $t=90 \\mu \\mathrm{m}$, the hatching space variations must be limited to the 110 to $220 \\mu \\mathrm{m}$ range.", "start_char_idx": 139645, "end_char_idx": 142948, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a2a0c635-e82d-414a-a1db-68b43852e588": {"__data__": {"id_": "a2a0c635-e82d-414a-a1db-68b43852e588", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7e8fc634-6cc5-4310-b610-1d5745453ad4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "85f8824eda9e554ec9ad95eefd2a7d660b92d3701b23a57709931e8c402e973d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "dc7be2f8-1d6c-4d7f-b33d-485488bd8649", "node_type": "1", "metadata": {}, "hash": "acfdd12274325d5162f7ba5b5c4ae5f2b498354056ffe7603e0542adba9b0b67", "class_name": "RelatedNodeInfo"}}, "text": "To establish such a condition, the previously developed model was used to plot the density of IN625 components as a function of the $h / t$ ratio for different layer thicknesses (Figure 8a). From this plot, it is clear that to maximize the material density, the selection of a hatching space must be related to the selection of a layer thickness (Figure 8b). For example, to guarantee the maximum material density $\\geq 99.8 \\%$, with a layer thickness of $t=30 \\mu \\mathrm{m}$, the hatching space variations must be limited to the 50 to $80 \\mu \\mathrm{m}$ range, while for a layer thickness of $t=90 \\mu \\mathrm{m}$, the hatching space variations must be limited to the 110 to $220 \\mu \\mathrm{m}$ range.\n\nThese results are shown in Figure $8 \\mathrm{~b}$ to present the $h-t$ area corresponding to the maximum density of IN625 parts. In the same figure, corresponding $h-t$ areas are plotted for AlSi10Mg (Table 3) and Ti64 (Table 4) alloys, for comparison. Finally, once obtained, such plots provide guidance for the selection of the most appropriate hatching space/layer thickness combinations.\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-09}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-09(1)}\n\\end{center}\n\nFigure 8. Hatching space/Layer thickness relations: (a) density as a function of the $h / t$ ratio; (b) hatching space as a function of the layer thickness for maximum density $\\geq 99.5 \\%$ (IN625, AlSi10Mg and Ti64 powders for an EOS M280 LPBF system).\n\nNote that even though this combined modeling-experiment approach was validated for only one specific LPBF system (EOS M 280), we hypothesize that it can be extended to any LPBF system, provided an adequate calibration experiment is carried out. To this end, after generating the first processing map assuming the physical properties of the material taken from the literature and a powder bed density of $60 \\%$, a series of calibration coupons must be printed. Once the density of the printed coupons is measured, the model must be adjusted to fit the experimentally obtained values, by modifying the coefficients of Equation 6 . Finally, the relation between the hatching space and the layer thickness can be plotted for a maximum printed material density (see Figure 8b). Once all these conditions are met, the LPBF processing parameters (laser powder, scanning speed, hatching space and layer thickness) can be determined using the following protocol:\n\n\\begin{enumerate}\n  \\item The layer thickness is selected first to provide a required precision/performance relationship (Figure 9a). If we take $t=40 \\mu \\mathrm{m}$ to favor precision, the processing map for this layer thickness can be built as shown in Figure 9c.\n\n  \\item As, in this case, $h$ can vary from 50 to $110 \\mu \\mathrm{m}$ (Figure 9b), the highest hatch value of $110 \\mu \\mathrm{m}$ can be specified to improve the process productivity.\n\n  \\item To print components with a material density $\\geq 99.8 \\%$ and a maximum allowable build rate of $B R=15 \\mathrm{~cm}^{3} / \\mathrm{h}$ (Figure 9), the corresponding volumetric laser energy density corresponds to $E=67 \\mathrm{~J} / \\mathrm{mm}^{3}$ (see the dot in Figure 9c). Since $t=40 \\mu \\mathrm{m}$ and $h=110 \\mu \\mathrm{m}$, the remaining LPBF parameters can easily be defined using the energy density and build rate definitions of Equations (7) and (8): laser power $\\sim 285 \\mathrm{~W}$ and scanning speed $\\sim 960 \\mathrm{~mm} / \\mathrm{s}$ [36].", "start_char_idx": 142242, "end_char_idx": 145801, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "dc7be2f8-1d6c-4d7f-b33d-485488bd8649": {"__data__": {"id_": "dc7be2f8-1d6c-4d7f-b33d-485488bd8649", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a2a0c635-e82d-414a-a1db-68b43852e588", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a940dd7bd6c757f7f8edc7bc62ff1f1b73654fef22dedc39e9f50302c39d2b27", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "92ea837f-1cf8-419e-aacd-bdefbd3da3bd", "node_type": "1", "metadata": {}, "hash": "bc6f53f02e0275ef8fa9996f47c7276f0c2de9a25990944b07f9fa13a600ee3a", "class_name": "RelatedNodeInfo"}}, "text": "\\item To print components with a material density $\\geq 99.8 \\%$ and a maximum allowable build rate of $B R=15 \\mathrm{~cm}^{3} / \\mathrm{h}$ (Figure 9), the corresponding volumetric laser energy density corresponds to $E=67 \\mathrm{~J} / \\mathrm{mm}^{3}$ (see the dot in Figure 9c). Since $t=40 \\mu \\mathrm{m}$ and $h=110 \\mu \\mathrm{m}$, the remaining LPBF parameters can easily be defined using the energy density and build rate definitions of Equations (7) and (8): laser power $\\sim 285 \\mathrm{~W}$ and scanning speed $\\sim 960 \\mathrm{~mm} / \\mathrm{s}$ [36].\n\n\\end{enumerate}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-10}\n\\end{center}\n\n\\begin{enumerate}\n  \\item Selection of $\\mathrm{t}$ (b)\n\\end{enumerate}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-10(1)}\n\\end{center}\n\n\\begin{enumerate}\n  \\setcounter{enumi}{1}\n  \\item Determination of $\\mathrm{h}$\n\\end{enumerate}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_fc09789349ca6c152437g-10(2)}\n\\end{center}\n\n\\begin{enumerate}\n  \\setcounter{enumi}{2}\n  \\item Simulation and determination of $\\mathrm{P}$ and $\\mathrm{v}$\n\\end{enumerate}\n\nFigure 9. Steps needed for the printing parameters determination from a processing map: (a) selection of a layer thickness, (b) selection of an appropriate hatching space, and (c) determination of the corresponding laser power and scanning speed values.\n\nAs it is widely assumed that the smaller the layer thickness, the better the surface finish and part precision, but the lower the build rate, it is recommended to work with layer thicknesses of 30 or $40 \\mu \\mathrm{m}$ when precision is required, and of 50 or $60 \\mu \\mathrm{m}$, when process productivity is more important.\n\n\\section*{5. Conclusions}\nA simplified analytical model of the LPBF process was used to develop the density prediction algorithm for a given powder feedstock and a given LPBF system. Using a set of density calibration coupons built with the laser power varying from 160 to $350 \\mathrm{~W}$; the scanning speed, from 500 to $2800 \\mathrm{~mm} / \\mathrm{s}$; the hatching space, from 30 to $550 \\mu \\mathrm{m}$, and the layer thickness, from 30 to $60 \\mu \\mathrm{m}$, this model was adapted for the IN625 alloy powder and an M280 EOS LPBF system. This approach was then validated for different alloys and processing conditions using literature data, thus demonstrating its potential for the LPBF process optimization. It was also shown that the layer thickness value has a direct influence on the creation of the processing map and must be taken into account during the calibration\\\\\nstep. This step represents a must-follow requirement to improve the prediction capability of the model because it takes into account the specificities of a given LPBF system related to particular powder recoating and heat transfer conditions, which differ from one printer to another, and influence the final density of the manufactured parts. However, once calibrated for a selected LPBF system, the model could be used for different alloys processed with this same system, avoiding trial-and-error-based process optimization routines.\n\nTo further this work, a comprehensive study should be conducted to evaluate the influence of parts' geometry, size, orientation and support on the density predictions.\n\nAuthor Contributions: The work plan was developed by M.L. to meet the study objectives defined by himself and V.B. The specimen design and the alloy selection were carried out by all the coauthors based upon the state of the art, previous research of V.B., and the current trends in the field. The design, fabrication and testing of the specimens were performed by M.L., V.B. contributed to the data organization, results interpretation and manuscript redaction.\n\nFunding: This research received no external funding.", "start_char_idx": 145235, "end_char_idx": 149135, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "92ea837f-1cf8-419e-aacd-bdefbd3da3bd": {"__data__": {"id_": "92ea837f-1cf8-419e-aacd-bdefbd3da3bd", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "dc7be2f8-1d6c-4d7f-b33d-485488bd8649", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b6982a9edee1c7e35b138603a6efa98b80fe8a612f0b873004b929d63a0a200a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3a3c7a0a-7eba-4e10-80dd-01e817c677bd", "node_type": "1", "metadata": {}, "hash": "75450c591f6aa1075fdd11ab11152d4acc6d03338e24139d0800330ac8136312", "class_name": "RelatedNodeInfo"}}, "text": "However, once calibrated for a selected LPBF system, the model could be used for different alloys processed with this same system, avoiding trial-and-error-based process optimization routines.\n\nTo further this work, a comprehensive study should be conducted to evaluate the influence of parts' geometry, size, orientation and support on the density predictions.\n\nAuthor Contributions: The work plan was developed by M.L. to meet the study objectives defined by himself and V.B. The specimen design and the alloy selection were carried out by all the coauthors based upon the state of the art, previous research of V.B., and the current trends in the field. The design, fabrication and testing of the specimens were performed by M.L., V.B. contributed to the data organization, results interpretation and manuscript redaction.\n\nFunding: This research received no external funding.\n\nAcknowledgments: The authors would like to express their appreciation for the financial support provided by NSERC (Natural Sciences and Engineering Research Council of Canada) and for the technical support provided by M. Samoilenko.\n\nConflicts of Interest: The authors declare no conflict of interest.\n\n\\section*{Appendix A}\nTable A1. Printing parameters, melt pool geometry and density of IN625 test coupons (M280 EOS).\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n\\multirow{2}{*}{Spec.} & \\multirow{2}{*}{}\\begin{tabular}{l}\nPower, \\\\\n$W$ \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{c}\nSpeed, \\\\\n$\\mathrm{m} / \\mathrm{s}$ \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{c}\nHatching \\\\\nspace, $\\mathrm{mm}$ \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{l}\nEnergy density, \\\\\n$\\mathrm{J} / \\mathrm{mm}^{3}$ \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{l}\nBuild rate, \\\\\n$\\mathrm{cm}^{3} / \\mathrm{h}$ \\\\\n\\end{tabular} & \\multicolumn{3}{|c|}{Mel pool geometry} & \\multirow{2}{*}{}\\begin{tabular}{c}\nDensity, \\\\\n$\\%$ \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{l}\nSD \\\\\n$\\pm \\%$ \\\\\n\\end{tabular} \\\\\n\\hline\n &  &  &  &  &  & $D / t$ & W/h & $L / W$ &  &  \\\\\n\\hline\n1 & 160 & 2.8 & 0.092 & 15.6 & 37.0 & 1 & 1 & 5.7 & 78.3 & 0.7 \\\\\n\\hline\n2 & 160 & 2.8 & 0.061 & 23.3 & 24.7 & 1 & 1.5 & 5.7 & 87.6 & 0.2 \\\\\n\\hline\n3 & 160 & 2.8 & 0.052 & 27.4 & 21.0 & 1 & 1.76 & 5.7 & 91.6 & 0.3 \\\\\n\\hline\n4 & 160 & 2.8 & 0.046 & 31.1 & 18.5 & 1 & 2 & 5.7 & 95.6 & 0.1 \\\\\n\\hline\n5 & 160 & 2.8 & 0.037 & 38.9 & 14.8 & 1 & 2.5 & 5.7 & 95.6 & 0.1 \\\\\n\\hline\n6 & 160 & 2.8 & 0.031 & 46.7 & 12.3 & 1 & 3 & 5.7 & 97.7 & 0.1 \\\\\n\\hline\n7 & 225 & 1.94 & 0.265 & 10.9 & 74.1 & 1.5 & 0.5 & 5.7 & 79.03 & 1.1 \\\\\n\\hline\n8 & 225 & 1.94 & 0.133 & 21.", "start_char_idx": 148256, "end_char_idx": 150903, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3a3c7a0a-7eba-4e10-80dd-01e817c677bd": {"__data__": {"id_": "3a3c7a0a-7eba-4e10-80dd-01e817c677bd", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "92ea837f-1cf8-419e-aacd-bdefbd3da3bd", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3b18ba00847733b8d09e0ce2888c93264ed01ad1df75c6dfef36f9fd9699c8ea", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "93c20f21-585e-44fb-986f-77167013b0e0", "node_type": "1", "metadata": {}, "hash": "27e83774a1ec336d03a201ab0f68de023670379b9de3fc90d98756bf316e9996", "class_name": "RelatedNodeInfo"}}, "text": "7 & 95.6 & 0.1 \\\\\n\\hline\n5 & 160 & 2.8 & 0.037 & 38.9 & 14.8 & 1 & 2.5 & 5.7 & 95.6 & 0.1 \\\\\n\\hline\n6 & 160 & 2.8 & 0.031 & 46.7 & 12.3 & 1 & 3 & 5.7 & 97.7 & 0.1 \\\\\n\\hline\n7 & 225 & 1.94 & 0.265 & 10.9 & 74.1 & 1.5 & 0.5 & 5.7 & 79.03 & 1.1 \\\\\n\\hline\n8 & 225 & 1.94 & 0.133 & 21.9 & 37.1 & 1.5 & 1 & 5.7 & 92.5 & 0.2 \\\\\n\\hline\n9 & 225 & 1.94 & 0.088 & 32.8 & 24.7 & 1.5 & 1.5 & 5.7 & 97.3 & 0.1 \\\\\n\\hline\n10 & 225 & 1.94 & 0.075 & 38.5 & 21.1 & 1.5 & 1.76 & 5.7 & 98.7 & 0.1 \\\\\n\\hline\n11 & 225 & 1.94 & 0.066 & 43.7 & 18.5 & 1.5 & 2 & 5.7 & 99.5 & 0.1 \\\\\n\\hline\n12 & 225 & 1.94 & 0.053 & 54.6 & 14.8 & 1.5 & 2.5 & 5.7 & 99.6 & $<0.1$ \\\\\n\\hline\n13 & 225 & 1.94 & 0.044 & 65.6 & 12.4 & 1.5 & 3 & 5.7 & 99.6 & $<0.1$ \\\\\n\\hline\n14 & 350 & 1.68 & 0.347 & 15.0 & 83.9 & 2 & 0.5 & 5.4 & 85.0 & 0.3 \\\\\n\\hline\n15 & 350 & 1.68 & 0.173 & 30.0 & 42.0 & 2 & 1 & 5.4 & 96.4 & 0.1 \\\\\n\\hline\n16 & 350 & 1.68 & 0.116 & 45.0 & 28.0 & 2 & 1.5 & 5.4 & 99.1 & $<0.1$ \\\\\n\\hline\n17 & 350 & 1.68 & 0.099 & 52.8 & 23.8 & 2 & 1.76 & 5.4 & 99.4 & $<0.1$ \\\\\n\\hline\n18 & 350 & 1.68 & 0.087 & 60.0 & 21.0 & 2 & 2 & 5.4 & 99.6 & $<0.1$ \\\\\n\\hline\n19 & 350 & 1.68 & 0.069 & 75.1 & 16.8 & 2 & 2.5 & 5.4 & 99.4 & 0.1 \\\\\n\\hline\n20 & 350 & 1.68 & 0.058 & 90.1 & 14.0 & 2 & 3 & 5.4 & 99.6 & 0.1 \\\\\n\\hline\n21 & 350 & 1.18 & 0.388 & 19.1 & 65.9 & 2.45 & 0.5 & 5.0 & 93.0 & 0.6 \\\\\n\\hline\n22 & 350 & 1.18 & 0.194 & 38.2 & 32.9 & 2.45 & 1 & 5.0 & 98.9 & 0.1 \\\\\n\\hline\n23 & 350 & 1.18 & 0.129 & 57.", "start_char_idx": 150623, "end_char_idx": 152078, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "93c20f21-585e-44fb-986f-77167013b0e0": {"__data__": {"id_": "93c20f21-585e-44fb-986f-77167013b0e0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3a3c7a0a-7eba-4e10-80dd-01e817c677bd", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7fa34e93ece0884b491b0e477e44957309704b4777a5fce741b4cefa07e64dbd", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "063d63b4-543e-43dd-ae8d-3eba678751b3", "node_type": "1", "metadata": {}, "hash": "c601939986b4e087c6cc0c502db289243f232a989e5e753e89203927ab34b63d", "class_name": "RelatedNodeInfo"}}, "text": "5 & 5.4 & 99.4 & 0.1 \\\\\n\\hline\n20 & 350 & 1.68 & 0.058 & 90.1 & 14.0 & 2 & 3 & 5.4 & 99.6 & 0.1 \\\\\n\\hline\n21 & 350 & 1.18 & 0.388 & 19.1 & 65.9 & 2.45 & 0.5 & 5.0 & 93.0 & 0.6 \\\\\n\\hline\n22 & 350 & 1.18 & 0.194 & 38.2 & 32.9 & 2.45 & 1 & 5.0 & 98.9 & 0.1 \\\\\n\\hline\n23 & 350 & 1.18 & 0.129 & 57.4 & 22.0 & 2.45 & 1.5 & 5.0 & 99.3 & $<0.1$ \\\\\n\\hline\n24 & 350 & 1.18 & 0.110 & 67.3 & 18.7 & 2.45 & 1.76 & 5.0 & 99.5 & 0.1 \\\\\n\\hline\n25 & 350 & 1.18 & 0.097 & 76.5 & 16.5 & 2.45 & 2 & 5.0 & 99.4 & 0.1 \\\\\n\\hline\n26 & 350 & 1.18 & 0.078 & 95.6 & 13.2 & 2.45 & 2.5 & 5.0 & 99.6 & 0.1 \\\\\n\\hline\n27 & 350 & 1.18 & 0.065 & 114.7 & 11.0 & 2.45 & 3 & 5.0 & 99.7 & 0.2 \\\\\n\\hline\n28 & 345 & 1.06 & 0.429 & 19.0 & 65.4 & 2.5 & 0.5 & 4.5 & 93.3 & 0.1 \\\\\n\\hline\n29 & 345 & 1.06 & 0.214 & 38.0 & 32.7 & 2.5 & 1 & 4.5 & 98.7 & 0.2 \\\\\n\\hline\n30 & 345 & 1.06 & 0.143 & 57.0 & 21.8 & 2.5 & 1.5 & 4.5 & 99.3 & 0.2 \\\\\n\\hline\n31 & 345 & 1.06 & 0.122 & 66.8 & 18.6 & 2.5 & 1.76 & 4.5 & 99.4 & 0.1 \\\\\n\\hline\n32 & 345 & 1.06 & 0.107 & 75.9 & 16.4 & 2.5 & 2 & 4.5 & 99.4 & $<0.1$ \\\\\n\\hline\n33 & 345 & 1.06 & 0.086 & 94.9 & 13.1 & 2.5 & 2.5 & 4.5 & 99.5 & $<0.1$ \\\\\n\\hline\n34 & 345 & 1.06 & 0.071 & 113.9 & 10.9 & 2.5 & 3 & 4.5 & 99.7 & 0.1 \\\\\n\\hline\n35 & 350 & 0.8 & 0.469 & 23.3 & 54.1 & 3 & 0.5 & 3.9 & 94.3 & 0.1 \\\\\n\\hline\n36 & 350 & 0.8 & 0.235 & 46.6 & 27.0 & 3 & 1 & 3.9 & 99.1 & 0.1 \\\\\n\\hline\n37 & 350 & 0.8 & 0.156 & 69.9 & 18.0 & 3 & 1.5 & 3.9 & 99.5 & $<0.1$ \\\\\n\\hline\n38 & 350 & 0.", "start_char_idx": 151785, "end_char_idx": 153247, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "063d63b4-543e-43dd-ae8d-3eba678751b3": {"__data__": {"id_": "063d63b4-543e-43dd-ae8d-3eba678751b3", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "93c20f21-585e-44fb-986f-77167013b0e0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "dc6d732a5c0961729d15c7aeed5dde72a1259e9b1c9a45fedaddecab19020a86", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "786c6e2a-77f7-422c-af93-a571ca4bcbd4", "node_type": "1", "metadata": {}, "hash": "6aab70ebc8369292a3cae809c1d80f6e89b01b309113254910cb40d2b8605644", "class_name": "RelatedNodeInfo"}}, "text": "9 & 10.9 & 2.5 & 3 & 4.5 & 99.7 & 0.1 \\\\\n\\hline\n35 & 350 & 0.8 & 0.469 & 23.3 & 54.1 & 3 & 0.5 & 3.9 & 94.3 & 0.1 \\\\\n\\hline\n36 & 350 & 0.8 & 0.235 & 46.6 & 27.0 & 3 & 1 & 3.9 & 99.1 & 0.1 \\\\\n\\hline\n37 & 350 & 0.8 & 0.156 & 69.9 & 18.0 & 3 & 1.5 & 3.9 & 99.5 & $<0.1$ \\\\\n\\hline\n38 & 350 & 0.8 & 0.133 & 82.0 & 15.4 & 3 & 1.76 & 3.9 & 99.5 & 0.1 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable A1. Cont.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n\\multirow{2}{*}{Spec.}", "start_char_idx": 152957, "end_char_idx": 153441, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "786c6e2a-77f7-422c-af93-a571ca4bcbd4": {"__data__": {"id_": "786c6e2a-77f7-422c-af93-a571ca4bcbd4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "063d63b4-543e-43dd-ae8d-3eba678751b3", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "bbafa8ccf57d24acf62bac4934172314cc88d641e7dcdb7a63b5985d23529fd9", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "cfa01c24-94ae-47f7-8389-93c3128e6fef", "node_type": "1", "metadata": {}, "hash": "955583f8acbc35ca29344a813fe4a759f6b64cc0a42ba592fa98db9dfee8e7ab", "class_name": "RelatedNodeInfo"}}, "text": "9 & 99.1 & 0.1 \\\\\n\\hline\n37 & 350 & 0.8 & 0.156 & 69.9 & 18.0 & 3 & 1.5 & 3.9 & 99.5 & $<0.1$ \\\\\n\\hline\n38 & 350 & 0.8 & 0.133 & 82.0 & 15.4 & 3 & 1.76 & 3.9 & 99.5 & 0.1 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable A1. Cont.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n\\multirow{2}{*}{Spec.} & \\multirow{2}{*}{}\\begin{tabular}{l}\nPower, \\\\\nW \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{c}\nSpeed, \\\\\n$\\mathrm{m} / \\mathrm{s}$ \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{l}\nHatching \\\\\nspace, $\\mathrm{mm}$ \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{c}\nEnergy density, \\\\\n$\\mathrm{J} / \\mathrm{mm}^{3}$ \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{l}\nBuild rate, \\\\\n$\\mathrm{cm}^{3} / \\mathrm{h}$ \\\\\n\\end{tabular} & \\multicolumn{3}{|c|}{Mel pool geometry} & \\multirow{2}{*}{}\\begin{tabular}{c}\nDensity, \\\\\n$\\%$ \\\\\n\\end{tabular} & \\multirow{2}{*}{}\\begin{tabular}{l}\nSD \\\\\n$\\pm \\%$ \\\\\n\\end{tabular} \\\\\n\\hline\n &  &  &  &  &  & $D / t$ & W/h & $L / W$ &  &  \\\\\n\\hline\n39 & 350 & 0.8 & 0.117 & 93.2 & 13.5 & 3 & 2 & 3.9 & 99.7 & 0.1 \\\\\n\\hline\n40 & 350 & 0.8 & 0.094 & 116.5 & 10.8 & 3 & 2.5 & 3.9 & 99.4 & 0.1 \\\\\n\\hline\n41 & 340 & 0.56 & 0.551 & 27.5 & 44.4 & 3.5 & 0.5 & 3.4 & 96.3 & 0.1 \\\\\n\\hline\n42 & 340 & 0.56 & 0.276 & 55.1 & 22.2 & 3.5 & 1 & 3.4 & 99.4 & 0.1 \\\\\n\\hline\n43 & 340 & 0.56 & 0.184 & 82.6 & 14.8 & 3.5 & 1.5 & 3.4 & 99.4 & 0.2 \\\\\n\\hline\n44 & 340 & 0.56 & 0.157 & 97.0 & 12.6 & 3.5 & 1.76 & 3.4 & 99.5 & 0.1 \\\\\n\\hline\n45 & 340 & 0.56 & 0.138 & 110.2 & 11.1 & 3.5 & 2 & 3.4 & 99.2 & 0.2 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\section*{References}\n\\begin{enumerate}\n  \\item Huang, Y.; Leu, M.C.; Mazumder, J.; Donmez, A. 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[CrossRef]\n\n  \\item Abd-Elghany, K.; Bourell, D. Property evaluation of $304 \\mathrm{~L}$ stainless steel fabricated by selective laser melting. Rapid Prototyp. J. 2012, 18, 420-428. [CrossRef]\n\n  \\item Spierings, A.B.; Levy, G. Comparison of density of stainless steel 316L parts produced with selective laser melting using different powder grades. In Proceedings of the Annual International Solid Freeform Fabrication Symposium, Austin, TX, USA, 3-5 August 2009.\n\n  \\item Jacob, G.; Brown, C.U.; Donmez, M.A. The Influence of Spreading Metal Powders with Different Particle Size Distributions on the Powder Bed Density in Laser-Based Powder Bed Fusion Processes; Advanced Manufacturing Series (NIST AMS) 100-17; National Institute of Standards and Technology (NIST): Gaithersburg, MD, USA, 2018.\n\n  \\item Polmear, I.J. Light Alloys: From Traditional Alloys to Nanocrystals, 4th ed.; Elsevier: Oxford, UK, 2005.\n\n  \\item Krishnan, M.; Atzeni, E.; Canali, R.; Calignano, F.; Manfredi, D.; Ambrosio, E.P.; Iuliano, L. On the effect of process parameters on properties of AlSi10Mg parts produced by DMLS. Rapid Prototyp. J. 2014, 20, 449-458. [CrossRef]\n\n  \\item Poulin, J.-R.", "start_char_idx": 159453, "end_char_idx": 162399, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "70f53e2b-d2ac-4211-9184-a2b32f49dbb8": {"__data__": {"id_": "70f53e2b-d2ac-4211-9184-a2b32f49dbb8", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a9640c6b-277a-48d5-b70f-3cd4c61bfe36", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "5f70d0d8f745e4daf45d45eea8519794d1ee06d99a4c7d7aeb9a825637b7d299", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "76f4bd7d-b836-4392-b732-bc9c3d56b58a", "node_type": "1", "metadata": {}, "hash": "c712ed7b2a6b6754d10ad246e433e457e788df0be3d4ec6a0ae8bc70c6001d7d", "class_name": "RelatedNodeInfo"}}, "text": "\\item Polmear, I.J. Light Alloys: From Traditional Alloys to Nanocrystals, 4th ed.; Elsevier: Oxford, UK, 2005.\n\n  \\item Krishnan, M.; Atzeni, E.; Canali, R.; Calignano, F.; Manfredi, D.; Ambrosio, E.P.; Iuliano, L. On the effect of process parameters on properties of AlSi10Mg parts produced by DMLS. Rapid Prototyp. J. 2014, 20, 449-458. [CrossRef]\n\n  \\item Poulin, J.-R.; Letenneur, M.; Terriault, P.; Brailovski, V. Influence of intentionally-induced porosity and post-processing conditions on the mechanical properties of laser powder bed fused inconel 625. In Selected Technical Papers (STP1620), Proceedings of ASTM Symposium on Structural Integrity of Additive Manufactured Parts, Washington, DC, USA, 6-8 November 2018; ASTM International: West Conshohocken, PA, USA, 2018.\n\n\\end{enumerate}\n\nC 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 (http:/ / \\href{http://creativecommons.org/licenses/by/4.0/}{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{Effects of laser processing parameters on thermal behavior and melting/solidification mechanism during selective laser melting of $\\mathrm{TiC} /$ Inconel 718 composites }\n\n\n\\author{Qimin Shi ${ }^{\\text {a,b }}$, Dongdong Gu ${ }^{\\text {a,b,* }}$, Mujian Xia ${ }^{\\text {a,b }}$, Sainan Cao ${ }^{\\text {a,b }}$, Ting Rong a,b\\\\\na College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing 210016, PR China\\\\\nb Institute of Additive Manufacturing (3D Printing), Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing 210016, PR China}\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", "start_char_idx": 162026, "end_char_idx": 164844, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "76f4bd7d-b836-4392-b732-bc9c3d56b58a": {"__data__": {"id_": "76f4bd7d-b836-4392-b732-bc9c3d56b58a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "70f53e2b-d2ac-4211-9184-a2b32f49dbb8", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7306462dc06f635ff43909f80fa89b646b384224bb87a9ce0da5fc0a5c3175bf", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "98e8ee05-5e06-4eb9-b497-d302e8641e6e", "node_type": "1", "metadata": {}, "hash": "1c4b4b049dfaee3b69dd58cdda5d8c97657364ea160af49f69570111fbaec1b9", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{A R T I C L E I N F O}\n\\section*{Article history:}\nReceived 18 December 2015\n\nReceived in revised form\n\n27 February 2016\n\nAccepted 14 April 2016\n\nAvailable online 29 April 2016\n\nKeywords:\n\nAdditive manufacturing\n\nSelective laser melting (SLM)\n\nNumerical simulation\n\nMelting/solidification mechanism\n\nTiC/Inconel 718\n\n\\begin{abstract}\nA B S T R A C T A three-dimensional finite element model is proposed to study the effects of laser power and scan speed on the thermal behavior and melting/solidification mechanism during selective laser melting (SLM) of TiC/Inconel 718 powder system. The cooling time during powder delivery is taken into account to simulate the actual production process well. It shows obviously the existence of heat accumulation effect in SLM process and, the tailored set of cooling time of $10 \\mathrm{~ms}$ during powder delivery alleviates that effectively. The maximum temperature gradient in the molten pool slightly increases from $1.30 \\times 10^{4}{ }^{\\circ} \\mathrm{C}$ / $\\mathrm{mm}$ to $2.60 \\times 10^{4} \\mathrm{C} / \\mathrm{mm}$ as the laser power is increased from $75 \\mathrm{~W}$ to $150 \\mathrm{~W}$. However, it is negligibly sensitive to the variation of scan speed. There is a positive corresponding relationship between the maximum rate of temperature change and processing parameters. A low laser power ( $75 \\mathrm{~W}$ ) or a high scan speed $(300 \\mathrm{~mm} / \\mathrm{s})$ is more energy efficient in Z-direction of the molten pool, giving rise to a deepnarrow cross section of the pool. Whereas, a high laser power ( $150 \\mathrm{~W}$ ) or a low scan speed ( $50 \\mathrm{~mm} / \\mathrm{s}$ ) causes a shallow-wide cross section of the molten pool, meaning it is more energy efficient in the Y-direction of the melt. The combination of a laser power of $125 \\mathrm{~W}$ and a scan speed of $100 \\mathrm{~mm} / \\mathrm{s}$ contributes to achieve a sound metallurgical bonding between the neighbor layers and tracks, due to the proper molten pool size (width: $109.3 \\mu \\mathrm{m}$; length: $120.7 \\mu \\mathrm{m}$; depth: $67.8 \\mu \\mathrm{m}$ ). The SLM experiments on $\\mathrm{TiC} /$ Inconel 718 powder system are performed to verify the reliability and accuracy of the physical model and, simulation results are proved to be correct.\n\\end{abstract}\n\n\u24d2 2016 Elsevier Ltd. All rights reserved.\n\n\\section*{1. Introduction}\nNickel-based superalloys are widely used as high-temperature service parts in industrial and aerospace fields in which perfect combination of elevated temperature workability and mechanical properties are required [1]. Inconel 718, the typical representative of nickel-based superalloys, due to its outstanding oxidation resistance, hot corrosion resistance and fatigue resistance, has been recognized as the most promising candidate for many applications such as turbine wheel blades, rocket motors, nuclear reactors and fossil fuel components at elevated temperature [2]. Furthermore, Inconel 718 based metal matrix composites (MMCs), reinforced with discontinuous TiC reinforcements, show the superiority compared with the pure parts for significantly increased not only of strength and hardness, but also of elasticity modulus and wear\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author at: College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing 210016, PR China.\n\\end{itemize}\n\nE-mail address: \\href{mailto:dongdonggu@nuaa.edu.cn}{dongdonggu@nuaa.edu.cn} (D. Gu).\n}\n\nresistance, amplifying effectively the serviceable range of Inconel 718 [3]. However, the poor wetting ability between the reinforcing particles and the matrix extremely reduces the particle/matrix interfacial bonding due to the formation of microcracks or pores, thus resulting in the premature failure of MMCs during mechanical loading [4].", "start_char_idx": 164848, "end_char_idx": 168724, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "98e8ee05-5e06-4eb9-b497-d302e8641e6e": {"__data__": {"id_": "98e8ee05-5e06-4eb9-b497-d302e8641e6e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "76f4bd7d-b836-4392-b732-bc9c3d56b58a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3b7decf5d183d5de6137bc169b598b627c4b6d9a44d2764f326ba30c43db99e1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "76c17294-5c5c-4e0d-854b-5afbd941c320", "node_type": "1", "metadata": {}, "hash": "cf827f5038b4c8b6060790be65b1bfd2e735a7f6f61812eafc3f4804bd980a9f", "class_name": "RelatedNodeInfo"}}, "text": "\\end{itemize}\n\nE-mail address: \\href{mailto:dongdonggu@nuaa.edu.cn}{dongdonggu@nuaa.edu.cn} (D. Gu).\n}\n\nresistance, amplifying effectively the serviceable range of Inconel 718 [3]. However, the poor wetting ability between the reinforcing particles and the matrix extremely reduces the particle/matrix interfacial bonding due to the formation of microcracks or pores, thus resulting in the premature failure of MMCs during mechanical loading [4]. Considerable research efforts are required to study the liquid wetting effect of powder particles for alleviating the pores and microcracks between the particle/matrix interface and, thus, improving their bonding ability. Meanwhile, the conventional manufacturing processes, such as casting process, easily cause the grain coarsening and shrinkage cavity/porosity and, they are difficult to manufacture Inconel 718 composites with complex geometry [5]. These put forward new requirements on the material forming techniques.\n\nSelective laser melting (SLM), as one of the most important branches of additive manufacturing (AM) techniques, exhibits a great potential for direct fabricating 3D parts with flexibility in materials and shapes [6-9]. During the SLM process, a large amount of powder comes up to the build table and a roller/blade spreads powder at the metal substrate in order to deposit powder\n\n\\section*{Nomenclature}\nA Laser energy absorptance of a material\n\n$T \\quad$ Temperature of the powder system or melt, ${ }^{\\circ} \\mathrm{C}$\n\n$T_{\\text {amb }} \\quad$ Ambient temperature, ${ }^{\\circ} \\mathrm{C}$\n\n$T_{\\mathrm{P}} \\quad$ Temperature of powder particles, ${ }^{\\circ} \\mathrm{C}$\n\n$t \\quad$ Interaction time, $s$\n\n$P \\quad$ Laser power, $\\mathrm{W}$\n\n$k \\quad$ Effective conductivity of powder bed, $\\mathrm{W} /\\left(\\mathrm{m}{ }^{\\circ} \\mathrm{C}\\right)$\n\n$k_{\\mathrm{f}} \\quad$ Thermal conductivity of the fluid, $\\mathrm{W} /\\left(\\mathrm{m}{ }^{\\circ} \\mathrm{C}\\right)$\n\n$k_{\\mathrm{s}} \\quad$ Thermal conductivity of the powder solid, $\\mathrm{W} /\\left(\\mathrm{m}{ }^{\\circ} \\mathrm{C}\\right)$\n\n$k_{\\mathrm{r}} \\quad$ Thermal conductivity portion due to the radiation, $\\mathrm{W} /$ $\\left(\\mathrm{m}{ }^{\\circ} \\mathrm{C}\\right)$\n\n$\\rho \\quad$ Material density, $\\mathrm{kg} / \\mathrm{m}^{3}$\n\n$\\rho_{\\mathrm{f}} \\quad$ Fluid density, $\\mathrm{kg} / \\mathrm{m}^{3}$\n\n$\\rho_{\\mathrm{s}} \\quad$ Density of the solid, $\\mathrm{kg} / \\mathrm{m}^{3}$\n\n$\\rho_{\\mathrm{p}} \\quad$ Density of the powder materials, $\\mathrm{kg} / \\mathrm{m}^{3}$\n\n$C_{\\mathrm{p}} \\quad$ Specific heat capacity, $\\mathrm{J} /\\left(\\mathrm{kg}{ }^{\\circ} \\mathrm{C}\\right)$\n\n$x, y, z \\quad$ Spatial co-ordinates, $\\mathrm{m}$\n\nQ Heat generated per volume, $\\mathrm{W} / \\mathrm{m}^{3}$\n\n$n \\quad$ Normal vector\n\n$q \\quad$ Input heat flux, $\\mathrm{W} / \\mathrm{m}^{2}$\n\n$q_{\\text {con }} \\quad$ Heat convection, $\\mathrm{W} / \\mathrm{m}^{2}$\n\n\\begin{center}\n\\begin{tabular}{ll}\n$q_{\\mathrm{rad}}$ & Heat radiation, $\\mathrm{W} / \\mathrm{m}^{2}$ \\\\\n$h$ & Coefficient of heat transfer, $\\mathrm{W} /\\left(\\mathrm{m}^{2}{ }^{\\circ} \\mathrm{C}\\right)$ \\\\\n$\\mathrm{Nu}$ & Nusselt number \\\\\n$\\mathrm{Pr}$ & Prandtl numbers \\\\\n$\\mathrm{Gr}$ & Grashof numbers \\\\\n$g$ & Gravitational acceleration, $\\mathrm{m} / \\mathrm{s}^{2}$ \\\\\n$\\beta_{\\mathrm{f}}$ & Volumetric expansivity,", "start_char_idx": 168278, "end_char_idx": 171600, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "76c17294-5c5c-4e0d-854b-5afbd941c320": {"__data__": {"id_": "76c17294-5c5c-4e0d-854b-5afbd941c320", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "98e8ee05-5e06-4eb9-b497-d302e8641e6e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "67c87e4bf3d5db9f730b6d17679a96ff78de03529993c9a8754299e372615b33", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "cf6da1ce-f20b-4e18-866f-287c960d29d6", "node_type": "1", "metadata": {}, "hash": "3c2915c93f80482894986103406a13e0b6913bdf4418f3bc4e0b522adaa89c89", "class_name": "RelatedNodeInfo"}}, "text": "$\\mathrm{W} / \\mathrm{m}^{2}$\n\n$q_{\\text {con }} \\quad$ Heat convection, $\\mathrm{W} / \\mathrm{m}^{2}$\n\n\\begin{center}\n\\begin{tabular}{ll}\n$q_{\\mathrm{rad}}$ & Heat radiation, $\\mathrm{W} / \\mathrm{m}^{2}$ \\\\\n$h$ & Coefficient of heat transfer, $\\mathrm{W} /\\left(\\mathrm{m}^{2}{ }^{\\circ} \\mathrm{C}\\right)$ \\\\\n$\\mathrm{Nu}$ & Nusselt number \\\\\n$\\mathrm{Pr}$ & Prandtl numbers \\\\\n$\\mathrm{Gr}$ & Grashof numbers \\\\\n$g$ & Gravitational acceleration, $\\mathrm{m} / \\mathrm{s}^{2}$ \\\\\n$\\beta_{\\mathrm{f}}$ & Volumetric expansivity, $/{ }^{\\circ} \\mathrm{C}$ \\\\\n$\\eta_{\\mathrm{f}}$ & Fluid viscosity, (Pa s) \\\\\n$\\sigma$ & Stefan-Boltzmann constant, $\\mathrm{W} /\\left(\\mathrm{m}^{2} \\mathrm{~K}^{4}\\right)$ \\\\\n$\\varepsilon$ & Emissivity \\\\\n$\\varepsilon_{\\mathrm{s}}$ & Emissivity of the powder particles \\\\\n$\\varepsilon_{\\mathrm{H}}$ & Emissivity of the hole \\\\\n$A_{\\mathrm{H}}$ & Area fraction \\\\\n$\\varphi$ & Porosity of the powder bed \\\\\n$R$ & Radius of the Gaussian laser beam, $\\mathrm{m}$ \\\\\n$r$ & Radial distance from a point to the center of the laser \\\\\n & beam, $\\mathrm{m}$ \\\\\n$H$ & Enthalpy, $\\mathrm{J} / \\mathrm{m}^{3}$ \\\\\n$F_{0}$ & View factor \\\\\n$D_{\\mathrm{P}}$ & Average diameter of the powder particles, $\\mathrm{m}$ \\\\\n$M$ & One of the material physical properties \\\\\n$M_{\\mathrm{n}}$ & Physical property of one of the components \\\\\n$x_{\\mathrm{n}}$ & Mass fraction of one of the components \\\\\n\\end{tabular}\n\\end{center}\n\nlayers with well designed thickness. Fully dense parts are created by a laser beam with a high intensity in a special scanning strategy, local melting and subsequent solidification of the powder bed in successive layers [10]. As the laser beam is scattered through the powder bed, the energy is absorbed by powder particles via both powder-coupling and bulk-coupling mechanisms [11]. The powder system experiences a rapid cooling rate (up to $10^{6-7}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ ) during the interaction between the powder particles and the laser beam, which has a substantial effect on the generation of fine and uniform microstructure, as well as resultant mechanical properties of final components $[12,13]$. The materials in SLM process have a tendency to experience a significant non-equilibrium physical and chemical metallurgical process, exhibiting multiple modes of heat, mass and momentum transfer [14]. The typical defects associated with SLM such as \"balling effect\", residual porosity, stress induced microcracks, warpage induced dimensional accuracy and delamination tend to occur under inappropriate processing parameters (laser power and scan speed) [15,16]. Therefore, to obtain the desired SLM-fabricated parts, the significant research efforts are required to study the relationship between processing parameters and melting/solidification mechanism. However, the experimental measurements of thermal-physical statistics during SLM process are considered to be difficult for it involves the fast moving of laser energy source, the limited liquid lifetime of the molten pool and the extremely high cooling rate of the elevated-temperature melt. Consequently, the numerical simulation approach is typically chosen as an alternative to solve the problems mentioned above.\n\nIn fact, some heat conduction three-dimensional models have been established to investigate the thermal behavior and further melting/solidification mechanism during SLM process recently. Gusarov et al. [17] simulated and analyzed the temperature distribution of steel $316 \\mathrm{~L}$ powder bed during SLM process. The analysis of the capillary stability of the segmental cylinder applied to the calculated melt pool estimated the stability of the process depending on the scanning velocity, powder layer thickness, and the material optical and thermal properties in the developed model.", "start_char_idx": 171071, "end_char_idx": 174896, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "cf6da1ce-f20b-4e18-866f-287c960d29d6": {"__data__": {"id_": "cf6da1ce-f20b-4e18-866f-287c960d29d6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "76c17294-5c5c-4e0d-854b-5afbd941c320", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9ff894628b0dcbc41a2192d38f7aa980d98b9ad5f56574e60fb51248a53a52d8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9935f49b-587b-4aee-9560-9a9c3cc25e76", "node_type": "1", "metadata": {}, "hash": "39f1e6c1edb4975a7f2f03152984a8e892576523e91a4701c2c301e15a6020c4", "class_name": "RelatedNodeInfo"}}, "text": "However, the experimental measurements of thermal-physical statistics during SLM process are considered to be difficult for it involves the fast moving of laser energy source, the limited liquid lifetime of the molten pool and the extremely high cooling rate of the elevated-temperature melt. Consequently, the numerical simulation approach is typically chosen as an alternative to solve the problems mentioned above.\n\nIn fact, some heat conduction three-dimensional models have been established to investigate the thermal behavior and further melting/solidification mechanism during SLM process recently. Gusarov et al. [17] simulated and analyzed the temperature distribution of steel $316 \\mathrm{~L}$ powder bed during SLM process. The analysis of the capillary stability of the segmental cylinder applied to the calculated melt pool estimated the stability of the process depending on the scanning velocity, powder layer thickness, and the material optical and thermal properties in the developed model. The results showed that the thermal-physical phenomenon was highly dependent on the processing parameters (laser power, scan speed, thickness of powder layer, properties of materials, etc.). Roberts et al. [18] proposed a three dimensional thermal model for fabrication of TiAl6V4 parts, considering the temperature-dependent thermal-physical properties, which is beneficial to improve the computational accuracy. This model involving multiple layers was equally of great importance because the thermal interactions of successive layers affected the temperature gradients, which governed the heat transfer and thermal stress development mechanisms. The work predicted the transient temperature distribution during the production. It was found that the laser region experienced rapid thermal cycles accompanied with commensurate stress cycles. Ali Foroozmehr et al. [19] conducted the finite element simulation of steel $316 \\mathrm{~L}$ SLM process considering optical penetration depth and, each calculating step is divided into some smaller sub-steps where the change in the materials properties from \"powder\" to \"solid\" occurred for improving calculation precision. They paid attention to the influences of the different scan speeds on the melt pool depth, width, and length. It suggested that the melt pool size varied from the beginning of a track to its end and from the first track to the next one. The melt pool size, however, reached a stable condition after a few tracks. To date, although there are some numerical simulations have been carried out to investigate the thermal behavior during laser processing of metal powder system, the rare researches focus on the thermal behavior and melting/solidification mechanism during SLM of TiC/Inconel 718 powder system. Meanwhile, the simulation three-dimensional models are needed to be further perfected and optimized for more precise calculation and simulating the actual fabrication process excellently.\n\nIn this investigation, a three-dimensional finite element model was established based on the models mentioned above to predict the relationship between melting/solidification mechanism and processing parameters, using ANSYS 13.0 software. Latent heat of phase change, multiple heat transfer mechanisms, temperaturedependent thermal physical properties and cooling time during powder delivery were considered in order to precisely simulate the actual production process, as well as improve the calculation accuracy. Moreover, the movement of Gaussian laser source and the laser energy loading of multi-layer and multi-track were realized using APDL secondary development language. The effects of\\\\\nlaser power and scan speed on the thermal behavior and the forming mechanism of cross-sectional configuration of the molten pool were analyzed. The formation mechanisms of processing defects, such as \"balling effect\", warpage, pores, microcracks, delamination, etc. were discussed in order to optimize the processing parameters and obtain desired SLM-produced parts. Meanwhile, the corresponding experiments were also implemented to investigate the microstructure of the SLM-produced components with different laser processing conditions for verifying the reliability and accuracy of the model proposed in this paper.\n\n\\section*{2. Model descriptions for SLM process}\n\\subsection*{2.1. Physical description of SLM}\nFig. 1 depicts the schematic overview of the interaction zone between laser radiation and powder. As the top surface of the powder bed is irradiated by the incident laser beam, a small fraction of laser energy is dissipated by radiation and convection. The remainder, the vast majority of laser energy, is absorbed by powder particles, leading to the rapid heating and resultant localized melting. After the moving Gaussian laser heat source leaves the melt region, which is called molten pool, rapid consolidation of the melt occurs. Then the metallurgical bonding is formed between the adjacent tracks and the neighbor layers. The heat transfer mechanism of SLM process mainly includes laser radiation to powder bed, heat conduction among metal base plate and powder particles and heat convection between the boundaries of powder layer and chamber atmosphere.", "start_char_idx": 173888, "end_char_idx": 179134, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9935f49b-587b-4aee-9560-9a9c3cc25e76": {"__data__": {"id_": "9935f49b-587b-4aee-9560-9a9c3cc25e76", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "cf6da1ce-f20b-4e18-866f-287c960d29d6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "555d31fe4f3786429de0c3de578346e6ab32e66e096f0d5576bfeb7d10ce6931", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ea893c55-336b-4151-946e-62c94a0a5e9c", "node_type": "1", "metadata": {}, "hash": "75e21d4f273139f0f531b6c1b07391f869a5b6b808460fd6bcf9b4b7ffc6c80e", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{2. Model descriptions for SLM process}\n\\subsection*{2.1. Physical description of SLM}\nFig. 1 depicts the schematic overview of the interaction zone between laser radiation and powder. As the top surface of the powder bed is irradiated by the incident laser beam, a small fraction of laser energy is dissipated by radiation and convection. The remainder, the vast majority of laser energy, is absorbed by powder particles, leading to the rapid heating and resultant localized melting. After the moving Gaussian laser heat source leaves the melt region, which is called molten pool, rapid consolidation of the melt occurs. Then the metallurgical bonding is formed between the adjacent tracks and the neighbor layers. The heat transfer mechanism of SLM process mainly includes laser radiation to powder bed, heat conduction among metal base plate and powder particles and heat convection between the boundaries of powder layer and chamber atmosphere. These three coupled heat transfer mechanisms make the thermal behavior of SLM process become extremely complex [20].\n\n\\subsection*{2.2. Basic setup of the finite element model}\nThe numerical simulation is carried out using ANSYS multiphysics finite element package to obtain a thorough understanding of the temperature evolution behavior and resultant phenomenon like temperature gradient, metallurgical defects and deformation during SLM process. The established three-dimensional finite model and laser scan strategy during SLM process are shown in Fig. 2. The dimensions of the computational model of TiC/Inconel 718 powder bed are $1.4 \\mathrm{~mm} \\times 0.385 \\mathrm{~mm} \\times 0.1 \\mathrm{~mm}$ with two layers. The height of each power layer is $50 \\mu \\mathrm{m}$ and, the C45 medium carbon steel block with the dimensions of $1.7 \\mathrm{~mm} \\times 0.7 \\mathrm{~mm} \\times 0.3 \\mathrm{~mm}$ is taken as the metal substrate\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3d8b51f9bfd3b941d680g-03}\n\\end{center}\n\nFig. 1. Schematic overview of the interaction zone between laser radiation and powder bed. beneath the powder layers. The coordinate origin of this physical model lies at the left bottom of the second powder layer as shown in Fig. 2(a) and, its X-axis, Y-axis and Z-axis are located along the laser scan direction, perpendicular to the laser scan direction and from top surface to bottom of the powder layers. Considering the computational precision and simulation efficiency, the ANSYS Solid70 hexahedron element with the fine mesh of $0.0175 \\mathrm{~mm} \\times 0.0175 \\mathrm{~mm} \\times 0.025 \\mathrm{~mm}$ is utilized in the powder bed, while, a relatively coarse tetrahedron mesh is adopted in the substrate. The three-dimensional simulation model is meshed into 11,745 nodes and 25,532 elements in all. In order to mimic the cooling time involved during the delivery of each powder layer, there is a $10-\\mathrm{ms}$ cooling time between the fabrications of neighbor layers. This time is converted by the real time during powder delivery of actual laser processing according to the ratio of the top surface area of the physical model and the area of the real powder delivery during previous experiments. Every calculating step is divided into two smaller sub-steps for improving calculation precision. Each powder layer is processed track by track in a reciprocating raster pattern as shown in Fig. 2(b). Point 1, Point 2 and Point 3 lie at the center of the first scan track, second scan track and fourth scan track, respectively. Path A-B locates on the top surface of the first powder layer along the $\\mathrm{Y}$ direction at $\\mathrm{X}=0.7 \\mathrm{~mm}$ and $\\mathrm{Z}=0.05 \\mathrm{~mm}$. The applied laser processing parameters are listed in Table 1.\n\n\\subsection*{2.3. Governing equations}\nIn selective laser melting, the localized heating of the powder bed by the laser beam results in a heat transfer in the material dominated by conductive heat transfer.", "start_char_idx": 178177, "end_char_idx": 182150, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ea893c55-336b-4151-946e-62c94a0a5e9c": {"__data__": {"id_": "ea893c55-336b-4151-946e-62c94a0a5e9c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9935f49b-587b-4aee-9560-9a9c3cc25e76", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e3d1993a9f21cfb2c15e6622cbff625c4054c9c345fa281a963988d6d4f48c90", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "38136c93-10b5-47e6-9388-8da3af3ae3d5", "node_type": "1", "metadata": {}, "hash": "e7da15d67aa87e9e0b2f7e74de9eb48de6dbad6b65b6021cb056f6e1e9be4004", "class_name": "RelatedNodeInfo"}}, "text": "Every calculating step is divided into two smaller sub-steps for improving calculation precision. Each powder layer is processed track by track in a reciprocating raster pattern as shown in Fig. 2(b). Point 1, Point 2 and Point 3 lie at the center of the first scan track, second scan track and fourth scan track, respectively. Path A-B locates on the top surface of the first powder layer along the $\\mathrm{Y}$ direction at $\\mathrm{X}=0.7 \\mathrm{~mm}$ and $\\mathrm{Z}=0.05 \\mathrm{~mm}$. The applied laser processing parameters are listed in Table 1.\n\n\\subsection*{2.3. Governing equations}\nIn selective laser melting, the localized heating of the powder bed by the laser beam results in a heat transfer in the material dominated by conductive heat transfer. The spatial and temporal distribution of the temperature field satisfies the heat conduction equation, which can be expressed as [22]:\n\n$\\rho C_{\\mathrm{p}} \\frac{\\partial T}{\\partial t}=\\frac{\\partial}{\\partial x}\\left(k \\frac{\\partial T}{\\partial x}\\right)+\\frac{\\partial}{\\partial y}\\left(k \\frac{\\partial T}{\\partial y}\\right)+\\frac{\\partial}{\\partial z}\\left(k \\frac{\\partial T}{\\partial z}\\right)+\\dot{Q}$\n\nwhere $T$ is the temperature of the powder system, $t$ is the interaction time between laser beam and powder bed, $(x, y, z)$ are the spatial co-ordinates, $k$ is the effective thermal conductivity of powder bed, $\\rho$ is the material density, $C_{\\mathrm{p}}$ is the specific heat capacity and, $Q$ is the heat generated per volume within the component.\n\nThe initial condition of the temperature distribution in the powder bed and substrate at time $t=0$ is defined as:\n\n$\\left.T(x, y, z, t)\\right|_{t=0}=T_{\\text {amb }} \\quad(x, y, z) \\in D$\n\nwhere $T_{\\mathrm{amb}}$ is the ambient temperature and is taken as $20^{\\circ} \\mathrm{C}$.\n\nThe thermal boundary conditions for powder, liquid and solid can be expressed by [23]:\n\n$k \\frac{\\partial T}{\\partial n}-q+q_{\\mathrm{con}}+q_{\\mathrm{rad}}=0 \\quad(x, y, z) \\in S$\n\nwhere $S$ represents the surfaces which are attached to imposed heat fluxes, radiation and convection, $n$ is the normal vector of surface $S$, the input heat flux $q$ is presented in the following by Eq. (14). The heat loss $q_{\\text {con }}$ due to natural convection of the fluid around the powder bed is described by:\n\n$q_{\\mathrm{con}}=h\\left(T-T_{\\mathrm{amb}}\\right)$\n\nwhere $h$ is the coefficient of heat transfer. $h$ is size- and temperature-dependent and can be expressed as:\n\n$h=\\frac{N u k_{\\mathrm{f}}}{L}$\n\nwhere $L$ is the characteristic length of the specimen, $N u$ is the\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3d8b51f9bfd3b941d680g-04}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3d8b51f9bfd3b941d680g-04(1)}\n\\end{center}\n\nFig. 2. The established three-dimensional finite element model (a) and laser scan strategy (b) during SLM process (Point 1, Point 2 and Point 3 at the center of the 1 st scan track, 2nd scan track and 4th scan track, respectively).\n\nTable 1\n\nFinite element simulation parameters.", "start_char_idx": 181388, "end_char_idx": 184476, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "38136c93-10b5-47e6-9388-8da3af3ae3d5": {"__data__": {"id_": "38136c93-10b5-47e6-9388-8da3af3ae3d5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ea893c55-336b-4151-946e-62c94a0a5e9c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "31b4f6e798edc3405663868d0ebd0a47942f86b9d4d2d35a5980e00e8cdecd9a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "96eb8651-1aba-47b6-8f00-562ce1a64b55", "node_type": "1", "metadata": {}, "hash": "6caacc7568fc70ec14f47f808948ed856fc238ae250a3e7759a18b6c05e93608", "class_name": "RelatedNodeInfo"}}, "text": "2. The established three-dimensional finite element model (a) and laser scan strategy (b) during SLM process (Point 1, Point 2 and Point 3 at the center of the 1 st scan track, 2nd scan track and 4th scan track, respectively).\n\nTable 1\n\nFinite element simulation parameters.\n\n\\begin{center}\n\\begin{tabular}{ll}\n\\hline\nParameter & Value \\\\\n\\hline\nAbsorptivity, $A$ & $0.72[21]$ \\\\\nPowder layer thickness, $d$ & $50 \\mu \\mathrm{m}$ \\\\\nLaser spot size, $D$ & $70 \\mu \\mathrm{m}$ \\\\\nHatch spacing, $s$ & $50 \\mu \\mathrm{m}$ \\\\\nAmbient temperature, $T_{0}$ & $20^{\\circ} \\mathrm{C}$ \\\\\nLaser power, $P$ & $75,100,125,150 \\mathrm{~W}$ \\\\\nScan speed, $v$ & $50,100,200,300 \\mathrm{~mm} / \\mathrm{s}$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nNusselt number and $k_{\\mathrm{f}}$ is the thermal conductivity of the fluid in the atmosphere. $\\mathrm{Nu}$ is equal to:\n\n$\\sqrt{N u}=\\sqrt{N u_{0}}+\\left[\\frac{\\operatorname{GrPr} / 300}{\\left(1+(0.5 / \\operatorname{Pr})^{9 / 16}\\right)^{16 / 9}}\\right]^{1 / 6}$\n\nwhere $\\mathrm{Pr}$ and $\\mathrm{Gr}$ are Prandtl numbers and Grashof numbers, respectively, which can be estimated by:\n\n$G r=g \\frac{L^{3} \\rho_{\\mathrm{f}}^{2} \\beta_{\\mathrm{f}}\\left(T-T_{\\mathrm{amb}}\\right)}{\\eta_{\\mathrm{f}}^{2}}$\n\nand\n\n$\\operatorname{Pr}=\\frac{C_{\\mathrm{p}} \\eta_{\\mathrm{f}}}{k_{\\mathrm{f}}}$\n\nwhere $g$ is the gravitational acceleration, $\\rho_{\\mathrm{f}}$ is the fluid density, $\\beta_{\\mathrm{f}}$ is the volumetric expansivity, $\\eta_{\\mathrm{f}}$ is the fluid viscosity and $C_{\\mathrm{p}}$ is the specific heat of the fluid.\n\nThe heat loss qrad due to radiation of the powder layer is equal to:\n\n$q_{\\mathrm{rad}}=\\sigma \\varepsilon\\left(T^{4}-T_{\\mathrm{amb}}^{4}\\right)$\n\nwhere $\\sigma$ is the Stefan-Boltzmann constant $\\left(5.67 \\times 10^{-8} \\mathrm{~W} /\\left(\\mathrm{m}^{2} \\mathrm{~K}^{4}\\right)\\right)$ and $\\varepsilon$ is the emissivity of powder bed which can be expressed as:\n\n$\\varepsilon=A_{\\mathrm{H}} \\varepsilon_{\\mathrm{H}}+\\left(1-A_{\\mathrm{H}}\\right) \\varepsilon_{\\mathrm{s}}$\n\nwhere $\\varepsilon_{\\mathrm{s}}$ is the emissivity of the powder particles.", "start_char_idx": 184202, "end_char_idx": 186310, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "96eb8651-1aba-47b6-8f00-562ce1a64b55": {"__data__": {"id_": "96eb8651-1aba-47b6-8f00-562ce1a64b55", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "38136c93-10b5-47e6-9388-8da3af3ae3d5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "fbe8df632590ffd32624f4952e8f03099ac2f5442563b5182452ef5ea6880210", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ee5f7e67-c2c1-47ee-a54c-77541af9c2d3", "node_type": "1", "metadata": {}, "hash": "7666078f75ba1b3c1499c81f3b9955d58fe456592263112fb5b22637ca060599", "class_name": "RelatedNodeInfo"}}, "text": "The heat loss qrad due to radiation of the powder layer is equal to:\n\n$q_{\\mathrm{rad}}=\\sigma \\varepsilon\\left(T^{4}-T_{\\mathrm{amb}}^{4}\\right)$\n\nwhere $\\sigma$ is the Stefan-Boltzmann constant $\\left(5.67 \\times 10^{-8} \\mathrm{~W} /\\left(\\mathrm{m}^{2} \\mathrm{~K}^{4}\\right)\\right)$ and $\\varepsilon$ is the emissivity of powder bed which can be expressed as:\n\n$\\varepsilon=A_{\\mathrm{H}} \\varepsilon_{\\mathrm{H}}+\\left(1-A_{\\mathrm{H}}\\right) \\varepsilon_{\\mathrm{s}}$\n\nwhere $\\varepsilon_{\\mathrm{s}}$ is the emissivity of the powder particles. $A_{\\mathrm{H}}$ and $\\varepsilon_{\\mathrm{H}}$ are the area fraction of the surface that is occupied by the radiationemitting holes and the emissivity of the hole, respectively and\n\n$A_{\\mathrm{H}}=\\frac{0.908 \\varphi^{2}}{1.908 \\varphi^{2}-2 \\varphi+1}$\n\nand\n\n$\\varepsilon_{\\mathrm{H}}=\\frac{\\varepsilon_{S}\\left[2+3.082\\left(\\frac{1-\\varphi}{\\varphi}\\right)^{2}\\right]}{\\varepsilon_{\\mathrm{S}}\\left[1+3.082\\left(\\frac{1-\\varphi}{\\varphi}\\right)^{2}\\right]+1}$\n\nwhere $\\varphi$ is the porosity of the powder bed which can be written as\\\\\n[20]:\n\n$\\varphi=\\frac{\\rho_{\\mathrm{s}}-\\rho_{\\mathrm{p}}}{\\rho_{\\mathrm{s}}}$\n\nwhere $\\rho_{\\mathrm{s}}$ and $\\rho_{\\mathrm{p}}$ are the density of the solid and powder materials, respectively. The porosity is assumed to vary from $\\varphi=0.4$ for powder to $\\varphi=0$ for solid and it is taken as 0.4 in this paper.\n\n\\subsection*{2.4. Design of moving Gaussian heat source model}\nPowder bed is rapid heated and localized melt by laser heat source and the distribution of the laser beam intensity follows nearly a Gaussian relationship, which was mathematically presented as [24]:\n\n$q=\\frac{2 A P}{\\pi R^{2}} \\exp \\left(-\\frac{2 r^{2}}{R^{2}}\\right)$\n\nwhere $A$ is the laser energy absorptivity of TiC/Inconel 718 powder system as shown in Table 1, $P$ is the laser power, $R$ represents the radius of the Gaussian laser beam, which denotes the distance from the center of the laser beam to the point at which the energy reduced to its $1 / \\mathrm{e}^{2}$ and $r$ is the radial distance from a point on the powder bed surface to the center of the laser beam.\n\nThe latent heat occurred in the phase change, such as melting and solidification phenomenon in laser processing, cannot be negligible for the precision of simulation. In that case, the enthalpy is utilized to define the latent heat and expressed as a function of temperature:\n\n$H=\\int \\rho C_{\\mathrm{p}} d T$\n\nwhere $H$ is the enthalpy, $\\rho$ is the material density, $C_{\\mathrm{p}}$ is the specific heat capacity and $T$ is the temperature of the melt formed in SLM process.\n\n\\subsection*{2.5. Determination of thermal-physical parameters}\nEffective thermal conductivity of the powder layer, $k$, is defined by [25]:", "start_char_idx": 185759, "end_char_idx": 188536, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ee5f7e67-c2c1-47ee-a54c-77541af9c2d3": {"__data__": {"id_": "ee5f7e67-c2c1-47ee-a54c-77541af9c2d3", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "96eb8651-1aba-47b6-8f00-562ce1a64b55", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e7fa8d36fdee2f836bac699154aa4770687c53a26e029e246a81682ca59ad4b4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "14301aed-5dc8-4d1f-9dce-824bdf88fb91", "node_type": "1", "metadata": {}, "hash": "46876629be4cb9bc9b1794d653ee8f9586135e0cdbe6cb30c1c11df86dd41a7f", "class_name": "RelatedNodeInfo"}}, "text": "The latent heat occurred in the phase change, such as melting and solidification phenomenon in laser processing, cannot be negligible for the precision of simulation. In that case, the enthalpy is utilized to define the latent heat and expressed as a function of temperature:\n\n$H=\\int \\rho C_{\\mathrm{p}} d T$\n\nwhere $H$ is the enthalpy, $\\rho$ is the material density, $C_{\\mathrm{p}}$ is the specific heat capacity and $T$ is the temperature of the melt formed in SLM process.\n\n\\subsection*{2.5. Determination of thermal-physical parameters}\nEffective thermal conductivity of the powder layer, $k$, is defined by [25]:\n\n\n\\begin{align*}\n\\frac{k}{k_{\\mathrm{f}}}= & (1-\\sqrt{1-\\varphi})\\left(1+\\frac{\\varphi k_{\\mathrm{r}}}{\\mathrm{k}_{\\mathrm{f}}}\\right) \\\\\n& +\\sqrt{1-\\varphi} \\times\\left\\{\\frac{2}{1-\\frac{k_{\\mathrm{f}}}{k_{\\mathrm{s}}}}\\left[\\frac{1}{\\left(1-\\frac{k_{\\mathrm{f}}}{k_{\\mathrm{s}}}\\right)^{2}}\\left(1-\\frac{k_{\\mathrm{f}}}{k_{\\mathrm{s}}}\\right) \\ln \\left(\\frac{k_{\\mathrm{s}}}{k_{\\mathrm{f}}}\\right)-1\\right]+\\frac{k_{\\mathrm{r}}}{k_{\\mathrm{f}}}\\right\\} \\tag{16}\n\\end{align*}\n\n\nwhere $\\varphi$ is the porosity of the powder bed, $k_{\\mathrm{f}}$ is the thermal conductivity of the fluid surrounding the powder and substrate, i.e. argon in this case. $k_{\\mathrm{s}}$ is the thermal conductivity of the powder solid and $k_{\\mathrm{r}}$ is the thermal conductivity portion due to the radiation among powder particles which follows the expression:\n\n$k_{\\mathrm{r}}=4 F_{0} \\sigma T_{\\mathrm{P}}^{3} D_{\\mathrm{P}}$\n\nTable 2\n\nThermal-physical parameters of Inconel 718 [26].\n\n\\begin{center}\n\\begin{tabular}{lrrrrrrr}\n\\hline\n$T\\left[{ }^{\\circ} \\mathrm{C}\\right]$ & 20 & 100 & 200 & 400 & 600 & 800 & 1300 \\\\\n\\hline\n$k_{s}\\left[\\mathrm{~W} /\\left(\\mathrm{m}{ }^{\\circ} \\mathrm{C}\\right)\\right]$ & 10 & 12 & 14 & 17 & 20 & 26 & 31 \\\\\n$c\\left[\\mathrm{~J} /\\left(\\mathrm{kg}^{\\circ} \\mathrm{C}\\right)\\right]$ & 362 & 378 & 400 & 412 & 460 & 544 & 583 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nwhere $F_{0}$ is a view factor which is approximately taken as $1 / 3, T_{\\mathrm{P}}$ is the temperature of powder particles and $D_{\\mathrm{P}}$ is the average diameter of the powder particles.\n\nThermal-physical properties of the mixture like TiC/Inconel 718 in that case can be estimated by:\n\n$M=\\sum_{\\mathrm{n}} x_{\\mathrm{n}} M_{\\mathrm{n}}$\n\nwhere $M$ is one of the material physical properties, $M_{\\mathrm{n}}$ and $x_{\\mathrm{n}}$ are the physical property of one of the components in the powder and the mass fraction of this component among all the components. The weight ratio of $\\mathrm{TiC} /$ Inconel 718 is $0.25: 0.75$ in this paper. The melting point of Inconel 718 is $1300{ }^{\\circ} \\mathrm{C}$ with the density of $8200 \\mathrm{~kg} / \\mathrm{m}^{3}$, while reinforcing TiC particle has a relatively high melting point of $3067{ }^{\\circ} \\mathrm{C}$ and a density of $4910 \\mathrm{~kg} / \\mathrm{m}^{3}$.", "start_char_idx": 187916, "end_char_idx": 190848, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "14301aed-5dc8-4d1f-9dce-824bdf88fb91": {"__data__": {"id_": "14301aed-5dc8-4d1f-9dce-824bdf88fb91", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ee5f7e67-c2c1-47ee-a54c-77541af9c2d3", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "38a51b755fae85490a96ccecf7b146b2710494277e91f60f1cd9e2c22c7730af", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fb404a9a-d53d-41db-a082-eefe744a0bf5", "node_type": "1", "metadata": {}, "hash": "4aa4b56843ce45a6bff097d0ac317f4180ddd52ae24f5feb24e83e207a1f7d6b", "class_name": "RelatedNodeInfo"}}, "text": "The weight ratio of $\\mathrm{TiC} /$ Inconel 718 is $0.25: 0.75$ in this paper. The melting point of Inconel 718 is $1300{ }^{\\circ} \\mathrm{C}$ with the density of $8200 \\mathrm{~kg} / \\mathrm{m}^{3}$, while reinforcing TiC particle has a relatively high melting point of $3067{ }^{\\circ} \\mathrm{C}$ and a density of $4910 \\mathrm{~kg} / \\mathrm{m}^{3}$. Other thermal-physical parameters of solid of Inconel 718 and TiC involved in the numerical calculation are shown in Tables 2 and 3. However, it has to be noted that the properties of the powder and the solid are radically different, especially the thermal conductivities and specific heat capacity. The properties of powder can be defined by:\n\n$M=M_{\\mathrm{n}}(1-\\varphi)$\n\nwhere $M$ is one of the material physical properties, $M_{n}$ is the physical property of one of the components in the powder and $\\varphi$ is the porosity of the powder bed.\n\n\\section*{3. Experiments}\n\\subsection*{3.1. Powder materials}\nThe powder used in this study as starting materials includes the spherical Inconel 718 powder with a size distribution of 15$45 \\mu \\mathrm{m}$, which is produced by gas atomization method, the TiC nanopowder with polygonal shape and its size in an average of $50 \\mathrm{~nm}$. The chemical compositions of Inconel 718 powder are shown in Table 4. The Inconel 718 and TiC components with a weight ratio of $0.75: 0.25$ are mixed homogeneously in a Fritch Pulverisette 6 planetary ball mill (Fritsch GmbH, Germany) with a rotation speed of the main disc of $200 \\mathrm{rpm}$, a ball-to-powder weight ratio of 5:1 and a milling time of $4 \\mathrm{~h}$.\n\n\\subsection*{3.2. Laser processing}\nThe SLM experimental equipment developed by the Fraunhofer ILT is used in the SLM process experiment. The equipment mainly consists of a YLR-200-SM fiber laser with a output power of $\\sim 200 \\mathrm{~W}$ and a spot diameter of $70 \\mu \\mathrm{m}$, an automatic system for powder delivery and a computer system for process control. The\n\nTable 3\n\nThermal-physical parameters of TiC [27].\n\n\\begin{center}\n\\begin{tabular}{lrrrrrrr}\n\\hline\n$T\\left[{ }^{\\circ} \\mathrm{C}\\right]$ & 20 & 100 & 200 & 400 & 600 & 800 & 1300 \\\\\n\\hline\n$k_{s}\\left[\\mathrm{~W} /\\left(\\mathrm{m}^{\\circ} \\mathrm{C}\\right)\\right]$ & 23 & 24 & 25 & 29 & 32 & 34 & 39 \\\\\n$c\\left[\\mathrm{~J} /\\left(\\mathrm{kg}^{\\circ} \\mathrm{C}\\right)\\right]$ & 543 & 623 & 683 & 772 & 840 & 870 & 899 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 4\n\nChemical compositions of Inconel 718 powder (in weight percent, wt\\%).\n\n\\begin{center}\n\\begin{tabular}{llllllll}\n\\hline\n$\\mathrm{Cr}$ & $\\mathrm{Mo}$ & $\\mathrm{Al}$ & $\\mathrm{Ti}$ & $\\mathrm{Fe}$ & $\\mathrm{Nb}$ & $\\mathrm{C}$ & $\\mathrm{Ni}$ \\\\\n\\hline\n18.4 & 4.2 & 0.3 & 0.9 & 17.7 & 5.1 & 0.08 & Balance \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nentire SLM process is conducted in the protection of argon atmosphere. The processing parameters in the experiments are same as those in the simulation listed in the Table 1. The samples for metallographic examinations were cut, ground and polished according to standard procedures strictly.", "start_char_idx": 190492, "end_char_idx": 193594, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fb404a9a-d53d-41db-a082-eefe744a0bf5": {"__data__": {"id_": "fb404a9a-d53d-41db-a082-eefe744a0bf5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "14301aed-5dc8-4d1f-9dce-824bdf88fb91", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1609e13cc8d652c78dfeafc83dce4ccefb7357a063a296a90f02af81cb0963a9", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "433cd6e3-5274-471d-82a8-6579d80a231f", "node_type": "1", "metadata": {}, "hash": "a5db14cf7498e1c89330a471c1e4ba50605fbe8ad22f88c8f31995d8d9b71b83", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\begin{tabular}{llllllll}\n\\hline\n$\\mathrm{Cr}$ & $\\mathrm{Mo}$ & $\\mathrm{Al}$ & $\\mathrm{Ti}$ & $\\mathrm{Fe}$ & $\\mathrm{Nb}$ & $\\mathrm{C}$ & $\\mathrm{Ni}$ \\\\\n\\hline\n18.4 & 4.2 & 0.3 & 0.9 & 17.7 & 5.1 & 0.08 & Balance \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nentire SLM process is conducted in the protection of argon atmosphere. The processing parameters in the experiments are same as those in the simulation listed in the Table 1. The samples for metallographic examinations were cut, ground and polished according to standard procedures strictly. The cross-sectional microstructures of the SLM-produced TiC/Inconel 718 parts were characterized using a PMG3 optical microscopy (Olympus Corporation, Japan). The characteristic surface morphologies of the parts were characterized by scanning electron microscopy (SEM; Hitachi model S-4800, Japan) in secondary electron mode at $10 \\mathrm{kV}$.\n\n\\section*{4. Results and discussion}\n\\subsection*{4.1. Characteristics of temperature distributions in SLM process}\nFig. 3 shows the transient temperature distribution on the top surface and longitudinal view of the molten pool as laser beam reaches Point 1, Point 2 and Point 3, respectively, with $v$ of $100 \\mathrm{~mm} / \\mathrm{s}$ and $P$ of $125 \\mathrm{~W}$ (Fig. 2(b)). At the center of the first track (Point 1, Fig. 2(b)), the isotherm curves on the top surface of the molten pool are similar to a series of ellipses and, the ellipses of fore part are more intensive than those at the back-end of it. Meantime, it is asymmetry of isotherms along the laser scanning direction. However, this phenomenon is not conspicuous enough as shown in temperature contour pots (Fig. 3). The dashed line circle shown in the temperature contour plots presents the melting temperature of Inconel $718\\left(1300^{\\circ} \\mathrm{C}\\right)$. The temperature in this dashed line circle is higher compared with the melting point of Inconel 718, which induces a small molten pool within this region. The predicted operative temperature of the molten pool reduces from $2113{ }^{\\circ} \\mathrm{C}$ in the center of the melt to $1182^{\\circ} \\mathrm{C}$ at the edge of the molten pool as the laser beam reaches Point 1. Three dimensions of the molten pool are approximately $95.5 \\mu \\mathrm{m}$ (width), $106.5 \\mu \\mathrm{m}$ (length) and $61.3 \\mu \\mathrm{m}$ (depth), respectively (Fig. 3(a) and (b)). Then the laser spot further moves to the Point 2, the working temperature of the molten pool decreases from $2291{ }^{\\circ} \\mathrm{C}$ in the center to $1290{ }^{\\circ} \\mathrm{C}$ at the edge of the molten pool. There, then, is a cooling time of $10-\\mathrm{ms}$ after the fabrication of $\\mathrm{n}$ layer is completed by scanning track by track and, then, the SLM process of $n+1$ layer continues. The predicted working temperature of the molten pool ranges from $2348{ }^{\\circ} \\mathrm{C}$ in the center to $1345^{\\circ} \\mathrm{C}$ at the edge of the pool as the laser beam reaches Point 3. Comparing three dimensions of molten pool in Point 2 with these three figures of the pool in Point 1, the width $(109.3 \\mu \\mathrm{m})$, length $(120.7 \\mu \\mathrm{m})$ and depth $(67.8 \\mu \\mathrm{m})$ of the melt pool at Point 2 increases by $14.5 \\%, 13.3 \\%$ and 10.6\\%, respectively, to these at Point 1 (Fig. 3(c) and (d)).", "start_char_idx": 193029, "end_char_idx": 196365, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "433cd6e3-5274-471d-82a8-6579d80a231f": {"__data__": {"id_": "433cd6e3-5274-471d-82a8-6579d80a231f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fb404a9a-d53d-41db-a082-eefe744a0bf5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "25f1978a1ba432978ad36ff2c3001174a4da55f726630a40f228f5793056fda1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9d76fb0d-367b-40d5-a50a-0262615b95d6", "node_type": "1", "metadata": {}, "hash": "b15c53d22c9e46c15e286c2b980b5395e08b4c526b844bbd0f39c30587ab087c", "class_name": "RelatedNodeInfo"}}, "text": "The predicted working temperature of the molten pool ranges from $2348{ }^{\\circ} \\mathrm{C}$ in the center to $1345^{\\circ} \\mathrm{C}$ at the edge of the pool as the laser beam reaches Point 3. Comparing three dimensions of molten pool in Point 2 with these three figures of the pool in Point 1, the width $(109.3 \\mu \\mathrm{m})$, length $(120.7 \\mu \\mathrm{m})$ and depth $(67.8 \\mu \\mathrm{m})$ of the melt pool at Point 2 increases by $14.5 \\%, 13.3 \\%$ and 10.6\\%, respectively, to these at Point 1 (Fig. 3(c) and (d)). In addition, comparing these three figures of Point 3 with these of Point 1 , the width $(124.1 \\mu \\mathrm{m})$, length $(132.2 \\mu \\mathrm{m})$ and depth $(73.1 \\mu \\mathrm{m})$ of the molten pool at Point 3 are also slightly larger than these at Point 2, increasing by $13.5 \\%, 9.5 \\%$ and $7.8 \\%$, respectively (Fig. 3 (e) and (f)).\n\nThe simulation temperature contour plots show that the isotherm ellipses of the fore-part of molten pool (unscanned region) arrange more intensive than these at back-end of the melt (scanned region). This is mainly attributed to the change of thermal conductivities of $\\mathrm{TiC}$ /Inconel 718 , which are listed partly in Tables 2 and 3, due to the transition from powder to solid. This kind of transformation from powder to block contributes to the\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3d8b51f9bfd3b941d680g-06}\n\n(b)\n\nLongitudinal view of Point 1\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3d8b51f9bfd3b941d680g-06(1)}\n\nFig. 3. Temperature contour plots during SLM processing ( $v=100 \\mathrm{~mm} / \\mathrm{s}$ and $P=125 \\mathrm{~W}$ ). (a), (c) and (e): top surface of the molten pool of Point 1 , Point 2 and Point 3 , respectively; (b), (d) and (f): longitudinal view of the molten pool of Point 1, Point 2 and Point 3, respectively.\n\nheat transmission in the powder layer. Meantime, there is inconspicuous asymmetry of isotherms along the laser scanning direction since the special thermal-physical properties of materials, especially the thermal conductivities of $\\mathrm{TiC} /$ Inconel 718 . The differences between thermal conductivities of high-temperature and low-temperature are small (Tables 2 and 3), leading to the inconspicuous discrepancy of thermal conductive ability on two sides of unprocessed region and processed region along scanning\\\\\ndirection. During SLM process, the fabrication is completed track by track and then layer by layer. The average temperature and molten pool size described in simulation results are increasing gradually. This is mainly due to the fact that the heat stored in previous produced part has a significant influence on the next processing tracks and layers, i.e. heat accumulation effect. Furthermore, the energy losses caused by conduction are higher than the radiation and convection during processing layer by layer, and the development of shaped layers will weaken the ability of heat dissipation by conduction [28]. This phenomenon leads to a higher temperature and a larger molten pool. Fortunately, the existence of cooling time of $10-\\mathrm{ms}$ between productions of neighbor layers can relieve heat accumulation to a certain extent, then controlling the molten pool size change in a qualified scope. Excellent dimensional stability of molten pool size guarantees the homogeneity of liquid column size and, resultantly, improving the quality of SLMproduces parts.\n\n\\subsection*{4.2. Molten pool dimensions at different SLM processing parameters}\nFig. 4 depicts the three dimensions of the molten pool under different laser powers and scan speeds during SLM process of TiC/ Inconel 718. It is observed that the length, width and depth of the molten pool are approximately in positive liner relationship with the applied laser power.", "start_char_idx": 195839, "end_char_idx": 199648, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9d76fb0d-367b-40d5-a50a-0262615b95d6": {"__data__": {"id_": "9d76fb0d-367b-40d5-a50a-0262615b95d6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "433cd6e3-5274-471d-82a8-6579d80a231f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b507d49740f0bada14d281573ebb4d1a08a75623d3affcdb1421f64599354257", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5b899f71-ae1f-4933-bffa-90620f554d09", "node_type": "1", "metadata": {}, "hash": "75c179969842f9ce8fdd98a3caa5c45ee30eb6d7e21727c0869451890f34e2ab", "class_name": "RelatedNodeInfo"}}, "text": "This phenomenon leads to a higher temperature and a larger molten pool. Fortunately, the existence of cooling time of $10-\\mathrm{ms}$ between productions of neighbor layers can relieve heat accumulation to a certain extent, then controlling the molten pool size change in a qualified scope. Excellent dimensional stability of molten pool size guarantees the homogeneity of liquid column size and, resultantly, improving the quality of SLMproduces parts.\n\n\\subsection*{4.2. Molten pool dimensions at different SLM processing parameters}\nFig. 4 depicts the three dimensions of the molten pool under different laser powers and scan speeds during SLM process of TiC/ Inconel 718. It is observed that the length, width and depth of the molten pool are approximately in positive liner relationship with the applied laser power. As the utilized power is increased from $75 \\mathrm{~W}$ to $150 \\mathrm{~W}$, the pronounced enhancement of three dimensions of the molten pool, i.e. length (from $50.8 \\mu \\mathrm{m}$ to $217.2 \\mu \\mathrm{m}$ ), width (from $34.3 \\mu \\mathrm{m}$ to $211.9 \\mu \\mathrm{m}$ ) and depth (from $27.3 \\mu \\mathrm{m}$ to $85.3 \\mu \\mathrm{m}$ ), respectively, is observed (Fig. 4(a)). However, it can be seen that the three dimensions of the molten pool reduces with the increment of the applied scan speed. On increasing the applied scan speed from $50 \\mathrm{~mm} / \\mathrm{s}$ to $300 \\mathrm{~mm} / \\mathrm{s}$, the length of the molten pool decreases evidently from $239.8 \\mu \\mathrm{m}$ to $91.2 \\mu \\mathrm{m}$. Meanwhile, the width of the molten pool reduces from $215.2 \\mu \\mathrm{m}$ to $78.0 \\mu \\mathrm{m}$ and, the depth of the molten pool decreases from $91.6 \\mu \\mathrm{m}$ to $49.8 \\mu \\mathrm{m}$ (Fig. 4(b)). Further, the calculation results manifest that the decreasing tendency becomes less pronounced as the utilized scan speed is increased above $100 \\mathrm{~mm} / \\mathrm{s}$.\n\nSince SLM is a multi-track and multi-layer additive manufacturing based laser scanning, thus, a successful SLM fabrication should be realized by the well bonding between adjacent scan tracks and neighbor layers through rapid heating, complete melting and subsequent sufficient solidification [29]. The geometric dimension precision and density of the SLM-fabricated parts are pronounced affected by the metallurgical bonding ability between the neighbor layers and adjacent tracks. Furthermore, there is a significant connection between the metallurgical bonding and three-dimension of the molten pool. As the combination of scan speed of $100 \\mathrm{~mm} / \\mathrm{s}$ and laser power of $75 \\mathrm{~W}$ is applied, a narrow melt pool is obtained with its depth of $27.3 \\mu \\mathrm{m}$ and width of $34.3 \\mu \\mathrm{m}$, which is obviously less than the powder layer thickness $(50 \\mu \\mathrm{m})$ and hatch spacing $(50 \\mu \\mathrm{m})$, respectively, thus, leading to the poor metallurgical bonding between neighbor layers and adjacent tracks since the necessary overlap is not realized. At a relatively higher laser power of $100 \\mathrm{~W}$ combined with a constant scan speed of $100 \\mathrm{~mm} / \\mathrm{s}$, the obtained molten pool depth $(53.6 \\mu \\mathrm{m})$ approximately equals to the thickness of powder layer, resulting in a relatively weak metallurgical bonding between neighbor layers. Moreover, when a high laser power ( $150 \\mathrm{~W})$ with an extremely slow scan speed $(50 \\mathrm{~mm} / \\mathrm{s})$ is utilized, the three dimensions acquired (length: $239.8 \\mu \\mathrm{m}$, width: $215.2 \\mu \\mathrm{m}$ and depth: $91.6 \\mu \\mathrm{m})$ are obviously larger than results required. Excessive remelting of width and depth arising from large molten pool three dimensions results in the stress accumulation in the remelting region. It is responsible for the attendant microcracks in SLMprocessed parts and distortion of the parts.", "start_char_idx": 198826, "end_char_idx": 202715, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5b899f71-ae1f-4933-bffa-90620f554d09": {"__data__": {"id_": "5b899f71-ae1f-4933-bffa-90620f554d09", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9d76fb0d-367b-40d5-a50a-0262615b95d6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "47dcc84aa120d948509434f1df99c003175b6bff5e32faeb57cb12e30c24a29d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fd124f04-9150-4d1b-be60-7b01dc13da0e", "node_type": "1", "metadata": {}, "hash": "f5927db1720fbcefc9ff48cf3d83bc66a4e896aeda0e24be99eacada2171ecb4", "class_name": "RelatedNodeInfo"}}, "text": "Moreover, when a high laser power ( $150 \\mathrm{~W})$ with an extremely slow scan speed $(50 \\mathrm{~mm} / \\mathrm{s})$ is utilized, the three dimensions acquired (length: $239.8 \\mu \\mathrm{m}$, width: $215.2 \\mu \\mathrm{m}$ and depth: $91.6 \\mu \\mathrm{m})$ are obviously larger than results required. Excessive remelting of width and depth arising from large molten pool three dimensions results in the stress accumulation in the remelting region. It is responsible for the attendant microcracks in SLMprocessed parts and distortion of the parts. It thus can be concluded that a SLM-fabricated part with high density and outstanding metallurgical bonding ability cannot be obtained under the above mentioned laser processing conditions.\n\n\\subsection*{4.3. Effect of laser processing conditions on thermal behavior}\nFig. 5 shows the effects of laser processing parameters on the temperature distribution during SLM of TiC/Inconel 718 powder system along the $Y$-direction at $X=0.7 \\mathrm{~mm}$ and $Z=0.05 \\mathrm{~mm}$ (path A-B), and Z-direction at Point 2 (Fig. 2(b)). The slope of the curves shown in the figures presents the temperature gradient of the powder bed, and a steep slope means a relatively high temperature gradient. When the laser power is increased from $75 \\mathrm{~W}$ to $150 \\mathrm{~W}$, the maximum temperature gradient along the path A-B pronouncedly increases from $1.30 \\times 10^{4}{ }^{\\circ} \\mathrm{C} / \\mathrm{mm}$ to $2.60 \\times 10^{4}{ }^{\\circ} \\mathrm{C}$ / $\\mathrm{mm}$ (Fig. 5(a)). The maximum temperature gradient along the Z-direction also significantly increases from $1.36 \\times 10^{4}{ }^{\\circ} \\mathrm{C} / \\mathrm{mm}$ to $2.62 \\times 10^{4}{ }^{\\circ} \\mathrm{C} / \\mathrm{mm}$. Furthermore, the temperature trend of each curve along Z-direction is obviously divided into four parts. Part (1) and part (2) present the fabricating powder layer. Part (3) and part (4) mean the previous powder layer or metal substrate. The temperature distribution in every powder layer consists of two different segments and the temperature gradient of upper powder layer is higher than that of bottom powder layer. Taking the temperature distribution under processing condition of $P=125 \\mathrm{~W}$ and $v=100 \\mathrm{~mm} / \\mathrm{s}$ as an example, the temperature gradients are $1.68 \\times 10^{4}{ }^{\\circ} \\mathrm{C} / \\mathrm{mm}, \\quad 7.40 \\times 10^{3}{ }^{\\circ} \\mathrm{C} / \\mathrm{mm}, \\quad 2.16 \\times 10^{4}{ }^{\\circ} \\mathrm{C} / \\mathrm{mm} \\quad$ and $1.01 \\times 10^{4} \\mathrm{C} / \\mathrm{mm}$, respectively, from the top surface of building\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3d8b51f9bfd3b941d680g-07}\n\nFig. 4. Three dimensions of the molten pool during SLM process of TiC/Inconel 718 powder system with different processing parameters. (a) different laser powers $(v=100 \\mathrm{~mm} / \\mathrm{s})$; (b) different scan speeds $(P=125 \\mathrm{~W})$.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3d8b51f9bfd3b941d680g-08(1)}\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3d8b51f9bfd3b941d680g-08}\n\nFig. 5. Temperature distribution during SLM of TiC/Inconel 718 powder.", "start_char_idx": 202164, "end_char_idx": 205354, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fd124f04-9150-4d1b-be60-7b01dc13da0e": {"__data__": {"id_": "fd124f04-9150-4d1b-be60-7b01dc13da0e", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5b899f71-ae1f-4933-bffa-90620f554d09", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "880e9fb634e6c34cbc25f25a2d87bce6fbbe62f637b945e6bd1c97a3183b114f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6d3f403d-2721-4288-815e-2022472b2240", "node_type": "1", "metadata": {}, "hash": "aa74c68eab75f08a3079743ac0d5ce0b6dc2d7ea88a41d1b21318b3998ccf099", "class_name": "RelatedNodeInfo"}}, "text": "4. Three dimensions of the molten pool during SLM process of TiC/Inconel 718 powder system with different processing parameters. (a) different laser powers $(v=100 \\mathrm{~mm} / \\mathrm{s})$; (b) different scan speeds $(P=125 \\mathrm{~W})$.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3d8b51f9bfd3b941d680g-08(1)}\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3d8b51f9bfd3b941d680g-08}\n\nFig. 5. Temperature distribution during SLM of TiC/Inconel 718 powder. (a) along the path $A-B$ at $X=0.7 \\mathrm{~mm}$ and $Z=0.05 \\mathrm{~mm}$ on the top surface of the powder bed for different laser powers $(v=100 \\mathrm{~mm} / \\mathrm{s})$; (b) along the Z-direction at Point 2 for different laser powers $(v=100 \\mathrm{~mm} / \\mathrm{s})$; (c) along the path A-B at X=0.7 $\\mathrm{mm}$ and $\\mathrm{Z}=0.05 \\mathrm{~mm}$ on the top surface of the powder bed for different scan speeds $(P=125 \\mathrm{~W})$; (d) along the Z-direction at Point 2 for different scan speeds $(P=125 \\mathrm{~W})$.\n\nlayer to the bottom of previous layer or substrate (Fig. 5(b)). However, the maximum temperature gradient is affected negligibly by the variation of scan speed. When the laser scan speed is increased from $50 \\mathrm{~mm} / \\mathrm{s}$ to $300 \\mathrm{~mm} / \\mathrm{s}$, the maximum temperature gradient of different processing conditions fluctuates around $2.18 \\times 10^{3}{ }^{\\circ} \\mathrm{C} / \\mathrm{mm}$ along path A-B (Fig. 5(c)). Moreover, the temperature distribution curves of different operative speeds along Z-direction are approximately parallel arranged, where the maximum temperature gradient is about $2.40 \\times 10^{3}{ }^{\\circ} \\mathrm{C} / \\mathrm{mm}$. Similarly, the temperature distribution curves along Z-direction of molten pool are divided into four parts under varying scan speeds as same as these under different laser powers (Fig. 5(d)).\n\nThe temperature distribution of the powder bed is affected directly by the laser power and, the scan speed indirectly influences temperature contour plots by changing the interaction time between the powder particles and laser beam. Or more precisely, the laser power has a more pronounced influence on the temperature gradient around the molten pool than the scan speed, as depicted by Fig. 5. Moreover, the maximum temperature gradient in Z-direction of the melt pool is relatively larger than that observed in Y-direction of the pool, which attributes to the heat flow direction in the molten pool. During SLM, the majority of laser energy is mainly dissipated through the pre-fabricated layers or metal substrate for the relatively higher thermal conductivity in this region. So the heat flow direction during the SLM process is approximately perpendicular to the surface of pre-processed layers and the temperature gradient in this direction is highest [30]. This high temperature gradient along Z-direction presents that rapid heating and solidification during SLM is an unsteady-state process. The microstructural features, like grain morphology, grain size and its size distribution, in SLM-fabricated parts show some interesting variation along Z-direction correspondingly. Hofmeister et al. [31] noted that the microstructure scale shows more sensitive to variations in Z-direction height than to differences in laser power and traverse velocity. Furthermore, when a relatively high laser power $(150 \\mathrm{~W})$ is utilized, the finally solidified parts may suffer from residual stress accumulation due to the large temperature gradient $\\left(2.62 \\times 10^{4}{ }^{\\circ} \\mathrm{C} / \\mathrm{mm}\\right)$ between the hot melt region and the relatively cold substrate. This residual internal stress is responsible for the local inaccuracy, warpage and even delamination $[32,33]$.\n\nFig. 6 depicts the variation of the maximum rate of temperature change with different processing conditions.", "start_char_idx": 204866, "end_char_idx": 208764, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "6d3f403d-2721-4288-815e-2022472b2240": {"__data__": {"id_": "6d3f403d-2721-4288-815e-2022472b2240", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fd124f04-9150-4d1b-be60-7b01dc13da0e", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1ccf0f5c4473d739a4d649cd2a8cb0296daf0588b1757871b40827a4c294c726", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "44b766c9-6394-4b4d-9619-5f750867ef0a", "node_type": "1", "metadata": {}, "hash": "d5bddeeeda9568d1353d85b7e267c0b655521b765f974537c5deb4659c8d90c5", "class_name": "RelatedNodeInfo"}}, "text": "The microstructural features, like grain morphology, grain size and its size distribution, in SLM-fabricated parts show some interesting variation along Z-direction correspondingly. Hofmeister et al. [31] noted that the microstructure scale shows more sensitive to variations in Z-direction height than to differences in laser power and traverse velocity. Furthermore, when a relatively high laser power $(150 \\mathrm{~W})$ is utilized, the finally solidified parts may suffer from residual stress accumulation due to the large temperature gradient $\\left(2.62 \\times 10^{4}{ }^{\\circ} \\mathrm{C} / \\mathrm{mm}\\right)$ between the hot melt region and the relatively cold substrate. This residual internal stress is responsible for the local inaccuracy, warpage and even delamination $[32,33]$.\n\nFig. 6 depicts the variation of the maximum rate of temperature change with different processing conditions. It shows that the maximum rate of temperature change including the maximum heating rate and the maximum cooling rate is generally in positive linear relation with the utilized laser power and scan speed. The maximum heating rate is higher slightly than the maximum cooling rate (Figs. 6(a) and (b)). When the laser power is increased from $75 \\mathrm{~W}$ to $150 \\mathrm{~W}$, the maximum heating rate increases slightly from $2.70 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ to $5.42 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$. The maximum cooling rate follows the similar variation tendency and it increases from $2.63 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ to $5.25 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$. On increasing the applied scan speed from $50 \\mathrm{~mm} / \\mathrm{s}$ to $300 \\mathrm{~mm} / \\mathrm{s}$, the maximum heating rate increases obviously from $2.30 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ to $1.30 \\times 10^{7}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$. Meantime, the maximum cooling rate increase from $2.21 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ to $1.26 \\times 10^{7} \\mathrm{C} / \\mathrm{s}$. Comparing the data from Fig. 6(a) and (b), it reveals that the scan speed has a more significant effect than the laser power on the rate of temperature change. More precisely, the rate of temperature change in the molten pool during SLM is more sensitive to the scan speed than to the laser power.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3d8b51f9bfd3b941d680g-09(1)}\n\nFig. 6. The variation of the maximum rate of temperature change with (a) different laser powers $(\\nu=100 \\mathrm{~mm} / \\mathrm{s})$ and (b) different scan speeds ( $P=125 \\mathrm{~W})$.\n\nAs the track-by-track and layer-by-layer rapid melting and subsequent solidification process continues, the powder bed experiences a complex iteration behavior of heating and cooling, implying the latent heat of phase change and thermal cycles accompanied with stress cycles. On the other hand, the processing conditions play a crucial role in influencing thermal behavior and attendant mechanical properties of as-fabricated parts. When the laser beam scans through the powder bed with a high speed $(300 \\mathrm{~mm} / \\mathrm{s})$ or a relatively high laser power $(150 \\mathrm{~W})$, the particles within the laser radiation region undergo an extremely rapid heating process with the maximum heating rate of $1.30 \\times 10^{7} \\mathrm{C} / \\mathrm{s}$, which potentially results in thermo-capillary instability in the molten pool and droplets splashing from the melt pool. It is responsible for the balling effect on the top surface of every fabricating layer (Fig. 1).", "start_char_idx": 207861, "end_char_idx": 211490, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "44b766c9-6394-4b4d-9619-5f750867ef0a": {"__data__": {"id_": "44b766c9-6394-4b4d-9619-5f750867ef0a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "6d3f403d-2721-4288-815e-2022472b2240", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0db30baadd3cb9af50ec7e3e423d0ce9559c31c7d73c8da40f34c34130689200", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d442c4fe-a8a3-4338-8f6f-8c032bec6c1d", "node_type": "1", "metadata": {}, "hash": "8c28783f068daf372b5452f43c9fbb31e67ef6abcb75fdca7d2b365ba09c67d5", "class_name": "RelatedNodeInfo"}}, "text": "On the other hand, the processing conditions play a crucial role in influencing thermal behavior and attendant mechanical properties of as-fabricated parts. When the laser beam scans through the powder bed with a high speed $(300 \\mathrm{~mm} / \\mathrm{s})$ or a relatively high laser power $(150 \\mathrm{~W})$, the particles within the laser radiation region undergo an extremely rapid heating process with the maximum heating rate of $1.30 \\times 10^{7} \\mathrm{C} / \\mathrm{s}$, which potentially results in thermo-capillary instability in the molten pool and droplets splashing from the melt pool. It is responsible for the balling effect on the top surface of every fabricating layer (Fig. 1). Meanwhile, local residual stress accumulation maybe occurs for the enormous cooling rate of $1.26 \\times 10^{7}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ under scan speed of $300 \\mathrm{~mm} / \\mathrm{s}$ or laser power of $150 \\mathrm{~W}$. It possibly gives rise to the increment of cracking susceptibility, distortion of SLM-processed parts and delamination between neighbor layers. It is worth noting that the combination of the lower heating rate of $4.52 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ and cooling rate of $4.38 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ has a tendency to reduce the possibility of these above metallurgical defects under a relatively low scan speed of $100 \\mathrm{~mm} / \\mathrm{s}$ and a laser power of $125 \\mathrm{~W}$. In addition, it is contributory to the refinement of microstructure and, thus resultant synthesized mechanical properties of final components for the rapid melting/rapid solidification mechanism.\n\nThe variation of the maximum temperature and the liquid lifetime of molten pool during SLM process with different parameters are shown in Fig. 7. It can be found clearly that the maximum temperature and the liquid lifetime are generally linear to the applied laser power. When the laser power increased from $75 \\mathrm{~W}$ to $150 \\mathrm{~W}$, the maximum temperature enhances sharply from $1524^{\\circ} \\mathrm{C}$ to $2690^{\\circ} \\mathrm{C}$ as a result of the higher laser energy density input. Meanwhile, the liquid lifetime of molten pool increased similarly from $0.51 \\mathrm{~ms}$ to $2.15 \\mathrm{~ms}$ (Fig. 7(a)). On the other hand, as the utilized scan speed increased from $50 \\mathrm{~mm} / \\mathrm{s}$ to $300 \\mathrm{~mm} / \\mathrm{s}$, the maximum temperature undergoes a slight decrement from $2495^{\\circ} \\mathrm{C}$ to $2080^{\\circ} \\mathrm{C}$ as an indirect response of the shorter interaction time between powder particles and laser beam. Accordingly, the liquid lifetime also shortens from $5.15 \\mathrm{~ms}$ to $0.30 \\mathrm{~ms}$. Moreover, it should be noted that the enhancement tendency of maximum temperature and liquid lifetime are alleviated when the scan speed is increased above $100 \\mathrm{~mm} / \\mathrm{s}$ (Fig. 7(b)). In addition, comparing the data from Fig. 7(a) and (b), it reveals that the laser power has a more pronounced effect than the scan speed on the maximum temperature and, the liquid lifetime of the molten pool during SLM is more sensitive to the scan speed than to the laser power.\n\nThe TiC/Inconel 718 powder system is melted by the laser energy, which is directly influenced by the laser power and indirectly affected by the scan speed, to yield a high-temperature molten pool during SLM process. The thermal-physical parameters are changed for the transition of TiC/Inconel 718 form powder to solid, contributing to heat transmission in powder bed and resultant liquid phase with lower viscosity. It is helpful to improve the metal liquid wetting effect around TiC particles and, thus, enhance particle/matrix interfacial bonding ability, so that optimize comprehensive performance of the SLM-fabricated parts.", "start_char_idx": 210792, "end_char_idx": 214632, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d442c4fe-a8a3-4338-8f6f-8c032bec6c1d": {"__data__": {"id_": "d442c4fe-a8a3-4338-8f6f-8c032bec6c1d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "44b766c9-6394-4b4d-9619-5f750867ef0a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e6e3378781b06521637390664e249bba9cf2ed2e8fd18d274f1dc8fb55406141", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f843eb16-9c4b-4300-84a7-ca60ae6659ea", "node_type": "1", "metadata": {}, "hash": "7a79e9340b4f5d1df92a3c5006ac5cec369cbbbf40a9c4161d25f5750f0926dd", "class_name": "RelatedNodeInfo"}}, "text": "7(b)). In addition, comparing the data from Fig. 7(a) and (b), it reveals that the laser power has a more pronounced effect than the scan speed on the maximum temperature and, the liquid lifetime of the molten pool during SLM is more sensitive to the scan speed than to the laser power.\n\nThe TiC/Inconel 718 powder system is melted by the laser energy, which is directly influenced by the laser power and indirectly affected by the scan speed, to yield a high-temperature molten pool during SLM process. The thermal-physical parameters are changed for the transition of TiC/Inconel 718 form powder to solid, contributing to heat transmission in powder bed and resultant liquid phase with lower viscosity. It is helpful to improve the metal liquid wetting effect around TiC particles and, thus, enhance particle/matrix interfacial bonding ability, so that optimize comprehensive performance of the SLM-fabricated parts. However, An low scan speed $(50 \\mathrm{~mm} / \\mathrm{s})$ or an intense laser power ( $150 \\mathrm{~W}$ ) applied in the SLM process yields an extremely long liquid lifetime\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3d8b51f9bfd3b941d680g-09}\n\nFig. 7. The maximum temperature and the liquid lifetime of the molten pool during SLM process using different processing parameters. (a) different laser powers $(v=100 \\mathrm{~mm} / \\mathrm{s})$; (b) different scan speeds $(P=125 \\mathrm{~W}$ ).\n\n( $5.15 \\mathrm{~ms})$, maybe, resulting in the formation of gas since the gas atoms release from the lattice in heat affected zone, as proposed by Weingarten [34]. This phenomenon causes the appearance of spherical pores and the attendant high porosity in SLM-produced parts. Moreover, these pores appear generally in the back-end of the molten pool, as revealed by Fig. 1. Meanwhile, when an overwhelmingly high scan speed $(300 \\mathrm{~mm} / \\mathrm{s})$ or an exceedingly low laser power $(75 \\mathrm{~W})$ is used, an extremely short liquid lifetime $(0.30 \\mathrm{~ms})$ and low temperature $\\left(1524^{\\circ} \\mathrm{C}\\right)$ occur, causing the formation of a small amount of liquid phase with a relatively high viscosity. It is detrimental for the wetting of the liquid phase among the gaps of powders, generating the appearance of irregular pores and the attendant high porosity in SLM-produced parts. In conclusion, an appropriate scan speed $(100 \\mathrm{~mm} / \\mathrm{s})$ combined with a suitable laser power ( $125 \\mathrm{~W}$ ) plays a paramount role in SLM process of TiC/Inconel 718 with an appropriate temperature of $2291{ }^{\\circ} \\mathrm{C}$ and a proper liquid lifetime of $1.41 \\mathrm{~ms}$.\n\n\\subsection*{4.4. Effects of different processing parameters on molten pool configuration}\nFig. 8 shows the melt depth and width divided by the total energy input (i.e. the melt depth per energy, $D_{\\text {per }}$; the melt width per energy, $W_{\\text {per }}$ ) at different powers and scan speeds. The ratio of the depth per energy/the width per energy (i.e. $R_{\\mathrm{D} / \\mathrm{W}}$ ) under the same processing parameters is depicted in Fig. 9, as well as the configuration of the molten pool formed under corresponding fabrication conditions in Fig. 10. It can be seen that $D_{\\text {per }}$ and $W_{\\text {per }}$ both increase as the laser power is increased and, both reduce with the decrease of scan speed. As the laser power is enhanced from $75 \\mathrm{~W}$ to $150 \\mathrm{~W}$, the $W_{\\text {per }}$ increases obviously from $2.61 \\mathrm{~mm} / \\mathrm{J}$ to $8.07 \\mathrm{~mm} / \\mathrm{J}$ and, the $D_{\\text {per }}$ elevates slightly from $2.08 \\mathrm{~mm} / \\mathrm{J}$ to $3.25 \\mathrm{~mm} / \\mathrm{J}$.", "start_char_idx": 213714, "end_char_idx": 217402, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f843eb16-9c4b-4300-84a7-ca60ae6659ea": {"__data__": {"id_": "f843eb16-9c4b-4300-84a7-ca60ae6659ea", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d442c4fe-a8a3-4338-8f6f-8c032bec6c1d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "190e5fedc7e813c2a80fdd6aa162206af578c12aa326ea732c0e2f5192bb693d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2032a689-ac2c-4505-bf7a-f98618e1f37f", "node_type": "1", "metadata": {}, "hash": "3b4ef8ff8dd025aa41a61e3fd552ad1dba9fb300886e040f22a53269aad0002d", "class_name": "RelatedNodeInfo"}}, "text": "9, as well as the configuration of the molten pool formed under corresponding fabrication conditions in Fig. 10. It can be seen that $D_{\\text {per }}$ and $W_{\\text {per }}$ both increase as the laser power is increased and, both reduce with the decrease of scan speed. As the laser power is enhanced from $75 \\mathrm{~W}$ to $150 \\mathrm{~W}$, the $W_{\\text {per }}$ increases obviously from $2.61 \\mathrm{~mm} / \\mathrm{J}$ to $8.07 \\mathrm{~mm} / \\mathrm{J}$ and, the $D_{\\text {per }}$ elevates slightly from $2.08 \\mathrm{~mm} / \\mathrm{J}$ to $3.25 \\mathrm{~mm} / \\mathrm{J}$. Whereas the increasing tendency of the $D_{\\text {per }}$ is moderate as the applied laser power is increased above $100 \\mathrm{~W}$ (Fig. 8 (a)), leading to a decrement of the $R_{\\mathrm{D} / \\mathrm{W}}$ from 0.80 to 0.40 (Fig. 9 (a)) and a wide-shallow cross section of the molten pool correspondingly (Fig. 10(a)). On increasing the applied scan speed from $50 \\mathrm{~mm} / \\mathrm{s}$ to $300 \\mathrm{~mm} / \\mathrm{s}$, the $W_{\\text {per }}$ increases extremely from $4.92 \\mathrm{~mm} / \\mathrm{J}$ to $10.70 \\mathrm{~mm} / \\mathrm{J}$, the $D_{\\text {per }}$ enhances considerately from $2.09 \\mathrm{~mm} / \\mathrm{J}$ to $6.83 \\mathrm{~mm} / \\mathrm{J}$ (Fig. 8(a)). As a result, the $R_{\\mathrm{D} / \\mathrm{w}}$ elevates monotonously from 0.42 to 0.63 (Fig. 9(b)) and, consequently, a relatively deep-narrow configuration of molten pool along the Y-direction is formed as a high scan speed is utilized (Fig. 10(b)).\n\nA superior SLM-fabricated part is bonded by neighbor liquid columns with homogeneous and appropriate radius, thus a further understanding regarding the influential factors of the dimensions and configuration of liquid columns contributes to optimize the processing parameters and improve mechanical properties correspondingly. Fig. 8(a) and (b) reflect the energy efficiency in Z-direction and Y-direction of the molten pool, where the laser beam and powder particles interact between each other, indicating the heat flow direction in the melt. They suggest that low power $(75 \\mathrm{~W})$ and high scan speed $(300 \\mathrm{~mm} / \\mathrm{s})$ are more energy efficient in Z-direction of the molten pool. More precisely, the relatively higher laser energy flows along Z-direction, leading to a higher $R_{\\mathrm{D} / \\mathrm{W}}(0.80)$ and a resultantly deep-narrow cross sectional view of the molten pool (Fig. 8-10). Whereas a high laser power ( $150 \\mathrm{~W}$ ) or a low scan speed $\\left(50 \\mathrm{~mm} / \\mathrm{s}\\right.$ ) causes a low $R_{\\mathrm{D} / \\mathrm{W}}(0.40)$ and a wide-shallow cross section of the molten pool, meaning it is more energy efficient in the Y-direction of the melt (Fig. 8-10). The forming mechanism of the cross-sectional configuration of the molten pool at different processing conditions can be concluded as follows:\n\n(1) The fusion enthalpy of TiC/Inconel 718 powder system is the energy barrier for melting powder particles. The melt generates when accumulated heat reaches the energy barrier.\n\n(2) The laser beam with Gaussian power distribution reveals that the energy intensity of the laser beam periphery is pronounced weaker than that in the center.\n\n(3) The energy $(W=P t)$ accumulated in the periphery region cannot satisfy the fusion enthalpy, i.e. energy barrier, to hinder the generation of the melt under a low laser power or a high scan speed.", "start_char_idx": 216819, "end_char_idx": 220239, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2032a689-ac2c-4505-bf7a-f98618e1f37f": {"__data__": {"id_": "2032a689-ac2c-4505-bf7a-f98618e1f37f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f843eb16-9c4b-4300-84a7-ca60ae6659ea", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "64f8db3a09baf74cc37f48be7b609ca0be9e36b41f25906f702a33e0d546b67d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "23cf90a4-809d-4fc6-a21d-996a21f827eb", "node_type": "1", "metadata": {}, "hash": "80559e3fd7aa0d7f54012ba20f4da03236debe0dcdacba883a0e7c843ca66689", "class_name": "RelatedNodeInfo"}}, "text": "8-10). The forming mechanism of the cross-sectional configuration of the molten pool at different processing conditions can be concluded as follows:\n\n(1) The fusion enthalpy of TiC/Inconel 718 powder system is the energy barrier for melting powder particles. The melt generates when accumulated heat reaches the energy barrier.\n\n(2) The laser beam with Gaussian power distribution reveals that the energy intensity of the laser beam periphery is pronounced weaker than that in the center.\n\n(3) The energy $(W=P t)$ accumulated in the periphery region cannot satisfy the fusion enthalpy, i.e. energy barrier, to hinder the generation of the melt under a low laser power or a high scan speed. However, the relatively more powerful laser energy in the center of the beam is absorbed through radiation on the top surface and conduction in the powder bed to melt powder along Z-direction, leading to a deep-narrow cross section of the molten pool. Differently, when a high laser power or a low scan speed is applied, it is easily to melt powder bed in both periphery and center region of the laser beam since enough energy accumulated. That is responsible to generate a wide and relatively shallow configuration of the molten pool.\n\nConsequently, it is beneficial to reduce the hatch spacing when the molten pool configuration is deep and narrow and, improve that when a wide-shallow configuration generates for a comparatively smooth surface and excellent bonding properties.\n\n\\subsection*{4.5. Experimental investigation}\nThe typical etched cross-sectional metallographic microstructures of shaped samples with varying laser powers are shown in Fig. 11, in order to investigate the layer-by-layer bonding\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3d8b51f9bfd3b941d680g-10}\n\nFig. 8. Numerical results of the melt depth/width per energy under (a) varying laser powers $(v=100 \\mathrm{~mm} / \\mathrm{s})$ and (b) scan speeds $(P=125 \\mathrm{~W})$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3d8b51f9bfd3b941d680g-11}\n\\end{center}\n\n(a) The ratio of depth per energy/width per energy\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3d8b51f9bfd3b941d680g-11(1)}\n\\end{center}\n\n(b)\n\nThe ratio of depth per energy/width per energy\n\nFig. 9. The ratio of the depth per energy/the width per energy with (a) varying laser powers $(\\nu=100 \\mathrm{~mm} / \\mathrm{s})$ and (b) scan speeds $(P=125 \\mathrm{~W})$.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3d8b51f9bfd3b941d680g-11(2)}\n\nFig. 10. The configuration of the molten pool under (a) different laser powers $(v=100 \\mathrm{~mm} / \\mathrm{s}$ ) and (b) different scan speeds ( $P=125 \\mathrm{~W}$ ).\n\nproperties of the final TiC/Inconel 718 samples. Layerwise microstructure features were observed legibly, especially under the condition of laser power of $125 \\mathrm{~W}$, as a result of layer-by-layer melting and subsequent solidification of SLM process. At a lower laser power of $75 \\mathrm{~W}$, the irregular pores with large size which crossed over several layers, as well as the tiny molten pool width of $35 \\mu \\mathrm{m}$ and pool depth of $28 \\mu \\mathrm{m}$ shown using white dot line in the figure, were found (Fig. 11(a)). On enhancing the applied laser power to $100 \\mathrm{~W}$, large-sized irregular pores disappeared while small spherical pores occurred, which generally aggregated in the back-end of the molten pool (Figs. 11(b) and 1). Meantime, the width and depth of the molten pool increase to $76 \\mu \\mathrm{m}$ and $45 \\mu \\mathrm{m}$, respectively.", "start_char_idx": 219549, "end_char_idx": 223142, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "23cf90a4-809d-4fc6-a21d-996a21f827eb": {"__data__": {"id_": "23cf90a4-809d-4fc6-a21d-996a21f827eb", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2032a689-ac2c-4505-bf7a-f98618e1f37f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "148e491655b8fca3515eb270ad0a3b5703c653b051c629e9407792358fc9ea19", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "66f3818b-61f5-4384-9602-6ba32141c426", "node_type": "1", "metadata": {}, "hash": "58a3088547d258c5b4af0859b3c50071935a7ba693b352e2273d0a52c06222d0", "class_name": "RelatedNodeInfo"}}, "text": "At a lower laser power of $75 \\mathrm{~W}$, the irregular pores with large size which crossed over several layers, as well as the tiny molten pool width of $35 \\mu \\mathrm{m}$ and pool depth of $28 \\mu \\mathrm{m}$ shown using white dot line in the figure, were found (Fig. 11(a)). On enhancing the applied laser power to $100 \\mathrm{~W}$, large-sized irregular pores disappeared while small spherical pores occurred, which generally aggregated in the back-end of the molten pool (Figs. 11(b) and 1). Meantime, the width and depth of the molten pool increase to $76 \\mu \\mathrm{m}$ and $45 \\mu \\mathrm{m}$, respectively. On further increasing the laser power to $125 \\mathrm{~W}$, the dense morphology without any apparent pores, as well as the appropriate width of $95 \\mu \\mathrm{m}$ and depth of $60 \\mu \\mathrm{m}$, was formed, indicating a pleasurable bonding between neighbor layers and adjacent tracks (Fig. 11(c)).\n\nDuring the SLM process, the operative temperature and the amount of liquid phase with its viscosity are closely related with the laser energy. The powerful laser energy gives rise to a large amount of liquid formation with high temperature and low viscosity, which in turn promotes the liquid spreading out to fill the voids among particles and, thus, improve the metallurgical bonding properties between the neighbor layers. In view of the above experimental analyses, as well as the numerical simulation results, it can be found that the metallurgical bonding properties experienced a significant improvement as the laser power is increased from $75 \\mathrm{~W}$ to $125 \\mathrm{~W}$. At a lower laser power of $75 \\mathrm{~W}$, a considerably small amount of liquid phase of TiC/Inconel 718 with higher viscosity is formed due to the lower temperature of $1524^{\\circ} \\mathrm{C}$, resulting in a shallower penetration of $28 \\mu \\mathrm{m}$ (Figs. 7 (a) and 11(a)). It is responsible for the appearance of large-sized irregular pores among layers and resultant poor metallurgical bonding behavior between adjacent layers (Fig. 11(a)). On increasing the laser power to $100 \\mathrm{~W}$, the volume of liquid phase and penetration increase, resulting from the enhancement of molten pool temperature of $1901^{\\circ} \\mathrm{C}$ (Figs. 7(a) and 11(b)). The irregular pores with large size are alleviated due to more liquid spreading and filling among particles. Whereas some spherical pores with small size generate in the back-end of the molten pool since the gas atoms release from the lattice in heat affected zone possibly, as demonstrated by Weingarten (Figs. 1 and 11(b)) [34]. On further increasing the applied laser power to $125 \\mathrm{~W}$, a sufficient amount liquid phase with lower viscosity, as well as the appropriate width of $95 \\mu \\mathrm{m}$ and depth of $60 \\mu \\mathrm{m}$, is formed for a higher temperature of $2291{ }^{\\circ} \\mathrm{C}$ (Figs. 7(a) and 11(c)). The smoothly spread liquid and the appropriate molten pool dimensions guarantee the sound metallurgical bonding ability between adjacent layers and resultant high density of final SLM-fabricated parts (Fig. 11(c)). The dimensions of the molten pool measured by size calculation in Fig. 11 are in a relatively good agreement with the results predicted by simulation above (Figs. 4 and 11).\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3d8b51f9bfd3b941d680g-12(1)}\n\nFig. 11. OM images showing microstructures on cross-sectional view of SLM-processed parts at different laser powers $(v=100 \\mathrm{~mm} / \\mathrm{s}$ ). (a) $P=75 \\mathrm{~W}$; (b) $P=100 \\mathrm{~W}$; (c) $P=125 \\mathrm{~W}$.\n\nFig. 12 elucidates the typical surface morphologies of SLMproceed samples using different scan speeds.", "start_char_idx": 222522, "end_char_idx": 226246, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "66f3818b-61f5-4384-9602-6ba32141c426": {"__data__": {"id_": "66f3818b-61f5-4384-9602-6ba32141c426", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "23cf90a4-809d-4fc6-a21d-996a21f827eb", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a89fd36efd28fb4d060475dd49b92a7bc189e2c30c7efd8dfbc769817622cc26", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d313db08-5fb4-43ad-aece-818a798bb4e1", "node_type": "1", "metadata": {}, "hash": "fa002442fd44946847db220411be044688e4b829206bde7cd70f75363c3e9be3", "class_name": "RelatedNodeInfo"}}, "text": "11(c)). The dimensions of the molten pool measured by size calculation in Fig. 11 are in a relatively good agreement with the results predicted by simulation above (Figs. 4 and 11).\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3d8b51f9bfd3b941d680g-12(1)}\n\nFig. 11. OM images showing microstructures on cross-sectional view of SLM-processed parts at different laser powers $(v=100 \\mathrm{~mm} / \\mathrm{s}$ ). (a) $P=75 \\mathrm{~W}$; (b) $P=100 \\mathrm{~W}$; (c) $P=125 \\mathrm{~W}$.\n\nFig. 12 elucidates the typical surface morphologies of SLMproceed samples using different scan speeds. At a relatively high scan speed of $300 \\mathrm{~mm} / \\mathrm{s}$, an unfavorable surface quality characterized by large pores and microcracks was obtained on the solidified surface, which severely impeded densification response to a great degree (Fig. 12(a)). As the applied scan speed was\n\n(a)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3d8b51f9bfd3b941d680g-12}\n\nFig. 12. SEM images showing microstructures on top surface of SLM-processed parts at different scan speeds $(P=125 \\mathrm{~W}$ ). (a) $v=300 \\mathrm{~mm} / \\mathrm{s}$; (b) $v=200 \\mathrm{~mm} / \\mathrm{s}$; (c) $v=100 \\mathrm{~mm} / \\mathrm{s}$.\\\\\ndecreased to $200 \\mathrm{~mm} / \\mathrm{s}$, the large-sized pores disappeared and a great area of dense surface was obtained, while, balling effect on the top surface occurred (Fig. 12(b)). On further decreasing scan speed to $100 \\mathrm{~mm} / \\mathrm{s}$, a near-full dense and comparatively smooth surface free of obvious balling was obtained, indicating the formation of continuous and stable tracks and coherent bonding behavior between the adjacent tracks (Fig. 12(c)).\n\nDuring the track-by-track SLM process, the superior metallurgical bonding performance between the adjacent tracks plays a pronounced role to improve the densification behavior of SLMproduced parts. At a comparatively higher scan speed of $300 \\mathrm{~mm} /$ s, a small amount of liquid phase of TiC/Inconel 718 with a relatively high viscosity was yielded, resulting from the lower working temperature of $2080^{\\circ} \\mathrm{C}$ and extremely short liquid lifetime of $0.30 \\mathrm{~ms}$ (Fig. 7(b)). It is unbeneficial for the formed liquid to spread out smoothly for filling the voids among particles, which in turn gives rise to the large-sized pores. Meanwhile, the extremely high cooling rate of $1.26 \\times 10^{7}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ under high scan speed of $300 \\mathrm{~mm} / \\mathrm{s}$ results in the local residual stress accumulation and resultant increment of cracking susceptibility (Figs. 6(b) and 12(a)). As the applied scan speed is decreased to $200 \\mathrm{~mm} / \\mathrm{s}$, the increasing volume of liquid $\\mathrm{TiC} /$ Inconel 718 and decreasing of viscosity give rise to the improvement of the inter-track bonding and the density of final SLM-produced parts. Whereas, there is a comparatively higher heating rate of $8.84 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ at the scan speed of $200 \\mathrm{~mm} /$ $\\mathrm{s}$, which causes the thermo-capillary instability in the molten pool and droplets to splash from melt pool. It is responsible for the balling effect on the top surface of fabricated layer, as shown by the Figs. 1 and 12(b). On further decreasing the applied scan speed to $100 \\mathrm{~mm} / \\mathrm{s}$, the higher working temperature of $2291^{\\circ} \\mathrm{C}$ guarantees the formation of sufficient amount of TiC/Inconel 718 liquid phase with appropriate viscosity (Fig. 7(b)).", "start_char_idx": 225643, "end_char_idx": 229215, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d313db08-5fb4-43ad-aece-818a798bb4e1": {"__data__": {"id_": "d313db08-5fb4-43ad-aece-818a798bb4e1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "66f3818b-61f5-4384-9602-6ba32141c426", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "352a8c92f609c17c1f9191ad69769ebaebb59ead58ea8a681723ec7e2ce25b24", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b316ce8f-952a-4c45-8ae7-47a0a72f4458", "node_type": "1", "metadata": {}, "hash": "4248f19ada1328c9c280916720a736298ffb062f1d55f0f0a521198e03445b79", "class_name": "RelatedNodeInfo"}}, "text": "Whereas, there is a comparatively higher heating rate of $8.84 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ at the scan speed of $200 \\mathrm{~mm} /$ $\\mathrm{s}$, which causes the thermo-capillary instability in the molten pool and droplets to splash from melt pool. It is responsible for the balling effect on the top surface of fabricated layer, as shown by the Figs. 1 and 12(b). On further decreasing the applied scan speed to $100 \\mathrm{~mm} / \\mathrm{s}$, the higher working temperature of $2291^{\\circ} \\mathrm{C}$ guarantees the formation of sufficient amount of TiC/Inconel 718 liquid phase with appropriate viscosity (Fig. 7(b)). In addition, the heating rate $\\left(4.52 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}\\right)$ and cooling rate $\\left(4.38 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}\\right)$ of the molten pool alleviate as the scan speed is elevated (Fig. 6(b)). The sound bonding ability between adjacent tracks and fully dense surface are achieved in the SLM-fabricated samples accordingly (Fig. 12(c)).\n\n\\section*{5. Conclusions}\nThe three-dimensional finite element model, considering the cooling time for powder delivery, temperature-dependent properties, multiple heat transfer mechanisms and latent heat of phase change, was established to mainly focus on the effects of processing conditions on the thermal behavior and further melting/solidification mechanism, as well as forming mechanism of the molten pool configuration, and the following conclusions were drawn.\n\n(1) The maximum temperature, the width, the length, and the depth of the molten pool increases by $8.4 \\%, 14.5 \\%, 13.3 \\%$ and $10.6 \\%$, respectively, comparing the Point 2 with Point 1 . While they are $2.5 \\%, 13.5 \\%, 9.5 \\%$ and $7.8 \\%$, respectively, comparing the Point 3 with Point 2 . This is mainly due to the heat accumulation effect and the superior ability of conductions in powder bed than convection/radiation. The set of cooling time of 10$\\mathrm{ms}$ is obviously beneficial for alleviating the heat accumulation effect and, thus, controlling the liquid column size and resultant quality of final SLM parts.\n\n(2) The maximum temperature gradient in the molten pool slightly increases (from $1.30 \\times 10^{4}{ }^{\\circ} \\mathrm{C} / \\mathrm{mm}$ to $2.60 \\times 10^{4}{ }^{\\circ} \\mathrm{C} / \\mathrm{mm}$ along the path A-B; from $1.36 \\times 10^{4}{ }^{\\circ} \\mathrm{C} / \\mathrm{mm}$ to $2.62 \\times 10^{4}{ }^{\\circ} \\mathrm{C}$ / $\\mathrm{mm}$ in Z-direction) as the laser power is increased from $75 \\mathrm{~W}$ to $150 \\mathrm{~W}$. Whereas, it is affected negligibly by the variation of scan speed.\\\\\n(3) The maximum rate of temperature change obviously increases (heating: from $2.70 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ to $5.42 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$; cooling: from $2.63 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ to $\\left.5.25 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}\\right)$ when the laser power is elevated from $75 \\mathrm{~W}$ to $150 \\mathrm{~W}$.", "start_char_idx": 228568, "end_char_idx": 231631, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b316ce8f-952a-4c45-8ae7-47a0a72f4458": {"__data__": {"id_": "b316ce8f-952a-4c45-8ae7-47a0a72f4458", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d313db08-5fb4-43ad-aece-818a798bb4e1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "22b3ebd2da181a363b74cdee7bcfadd6af558199adcfc09fe3f1fa1176d66bb7", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "822df0f1-fcfd-48d5-8954-dd17ce6697fd", "node_type": "1", "metadata": {}, "hash": "f6191c7fcced6762a54f3758c51b99fc5c62e920fcee608456f5cc325407579e", "class_name": "RelatedNodeInfo"}}, "text": "Whereas, it is affected negligibly by the variation of scan speed.\\\\\n(3) The maximum rate of temperature change obviously increases (heating: from $2.70 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ to $5.42 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$; cooling: from $2.63 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ to $\\left.5.25 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}\\right)$ when the laser power is elevated from $75 \\mathrm{~W}$ to $150 \\mathrm{~W}$. On increasing the applied scan speed from $50 \\mathrm{~mm} / \\mathrm{s}$ to $300 \\mathrm{~mm} / \\mathrm{s}$, the maximum rate of temperature change similarly increases (heating: from $2.30 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ to $1.30 \\times 10^{7}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$; cooling: from $2.21 \\times 10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ to $\\left.1.26 \\times 10^{7}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}\\right)$.\n\n(4) A low power ( $75 \\mathrm{~W})$ or a high scan speed $(300 \\mathrm{~mm} / \\mathrm{s})$ is more energy efficient in Z-direction of the molten pool, leading to a deep-narrow cross sectional view of the pool. Whereas, a high laser power $(150 \\mathrm{~W})$ or a low scan speed $(50 \\mathrm{~mm} / \\mathrm{s})$ causes a low $R_{\\mathrm{D} / \\mathrm{W}}(0.40)$ and a wide-shallow cross sectional configuration of the molten pool, meaning it is more energy efficient in the Y-direction of the melt.\n\n(5) The microstructures on cross-sectional view and surface morphology of final parts were experimentally acquired, which validated indirectly the results by simulation. These indicated the sound metallurgical bonding between the neighbor layers and adjacent tracks at the optimized combination of $P=125 \\mathrm{~W}$ and $v=100 \\mathrm{~mm} / \\mathrm{s}$, due to the appropriate three dimensions of the molten pool (width: $109.3 \\mu \\mathrm{m}$; length: $120.7 \\mu \\mathrm{m}$; depth: $67.8 \\mu \\mathrm{m}$ ).\n\n(6) The physical phenomena considered in this study are general issues of temperature field simulation and thermal behavior investigation during SLM process. Therefore, the SLM physical model established in this paper is suitable for other material system.\n\n\\section*{Acknowledgments}\nThe authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Nos. 51575267 and 51322509), the Top-Notch Young Talents Program of China, the Outstanding Youth Foundation of Jiangsu Province of China (No. BK20130035), the Program for New Century Excellent Talents in University (No. NCET-13-0854), the Science and Technology Support Program (The Industrial Part), Jiangsu Provincial Department of Science and Technology of China (No. BE2014009-2), the 333 Project (No. BRA2015368), the Aeronautical Science Foundation of China (No. 2015ZE52051), the Shanghai Aerospace Science and Technology Innovation Fund (No. SAST2015053), the Fundamental Research Funds for the Central Universities (Nos. NE2013103, NP2015206 and NZ2016108), and the Priority Academic Program Development of Jiangsu Higher Education Institutions.\n\n\\section*{References}\n[1] H.N. Moosavy, M.R. Aboutalebi, S.H. Seyedein, M. Goodarzi, M. Khodabakhshi, C. Mapelli, S. Barella, Modern fiber laser beam welding of the newly-designed precipitation-strengthened nickel-base superalloys, Opt. Laser Technol. 57 (2014) 12-20.\n\n[2] B.S.", "start_char_idx": 231150, "end_char_idx": 234517, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "822df0f1-fcfd-48d5-8954-dd17ce6697fd": {"__data__": {"id_": "822df0f1-fcfd-48d5-8954-dd17ce6697fd", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b316ce8f-952a-4c45-8ae7-47a0a72f4458", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4b03fc2eb1086d2001aa0a78b31e9ff6e653cbd90ae60311179e373a0726675d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ff578666-e81b-4556-94e0-0a060fb3f7db", "node_type": "1", "metadata": {}, "hash": "8063317248b941b614b21c9e1c5cae9c53c4cc72522f4794e10724aff2925970", "class_name": "RelatedNodeInfo"}}, "text": "BRA2015368), the Aeronautical Science Foundation of China (No. 2015ZE52051), the Shanghai Aerospace Science and Technology Innovation Fund (No. SAST2015053), the Fundamental Research Funds for the Central Universities (Nos. NE2013103, NP2015206 and NZ2016108), and the Priority Academic Program Development of Jiangsu Higher Education Institutions.\n\n\\section*{References}\n[1] H.N. Moosavy, M.R. Aboutalebi, S.H. Seyedein, M. Goodarzi, M. Khodabakhshi, C. Mapelli, S. Barella, Modern fiber laser beam welding of the newly-designed precipitation-strengthened nickel-base superalloys, Opt. Laser Technol. 57 (2014) 12-20.\n\n[2] B.S. Yilbas, H. Ali, N. Al-Aqeeli, C. Karatas, Laser treatment of Inconel 718 alloy and surface characteristics, Opt. Laser Technol. 78 (2016) 153-158.\n\n[3] K. Venkatesan, R. Ramanujam, P. Kuppan, Parametric modeling and optimization of laser scanning parameters during laser assisted machining of Inconel 718, Opt. Laser Technol. 78 (2016) 10-18.\n\n[4] V. Ocel\u00edk, D. Matthews, J.T.M. De Hosson, Sliding wear resistance of metal matrix composite layers prepared by high power laser, Surf. Coat. Technol. 197 (2005) 303-315.\n\n[5] Y. Ma, J.H. Sun, X.H. Xie, Y.H. Hu, J.C. Zhao, P. 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Sih, J.W. Barlow, in: Proceedings of the 5th Annual SFF Symposium, The University of Texas, Austin, 1994.\n\n[26] J. D\u00edaz-\u00c1lvarez, J.L. Cantero, H. Migu\u00e9lez, X. Soldani, Numerical analysis of thermomechanical phenomena influencing tool wear in finishing turning of Inconel 718, Int. J. Mech. Sci. 82 (2014) 161-169.\n\n[27] A.V. Nikhil, V.B. Upendra, S.J. Suhas, A finite element model to predict the ablation depth in pulsed laser ablation, Thin Solid Films 519 (2010) 1421-1430.\n\n[28] M. Alimardani, E. Toyserkani, J.P. Huissoon, C.P. Paul, On the delamination and crack formation in a thin wall fabricated using laser solid freeform fabrication process: an experimental-numerical investigation, Opt. Lasers Eng. 47 (2009) 1160-1168.\n\n[29] D.Y. Zhang, W. Niu, X.Y. Cao, Z. Liu, Effect of standard heat treatment on the microstructure and mechanical properties of selective laser melting manufactured Inconel 718 superalloy, Mater. Sci. Eng. A 644 (2015) 32-40.\n\n[30] F.C. Liu, X. Lin, C.P. Huang, M.H. Song, G.L. Yang, J. Chen, W.D. Huang, The effect of laser scanning path on microstructures and mechanical properties of laser solid formed nickel-base superalloy Inconel 718, J. Alloy. Compd. 509 (2011) 4505-4509.\n\n[31] W. Hofmeister, M. Griffith, M. Ensz, J. Smugeresky, Solidification in Direct Metal Deposition by LENS Processing, J. Miner. Met. Mater. Soc. 53 (2001) 30-34.\n\n[32] J.D. Penot, D. Massy, F. Rieutord, F. Mazen, S. Reboh, F. Madeira, L. Capello, D. Landru, O. Kononchuk, Development of microcracks in hydrogen-implanted silicon substrates, J. Appl. Phys. 114 (2013) 123513.\n\n[33] P.Y. Lin, Z.H. Zhang, L.Q. Ren, The mechanical properties and microstructures of AZ91D magnesium alloy processed by selective laser cladding with $\\mathrm{Al}$ powder, Opt. Laser Technol. 60 (2014) 61-68.\n\n[34] C. Weingarten, D. Buchbinder, N. Pirch, W. Meiners, K. Wissenbach, R. Poprawe, Formation and reduction of hydrogen porosity during selective laser melting of AlSi10Mg, J. Mater. Process Technol. 221 (2015) 112-120.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3d8b51f9bfd3b941d680g-14(1)}\n\\end{center}\n\n\\#1 Qimin Shi Nanjing University of Aeronautics and Astronautics, Nanjing, China. Qimin Shi is currently doing his master's degree in College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics (NUAA), PR China. He received the bachelor degree in Materials Processing Engineering from NUAA in Jun. 2015. His principal research interest is laser additive manufacturing including selective laser melting (SLM), and laser metal deposition (LMD) especially majoring in the experiments and simulation of nickel-based composites processed by SLM.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3d8b51f9bfd3b941d680g-14(3)}\n\\end{center}\n\n\\#2 Dongong Gu (Corresponding author) Nanjing University of Aeronautics and Astronautics, Nanjing China.", "start_char_idx": 238652, "end_char_idx": 241609, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ef45efde-fd42-4386-af67-93170fe0fa06": {"__data__": {"id_": "ef45efde-fd42-4386-af67-93170fe0fa06", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0b445574-bce5-4193-87d1-19f918633260", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4af6e5997cc6fc56ca829fffae0e19cec2dab862d59596d2eb03e8012f573904", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "49df268a-e955-4215-a2e3-07d7616d1ff1", "node_type": "1", "metadata": {}, "hash": "4451472971f83b07502e166a6e3fdcc8faddabf1da1593b741c98a886cb144b0", "class_name": "RelatedNodeInfo"}}, "text": "Qimin Shi is currently doing his master's degree in College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics (NUAA), PR China. He received the bachelor degree in Materials Processing Engineering from NUAA in Jun. 2015. His principal research interest is laser additive manufacturing including selective laser melting (SLM), and laser metal deposition (LMD) especially majoring in the experiments and simulation of nickel-based composites processed by SLM.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3d8b51f9bfd3b941d680g-14(3)}\n\\end{center}\n\n\\#2 Dongong Gu (Corresponding author) Nanjing University of Aeronautics and Astronautics, Nanjing China. Professor Dongdong Gu is currently a Full Professor in College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics (NUAA), PR China. He received the Ph. D. in Materials Processing Engineering from NUAA in Jun. 2007. From Sep. 2009 to Aug. 2011, he worked in Fraunhofer Institute for Laser Technology ILT as the Alexander von Humboldt Research Fellow. His principal research interest is laser-based additive manufacturing including selective laser melting (SLM), direct metal laser sintering (DMLS), and laser metal deposition (LMD). Prof Gu has authored/co-authored 3 books and more than 100 papers in a number of internationally recognized peer-reviewed journals.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3d8b51f9bfd3b941d680g-14(4)}\n\\end{center}\n\n\\#3 Mujian Xia Nanjing University of Aeronautics and Astronautics, Nanjing, China. Mujian Xia is currently a $\\mathrm{Ph}$. D candidate in College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics (NUAA), PR China. He received the Master Degree in Materials Processing Engineering from Jiangsu University in Jun. 2012. Starting from Sep. 2015 he studied in College of Materials Science and Technology, NUAA. His principal research interest is laserbased additive manufacturing including selective laser melting (SLM) and direct metal laser sintering (DMLS), especially majoring in the experiments and simulation of nickel-based composite materials by SLM.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3d8b51f9bfd3b941d680g-14}\n\\end{center}\n\n\\#4 Sainan Cao Nanjing University of Aeronautics and Astronautics, Nanjing, China. Sainan Cao is currently pursuing for a master's degree in College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics (NUAA), PR China. She received the bachelor degree in Materials Processing Engineering from NUAA in Jun. 2014. Her principal research interest is laser additive manufacturing including selective laser melting (SLM), direct metal laser sintering (DMLS), and laser metal deposition (LMD) She has authored/co-authored 3 papers in internationally recognized peer-reviewed journals including J Laser Appl, Mater Sci Eng A, J Mater Res.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3d8b51f9bfd3b941d680g-14(2)}\n\\end{center}\n\n\\#5 Ting Rong Nanjing University of Aeronautics and Astronautics, Nanjing, China. Ting Rong is pursuing her master's degree in College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics (NUAA), PR China. She received the bachelor degree in Materials Processing Engineering from NUAA in Jun.2015. Her principal research interest is laser additive manufacturing including selective laser melting (SLM), and laser melting deposition (LMD), especially majoring in the experiments of nickel-based composites processed by SLM.\n\n\\begin{itemize}\n  \\item \n\\end{itemize}", "start_char_idx": 240901, "end_char_idx": 244594, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "49df268a-e955-4215-a2e3-07d7616d1ff1": {"__data__": {"id_": "49df268a-e955-4215-a2e3-07d7616d1ff1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ef45efde-fd42-4386-af67-93170fe0fa06", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "eb9a652fbeff75c78968c9e35872d42f387e450fe5997394b3cc584d34411069", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "4d57cb21-adca-4100-b71d-9ef83083e85a", "node_type": "1", "metadata": {}, "hash": "c4f3855fcdd3a35db57a89e0791ce3d121e0805d876b837c2693ee2d3b5eaa01", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3d8b51f9bfd3b941d680g-14(2)}\n\\end{center}\n\n\\#5 Ting Rong Nanjing University of Aeronautics and Astronautics, Nanjing, China. Ting Rong is pursuing her master's degree in College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics (NUAA), PR China. She received the bachelor degree in Materials Processing Engineering from NUAA in Jun.2015. Her principal research interest is laser additive manufacturing including selective laser melting (SLM), and laser melting deposition (LMD), especially majoring in the experiments of nickel-based composites processed by SLM.\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{An investigation into the effect of process parameters on melt pool geometry, cell spacing, and grain refinement during laser powder bed fusion }\n\n\n\\author{Ali Keshavarzkermani ${ }^{a}$, Ehsan Marzbanrad ${ }^{a}$, Reza Esmaeilizadeh ${ }^{a}$, Yahya Mahmoodkhani ${ }^{\\text {a }}$,\\\\\nUsman Ali ${ }^{\\mathrm{a}}$, Pablo D. Enrique ${ }^{\\mathrm{a}}$, Norman Y. Zhou ${ }^{\\mathrm{a}}$, Ali Bonakdar ${ }^{\\mathrm{b}}$, Ehsan Toyserkani ${ }^{\\mathrm{a}, *}$\\\\\n${ }^{a}$ University of Waterloo, 200 University Ave W, Waterloo, Ontario N2L 3G1, Canada\\\\\nbiemens Canada Limited, 9545 C\u00f4te-de-Liesse, Montr\u00e9al, Qu\u00e9bec H9P 1A5, Canada}\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\n\n\n\\section*{H I G HLI G H T S}\n\\begin{itemize}\n  \\item Laser power to velocity ratio (LED) was investigated for various melt pool features.\n  \\item Laser power has a higher effect than scanning velocity on the melt pool dimensions.\n  \\item Same LED results in finer cell structure with lower power due to high cooling rate.\n  \\item Due to wider melt pool cooler band, more grains are observed at higher laser power.\n  \\item It is proposed that partially melted particles act as nuclei during solidification.", "start_char_idx": 243889, "end_char_idx": 246839, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "4d57cb21-adca-4100-b71d-9ef83083e85a": {"__data__": {"id_": "4d57cb21-adca-4100-b71d-9ef83083e85a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "49df268a-e955-4215-a2e3-07d7616d1ff1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "67ba5061c0926c3b5fc0e9869c5591f83b6cc47a88972c05e82846af56c663f4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "8609298b-e70b-4f44-ba82-f8e2f87d5fe3", "node_type": "1", "metadata": {}, "hash": "167ec4558ccf9c00202dc3643a9c61a3cf98a115bdb2c46a455aef32419a54ba", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{H I G HLI G H T S}\n\\begin{itemize}\n  \\item Laser power to velocity ratio (LED) was investigated for various melt pool features.\n  \\item Laser power has a higher effect than scanning velocity on the melt pool dimensions.\n  \\item Same LED results in finer cell structure with lower power due to high cooling rate.\n  \\item Due to wider melt pool cooler band, more grains are observed at higher laser power.\n  \\item It is proposed that partially melted particles act as nuclei during solidification.\n\\end{itemize}\n\n\\section*{A R T I C L E I N F O}\n\\section*{Keywords:}\nAdditive manufacturing\n\nLaser powder bed fusion\n\nSingle track\n\nLaser energy density (LED)\n\nMicrostructure\n\nHastelloy $\\mathrm{X}$\n\n\\begin{abstract}\nA B S T R A C T An applied energy density approach defined as the ratio of laser power and scanning velocity is often used as a guideline for selecting appropriate process parameters in laser powder bed fusion (LPBF). In this study, amongst the many variables related to input energy, we investigate the effectiveness of laser energy density (LED) on the melt pool geometry and microstructure of Hastelloy X single tracks produced by fixed LED values at different laser powers and scanning velocities. The results reveal that for a fixed LED, the higher laser power has a higher effect on the melt pool depth. In addition, compared to the scanning velocity, laser power has a higher influence on the melt pool geometry. Moreover, it is proposed that the finer cell structure observed in the melt pool of high laser power is due to the higher cooling rates. Finally, the higher number of new grains observed in melt pools created with higher laser power and fixed LED are likely due to the grain detachment caused by the increase in the partially melted particles.\n\\end{abstract}\n\n\\section*{1. Introduction}\nAdditive manufacturing (AM) of metallic parts has grown in popularity due to its ability to fabricate parts with complex designs [1]. Laser powder-bed fusion (LPBF) is one of several AM techniques that builds parts in a layer by layer fashion. This versatile powder bed process has been used to manufacture parts with adjustable parameters such as laser power, scanning velocity, and layer thickness that can be optimized to print defect-free parts. To achieve acceptable part quality with no porosity, it is necessary to have consolidated layers made of single lines. Thus, an in-depth understanding of the effect of process parameters on a single track melt pool and the subsequent fast solidification is required to produce condensed layers leading to high-quality parts with low porosity and high strength.\n\\footnotetext{*Corresponding author.\n\nE-mail address: \\href{mailto:ehsan.toyserkani@uwaterloo.ca}{ehsan.toyserkani@uwaterloo.ca} (E. Toyserkani).\n}\n\nAmong all LPBF process parameters, energy input density has been considered as one of the most significant variables [2,3]. The energy input can be written as a function of laser power, scanning velocity, layer thickness, hatching distance, and other variables [1,4,5]. However, based on the previous studies [6-8], laser power and scanning velocity are considered as the most effective parameters. Some aspects of the single track formation (such as melt pool and bead geometry) under different sets of process parameters (laser power, scanning velocity, layer thickness, and hatching distance) have been studied for a few materials [2,3,9-11]. The laser energy density (LED) is one of the proposed energy input density functions and is defined as the ratio of laser power to scanning velocity $\\frac{P}{V}\\left(\\frac{J}{m m}\\right)[12]$. LED has been used to find the process window for deposition of different materials in the LPBF\\\\\nprocess $[2,6]$. In addition, LED has also been utilized to avoid balling, irregular and discontinuous track shapes in LPBF [9,12]. It has also been observed that incomplete melting can be the result of a low LED deposition, while a high LED deposition may introduce keyhole pores, which are detrimental for additively manufactured parts [10].\n\nInteraction of powder particles with laser irradiation during LPBF results in melting and solidification of molten metal. Similar to melting process, understanding the solidification of melted particles and microstructure formation in the melt pool is essential to reach the desired mechanical properties. Since the process parameters directly affect the geometry of the melt pool, changes in microstructure are expected to occur with different process parameters.", "start_char_idx": 246334, "end_char_idx": 250870, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "8609298b-e70b-4f44-ba82-f8e2f87d5fe3": {"__data__": {"id_": "8609298b-e70b-4f44-ba82-f8e2f87d5fe3", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "4d57cb21-adca-4100-b71d-9ef83083e85a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c29696d033e3055dd18e2f6ec7c3424ea754cd61fc06c2377793fba7c7a5e485", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "120ad710-d93e-4c10-ab2f-e9482c0714f0", "node_type": "1", "metadata": {}, "hash": "94af7e45e7ac64bdd368ff2789a04dbdc1ef92d8f7ebab504a89245d637f380a", "class_name": "RelatedNodeInfo"}}, "text": "LED has been used to find the process window for deposition of different materials in the LPBF\\\\\nprocess $[2,6]$. In addition, LED has also been utilized to avoid balling, irregular and discontinuous track shapes in LPBF [9,12]. It has also been observed that incomplete melting can be the result of a low LED deposition, while a high LED deposition may introduce keyhole pores, which are detrimental for additively manufactured parts [10].\n\nInteraction of powder particles with laser irradiation during LPBF results in melting and solidification of molten metal. Similar to melting process, understanding the solidification of melted particles and microstructure formation in the melt pool is essential to reach the desired mechanical properties. Since the process parameters directly affect the geometry of the melt pool, changes in microstructure are expected to occur with different process parameters. Several studies have been conducted to evaluate the influence of process parameters on microstructure of LPBF parts [2,13-16]. Single track deposition of Inconel 718 showed that the beads produced with low LED result in columnar grains growing upwards, while high LED values lead to grains converging at the center of the bead $[13,15]$. These long columnar grains observed in the microstructure of LPBF parts highlight the re-melting of previous layers resulting in the continuation of the crystallographic grain growth from grains in the former layers [2,14]. In addition, it was reported that formation of slender columnar grains may be due to the high cooling rate during LPBF with different manufacturing conditions [16].\n\nIn this study, the effect of laser power, scanning velocity, and LED values on the melt pool geometry and corresponding microstructure are investigated for Hastelloy X single tracks printed using a LPBF system. As discussed previously, LED values have been used as a guideline for printing effective LPBF parts. However, it has not been evaluated if the LED criterion is valid for different materials produced with different LED values. In addition, it is important to study the differences, if any, between the observed melt pool geometry and solidified microstructure at fixed LED values to evaluate the use of LED as a guideline for printing LPBF parts. To conduct this research, a series of single track depositions of Hastelloy X were performed to study the effect of changes in the laser power and scanning velocity with fixed LED values on the geometry and microstructure of melt pool. Results reveal that for a fixed LED, laser power has a higher influence on the melt pool dimensions (width and depth) while an increase in laser power has a higher effect on the melt pool depth. A finer cell structure is observed in the melt pool of high laser power and is thought to be due to the higher cooling rates observed at higher laser power. Finally, it is proposed that the grain detachment caused by the increase in number of partially melted particles (PMP) is the mechanism for the higher number of new grains observed in melt pools created with higher laser power.\n\n\\section*{2. Materials and methods}\nHastelloy X gas-atomized powder supplied by EOS GmbH, with the chemical composition listed in Table 1 was used to fabricate the LPBF parts with a $D_{10}, D_{50}$, and $D_{90}$ of $46.4 \\mu \\mathrm{m}, 30 \\mu \\mathrm{m}$ and $15.5 \\mu \\mathrm{m}$ respectively. As shown in Fig. 1, powder particles are mostly spherical in shape with attached satellite particles.\n\nThe experimental study was designed to manufacture12 rectangular substrates of Hastelloy $X$ with base dimensions of $25 \\mathrm{~mm} \\times 17.5 \\mathrm{~mm} \\times 5 \\mathrm{~mm}$. Six single laser scans were applied on top of the 3D printed substrates to form single tracks of length $25 \\mathrm{~mm}$. Single tracks with varying laser scanning velocity and power were printed on different substrates while single tracks with the same laser scanning velocity and power but different nominal layer thickness were\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_829fb3f692a2db4864deg-2}\n\\end{center}\n\nFig. 1. SEM image of powder metal showing the spherical morphology of particles with attached satellites.\n\nprinted on the same substrate.", "start_char_idx": 249964, "end_char_idx": 254230, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "120ad710-d93e-4c10-ab2f-e9482c0714f0": {"__data__": {"id_": "120ad710-d93e-4c10-ab2f-e9482c0714f0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8609298b-e70b-4f44-ba82-f8e2f87d5fe3", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "aab818d2cb03bc0eb8eab6f46797cacf8d42fe584d34865d19cd897752b9db70", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "e8fc22ca-fe89-4250-9854-462b6e2c5597", "node_type": "1", "metadata": {}, "hash": "bdaa344a80983d7b2a6411ecffac81d191439348cc599d10623bac09a88bfa26", "class_name": "RelatedNodeInfo"}}, "text": "The experimental study was designed to manufacture12 rectangular substrates of Hastelloy $X$ with base dimensions of $25 \\mathrm{~mm} \\times 17.5 \\mathrm{~mm} \\times 5 \\mathrm{~mm}$. Six single laser scans were applied on top of the 3D printed substrates to form single tracks of length $25 \\mathrm{~mm}$. Single tracks with varying laser scanning velocity and power were printed on different substrates while single tracks with the same laser scanning velocity and power but different nominal layer thickness were\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_829fb3f692a2db4864deg-2}\n\\end{center}\n\nFig. 1. SEM image of powder metal showing the spherical morphology of particles with attached satellites.\n\nprinted on the same substrate. The 20, 40 and $60 \\mu \\mathrm{m}$ single tracks were printed with a base nominal layer thickness of $20 \\mu \\mathrm{m}$ where the laser irradiation was skipped for 1 and 2 layers for the 40 and $60 \\mu \\mathrm{m}$, single tracks. Every single track, with its respective dimensions, was printed twice adjacent to each other (Fig. 2) and parallel to the direction of the recoater movement.\n\nEOS M290, equipped with a Ytterbium fiber laser, was used for fabricating the substrates and single tracks. As the laser spot size is considered to be a major contributing parameter to melt pool formation $[18,19]$, it is important to mention the effective laser spot size of $80 \\mu \\mathrm{m}$ was utilized in this experiment. All substrates were designed with the same process parameters as default EOS Hastelloy X parameters. Printed substrates were double scanned on the last layer to get a smooth surface. After reviewing the process parameters used in available literatures for Hastelloy X [20-23], a specific range of laser power and scanning velocity were selected in this study. Three values of LED were chosen for single tracks at different laser powers and scanning velocities, as listed in Table 2. Design of experiments for single line tracks consisted of varying laser powers (from $150 \\mathrm{~W}$ to $300 \\mathrm{~W}$ ) and scanning speeds (from $600 \\mathrm{~mm} / \\mathrm{s}$ to $2000 \\mathrm{~mm} / \\mathrm{s}$ ). The laser power and velocity were selected based on different LED values as shown in the 1st column of Table 2. The completed specimens were cross-sectioned (4 repetitions at $2.5 \\mathrm{~mm}$ offsets from the ends of substrate) using a Struers Accutom-50 precision cutter for a total of 4 cross-sections per single track condition.\n\nThe samples were manually polished using progressively finer SiC grinding papers from 320 to 4000 grit sizes. Finally, the samples were polished with $1,0.1$ and $0.05 \\mu \\mathrm{m}$ alumina slurry and rinsed with ethanol to remove residual alumina from the surface of the samples. Polished samples were kept in Glyceregia [24] (HCl 50ml - - HNO3 10ml - Glycerol 10ml) solution for about one minute for etching. The melt pool observation of cross-sectioned parts was performed using a Keyence VK-X250 confocal laser microscope. A Zeiss ULTRA SEM equipped with an EDS detector was used to study the microstructure and chemical composition of deposited single tracks. Electron back scattering diffraction (EBSD) analysis was performed using a JEOL7000F SEM equipped with an Oxford EBSD detector to investigate the grain structure of the fabricated single tracks with different process parameters. Data collection during the EBSD analysis was performed using AZtecHKL and post processing for data analysis was performed with HKL Channel 5.\n\nTable 1\n\nNominal composition (in wt.\\%) of Hastelloy X gas-atomized powder used for selective laser melting process [17].", "start_char_idx": 253473, "end_char_idx": 257151, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "e8fc22ca-fe89-4250-9854-462b6e2c5597": {"__data__": {"id_": "e8fc22ca-fe89-4250-9854-462b6e2c5597", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "120ad710-d93e-4c10-ab2f-e9482c0714f0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "847df97fc6a4538e81da8226351d160ac6dc8459adfc93bd059d4c13f35d885c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "00478d7d-c9a2-4c0b-8335-ac7d5f750d29", "node_type": "1", "metadata": {}, "hash": "e8b368c932bb8a3ef4a98b65d3f0059a1b307b29b2e2829eb5f0dd44870580e0", "class_name": "RelatedNodeInfo"}}, "text": "The melt pool observation of cross-sectioned parts was performed using a Keyence VK-X250 confocal laser microscope. A Zeiss ULTRA SEM equipped with an EDS detector was used to study the microstructure and chemical composition of deposited single tracks. Electron back scattering diffraction (EBSD) analysis was performed using a JEOL7000F SEM equipped with an Oxford EBSD detector to investigate the grain structure of the fabricated single tracks with different process parameters. Data collection during the EBSD analysis was performed using AZtecHKL and post processing for data analysis was performed with HKL Channel 5.\n\nTable 1\n\nNominal composition (in wt.\\%) of Hastelloy X gas-atomized powder used for selective laser melting process [17].\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n$\\mathrm{Ti}$ & $\\mathrm{Al}$ & $\\mathrm{Cu}$ & Mn & $\\mathrm{Si}$ & $\\mathrm{C}$ & Co & $\\mathrm{W}$ & Mo & $\\mathrm{Fe}$ & $\\mathrm{Cr}$ & $\\mathrm{Ni}$ \\\\\n\\hline\n$<0.15$ & $<0.5$ & $<0.5$ & $<1$ & $<1$ & $<0.1$ & $1.5 \\pm 1$ & $0.6 \\pm 0.4$ & $9 \\pm 1$ & $18.5 \\pm 1.5$ & $21.75 \\pm 1.25$ & Balance \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_829fb3f692a2db4864deg-3}\n\\end{center}\n\nFig. 2. Printed substrate and location of laser path on top of the substrate to manufacture single tracks.\n\n\\section*{3. Results and discussion}\nAs mentioned previously, single tracks of Hastelloy $\\mathrm{X}$ on the LPBFmade substrate were produced with the laser power range from 150 to $300 \\mathrm{~W}$ with scanning velocities from 600 to $2000 \\mathrm{~mm} / \\mathrm{s}$ and layer thickness from 20 to $60 \\mu \\mathrm{m}$. Fig. 3(a) and 3(b) show the depth and width of the melt pool region as a function of laser power in which the red, green, and blue colors represent LED values of $0.25 \\mathrm{~J} / \\mathrm{mm}, 0.20 \\mathrm{~J} /$ $\\mathrm{mm}$, and $0.15 \\mathrm{~J} / \\mathrm{mm}$, respectively. Similarly, triangular, circular, and rectangular markers represent a layer thickness of $20 \\mu \\mathrm{m}, 40 \\mu \\mathrm{m}$ and $60 \\mu \\mathrm{m}$, respectively. Fig. 3(a) and 3(b) demonstrate that the width of the melt pool is increasing from $93 \\pm 9 \\mu \\mathrm{m}$ to $121 \\pm 8 \\mu \\mathrm{m}$ and depth of the melt pool is increasing from $41.8 \\pm 6 \\mu \\mathrm{m}$ to $94 \\pm 9 \\mu$ mwhile the LED increased from $0.15 \\mathrm{~J} / \\mathrm{mm}$ to $0.25 \\mathrm{~J} / \\mathrm{mm}$ at a fixed laser power of $300 \\mathrm{~W}$. A similar trend was also observed by Sadowski et al for LPBF of Inconel 718 [2]. However, here, a general upward trend for both width and depth of the melt pool is observed while increasing the laser power at a constant LED. For instance, at a constant LED of $0.25 \\mathrm{~J} / \\mathrm{mm}$, the melt pool depth and width change around $25 \\%$ and $4 \\%$, respectively with changing laser power from $150 \\mathrm{~W}$ to $300 \\mathrm{~W}$ and scanning speeds from $600 \\mathrm{~mm} / \\mathrm{s}$ to $1200 \\mathrm{~mm} / \\mathrm{s}$.", "start_char_idx": 256404, "end_char_idx": 259447, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "00478d7d-c9a2-4c0b-8335-ac7d5f750d29": {"__data__": {"id_": "00478d7d-c9a2-4c0b-8335-ac7d5f750d29", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e8fc22ca-fe89-4250-9854-462b6e2c5597", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8084161cc2d58c3d89f851e331cbbf2b2eac226ead0924591c0afeb9ef5d95e5", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "744dd7b7-d817-448c-8ee9-acf66bcfdbe2", "node_type": "1", "metadata": {}, "hash": "e7bd4a649710e71690ecb77c98ef0e484e31ec11be40185e0a6eea2b665d767e", "class_name": "RelatedNodeInfo"}}, "text": "A similar trend was also observed by Sadowski et al for LPBF of Inconel 718 [2]. However, here, a general upward trend for both width and depth of the melt pool is observed while increasing the laser power at a constant LED. For instance, at a constant LED of $0.25 \\mathrm{~J} / \\mathrm{mm}$, the melt pool depth and width change around $25 \\%$ and $4 \\%$, respectively with changing laser power from $150 \\mathrm{~W}$ to $300 \\mathrm{~W}$ and scanning speeds from $600 \\mathrm{~mm} / \\mathrm{s}$ to $1200 \\mathrm{~mm} / \\mathrm{s}$.\n\nThe higher LED results in a higher energy input into the system, therefore it is expected to produce a bigger melt pool dimensions which can be confirmed by the data presented in Fig. 3(a) and 3(b). It is also reported by Aversa et al [3] that a higher LED value for a single line dramatically increases the depth of the melt pool of AlSi10Mg alloy. A lower LED with a shallower melt pool results in a smaller contact area between the molten metal and the substrate. As a result, there is less wetting of the molten metal on the surface and the tracks become more irregular or undergo balling before solidification [25]. To avoid this, process parameters need to be carefully selected to create an appropriate melt pool depth.\n\nResults in Fig. 3 can also be used to analyze the effect of layer thickness on the melt pool geometry of printed single tracks. However, it is in contrast to what has been observed in the literature where increasing layer thickness results to have shallower melt pools and more balling observed for single track [25]. Results from the current study show no specific deviation for the geometry of the melt pool when the nominal layer thickness changed from $20 \\mu \\mathrm{m}$ to $60 \\mu \\mathrm{m}$.\n\nAs was observed in Fig. 3, melt pool dimensions do not show any significant change with the change in layer thickness. Insignificant changes in the melt pool dimensions of single tracks with respect to different layer thicknesses may be due to the fact that the effective powder layer thickness is much bigger than the nominal or build layer thickness as reported by Mahmoodkhani et al. [26]. The actual layer thickness in LPBF is not constant and increases from the beginning of the process to reach a steady state known as the effective layer thickness (ELT) [27,28]. In this study, since only the last deposited layer's nominal thickness was changed from 20 to $60 \\mu \\mathrm{m}$, the effective layer thickness from former layers appears to be dominant in terms of controlling the melt pool geometry.\n\nInsignificant changes in the melt pool size by changing the layer thickness could also be explained due to the surface roughness of the previous layer. It is well known that the rough surface of the last deposited layer makes height to be different at different locations on the top surface during LPBF manufacturing process [29]. This leads to a non-uniform powder layer added by the recoater for subsequent layers which may be greater than the nominal layer thickness thus negating the effect of changing layer thickness on melt pool dimensions. Fig. 4 demonstrates the height map of the top surface of the printed Hastelloy $\\mathrm{X}$ substrate with printed single tracks. Measurement along the singletrack deposition (white line in Fig. 4) shows up to $80 \\mu \\mathrm{m}$ variation in height of the substrate, which is much larger than the maximum nominal layer thickness $(60 \\mu \\mathrm{m})$ used in this study. This variation in height affect the local layer thickness of powder during the next deposition step and therefore does not show any effect of layer thickness on melt pool dimensions of printed single tracks.\n\nExperimental results from melt pool dimensions with varying laser power and LED show the effect of melt pool width and depth with fixed LED. However, it is important to investigate the effect of laser power and velocity individually. Fig. 5 illustrates the effect of changing the LED from $0.15 \\mathrm{~J} / \\mathrm{mm}$ to $0.25 \\mathrm{~J} / \\mathrm{mm}$ on the melt pool dimensions at a\n\nTable 2\n\nSet of 12 groups of single tracks showing existing laser powers (P) and scanning velocity (V) for deposited tracks.", "start_char_idx": 258913, "end_char_idx": 263129, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "744dd7b7-d817-448c-8ee9-acf66bcfdbe2": {"__data__": {"id_": "744dd7b7-d817-448c-8ee9-acf66bcfdbe2", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "00478d7d-c9a2-4c0b-8335-ac7d5f750d29", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ce6f0776b58e52bc9681d478f0eb4633d43c4f19b3146fca4f3805ab47a17480", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "71260e39-b91f-4727-b3ab-18f6f5790f22", "node_type": "1", "metadata": {}, "hash": "7a50f9ac16fb421976f6196b4ed017e4cdfaedbde84fe912ad3b943f54f7bf48", "class_name": "RelatedNodeInfo"}}, "text": "This variation in height affect the local layer thickness of powder during the next deposition step and therefore does not show any effect of layer thickness on melt pool dimensions of printed single tracks.\n\nExperimental results from melt pool dimensions with varying laser power and LED show the effect of melt pool width and depth with fixed LED. However, it is important to investigate the effect of laser power and velocity individually. Fig. 5 illustrates the effect of changing the LED from $0.15 \\mathrm{~J} / \\mathrm{mm}$ to $0.25 \\mathrm{~J} / \\mathrm{mm}$ on the melt pool dimensions at a\n\nTable 2\n\nSet of 12 groups of single tracks showing existing laser powers (P) and scanning velocity (V) for deposited tracks.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\nLED (J/mm) & $\\mathrm{P}=150 \\mathrm{~W}$ & $P=200 W$ & $\\mathrm{P}=250 \\mathrm{~W}$ & $\\mathrm{P}=300 \\mathrm{~W}$ \\\\\n\\hline\n$0.25 \\pm 0.0(\\mathrm{~J} / \\mathrm{mm})$ & $\\mathrm{V}=600 \\mathrm{~mm} / \\mathrm{s}$ & $\\mathrm{V}=800 \\mathrm{~mm} / \\mathrm{s}$ & $\\mathrm{V}=1000 \\mathrm{~mm} / \\mathrm{s}$ & $\\mathrm{V}=1200 \\mathrm{~mm} / \\mathrm{s}$ \\\\\n\\hline\n$0.20 \\pm 0.01(\\mathrm{~J} / \\mathrm{mm})$ & $\\mathrm{V}=700 \\mathrm{~mm} / \\mathrm{s}$ & $\\mathrm{V}=1000 \\mathrm{~mm} / \\mathrm{s}$ & $\\mathrm{V}=1200 \\mathrm{~mm} / \\mathrm{s}$ & $\\mathrm{V}=1500 \\mathrm{~mm} / \\mathrm{s}$ \\\\\n\\hline\n$0.15 \\pm 0.006(\\mathrm{~J} / \\mathrm{mm})$ & $\\mathrm{V}=1000 \\mathrm{~mm} / \\mathrm{s}$ & $\\mathrm{V}=1300 \\mathrm{~mm} / \\mathrm{s}$ & $\\mathrm{V}=1600 \\mathrm{~mm} / \\mathrm{s}$ & $\\mathrm{V}=2000 \\mathrm{~mm} / \\mathrm{s}$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline\n\\begin{tabular}{c}\nLayer \\\\\nthickness \\\\\n\\end{tabular} & $20 \\mu \\mathrm{m}$ & $40 \\mu \\mathrm{m}$ & $60 \\mu \\mathrm{m}$ \\\\\n\\hline\nLED $\\sim 0.25$ & $\\triangle$ & $\\bigcirc$ & $\\square$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline\n\\begin{tabular}{c}\nLayer \\\\\nthickness \\\\\n\\end{tabular} & $20 \\mu \\mathrm{m}$ & $40 \\mu \\mathrm{m}$ & $60 \\mu \\mathrm{m}$ \\\\\n\\hline\nLED $\\sim 0.20$ & $\\triangle$ & $\\bigcirc$ & $\\square$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline\n\\begin{tabular}{c}\nLayer \\\\\nthickness \\\\\n\\end{tabular} & $20 \\mu \\mathrm{m}$ & $40 \\mu \\mathrm{m}$ & $60 \\mu \\mathrm{m}$ \\\\\n\\hline\nLED 0.15 & $\\Delta$ & $\\bigcirc$ & $\\square$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_829fb3f692a2db4864deg-4}\n\\end{center}\n\nFig. 3.", "start_char_idx": 262404, "end_char_idx": 264964, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "71260e39-b91f-4727-b3ab-18f6f5790f22": {"__data__": {"id_": "71260e39-b91f-4727-b3ab-18f6f5790f22", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "744dd7b7-d817-448c-8ee9-acf66bcfdbe2", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "5626ad1472706f74835f52d56c6367732df03889bf74424c460a7a094f0d5436", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "64ea306b-573a-48ee-905d-e1ba645536ef", "node_type": "1", "metadata": {}, "hash": "b8500b20942c8faff0d9bb9baecdcc8682182d74e1f6e1d39b9d44360e39251b", "class_name": "RelatedNodeInfo"}}, "text": "3. (a) Depth and (b) width of melt pool as a function of laser power in three different LED values of $0.15,0.2$, and $0.25(\\mathrm{~J} / \\mathrm{mm})$.\n\nconstant power or velocity. Results in Fig. 5(a) and (b) show that whilst keeping the scan velocity constant, decreasing the LED from $0.25 \\mathrm{~J} / \\mathrm{mm}$ to $0.15 \\mathrm{~J} / \\mathrm{mm}$ results in about a $65 \\%$ and $30 \\%$ decrease in melt pool depth and width, respectively. While with fixed power and decreasing LED from $0.25 \\mathrm{~J} / \\mathrm{mm}$ to $0.15 \\mathrm{~J} / \\mathrm{mm}$ results in about $38 \\%$ and $13 \\%$ reduction in melt pool depth and width correspondingly. Therefore, increasing the scanning velocity has a weaker influence on the melting regime compared to a proportional increase in laser power.\n\nAs discussed previously, the impact of change in laser power is stronger than corresponding changes in scanning velocity on the melt pool geometry. It is also observed that the melt pool width is larger than the laser beam spot size $(80 \\mu \\mathrm{m})$ due to the heat dissipation from molten metal to solid material. Considering the Gaussian distribution of the laser heat source, the average laser radiation intensity at the center of the beam profile is considerably higher than the intensity at the edges $[28,30]$. In addition, due to the Gaussian distribution, the input energy at the edges is less sensitive to the laser power or scanning velocity changes than at the center. The higher intensity at the center of the laser beam leads to an increase in the surface temperature of the melting metal to the boiling temperature of the metal, which causes recoil pressure on the melt pool and leads to the surface depression in this area [31-33]. This depression, along with higher temperatures at the central zone of the melt pool, provides a driving force for the melt pool penetration while increasing the melt pool depth. This explains the greater sensitivity of the melt pool depth when compared to the width when input energy is changed either by the varying scanning velocity or laser power.\n\nIt is well known that microstructure can be affected by variation in process parameter [11,13,34]. Fig. 6(a) and (b) show SEM images with LEDs of $0.25 \\mathrm{~J} / \\mathrm{mm}$ and $0.15 \\mathrm{~J} / \\mathrm{mm}$ at laser powers of $300 \\mathrm{~W}$ and $150 \\mathrm{~W}$ respectively. Results from Fig. 6(a) and (b) show the cellular structure of the melt pool area at low magnification from cross-sectioned deposited single tracks. Similar cellular structure is observed from Co-base and Ni-base LPBF parts with FCC crystal structure [35-38].\n\nSEM images at higher magnification were also captured to analyze the cellular spacing at fixed LED and varying laser power and velocity. Fig. 6(c) and (d) demonstrate the cellular microstructure of single tracks printed with a constant LED of $0.25 \\mathrm{~J} / \\mathrm{mm}$ with a laser power of $150 \\mathrm{~W}$ and $300 \\mathrm{~W}$, respectively. Comparing the microstructures reveals that at a fixed LED, the cell size increased from $0.285 \\pm 0.05 \\mu \\mathrm{m}$ to $0.5 \\pm 0.1 \\mu \\mathrm{m}$ when the laser power increases from $150 \\mathrm{~W}$ to $300 \\mathrm{~W}$. As cell size is directly related to mechanical properties such as hardness $[39,40]$, it is important to individually investigate the variation of cell spacing with respect to the fixed LED criteria. Reduction in cell spacing results in higher hardness $[39,40]$ due to higher number of cell boundaries enriched by dislocations [36,37].\n\nCell spacing in the microstructure strongly depends on the cooling rate at the solid-liquid interface during solidification [34]. High temperature gradients (G) and high solidification rate (R) in the melt pool result in higher cooling rate. This higher cooling rate leads to a higher super-cooling and finer cellular structure [41].", "start_char_idx": 264962, "end_char_idx": 268868, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "64ea306b-573a-48ee-905d-e1ba645536ef": {"__data__": {"id_": "64ea306b-573a-48ee-905d-e1ba645536ef", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "71260e39-b91f-4727-b3ab-18f6f5790f22", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ab6ee435ccce81f6f71ca7e6237715806243477f6ba24f02f46f196c356f16cc", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "08056bec-8ab2-4886-9f71-7b11b458a0f7", "node_type": "1", "metadata": {}, "hash": "791cb9ac7965dfd7959a19444a014eeb1a6bd15fe81ec400e7f82d7c41dbb477", "class_name": "RelatedNodeInfo"}}, "text": "As cell size is directly related to mechanical properties such as hardness $[39,40]$, it is important to individually investigate the variation of cell spacing with respect to the fixed LED criteria. Reduction in cell spacing results in higher hardness $[39,40]$ due to higher number of cell boundaries enriched by dislocations [36,37].\n\nCell spacing in the microstructure strongly depends on the cooling rate at the solid-liquid interface during solidification [34]. High temperature gradients (G) and high solidification rate (R) in the melt pool result in higher cooling rate. This higher cooling rate leads to a higher super-cooling and finer cellular structure [41]. As absorbed heat in the melt pool dissipates from the boundary of the melt pool to the\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_829fb3f692a2db4864deg-4(1)}\n\\end{center}\n\nFig. 4. Line scanning of the substrate parallel to single track deposition from top view shows about $80 \\mu \\mathrm{m}$ difference in height of the last deposited layer which makes the variation of nominal layer thickness (from 20 to $60 \\mu \\mathrm{m}$ ) for the last layer deposition insignificant.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_829fb3f692a2db4864deg-5}\n\nFig. 5. (a) Depth and (b) width of melt pool as a function of LED with two different passes of changing Velocity and laser power.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_829fb3f692a2db4864deg-5(1)}\n\nFig. 6. SEM micrographs showing cell structure from the cross-section of deposited single tracks with (a) LED value and laser power of 0.25 (J/ $\\mathrm{mm}$ ) and 300 (W) (b) LED value and laser power of $0.15(\\mathrm{~J} / \\mathrm{mm})$ and $150(\\mathrm{~W})$. In higher magnification, SEM micrographs at melt pool boundaries show the microstructure created by an LED value of $0.25(\\mathrm{~J} / \\mathrm{mm})$ and laser power of (c) 150 (W) and (d) $300(\\mathrm{~W})$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_829fb3f692a2db4864deg-5(2)}\n\nsurrounding substrate, an approximation of the cooling rate can be established based on the ratio of the melt pool volume $\\left(V_{s}\\right)$ to boundary area $\\left(S_{b}\\right)$. A smaller $\\frac{V_{s}}{S_{b}}$ would result in a faster heat dissipation to the substrate and hence, a higher cooling rate during the solidification. On the other hand, a larger $\\frac{V_{s}}{S_{b}}$ would result in a lower cooling rate. To be able to compare the solidification condition of single tracks fabricated at equivalent LED values with different laser powers, Fig. 7 shows the $\\frac{V_{s}}{S_{b}}$ ratio (which is estimated from the ratio of melt pool area to the melt pool boundary measured from the cross-sections considering a unit deep in the plate of single track images) as a function of laser power at constant LED of $0.25 \\mathrm{~J} / \\mathrm{mm}$. As observed, the higher laser power causes a larger $\\frac{V_{s}}{S_{b}}$ ratio, which leads to lower cooling rates during solidification. Similarly, a lower $\\frac{V_{s}}{S_{b}}$ ratio is observed at lower laser power which corresponds to higher cooling rates thus resulting in finer cellular structure compared to the higher laser power fabrication with an identical LED value (Fig. 6(c) and (d)).\n\nIt has been established that the cooling rate changes with different process parameters at the same LED. In addition, as cooling rate is directly proportional to the temperature gradient and solidification rate ( $\\dot{T}=G \\times R$ ), a change in cooling rate, suggests a change in $G$ and $R$ at different process parameters for the same LED. Moreover, it is well known that $\\frac{G}{R}$ can be employed to identify the solidification mode and resulting cellular, dendritic or equiaxed structures [34].", "start_char_idx": 268197, "end_char_idx": 271992, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "08056bec-8ab2-4886-9f71-7b11b458a0f7": {"__data__": {"id_": "08056bec-8ab2-4886-9f71-7b11b458a0f7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "64ea306b-573a-48ee-905d-e1ba645536ef", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0488a8301e6a67fa69264c6307c3444d91a397da1aeb71a5ed056e5975dc59d8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6186eacf-2e96-4762-95f7-cc5d35c50f29", "node_type": "1", "metadata": {}, "hash": "d3504dbe41406e96f26bf1faeeca95128435fa7ad99c4afc73ece9cca16fef1e", "class_name": "RelatedNodeInfo"}}, "text": "Similarly, a lower $\\frac{V_{s}}{S_{b}}$ ratio is observed at lower laser power which corresponds to higher cooling rates thus resulting in finer cellular structure compared to the higher laser power fabrication with an identical LED value (Fig. 6(c) and (d)).\n\nIt has been established that the cooling rate changes with different process parameters at the same LED. In addition, as cooling rate is directly proportional to the temperature gradient and solidification rate ( $\\dot{T}=G \\times R$ ), a change in cooling rate, suggests a change in $G$ and $R$ at different process parameters for the same LED. Moreover, it is well known that $\\frac{G}{R}$ can be employed to identify the solidification mode and resulting cellular, dendritic or equiaxed structures [34]. Hence, to investigate the possibility of changing solidification modes by varying process parameters of LPBF, two extremes of the current process window are selected (the lowest LED value with the lowest laser power and the highest LED value with the highest laser power). It is observed\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_829fb3f692a2db4864deg-6}\n\\end{center}\n\nFig. 7. The ratio of melt pool volume to the surface boundary as a function of laser power. Results measured from cross-sections of single tracks deposited with LED value of $0.25(\\mathrm{~J} / \\mathrm{mm})$.\n\nthat a cellular structure is the dominant solidification mode of the LPBF process within the range of selected process parameters (as shown in Fig. 6(a) and (b)). It is worth mentioning that the cellular growth of crystals is not restricted to the melt pool boundary region and continues during solidification as shown in Fig. 6 for both extreme parameters, leading to a cellular structure for the entire melt pool. Therefore, it can be concluded that the change in cooling rate at different process parameters affects the temperature gradient and solidification rate on the printed single tracks. However, this change in cooling rate does not affect the final solidification mode as the $\\frac{G}{R}$ is always in the range of cellular structure.\n\nThe cellular structure of additively manufactured parts is also reported for Co-29Cr-6Mo alloy which has cellular structures throughout the melt pool where the cooling rate is estimated to be around $2.2 \\times 10^{6} \\mathrm{~K} / \\mathrm{s}$ [38]. However, this is in contrast to what is observed at lower cooling rates of around $3.8 \\times 10^{4} \\mathrm{~K} / \\mathrm{s}$ in AlSi12 alloy, which has a clear transition from a dendritic (at the boundary) to microcellular structure (in the middle of melt pool) in the deposited layer [42]. On the other hand, AlSi10 shows an almost completely cellular structure in the LPBF part with an estimated cooling rate of $2 \\times 10^{6} \\mathrm{~K} / \\mathrm{s}$ [43]. This reveals that the solidification mode is material dependent, thus each material needs to be studied individually to analyze the associated microstructure. For Hastelloy X, the cooling rate can be estimated from $\\lambda=97 \\dot{T}^{-0.36}$ where $\\lambda$ is primary cell spacing and $\\dot{T}$ is the cooling rate $[35,38]$. Based on the current experiment, by changing the laser power at LED of $0.25 \\mathrm{~J} / \\mathrm{mm}$, the measured primary cell spacing changes from $0.285 \\pm 0.05 \\mu \\mathrm{m}$ to $0.5 \\pm 0.1 \\mu \\mathrm{m}$ (Figs. 6(c) and 5(d)) which lead to a cooling rate from $1.5 \\times 10^{7} \\mathrm{~K} / \\mathrm{s}$ to $2.2 \\times 10^{6} \\mathrm{~K} / \\mathrm{s}$. This decrease in the cooling rate of around $85 \\%$ occurs when the ratio of $\\frac{V_{s}}{S_{b}}$ increases by $\\sim 20 \\%$ at LED of $0.25 \\mathrm{~J} / \\mathrm{mm}$ and laser power of $150 \\mathrm{~W}$ and $300 \\mathrm{~W}$.", "start_char_idx": 271224, "end_char_idx": 274982, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "6186eacf-2e96-4762-95f7-cc5d35c50f29": {"__data__": {"id_": "6186eacf-2e96-4762-95f7-cc5d35c50f29", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "08056bec-8ab2-4886-9f71-7b11b458a0f7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2ef1316247b6bccafb22da2560d1d9e9c1372608537af956365818eb25c730b6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7cae6112-798e-4b22-8c74-f1eb4df25fc0", "node_type": "1", "metadata": {}, "hash": "54c9b845f7eb1f89bd99a4b91664766b7a0566922f3e33883c457350b83c896a", "class_name": "RelatedNodeInfo"}}, "text": "6(c) and 5(d)) which lead to a cooling rate from $1.5 \\times 10^{7} \\mathrm{~K} / \\mathrm{s}$ to $2.2 \\times 10^{6} \\mathrm{~K} / \\mathrm{s}$. This decrease in the cooling rate of around $85 \\%$ occurs when the ratio of $\\frac{V_{s}}{S_{b}}$ increases by $\\sim 20 \\%$ at LED of $0.25 \\mathrm{~J} / \\mathrm{mm}$ and laser power of $150 \\mathrm{~W}$ and $300 \\mathrm{~W}$.\n\nResults from the cell structure analysis of single tracks at fixed LED shows the variation in cell spacing due to the difference in cooling rates. However, it is also important to study the effect, if any, on the grain morphology. This is important as grain morphology has been linked to material performance such as yield strength [40,44,45]. Fig. 8a-b shows inverse pole-figure maps of two cross-sectioned single tracks at a LED value of $0.25 \\mathrm{~J} / \\mathrm{mm}$ with laser power of $150 \\mathrm{~W}$ and $300 \\mathrm{~W}$. Melt pool boundaries have been detected from optical images of etched samples and superimposed on the EBSD maps. EBSD results in Fig. 8 show the melt pool and the bead area from the cross-sectioned single tracks. Melt pool IPF maps show the grain growth due to epitaxial growth of grains at the melt pool boundary for both cross-sections in the building direction. Similar results of epitaxial growth have also been observed by other research groups from microstructure of LPBF parts $[5,13,36]$. In addition, a few number of nucleated grains are also observed in the middle of the melt pool with misorientation of more than $15^{\\circ}$ with neighboring grains. A total of 5 new grains (highlighted in Fig. 8(a)) were identified with the lower laser power ( $150 \\mathrm{~W})$, whereas 11 new grains (highlighted in Fig. 8(b)) were observed with the higher laser power $(300 \\mathrm{~W})$ at the same LED value. The average number for new grains, which are observed from different cross-sections, was calculated to be about $6 \\pm 2$ and $11 \\pm 1$ for laser power of $150 \\mathrm{~W}$ and $300 \\mathrm{~W}$, respectively. This difference in the number of grains, would result in a finer grain structure that would affect the mechanical properties of the printed parts.\n\nAs grain nucleation is observed in the melt pools from EBSD results, it is important to identify the nucleation mechanisms for the presence of new grains. Four different nucleation mechanisms namely; dendrite fragmentation, surface, homogenous/heterogeneous nucleation, and grain detachment have been identified during rapid solidification of metallic alloys [34]. Due to the existence of cellular structure observed in the single tracks (Fig. 6), the possibility of dendrite defragmentation mechanism is very low. Also, since epitaxial grain growth is observed in the melt pool of single tracks, surface nucleation is not a viable option. If the solute partition coefficient of alloying elements is less than 1 , it is possible to have solute pile-up in front of the solid-liquid boundary during solidification, which results in the segregation of alloying elements [46]. Segregation in front of the solid-liquid interface can lead to the high constitutional undercooling, which should be followed by homogenous nucleation of equiaxed grains in the middle of the melt pool [47]. However, according to the EDS line scanning analysis for the single track deposition, it is shown in Fig. 9 that there is no significant segregation of main alloying elements along the melt pool depth. EDS line scanning of melt pools was repeated for two different cross-sections of single tracks with LED of $0.15 \\mathrm{~J} / \\mathrm{mm}$ and LED of $0.25 \\mathrm{~J} / \\mathrm{mm}$. Results from both extreme LED values shows lack of segregation in printed Hastelloy X samples. This lack of segregation may be attributed due to the rapid solidification of the melt pool region during the LPBF process [35]. EDS results (Fig.", "start_char_idx": 274612, "end_char_idx": 278498, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7cae6112-798e-4b22-8c74-f1eb4df25fc0": {"__data__": {"id_": "7cae6112-798e-4b22-8c74-f1eb4df25fc0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "6186eacf-2e96-4762-95f7-cc5d35c50f29", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "25ea3d3894b0dcd163ae92903485b22abf1623b1de9565885ef01882c7455155", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "8f7978f2-5ffd-4706-9837-0aa37d23e463", "node_type": "1", "metadata": {}, "hash": "05f82065fe169dc7f0a22d4c95885a1866d83b8e58c34937642a1cf322a43873", "class_name": "RelatedNodeInfo"}}, "text": "Segregation in front of the solid-liquid interface can lead to the high constitutional undercooling, which should be followed by homogenous nucleation of equiaxed grains in the middle of the melt pool [47]. However, according to the EDS line scanning analysis for the single track deposition, it is shown in Fig. 9 that there is no significant segregation of main alloying elements along the melt pool depth. EDS line scanning of melt pools was repeated for two different cross-sections of single tracks with LED of $0.15 \\mathrm{~J} / \\mathrm{mm}$ and LED of $0.25 \\mathrm{~J} / \\mathrm{mm}$. Results from both extreme LED values shows lack of segregation in printed Hastelloy X samples. This lack of segregation may be attributed due to the rapid solidification of the melt pool region during the LPBF process [35]. EDS results (Fig. 9) show a lack of segregation in the concentration of alloying elements which would not change the undercooling temperature of the melted metal at the center of the melt pool. As homogeneous nucleation rate is linked to segregation of alloying elements [48], it can be concluded that the observed changes in nucleation rate in Hastelloy $\\mathrm{X}$ is not due to this mechanism.\n\nBased on the discussion presented thus far, grain detachment might be the best explanation for nucleation of the grains in the melt pool during solidification. Due to the Bernoulli effect, metal evaporation during the LPBF process enables the flow of inert gas (argon) toward the middle of the melt pool [28]. With the help of high-speed imaging, it is shown that this inert gas flow from the surrounding is strong enough to start the flow of powder particles towards the melt pool [28]. Some of these particles become part of the melt pool while others attach to the periphery. The partially melted particles attach to the solidified metal and may act as nucleation sites for grain growth. On the other hand, molten metal from these PMPs could enter the melt pool to create a potential nuclei inside the melt pool causing grain detachment. SEM secondary mode image and EBSD IPF maps from a cross-sectioned single track is presented in Fig. 10. In addition to that, Fig. 10 shows three attached particles surrounding the bead region (shown by red areas of A, B, and C). These attached particles might have originated from adjacent powders or spatter particles produced during LPBF. As new grains formed around the periphery of the attached particles do not show epitaxial growth, it can be concluded that grain detachment is the dominant mechanism. Results from attached particle show a significant amount of new orientated grains in the solidified bead region. All the attached particles (A-C) show detached grain growth along with heat flow direction after reaching a substantial under cooling temperature. The bigger size of the attached particle B leads to have more newly orientated grains in the microstructure on the left side of the melt pool when compared to the particle C in Fig. 10.\n\nIPF maps shown above highlight the formation mechanism for new grains in the solidified single track. However, results in Fig. 8 show a\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_829fb3f692a2db4864deg-7(1)}\n\\end{center}\n\nFig. 8. EBSD inverse pole-figure map from deposited single tracks with LED value of $0.25(\\mathrm{~J} / \\mathrm{mm})$ and laser power of (a) 150 (W) and (b) 300 (W). Dashed lines correspond to melt pool boundaries which are detected from OM pictures of etched cross-sectioned samples (shown as inserts).\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_829fb3f692a2db4864deg-7}\n\\end{center}\n\nFig. 9. EDS line scanning (counts versus depth distance) along with red line shown in the picture showing no specific amount of segregation of the main alloying element during the solidification of single track Hastelloy X. Analysis coming from cross-section of melt pool area deposited by LED value of 0.25 (J/ $\\mathrm{mm}$ ) and laser power of $300(\\mathrm{~W}$ ). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)\n\ndifference in the number of new grains between solidified melt pools from different laser powers at same LED.", "start_char_idx": 277663, "end_char_idx": 281938, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "8f7978f2-5ffd-4706-9837-0aa37d23e463": {"__data__": {"id_": "8f7978f2-5ffd-4706-9837-0aa37d23e463", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7cae6112-798e-4b22-8c74-f1eb4df25fc0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "43c55cf4cd57bd6f9d1a601c97eb3084eeaad7c220b8ace0d8fa36110e7b2eac", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "98662227-f5b3-4609-a009-0ac0fc40249c", "node_type": "1", "metadata": {}, "hash": "57f6c6aec63d74edafff20195c95c05a328d9f35a888f1b5037ff3adaa74d985", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_829fb3f692a2db4864deg-7}\n\\end{center}\n\nFig. 9. EDS line scanning (counts versus depth distance) along with red line shown in the picture showing no specific amount of segregation of the main alloying element during the solidification of single track Hastelloy X. Analysis coming from cross-section of melt pool area deposited by LED value of 0.25 (J/ $\\mathrm{mm}$ ) and laser power of $300(\\mathrm{~W}$ ). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)\n\ndifference in the number of new grains between solidified melt pools from different laser powers at same LED. It is observed, that the melt pool width always exceeds the laser beam diameter and the melt pool width is proportional to the laser power (Fig. 5(b)). Therefore, a higher laser power creates a melt pool larger than the laser diameter. This area can be distributed into the hot and cold regions where the hot region corresponds to the area under direct laser irradiation while the cold region corresponds to the difference between the direct laser irradiation and the melt pool width (Fig. 11(a)). Any powder in the hot section would melt completely. However, powder in the cooler band may partially melt and remain in the melt pool as a PMP. However, this cooler band is directly proportional to the laser power. For example, a cooler band increase from $\\sim 37 \\mu \\mathrm{m}$ to $\\sim 45 \\mu \\mathrm{m}$ is observed when the laser power is increased from $150 \\mathrm{~W}$ to $300 \\mathrm{~W}$ at fix LED. As the cooler band increases with laser power, the amount of PMPs in the melt pool would also increase. As these particles have been shown to cause nucleation in the melt pool, a higher number of PMPs would result in more grains inside the melt pool as shown in Fig. 8. Moreover, while the laser irradiation is directly above the area of interest, Marangoni convection of surface molten metal flows from the center to the periphery of the melt pool [49]. This pushes PMPs to cooler bands until the laser beam passes. This results in an average of 5 more nucleated grains within the melt pool with higher laser power at constant LED (Fig. 8).\n\nThe increase in PMP observed at higher power can also be attributed to the denudation zone created during laser irradiation [31]. It has been reported that higher laser power results in a wider denuded powder zone around the single track [50]. In addition, laser power has a higher effect than the scanning velocity on the denudation zone [50]. Based on this, higher laser power would result in addition of more powder particles in the melt pool which would increase the probability of existence of PMPs.\n\n\\section*{4. Conclusion}\nIn this work, independent of the laser power, scanning velocity and layer thickness, changing the LED (defined as the ratio of beam power to scanning velocity $\\frac{P}{V}\\left(\\frac{\\mathrm{J}}{\\mathrm{mm}}\\right)$ value) resulted in significant effects on the geometry of melt pool in Hastelloy X. However, keeping the LED constant at different laser powers and process speeds did not necessarily result in the same melt pool geometry or microstructure. The following points express the most important conclusions of this study:\n\n\\begin{enumerate}\n  \\item The laser power has a higher effect on the melt pool dimensions than the scanning velocity. Decreasing the laser power with fixed scanning velocity (LED from $0.25 \\mathrm{~J} / \\mathrm{mm}$ to $0.15 \\mathrm{~J} / \\mathrm{mm}$ ) results in about a $65 \\%$ and $30 \\%$ decrease in melt pool depth and width respectively. Similarly, increasing the scanning speed at a fixed power (LED from $0.25 \\mathrm{~J} / \\mathrm{mm}$ to $0.15 \\mathrm{~J} / \\mathrm{mm}$ ) results in about $38 \\%$ and $13 \\%$ reduction in melt pool depth and width respectively.\n\n  \\item At fixed LEDs, variation in melt pool dimensions is unavoidable due to the stronger influence of the laser power on the melting regime.", "start_char_idx": 281225, "end_char_idx": 285274, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "98662227-f5b3-4609-a009-0ac0fc40249c": {"__data__": {"id_": "98662227-f5b3-4609-a009-0ac0fc40249c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8f7978f2-5ffd-4706-9837-0aa37d23e463", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b5287eaf7fbfbd88e7056f46e8d8e040b75b657312affa36b7d7f384b699d586", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "99636ce2-1fa0-4820-884c-e6fcf557cb6a", "node_type": "1", "metadata": {}, "hash": "a9100cc76f6e35cc42272d864b888bd1c5e00712b209606d1a92831240d9d119", "class_name": "RelatedNodeInfo"}}, "text": "Decreasing the laser power with fixed scanning velocity (LED from $0.25 \\mathrm{~J} / \\mathrm{mm}$ to $0.15 \\mathrm{~J} / \\mathrm{mm}$ ) results in about a $65 \\%$ and $30 \\%$ decrease in melt pool depth and width respectively. Similarly, increasing the scanning speed at a fixed power (LED from $0.25 \\mathrm{~J} / \\mathrm{mm}$ to $0.15 \\mathrm{~J} / \\mathrm{mm}$ ) results in about $38 \\%$ and $13 \\%$ reduction in melt pool depth and width respectively.\n\n  \\item At fixed LEDs, variation in melt pool dimensions is unavoidable due to the stronger influence of the laser power on the melting regime. For example, at LED of $0.25 \\mathrm{~J} / \\mathrm{mm}$, increasing the laser power from $150 \\mathrm{~W}$ to $300 \\mathrm{~W}$ results in increasing the melt pool depth by $\\sim 56 \\%$.\n\n  \\item It is proposed that the difference in average primary cell spacing (from $285 \\mathrm{~nm}$ to $500 \\mathrm{~nm}$ at LED of $0.25 \\mathrm{~J} / \\mathrm{mm}$ ) with an increase in laser power from $150 \\mathrm{~W}$ to $300 \\mathrm{~W}$ is linked with the cooling rate and can be explained by the change in the ratio of $\\frac{\\text { meltpoolvolume }}{\\text { surfaceboundary }}$.\n\n  \\item In general, the microstructure of the cross-section single track melt pools shows a cellular structure with epitaxial growth of grains at melt pool boundaries. However, at fixed LED of $0.25 \\mathrm{~J} / \\mathrm{mm}$ a $\\sim 90 \\%$ increase in new grains is observed in the solidified melt pool which results in a finer microstructure at laser power of $150 \\mathrm{~W}$ and $350 \\mathrm{~W}$ respectively.\n\n  \\item Based on experimental EBSD results, it is proposed that the increase in the number of new grains observed in solidified melt pools is due to grain detachment caused by the higher number of survived\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_829fb3f692a2db4864deg-8(3)}\n\n\\end{enumerate}\n\nIPF-Z colouring\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_829fb3f692a2db4864deg-8}\n\nFig. 10. SEM secondary mode of imaging including EBSD inverse pole-figure map from highlighted areas of the single track deposited with an LED value of 0.25 (J/ $\\mathrm{mm}$ ) and laser power of $300(\\mathrm{~W})$. PMPs attached to single track show a significant amount of nucleation with new grains.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_829fb3f692a2db4864deg-8(2)}\n\nDetached particles acting\\\\\nas nucleation at the middle of melt pool\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_829fb3f692a2db4864deg-8(1)}\n\\end{center}\n\nFig. 11. Schematic overview of single track deposition with melt pool flow from (a) top view of single track and (b) longitudinal cross-section. (c) EBSD inverse-pole figure map showing random orientation of small crystals from PMP in the middle of melt pool region.\n\npartially melted particles (PMPs). The increase in the survived PMP at fixed LED of $0.25 \\mathrm{~J} / \\mathrm{mm}$ from $150 \\mathrm{~W}$ to $300 \\mathrm{~W}$ is probably due to the increase in the cooler band width (from $\\sim 37 \\mu \\mathrm{m}$ to $\\sim 45 \\mu \\mathrm{m}$ ) of molten metal that acts as nucleation sites during solidification.\n\n\\section*{Acknowledgments}\nThis work was supported by funding from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Federal Economic Development Agency for Southern Ontario (FedDev Ontario) and Siemens Canada Limited. The authors would like to acknowledge the help from members of Canadian Center of Electron Microscopy (CCEM) at McMaster University for Electron Backscatter Diffraction experiments.", "start_char_idx": 284673, "end_char_idx": 288301, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "99636ce2-1fa0-4820-884c-e6fcf557cb6a": {"__data__": {"id_": "99636ce2-1fa0-4820-884c-e6fcf557cb6a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "98662227-f5b3-4609-a009-0ac0fc40249c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "670dbba05ee31986d3b7aa495a0991f7eec55cb966ad85577bd84998af5cfc85", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "881436d3-a085-44dd-aeba-6ef9f0b22bb1", "node_type": "1", "metadata": {}, "hash": "8456a0c3767336e2b9b1656156df96040b04303b150a519fd0b6092ed66bc2ef", "class_name": "RelatedNodeInfo"}}, "text": "partially melted particles (PMPs). The increase in the survived PMP at fixed LED of $0.25 \\mathrm{~J} / \\mathrm{mm}$ from $150 \\mathrm{~W}$ to $300 \\mathrm{~W}$ is probably due to the increase in the cooler band width (from $\\sim 37 \\mu \\mathrm{m}$ to $\\sim 45 \\mu \\mathrm{m}$ ) of molten metal that acts as nucleation sites during solidification.\n\n\\section*{Acknowledgments}\nThis work was supported by funding from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Federal Economic Development Agency for Southern Ontario (FedDev Ontario) and Siemens Canada Limited. The authors would like to acknowledge the help from members of Canadian Center of Electron Microscopy (CCEM) at McMaster University for Electron Backscatter Diffraction experiments. The authors would also like to acknowledge the support from Jerry Ratthapakdee and Karl Rautenberg for helping with design and printing of LPBF parts.\n\n\\section*{Appendix A. Supplementary material}\nSupplementary data to this article can be found online at https:// \\href{http://doi.org/10.1016/j.optlastec.2019.03.012}{doi.org/10.1016/j.optlastec.2019.03.012}.\n\n\\section*{References}\n[1] H. Fayazfar, M. Salarian, A. Rogalsky, D. Sarker, P. Russo, V. Paserin, E. Toyserkani, A critical review of powder-based additive manufacturing of ferrous alloys: process parameters, microstructure and mechanical properties, Mater. Des. 144 (2018) 98-128, \\href{https://doi.org/10.1016/j.matdes.2018.02.018}{https://doi.org/10.1016/j.matdes.2018.02.018}.\n\n[2] M. Sadowski, L. Ladani, W. Brindley, J. Romano, Optimizing quality of additively manufactured Inconel 718 using powder bed laser melting process, Addit. Manuf. 11 (2016) 60-70, \\href{https://doi.org/10.1016/j.addma.2016.03.006}{https://doi.org/10.1016/j.addma.2016.03.006}.\n\n[3] A. Aversa, M. Moshiri, E. Librera, M. Hadi, G. Marchese, D. Manfredi, M. Lorusso, F. Calignano, S. Biamino, M. Lombardi, M. 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Matthews, G. Guss, S.A. Khairallah, A.M. Rubenchik, P.J. Depond, W.E. King, Denudation of metal powder layers in laser powder-bed fusion processes, Addit. Manuf. Handb. Prod. Dev. Def. Ind. 114 (2017) 677-693, \\href{https://doi.org/10.1201/}{https://doi.org/10.1201/} 9781315119106.\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{Influence of laser processing parameters on porosity in Inconel 718 during additive manufacturing }\n\n\n\\author{Pankaj Kumar ${ }^{1} \\cdot$ Jano Farah $^{2} \\cdot$ Javed Akram ${ }^{3} \\cdot$ Chong Teng $^{3} \\cdot$ Jon Ginn $^{3} \\cdot$ Mano Misra $^{1}$}\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\\DeclareUnicodeCharacter{0131}{$\\imath$}\n\n\\begin{document}\n\\maketitle\nReceived: 15 January 2019 / Accepted: 27 March 2019 /Published online: 6 April 2019\n\n(C) Springer-Verlag London Ltd., part of Springer Nature 2019\n\n\\begin{abstract}\nThe melt pool characteristics in terms of size and shape and the porosity development in laser powder bed fusion-processed Inconel 718 were investigated to determine how laser power and scan speed influence the porosity in the microstructure. The melt pool characteristics developed with both single-track and multilayer bulk laser deposition were evaluated. It was found that the melt pool characteristic is critical for the porosity development. It is shown that the porosity fraction and pore shape change depending on the melt pool size and shape. This result is explained based on the local energy density of a laser during the process. High-density (>99\\%) Inconel 718 samples were achieved over a wide range of laser energy densities $\\left(\\mathrm{J} / \\mathrm{mm}^{2}\\right)$. A careful assessment shows that the laser power and scan speed affect differently in developing the pores in the samples. The porosity decreased rapidly with the increase in laser power while it varied linearly with the scan speed. A proper combination, however, led to fully dense samples.", "start_char_idx": 302304, "end_char_idx": 305317, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b16632cf-bcd5-4266-9b97-dc844acc2484": {"__data__": {"id_": "b16632cf-bcd5-4266-9b97-dc844acc2484", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e8b3e4bc-908d-4716-babc-a9e4a6be927b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b79663743c931f15d4442cd0838b3ada01c09e56e42fffae80230be2132c23b8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "842f7de0-ab83-4c46-a9c4-6a6880a565fa", "node_type": "1", "metadata": {}, "hash": "bf20860620907c9fb76b92d5a45622a804ed487ec811b7a33077d6c85ced296b", "class_name": "RelatedNodeInfo"}}, "text": "The melt pool characteristics developed with both single-track and multilayer bulk laser deposition were evaluated. It was found that the melt pool characteristic is critical for the porosity development. It is shown that the porosity fraction and pore shape change depending on the melt pool size and shape. This result is explained based on the local energy density of a laser during the process. High-density (>99\\%) Inconel 718 samples were achieved over a wide range of laser energy densities $\\left(\\mathrm{J} / \\mathrm{mm}^{2}\\right)$. A careful assessment shows that the laser power and scan speed affect differently in developing the pores in the samples. The porosity decreased rapidly with the increase in laser power while it varied linearly with the scan speed. A proper combination, however, led to fully dense samples. The study reveals an optimum condition in terms of laser power and scan speed that can be adopted to fabricate high-density Inconel 718 parts using laser powder bed fusion-based additive manufacturing process.\n\\end{abstract}\n\nKeywords Additive manufacturing $\\cdot$ Selective laser melting $\\cdot$ Inconel $718 \\cdot$ Porosity $\\cdot$ Melt pool characteristics $\\cdot$ Laser powder bed fusion\n\n\\section*{1 Introduction}\nAdditive manufacturing (AM) of superalloys, such as Inconel 718 (IN 718), by laser powder bed fusion (L-PBF) for aerospace applications, creates a larger range of design possibilities for more efficient and powerful engines. With the ability to build layer by layer, complex structures that would be difficult or otherwise impossible with standard subtractive manufacturing are possible with additive manufacturing. However, critical parts produced using AM must be carefully\n\\footnotetext{$\\boxtimes$ Pankaj Kumar\n\n\\href{mailto:pkumar@unr.edu}{pkumar@unr.edu}\n\n$\\boxtimes$ Javed Akram\n\n\\href{mailto:javed.akram@ansys.com}{javed.akram@ansys.com}\n\n1 Chemical and Materials Engineering, University of Nevada, Reno, NV 89557, USA\n\n2 Metallurgical Engineering, University of Utah, Salt Lake City, UT 84112, USA\n\n3 Ansys, 1794 Olympic Parkway, Site\\#110, Park City, UT 84098, USA\n}\n\nevaluated to ensure the optimum structural property requirements are met. L-PBF based on selective laser sintering (SLS) is one of the few industrially attractive AM techniques that can produce fully dense nickel-based alloys [1-3]. This technique utilizes a localized and focused laser beam to melt the alloy particles and subsequently solidify the melted metal pool layer by layer in an optimized pattern to achieve a high-density 3D structure. Essentially, the 3D components produced by L-PBF result from the creation of micron-sized melt pools due to high energy-localized laser irradiation and rapid solidification of these melt pools. The effect of melt pool characteristics on the build quality of various materials has been widely studied and reported in the literature [4-10]. Small melt pool size (and depth) tends to reduce the processing efficiency by increasing the processing time. In contrast, a large melt pool can increase the processing efficiency but may vaporize the substrate/ powder leading to the formation of pores and increase the overall porosity in the materials $[5,9]$. Therefore, the quality of the build, including final density and the surface roughness, is primarily dependent on the melt pool characteristics (shape and size) which are largely controlled by the energy density of the laser beam. The similar dependency of melt pool characteristic on the energy density is also shown in selective\\\\\nelectron beam melting (SEBM) based AM [11]. It has been well established that the characteristic of the melt pool is related to the laser energy density which is essentially a measure of energy input applied during the processing of the materials [12]. Therefore, a controlled and optimized energy density of the L-PBF system for a given material can be achieved by controlling the predefined controllable parameters. The laser power $(P)$, scan speed $(v)$, hatch distance (melt pool overlaps, $d)$, and the layer thickness $(t)$ are the most important parameters and related to the laser energy density as $[9,13]$ :\n\n$E=\\frac{P}{v \\times d \\times t}$\n\nIn general, the laser beam diameter is fixed with uniform energy distribution while the parameters associated with the laser as mentioned above can be altered simultaneously/ individually to achieve the desired energy density. The resultant energy density affects favorably the melt pool characteristic and powder fusion quality for optimum density and microstructure of the build.", "start_char_idx": 304484, "end_char_idx": 309084, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "842f7de0-ab83-4c46-a9c4-6a6880a565fa": {"__data__": {"id_": "842f7de0-ab83-4c46-a9c4-6a6880a565fa", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b16632cf-bcd5-4266-9b97-dc844acc2484", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "003b304778c1b7a11d67d6edadd5b1eb9c7cfb16c0a04fadf62dab8cc27c0353", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6ad83a28-bacc-4bc4-87d4-bac6e3d484f2", "node_type": "1", "metadata": {}, "hash": "6354bb4295515027314b28a8127b75c950ddae73011d1e265f39473c90ce0955", "class_name": "RelatedNodeInfo"}}, "text": "It has been well established that the characteristic of the melt pool is related to the laser energy density which is essentially a measure of energy input applied during the processing of the materials [12]. Therefore, a controlled and optimized energy density of the L-PBF system for a given material can be achieved by controlling the predefined controllable parameters. The laser power $(P)$, scan speed $(v)$, hatch distance (melt pool overlaps, $d)$, and the layer thickness $(t)$ are the most important parameters and related to the laser energy density as $[9,13]$ :\n\n$E=\\frac{P}{v \\times d \\times t}$\n\nIn general, the laser beam diameter is fixed with uniform energy distribution while the parameters associated with the laser as mentioned above can be altered simultaneously/ individually to achieve the desired energy density. The resultant energy density affects favorably the melt pool characteristic and powder fusion quality for optimum density and microstructure of the build.\n\nSeveral studies of various materials including metal matrix composite have been pursued to understand the influence of processing parameters on the build quality, with the aim of developing the predictive model/strategy to manufacture defect-free components repeatedly by L-PBF [7, 9, 14-22]. An early study by Gu et al. [13] on stainless steel demonstrated that parameters such as laser power and scan speed affect differently on the porosity and microstructure evolution in LPBF processing. Yang et al. [23] experimentally showed that build quality is primarily controlled by the scan speed followed by the laser power and layer thickness. In a statistical study, the relative importance of each contributing process parameter was studied, demonstrating that the scan speed is the most influential parameter [24]. A low scan speed ensures the melting of particles and a dense structure; however, the processing efficiency is greatly reduced. At very slow scan speeds, melt pool instability causes irregular melting along each track leading to high surface roughness, distortion, and high volumetric porosity due to balling effects $[4,5]$. At high scan speeds, the short-time interaction between the materials and the laser beam causes narrow melt pools, which lead to increased surface roughness [5]. Additionally, very high scan speeds can contribute to increased porosity as well as thermally induced cracking as a consequence of extremely high cooling rates [14]. Thus, finding an optimum scan rate is a trade-off between build efficiency and build quality. The decrease in the mechanical properties of the materials in the presence of defects due to the processing is well reported in a recent study [25].\n\nConsiderable research has focused on the L-PBF of nickelbased alloys for melt pool and microstructure characterization in order to achieve the optimized conditions to manufacture high-density components [26-30]. Criales et al. [2] have shown that the L-PBF process parameters and scan strategy significantly affect the porosity in Inconel 625. In their elaborate experimental investigation, they established that porosity of the build is directly linked to the melt pool characteristics which are controlled by the process parameters. In recent studies $[9,13,31,32]$, single-track melt pool experiments have been developed to understand the effect of process parameters on porosity and microstructure evolution. Inconel 718 alloy is an age-hardened version of Inconel 625 with excellent strength (twice the strength of Inconel 625) [33, 34]. Exceptionally high tensile strength, fracture toughness, and wear resistance at relatively high temperature make this alloy an attractive material for application in high heat, wear, and corrosive environments such as turbine, nuclear reactors, jet engines, and combustion chambers. At the same time, these properties make it extremely difficult to machine [35-37]. Therefore, L-PBF is an attractive method to manufacture high-density Inconel 718 components. Extensive investigations have been carried out regarding the laser-based processing of Inconel 718 [6, 38-41], reporting the microstructure evolution and related mechanical properties. However, the effect of varying laser processing parameters on the porosity and the microstructure in Inconel 718 is rare [15]. In a limited study, the effect of laser energy density was investigated by processing Inconel 718 artifacts with different scan rates and laser power combinations [6, 42]. According to the study, the densification of the alloy is related to the laser energy density, and the highest possible density is achieved with an optimized laser energy density. However, the main effects of process parameters such as laser power, scan speed, and scan strategy on the porosity and microstructure in this alloy are not well understood.", "start_char_idx": 308092, "end_char_idx": 312938, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "6ad83a28-bacc-4bc4-87d4-bac6e3d484f2": {"__data__": {"id_": "6ad83a28-bacc-4bc4-87d4-bac6e3d484f2", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "842f7de0-ab83-4c46-a9c4-6a6880a565fa", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "caaf94e9f13fe1172bb7f647ebf68ec7bccc3d019549381ba99feaefb1506efb", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fc9bcefd-0d80-4a3e-8474-1efb14f5feb3", "node_type": "1", "metadata": {}, "hash": "2ae4c1230f43037219d8dd5cb31c4d4a4f2b2c6df30a0c7f987861a9dfcc9a4b", "class_name": "RelatedNodeInfo"}}, "text": "Therefore, L-PBF is an attractive method to manufacture high-density Inconel 718 components. Extensive investigations have been carried out regarding the laser-based processing of Inconel 718 [6, 38-41], reporting the microstructure evolution and related mechanical properties. However, the effect of varying laser processing parameters on the porosity and the microstructure in Inconel 718 is rare [15]. In a limited study, the effect of laser energy density was investigated by processing Inconel 718 artifacts with different scan rates and laser power combinations [6, 42]. According to the study, the densification of the alloy is related to the laser energy density, and the highest possible density is achieved with an optimized laser energy density. However, the main effects of process parameters such as laser power, scan speed, and scan strategy on the porosity and microstructure in this alloy are not well understood. The densification of any materials is critically linked with the melt pool characteristics, and affected by the contributing parameters of the energy density [43-47]. Additional studies are required to understand fully the processing variability in terms of melt pool characteristics to achieve the desired porosity and microstructure. Investigation of single-track deposits using various process parameters will provide a basic understanding of the effect on melt pool characteristics. This will help to identify and establish the optimized processing conditions for 3D components of Inconel 718.\n\nIn this investigation, the effect of L-PBF processing parameters, i.e., laser power and scan speed on the melt pool characteristics of Inconel 718, was studied. The melt pool geometry of L-PBF-processed single-track and bulk components under various processing conditions were evaluated with an aim to understand the effect of processing parameters on the density/porosity of the processed samples. The present study contributes to a gap of systematic research on the effect of machine/material processing parameters on the porosity evolution in Inconel\n\n\\begin{enumerate}\n  \\setcounter{enumi}{717}\n  \\item In addition, this research provides an optimized processing window for Inconel 718 that can be adopted at an industrial level.\n\\end{enumerate}\n\n\\section*{2 Experimental procedure}\n\\subsection*{2.1 L-PBF processing}\nA selective laser melting, $\\mathrm{SLM}^{\\mathrm{R}}$ 500, machine with a maximum power of $400 \\mathrm{~W}$ was used to fabricate single tracks (beads) and porosity cubes. Different sets of process parameters were used to examine the melt pool characteristics and porosity of the cubes.\n\nSingle-track laser deposition Single tracks with powder were deposited over a pad. The pads were fabricated using default settings of the machine. The dimension of pads is as follows: $45 \\mathrm{~mm}$ in width (perpendicular to scan direction) and $19 \\mathrm{~mm}$ in the scan direction of single tracks. Figure 1a illustrates the schematic of single tracks over pad. The purpose of putting single tracks over pads rather than wrought material was to capture the real heating phenomena occurring during the printing. The scanning direction of the single tracks was kept transverse to the scanning direction of the pad to provide maximum contrast upon analysis. Twelve (12) single tracks were deposited on a pad with different laser powers and scan speeds. A layer thickness of $40 \\mu \\mathrm{m}$ was maintained for single-track deposits with powder. The process parameter set for the singletrack experiment is listed in Table 1. To capture the statistical variation, three identical pads with the same process parameters (12 single beads on each pad) were produced.\n\nMultilayer-deposited cube samples To examine the porosity at different combinations of power and laser speed, simple cubes were printed using a bidirectional scan pattern with a $90^{\\circ}$ rotation at each layer as shown in Fig. 1b. Default support structure was built at the bottom of each cube for easy removal from base plate. The cubes were $10 \\times 10 \\times$ $5 \\mathrm{~mm}$ in dimension. Table 2 lists the set of process parameters used to fabricate the porosity cubes. Two replicates were produced for each process parameter set to capture the statistical variance.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5feb4058e560929d98a4g-03(1)}\n\\end{center}\n\nFig.", "start_char_idx": 312009, "end_char_idx": 316412, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fc9bcefd-0d80-4a3e-8474-1efb14f5feb3": {"__data__": {"id_": "fc9bcefd-0d80-4a3e-8474-1efb14f5feb3", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "6ad83a28-bacc-4bc4-87d4-bac6e3d484f2", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "551c966107ef7435bac44731af3900fcf02d17b7d04e86c08726c5e4cd48e624", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c814342e-39c0-4456-8874-4cc77b1d05f6", "node_type": "1", "metadata": {}, "hash": "e14c8004792b736a0fa942e67d9e40fc440c1341c6ba4442cae621327568b04d", "class_name": "RelatedNodeInfo"}}, "text": "Multilayer-deposited cube samples To examine the porosity at different combinations of power and laser speed, simple cubes were printed using a bidirectional scan pattern with a $90^{\\circ}$ rotation at each layer as shown in Fig. 1b. Default support structure was built at the bottom of each cube for easy removal from base plate. The cubes were $10 \\times 10 \\times$ $5 \\mathrm{~mm}$ in dimension. Table 2 lists the set of process parameters used to fabricate the porosity cubes. Two replicates were produced for each process parameter set to capture the statistical variance.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5feb4058e560929d98a4g-03(1)}\n\\end{center}\n\nFig. 1 Schematic of single-track laser deposition (a) and multilayerdeposited porosity cubes (b) with a scan strategy for analyzing melt\n\n\\subsection*{2.2 Characterization}\nThe melt pool dimensions and micrographs were examined using an optical microscope. The samples were cut cross-sectionally. The cut samples were mounted and polished following a standard metallurgical polishing method. The polished samples were etched lightly with Keller's reagent to reveal the melt pool in the microstructure. The porosity and microstructure of the cube samples were determined on the vertical plane of each cube. The porosity fraction, shape, and melt pool dimensions were determined with the aid of imageJ image analysis software.\n\n\\section*{3 Results and discussion}\n\\subsection*{3.1 Melt pool characteristics}\nMelt pool characteristics (source of the build quality) were studied by varying processing parameters. Melt pools obtained by the single-track laser deposition performed on the additively manufactured IN718 base pad were examined under an optical microscope. A characteristic melt pool which can easily be distinguished by the visible interface is shown in Fig. 2. The geometrical morphology and dimension of the melt pool in terms of width and depth can easily be identified. A symmetric melt pool was observed in all operating conditions while the width and depth of the melt pools changed with changes in laser power and scan speed. Figure 3 depicts the change in the shape of the melt pool when the energy density increases from 2.5 to $5 \\mathrm{~J} / \\mathrm{mm}^{2}$. It can be seen that the depth to width ratio increased with the energy level. The melt pool width is a critical parameter to consider in order to optimize the hatch distance. The hatch distance is important as it dictates the re-melting and solidification of previously solidified melt pool track during the subsequent laser passes. The process may lead to void formation, increase in surface roughness, and the complicated evolution of microstructure. Similar to width, the depth of melt pool influences the re-melting and solidification of already solidified layers in subsequent laser processing, which significantly impact the build quality. Therefore, it is essential to identify a range of optimized laser settings to achieve optimum melt pool geometry. In one study,\n\n(b)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_5feb4058e560929d98a4g-03}\n\npool characteristics and porosity.", "start_char_idx": 315720, "end_char_idx": 318889, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c814342e-39c0-4456-8874-4cc77b1d05f6": {"__data__": {"id_": "c814342e-39c0-4456-8874-4cc77b1d05f6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fc9bcefd-0d80-4a3e-8474-1efb14f5feb3", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e99538307ee6c45c4b7df541d53676cb8ce64c33e9b9521019db12813509a302", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "03a824af-796c-488e-8312-a2a41a0e485b", "node_type": "1", "metadata": {}, "hash": "8aecc50fd5ed22b2d69577cff7b232979eeaf5345c7572ee91fdabfa3371c8b1", "class_name": "RelatedNodeInfo"}}, "text": "It can be seen that the depth to width ratio increased with the energy level. The melt pool width is a critical parameter to consider in order to optimize the hatch distance. The hatch distance is important as it dictates the re-melting and solidification of previously solidified melt pool track during the subsequent laser passes. The process may lead to void formation, increase in surface roughness, and the complicated evolution of microstructure. Similar to width, the depth of melt pool influences the re-melting and solidification of already solidified layers in subsequent laser processing, which significantly impact the build quality. Therefore, it is essential to identify a range of optimized laser settings to achieve optimum melt pool geometry. In one study,\n\n(b)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_5feb4058e560929d98a4g-03}\n\npool characteristics and porosity. A scan strategy of $0-90$ is followed to fabricate the cube samples\n\nTable 1 Single-track laser deposition parameters\n\n\\begin{center}\n\\begin{tabular}{llll}\n\\hline\nPower $(\\mathrm{W})$ & \\begin{tabular}{l}\nSpeed \\\\\n$(\\mathrm{mm} / \\mathrm{s})$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nLayer thickness \\\\\n$(\\mathrm{mm})$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nEnergy density \\\\\n$\\left(\\mathrm{J} / \\mathrm{mm}^{2}\\right)$ \\\\\n\\end{tabular} \\\\\n\\hline\n75 & 800 & 0.04 & 2.3 \\\\\n75 & 1500 & 0.04 & 1.2 \\\\\n75 & 2200 & 0.04 & 0.8 \\\\\n150 & 800 & 0.04 & 4.6 \\\\\n150 & 1500 & 0.04 & 2.5 \\\\\n150 & 2200 & 0.04 & 1.7 \\\\\n225 & 800 & 0.04 & 7.0 \\\\\n225 & 1500 & 0.04 & 3.7 \\\\\n225 & 2200 & 0.04 & 2.5 \\\\\n300 & 800 & 0.04 & 9.3 \\\\\n300 & 1500 & 0.04 & 5.0 \\\\\n300 & 2200 & 0.04 & 3.4 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nit was demonstrated that melt pool geometry can change the melting characteristic from conduction to keyhole mode which eventually affects the build quality [23]. The melt pool width and depth obtained as a function of laser energy density by varying the scan rate and laser power are presented in Fig. 4. The melt pool width increases linearly with the increase in laser energy density $\\left(\\mathrm{J} / \\mathrm{mm}^{2}\\right)$ in the range of 2 to $10 \\mathrm{~J} / \\mathrm{mm}^{2}$. Similarly, the melt pool depth increases linearly with the energy density in the same energy density range (Fig. 4 inset). This indicates that the melt pool dimensions are directly related to the laser operating parameters. It is interesting to note that as the energy density increases, the scatter in the width and depth dimension of melt pool is also increased. A similar trend of increasing scattering in melt pool dimensions associated with increasing energy density can be observed in a recent study [48]. This demonstrates that at higher energy intensity levels, controlling the melt pool dimensions can be problematic. Large scattering in melt pool width and depth can cause uneven melting of the powder. For example, for a fixed laser beam diameter and hatch distance, some particles partially melt in the region where the hatch distance is larger than the melt pool dimension.", "start_char_idx": 317989, "end_char_idx": 321059, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "03a824af-796c-488e-8312-a2a41a0e485b": {"__data__": {"id_": "03a824af-796c-488e-8312-a2a41a0e485b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c814342e-39c0-4456-8874-4cc77b1d05f6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b5f1d33ffd55600d3d482865bd912c63ab132f07d34725a13fb40c00acedefe1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bd7679d1-6cf8-4112-b190-2a75c2d7ef53", "node_type": "1", "metadata": {}, "hash": "c7640bbcad63bcef6670ab9c891fd1f4d07002f394a9c33810fa312bac9f89ee", "class_name": "RelatedNodeInfo"}}, "text": "Similarly, the melt pool depth increases linearly with the energy density in the same energy density range (Fig. 4 inset). This indicates that the melt pool dimensions are directly related to the laser operating parameters. It is interesting to note that as the energy density increases, the scatter in the width and depth dimension of melt pool is also increased. A similar trend of increasing scattering in melt pool dimensions associated with increasing energy density can be observed in a recent study [48]. This demonstrates that at higher energy intensity levels, controlling the melt pool dimensions can be problematic. Large scattering in melt pool width and depth can cause uneven melting of the powder. For example, for a fixed laser beam diameter and hatch distance, some particles partially melt in the region where the hatch distance is larger than the melt pool dimension. In a region where the hatch distance\\\\\nTable 2 Cube deposition parameters\n\n\\begin{center}\n\\begin{tabular}{llll}\n\\hline\nPower $(\\mathrm{W})$ & \\begin{tabular}{l}\nSpeed \\\\\n$(\\mathrm{mm} / \\mathrm{s})$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nLayer thickness \\\\\n$(\\mathrm{mm})$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nEnergy density \\\\\n$\\left(\\mathrm{J} / \\mathrm{mm}^{2}\\right)$ \\\\\n\\end{tabular} \\\\\n\\hline\n75 & 800 & 0.04 & 2.3 \\\\\n75 & 1200 & 0.04 & 1.5 \\\\\n75 & 1600 & 0.04 & 1.1 \\\\\n75 & 2000 & 0.04 & 0.9 \\\\\n120 & 800 & 0.04 & 3.7 \\\\\n120 & 1200 & 0.04 & 2.5 \\\\\n120 & 1600 & 0.04 & 1.8 \\\\\n120 & 2000 & 0.04 & 1.5 \\\\\n165 & 800 & 0.04 & 5.1 \\\\\n165 & 1200 & 0.04 & 3.4 \\\\\n165 & 1600 & 0.04 & 2.5 \\\\\n165 & 2000 & 0.04 & 2.0 \\\\\n225 & 800 & 0.04 & 7.0 \\\\\n225 & 2000 & 0.04 & 2.8 \\\\\n285 & 800 & 0.04 & 8.9 \\\\\n285 & 2000 & 0.04 & 3.5 \\\\\n330 & 800 & 0.04 & 10.3 \\\\\n330 & 2000 & 0.04 & 4.1 \\\\\n375 & 800 & 0.04 & 11.7 \\\\\n375 & 2000 & 0.04 & 4.6 \\\\\n\\hline\n &  &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5feb4058e560929d98a4g-05}\n\\end{center}\n\nFig. 2 Melt pool geometry obtained by a single-track L-PBF deposition with a laser power of $300 \\mathrm{~W}$ at the scan speed of $1500 \\mathrm{~mm} / \\mathrm{s}$, equivalent of $\\sim 5 \\mathrm{~J} / \\mathrm{mm}^{2}$. The width and depth of the melt pool at this operating condition are $\\sim 142 \\mu \\mathrm{m}$ and $\\sim 115 \\mu \\mathrm{m}$ respectively\n\nis shorter than the melt pool dimension, the excessive energy may vaporize the particles. Both cases will result in the formation of voids which significantly impact the build quality. Based on this, it can be argued that the build quality can be compromised at higher energy densities $\\left(>10 \\mathrm{~J} / \\mathrm{mm}^{2}\\right.$ ) due to large scatter in melt pool dimension.\n\nThe representative microstructure development in a melt pool as a result of solidification can be seen in Fig. 2. The columnar grain formation is prevalent in the microstructure. The columnar grain developed along the building direction. Along with the course columnar grain parallel to the build height, the irregular columnar grain also developed. Typically, this microstructure developed when there is a large thermal gradient available.", "start_char_idx": 320173, "end_char_idx": 323331, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bd7679d1-6cf8-4112-b190-2a75c2d7ef53": {"__data__": {"id_": "bd7679d1-6cf8-4112-b190-2a75c2d7ef53", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "03a824af-796c-488e-8312-a2a41a0e485b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "016e1b2ed0c56e5c18e8a1d3a363db138f966a5906be70d4d90ea615bc7aec1f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1bff9b91-4a2a-4aec-a73c-89037a8c7f00", "node_type": "1", "metadata": {}, "hash": "be371985cb7ed5c690bec1277ea5c3e677862f393bfb68a288d183b8b6aa3c27", "class_name": "RelatedNodeInfo"}}, "text": "Both cases will result in the formation of voids which significantly impact the build quality. Based on this, it can be argued that the build quality can be compromised at higher energy densities $\\left(>10 \\mathrm{~J} / \\mathrm{mm}^{2}\\right.$ ) due to large scatter in melt pool dimension.\n\nThe representative microstructure development in a melt pool as a result of solidification can be seen in Fig. 2. The columnar grain formation is prevalent in the microstructure. The columnar grain developed along the building direction. Along with the course columnar grain parallel to the build height, the irregular columnar grain also developed. Typically, this microstructure developed when there is a large thermal gradient available. This characteristic microstructure developed in L-PBF process can be corroborated with the earlier study [15]. The columnar grain extends to the previous layer with a size approaching double the size of the melt pool height. This clearly indicates that during the laser scanning, the previous layer re-melted and solidified to form the columnar grain. Therefore, the thermal conditions in this approach encourage the formation of large elongated columnar grains that can extend to multiple layers.\n\nThe evaluation of melt pool characteristic in a single layer is extended to melt pools in multilayer cube sample. An optical image of the developed microstructure of the vertical section of the L-PBF-processed IN 718 cubes (scanned using 0-90 pattern and a laser energy density of $5.15 \\mathrm{~J} / \\mathrm{mm}^{2}$ [power $165 \\mathrm{~W}$, scan rate $800 \\mathrm{~mm} / \\mathrm{s}$, and layer thickness $0.04 \\mathrm{~mm}]$ ) is shown in Fig. 5. The melt pools as a result of multilayer laser scanning to fabricate a $1-\\mathrm{cm}$ cube can be clearly observed. Overlapped melt pools can be seen in the microstructure. This observation confirms that the excessive local energy can re-melt the\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5feb4058e560929d98a4g-05(1)}\n\\end{center}\n\nFig. 3 Representative melt pool geometries with change in energy density. Melt pool shape changes from short pyriform to long pyriform with increase in the energy density\n\npreviously solidified melt pool. The average width and the depth of the observed melt pool are $\\sim 112 \\pm 9 \\mu \\mathrm{m}$ and $\\sim$ $73 \\pm 10 \\mu \\mathrm{m}$, respectively. When compared, the melt pool dimensions are smaller than those obtained with singlelayer deposition with a similar energy density $\\left(5 \\mathrm{~J} / \\mathrm{mm}^{2}\\right)$. This difference in dimension can be attributed to error in measurement due to melt pool overlapping, assuming that the similar energy density has yielded a similar melt pool\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5feb4058e560929d98a4g-06}\n\\end{center}\n\nFig. 4 Melt pool width obtained by a single-track L-PBF deposition as a function of laser energy density. Inset diagram shows the melt pool depth obtained in the same experiments as a function of energy density. The laser energy density is varied by varying the laser power (75 to $300 \\mathrm{~W}$ ) and scan rate ( 800 to $2200 \\mathrm{~mm} / \\mathrm{s}$ )\n\nvolume. Also, a small fraction of randomly distributed fine porosity can also be observed.\n\nThe microstructure of an as-fabricated cube sample consists of large and interconnected directional columnar grains with random columnar grains. This suggests that the\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5feb4058e560929d98a4g-06(1)}\n\\end{center}\n\nFig. 5 Microstructure of the vertical section of the L-PBF fabricated with energy density $5.15 \\mathrm{~J} / \\mathrm{mm}^{2}$ (laser power $165 \\mathrm{~W}$, laser scan speed $800 \\mathrm{~mm} /$ $\\mathrm{s}$, and layer thickness $0.04 \\mathrm{~mm}$ ) cube. Melt pools and layer development in the sample can be clearly observed.", "start_char_idx": 322598, "end_char_idx": 326507, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1bff9b91-4a2a-4aec-a73c-89037a8c7f00": {"__data__": {"id_": "1bff9b91-4a2a-4aec-a73c-89037a8c7f00", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bd7679d1-6cf8-4112-b190-2a75c2d7ef53", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "090114048cbec24bd3208628372d4ff894d6334aa1ee366ac1454429d862d8d6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "81f5faa5-5f34-4136-a188-6b686661caf9", "node_type": "1", "metadata": {}, "hash": "f34f2fd7821ebdf4970387043667e3fb8c496fb69ad817f3601a826bad6a6927", "class_name": "RelatedNodeInfo"}}, "text": "Also, a small fraction of randomly distributed fine porosity can also be observed.\n\nThe microstructure of an as-fabricated cube sample consists of large and interconnected directional columnar grains with random columnar grains. This suggests that the\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5feb4058e560929d98a4g-06(1)}\n\\end{center}\n\nFig. 5 Microstructure of the vertical section of the L-PBF fabricated with energy density $5.15 \\mathrm{~J} / \\mathrm{mm}^{2}$ (laser power $165 \\mathrm{~W}$, laser scan speed $800 \\mathrm{~mm} /$ $\\mathrm{s}$, and layer thickness $0.04 \\mathrm{~mm}$ ) cube. Melt pools and layer development in the sample can be clearly observed. The columnar grains stretch to the multilayer characteristic microstructure of the melt pool in single-layer $\\mathrm{L}-\\mathrm{PBF}$ is preserved in the multilayer deposition process. The excess energy re-melts the already solidified layer and subsequently develops a large interconnected columnar grain in the direction of laser scanning.\n\n\\subsection*{3.2 Effect of laser processing parameters on the densification}\nThe first criteria to define a good quality build are directly related to the porosity present in the as-fabricated samples. A good build quality should be fully dense with no porosity present in the microstructure. Therefore, the L-PBF processing parameters should be first optimized to achieve fully dense samples. High density represents a lower fraction of porosity and vice versa. In order to achieve an optimized processing window for fully dense manufacturing of the IN 718 components, it is essential to understand the effect of individual laser processing parameters. The representative micrographs of the IN 718 as obtained from varying laser power and scan speed are shown in Fig. 6. The observed micrographs suggest that the density of a sample increases with the increase in laser power for a given scan speed. For example, the fraction of pores observed at $75 \\mathrm{~W}$ is significantly reduced when the laser power is increased to $285 \\mathrm{~W}$ at a scan speed of $800 \\mathrm{~mm} / \\mathrm{s}$. This observation is consistent with all the scan speeds considered in this study. Intuitively, it can be said that higher laser power provides sufficient energy to melt the particles resulting in larger melt pool volume. The sufficient melt pool volume ensures less porosity in the microstructure by interlayer bonding. The sample fabricated using the parameters $165 \\mathrm{~W}$ of laser power, $800 \\mathrm{~mm} / \\mathrm{s}$ of laser scan speed, and $0.04 \\mathrm{~mm}$ of layer thickness (energy density $5.15 \\mathrm{~J} / \\mathrm{mm}^{2}$ ) yielded a very low fraction of porosity in the microstructure. Increasing the energy density further to $\\sim 9 \\mathrm{~J} / \\mathrm{mm}^{2}$ ( $285 \\mathrm{~W}, 800 \\mathrm{~mm} / \\mathrm{s}$, and $0.04 \\mathrm{~mm}$ layer thickness) by increasing the laser power to $285 \\mathrm{~W}$ does not necessarily reduce the porosity fraction.\n\nIncreasing the scan rate, however, can significantly reduce the density of the L-PBF-processed IN 718 samples (Fig. 6). For instance, at the fixed laser power of $120 \\mathrm{~W}$, the pore fraction was significantly enhanced when the laser scan speed was increased from 800 to 2000 mm/s as shown in Fig. 6. It can be argued that at the higher scan speed, partial melting of powder occurs due to insufficient time available. The partial melting at high scan speeds causes the formation of voids, hence the poor density of samples $[49,50]$.\n\nThe laser scan speed can be increased to enhance the processing efficiency; however, increase in the scan speed is limited by the void formation at a given laser power. On the other hand, low scan speed can reduce the void formation but required a longer time to process the sample. Although a good build quality can be achieved with low scan speed at a given laser power, the processing efficiency reduces significantly.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5feb4058e560929d98a4g-07}\n\\end{center}\n\nFig.", "start_char_idx": 325816, "end_char_idx": 329909, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "81f5faa5-5f34-4136-a188-6b686661caf9": {"__data__": {"id_": "81f5faa5-5f34-4136-a188-6b686661caf9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1bff9b91-4a2a-4aec-a73c-89037a8c7f00", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "090796843963aba1cabc0d9e2efa755491f77862fb4d488b846d8c28d3123902", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "86aebaf0-1a9e-4f85-8513-7ecca6fd5ab6", "node_type": "1", "metadata": {}, "hash": "f7f4984dad111b1aaaa068d84e0326f70751b978dca5b5884fa28dbe86d9b3bc", "class_name": "RelatedNodeInfo"}}, "text": "6. It can be argued that at the higher scan speed, partial melting of powder occurs due to insufficient time available. The partial melting at high scan speeds causes the formation of voids, hence the poor density of samples $[49,50]$.\n\nThe laser scan speed can be increased to enhance the processing efficiency; however, increase in the scan speed is limited by the void formation at a given laser power. On the other hand, low scan speed can reduce the void formation but required a longer time to process the sample. Although a good build quality can be achieved with low scan speed at a given laser power, the processing efficiency reduces significantly.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5feb4058e560929d98a4g-07}\n\\end{center}\n\nFig. 6 Optical micrographs of the vertical section of L-PBF-fabricated cubes as a function of laser power and the laser scanning speed. The black regions in the micrographs represent the pores in the microstructure\n\nTherefore, these parameters are chosen in a way to yield the optimum build quality and fabrication efficiency. This can be achieved by simultaneously increasing or reducing the parameters as indicated in Fig. 6.\n\nA close inspection of the micrographs shown in Fig. 6 suggests that two different types of pores, irregular and round pores, are developed depending on the process conditions. The irregular pores are prevalent when laser energy input is low (low laser power (<120 W) and high scan speed (>1200 mm/s )). One plausible reason is that, in this condition, the melt pool dimensions (width and depth) are small and not sufficient to melt the particle in a volume enough to make strong bonding between the layers resulting in the formation of irregular pores (voids) $[45,51,52]$. The local melting occurs through localized conduction and convection process [9,23]. Due to a small melt pool and insufficient energy available during the process, the complete melting process does not occur leaving behind the partially melted IN 718 .\n\nThe small round pores are observed at high energy density, i.e., high laser power and low scan speed. In the present study, this is observed in the sample fabricated at a laser power above $165 \\mathrm{~W}$ and a scan speed of $800 \\mathrm{~mm} / \\mathrm{s}$ (Fig. 6). These pores are essentially formed due to characteristic heating and cooling cycles by the specific melt pool geometry. The large pyriform shape of melt pools from these operating conditions is observed (Fig. 3). In this case, due to large melt pool depth, the heat transfer and melting process occur in multi-layer deposits. Studies indicate that interlayer melting results in the small round pore formation $[53,54]$. The pore formation mechanism has been associated with the following: (i) shielding gas entrapment $[55,56]$ and (ii) local melting, vaporization, and entrapment during the laser processing, known as keyhole formation $[13,32,42,45]$. However, pore formation due to shielding gas entrapment phenomena is yet to be experimentally established. Nevertheless, it is well known that the interlayer melting results in the formation of fine round pores. Since the L-PBF process is dynamic in nature, the involved gases, such as vaporized melt and shielding gases, may entrap in the solidified melt pool resulting in the formation of the pores.\n\nThe effect of laser input power on the porosity can be analyzed by plotting the porosity obtained as a function of laser power as shown in Fig. 7. As evident from the figure, the porosity was reduced with the increase in the input laser\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5feb4058e560929d98a4g-08}\n\\end{center}\n\nFig. 7 Porosity obtained as a function of laser power at various laser scan speeds. Inset shows the porosity variation in the high-density samples\n\npower at all scanning speeds. A non-linear behavior of reducing porosity with the increase in laser power is observed. Near fully dense samples are observed for the sample processed at laser power above $165 \\mathrm{~W}$ at a scan speed of $800 \\mathrm{~mm} / \\mathrm{s}$. Increased scan speed from 800 to $2000 \\mathrm{~mm} / \\mathrm{s}$ can introduce porosity up to $40 \\%$ in the microstructure obtained with the laser power of $165 \\mathrm{~W}$.", "start_char_idx": 329140, "end_char_idx": 333428, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "86aebaf0-1a9e-4f85-8513-7ecca6fd5ab6": {"__data__": {"id_": "86aebaf0-1a9e-4f85-8513-7ecca6fd5ab6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "81f5faa5-5f34-4136-a188-6b686661caf9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f58e472a36fc8a849ef3405e77ba5d1192c3c93f5ccbac0e140063ca80ba6738", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fac9c0b3-4e1e-4794-a99d-cd2b3e2414ad", "node_type": "1", "metadata": {}, "hash": "300c7b6c1b87224abebd1aae2c84ae35ac74648f63a800d85e8baf9a8fb468c8", "class_name": "RelatedNodeInfo"}}, "text": "7 Porosity obtained as a function of laser power at various laser scan speeds. Inset shows the porosity variation in the high-density samples\n\npower at all scanning speeds. A non-linear behavior of reducing porosity with the increase in laser power is observed. Near fully dense samples are observed for the sample processed at laser power above $165 \\mathrm{~W}$ at a scan speed of $800 \\mathrm{~mm} / \\mathrm{s}$. Increased scan speed from 800 to $2000 \\mathrm{~mm} / \\mathrm{s}$ can introduce porosity up to $40 \\%$ in the microstructure obtained with the laser power of $165 \\mathrm{~W}$. The increased laser power allows the use of a high scan speed. For instance, at high scan speeds ( $\\sim 2000 \\mathrm{~mm} / \\mathrm{s}$ scan speed), the porosity reduced to $<10 \\%$ from $\\sim 40 \\%$ when the laser power increased from 165 to $265 \\mathrm{~W}$, and nearly $100 \\%$ density is observed when the laser input power is increased to above $330 \\mathrm{~W}$. The magnified view of the porosity variation in high density sample is shown as the inset figure. The inset figure clearly shows that the porosity level as low as $<1 \\%$ can be achieved with choosing an appropriate laser power for a given scan speed. This demonstrates that a fully dense sample can be achieved if the laser power is optimized.\n\nThe effect of laser scanning on the porosity variation can be analyzed using Fig. 8. As can be seen from Fig. 8, the porosity in the samples varies linearly with the scan speed. This\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5feb4058e560929d98a4g-08(2)}\n\\end{center}\n\nFig. 8 Variation in porosity as a function of scan speed at various laser power settings. Inset shows the porosity variation in the high-density samples observation is more evident when the laser input power is below $165 \\mathrm{~W}$. Also, it is observed that at $75 \\mathrm{~W}$ of laser power, the fully dense sample cannot be achieved with any scan speed considered in this study. However, from Fig. 8, it can be extrapolated to predict the required scan speed to achieve the high-density samples with a laser power of $75 \\mathrm{~W}$. For example, a scan speed of $<500 \\mathrm{~mm} / \\mathrm{s}$ is needed to achieve the highdensity IN 718 sample when processing with a laser power of $75 \\mathrm{~W}$. Thus, this figure can be used as a tool to predict the optimum scan speed required to achieve the highest possible density at a given laser power. The high-density samples plotted on Fig. 8 are magnified and shown in inset figure. A porosity fraction $<1 \\%$ is achieved at both low $(800 \\mathrm{~mm} / \\mathrm{s})$ and high scanning speeds $(2000 \\mathrm{~mm} / \\mathrm{s})$ with $>165 \\mathrm{~W}$ and $>$ $330 \\mathrm{~W}$ laser input power respectively. These indicate that both the laser power and speed are required to be chosen appropriately for desired porosity levels.\n\nAlternatively, the porosity variation due to laser power and scan speed can be analyzed by considering the laser energy density. The variation in porosity as a function of energy density is plotted in Fig. 9. It is clearly evident that the porosity level reduces abruptly with the increase in the laser energy density. The porosity reduced to $<1 \\%$ from $\\sim 100 \\%$ when the energy density increases from $\\sim 2.5$ to $4 \\mathrm{~J} / \\mathrm{mm}^{2}$. A nonlinear behavior of reducing porosity with energy density is evident from the present study. Furthermore, there is no observable change when the energy density increased above $4 \\mathrm{~J} /$ $\\mathrm{mm}^{2}$ as shown in the inset figure. All the samples processed in the range of 4 to $10 \\mathrm{~J} / \\mathrm{mm}^{2}$ show the porosity level $<1 \\%$. Dilip et al. [9] experimentally demonstrated the porosity pore formation by the keyhole mechanism at higher energy density.", "start_char_idx": 332836, "end_char_idx": 336671, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fac9c0b3-4e1e-4794-a99d-cd2b3e2414ad": {"__data__": {"id_": "fac9c0b3-4e1e-4794-a99d-cd2b3e2414ad", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "86aebaf0-1a9e-4f85-8513-7ecca6fd5ab6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "bee8f346018a43e5b2b575940a015d0954a9cc84d115245adb6d48cf1e44d5bb", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "41450995-1050-4163-9c37-116950d07cff", "node_type": "1", "metadata": {}, "hash": "1de75262a195ee366a377f2fecc3f56a4a3105970ede07460ea05eddb08d82f7", "class_name": "RelatedNodeInfo"}}, "text": "9. It is clearly evident that the porosity level reduces abruptly with the increase in the laser energy density. The porosity reduced to $<1 \\%$ from $\\sim 100 \\%$ when the energy density increases from $\\sim 2.5$ to $4 \\mathrm{~J} / \\mathrm{mm}^{2}$. A nonlinear behavior of reducing porosity with energy density is evident from the present study. Furthermore, there is no observable change when the energy density increased above $4 \\mathrm{~J} /$ $\\mathrm{mm}^{2}$ as shown in the inset figure. All the samples processed in the range of 4 to $10 \\mathrm{~J} / \\mathrm{mm}^{2}$ show the porosity level $<1 \\%$. Dilip et al. [9] experimentally demonstrated the porosity pore formation by the keyhole mechanism at higher energy density. The authors established that the porosity level reduced to a minimum and increased significantly with a further increase in energy density. This is the characteristic behavior when the porosity is formed by keyhole mechanism [51, 57]. At higher energy density, excessive vaporization can result in higher\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5feb4058e560929d98a4g-08(1)}\n\\end{center}\n\nFig. 9 Porosity observed as a function of laser energy density. Inset shows the porosity variation in the high-density samples\\\\\nporosity. In the present study, it is confirmed that density does not change with the increase in the laser energy density in the range of 4 to $10 \\mathrm{~J} / \\mathrm{mm}^{2}$. This behavior reveals that the round pore might not be formed by the keyhole mechanism. While the pore formation mechanism is not clear, it is reasonable to assume that the pores are likely to form due to inert shielding gas entrapment during the L-PBF processing in the present study.\n\n\\subsection*{3.3 Analyzing L-PBF processing parameters}\nIt is demonstrated that a high-density IN 718 sample with porosity below $1 \\%$ can be achieved by utilizing a laser energy density above $\\sim 4 \\mathrm{~J} / \\mathrm{mm}^{2}$. There is no appreciable change in porosity observed when the energy density increased up to $\\sim 10 \\mathrm{~J} / \\mathrm{mm}^{2}$. To understand the L-PBF processing parameter effects in order to achieve high-density sample ( $<1 \\%$ porosity), the laser power and scan speed are reproduced from the energy densities in the range of $\\sim 4$ to $10 \\mathrm{~J} / \\mathrm{mm}^{2}$ as given in Table 3. It can be noted that a porosity level of less than $1 \\%$ can be achieved with energy densities ranging from 4.7 to 10 . $3 \\mathrm{~J} / \\mathrm{mm}^{2}$. Therefore, it is vital to compare these energy densities in terms of scan speed and power input in order to optimize the processing conditions. Increasing scanning speed directs to the high fabrication efficiency while high laser power increases the cost of fabrication. The high scan speed is, therefore, a natural selection for fabrication. When compared, the laser processing condition of $800 \\mathrm{~mm} / \\mathrm{s}$ scan speed and $330 \\mathrm{~W}$ laser power produces a similar dense sample as the laser condition of $2000 \\mathrm{~mm} / \\mathrm{s}$ speed with $375 \\mathrm{~W}$. Although, the high-speed condition uses slightly more power, the parts can be fabricated about 2.5 times faster than the $800 \\mathrm{~mm} / \\mathrm{s}$ condition. This suggests that the fabrication efficiency is comparatively much higher which could eventually reduce the overall manufacturing cost. Even reducing the laser power to $225 \\mathrm{~W}$ with the scan speed of $800 \\mathrm{~mm} / \\mathrm{s}$, the comparative benefit is not significant.", "start_char_idx": 335935, "end_char_idx": 339516, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "41450995-1050-4163-9c37-116950d07cff": {"__data__": {"id_": "41450995-1050-4163-9c37-116950d07cff", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fac9c0b3-4e1e-4794-a99d-cd2b3e2414ad", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "435e82a0a781582781d3fef33a48e277b00c92fd51a0682a1f969409a5664720", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f20357fd-50bb-4d28-9761-f12bd097797c", "node_type": "1", "metadata": {}, "hash": "12ab8f9bbdb9494b99fbe57187af903b53ac565f98231bf9ccb81508793374d0", "class_name": "RelatedNodeInfo"}}, "text": "The high scan speed is, therefore, a natural selection for fabrication. When compared, the laser processing condition of $800 \\mathrm{~mm} / \\mathrm{s}$ scan speed and $330 \\mathrm{~W}$ laser power produces a similar dense sample as the laser condition of $2000 \\mathrm{~mm} / \\mathrm{s}$ speed with $375 \\mathrm{~W}$. Although, the high-speed condition uses slightly more power, the parts can be fabricated about 2.5 times faster than the $800 \\mathrm{~mm} / \\mathrm{s}$ condition. This suggests that the fabrication efficiency is comparatively much higher which could eventually reduce the overall manufacturing cost. Even reducing the laser power to $225 \\mathrm{~W}$ with the scan speed of $800 \\mathrm{~mm} / \\mathrm{s}$, the comparative benefit is not significant. Similarly, for the samples with\n\nTable 3 Laser density, scan speed, and power to achieve the porosity level $<1 \\%$ and $<2 \\%$\n\n\\begin{center}\n\\begin{tabular}{llll}\n\\hline\n\\begin{tabular}{l}\nPorosity \\\\\n$(\\%)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nEnergy \\\\\n$\\left(\\mathrm{J} / \\mathrm{mm}^{2}\\right)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nScan \\\\\nspeed \\\\\n$(\\mathrm{mm} / \\mathrm{s})$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nPower \\\\\n$(\\mathrm{W})$ \\\\\n\\end{tabular} \\\\\n\\hline\n$<1$ & 10.3 & 800 & 330 \\\\\n & 7.03 & 800 & 225 \\\\\n & 8.9 & 800 & 285 \\\\\n$<2$ & 4.7 & 2000 & 375 \\\\\n & 4.1 & 2000 & 330 \\\\\n & 5.1 & 800 & 165 \\\\\n & 11.7 & 800 & 375 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nItalicized data indicated the optimum laser power and speed to fabricate IN 718 parts using the L-PBF porosity $<2 \\%$, the comparative evaluation suggests that the optimum condition to fabricate parts is to use a high laser speed. Based on these arguments, the optimum operating window to fabricate IN 718 is identified (italicized data in Table 3). In addition, it is shown that the energy density is not the true parameter to optimize for fabricating AM parts. However, it can guide the amount of energy spent on fabrication. Depending on the energy spent locally, the microstructure of the build can significantly change [58]. Nevertheless, a comprehensive study of the microstructure evolution due to varying laser power and scanning speed is the scope of a future study.\n\n\\section*{4 Conclusion}\nThe effect of laser power and scan speed on melt pool dimensions and the porosity in the microstructure were systematically studied. The key contribution of this study is the demonstration that high-density IN 718 parts can be fabricated with laser powder bed fusion (L-PBF) by choosing the appropriate laser power and the scan speed. It is demonstrated that melt pool shape and dimension are the deciding factors for the porosity level and pore shapes in the final components. A linear correlation of melt pool dimension with the energy is observed in the range of 2 to $10 \\mathrm{~J} / \\mathrm{mm}^{2}$. The trend of melt pool characteristics as observed in the single-track deposition is preserved in the multilayer deposition. This information can be used to predict the multilayer build quality in laser-based AM processes by analyzing the melt pool characteristics in a single-layer deposition. A linear increase in porosity fraction was observed with the increase in laser scan speed. Surprisingly, a rapid reduction in the porosity fraction was seen with the increase in laser power. Based on this information, assessing energy density $\\left(\\mathrm{J} / \\mathrm{mm}^{2}\\right)$, a single parameter that includes variables such as laser scan speed and laser power, for the build quality is not practical. The same build quality can be achieved with a wide range of laser energy densities. Optimizing the processing condition based on the energy density is, therefore, not feasible. An optimized processing window is required to be established in terms of laser power and the scan speed.", "start_char_idx": 338746, "end_char_idx": 342593, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f20357fd-50bb-4d28-9761-f12bd097797c": {"__data__": {"id_": "f20357fd-50bb-4d28-9761-f12bd097797c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "41450995-1050-4163-9c37-116950d07cff", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9aa157dcbb86052510ad8ed97fe81a33a64bd0a607fdf4798707ab2bddf36e0a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "8001956f-2292-423f-96e8-f87e39517346", "node_type": "1", "metadata": {}, "hash": "a97266ac13650e04ea0f5f5f84110f02f69eac15c1263979ef0dee714fb81bf3", "class_name": "RelatedNodeInfo"}}, "text": "The trend of melt pool characteristics as observed in the single-track deposition is preserved in the multilayer deposition. This information can be used to predict the multilayer build quality in laser-based AM processes by analyzing the melt pool characteristics in a single-layer deposition. A linear increase in porosity fraction was observed with the increase in laser scan speed. Surprisingly, a rapid reduction in the porosity fraction was seen with the increase in laser power. Based on this information, assessing energy density $\\left(\\mathrm{J} / \\mathrm{mm}^{2}\\right)$, a single parameter that includes variables such as laser scan speed and laser power, for the build quality is not practical. The same build quality can be achieved with a wide range of laser energy densities. Optimizing the processing condition based on the energy density is, therefore, not feasible. An optimized processing window is required to be established in terms of laser power and the scan speed. This approach should be helpful to develop the operating condition criteria to achieve high-density ( $>99 \\%$ ) components. Based on the rigorous operating parameter analysis, an optimum laser power and scan speed window to fabricate IN 718 efficiently at low cost is devised in the present study.\n\nFunding information The authors PK, JF, and MM duly acknowledge the partial financial support from the Roger and Dawn Center for Renewable Energy Center at the University of Utah.\n\n\\section*{References}\n\\begin{enumerate}\n  \\item Ar\u0131soy YM, Criales LE, \u00d6zel T et al (2017) Influence of scan strategy and process parameters on microstructure and its optimization in additively manufactured nickel alloy 625 via laser powder bed fusion. Int J Adv Manuf Technol 90:1393-1417. \\href{https://doi}{https://doi}. org/10.1007/s00170-016-9429-z\n\n  \\item Criales LE, Arisoy YM, Lane B et al (2017) Laser powder bed fusion of nickel alloy 625: experimental investigations of effects of process parameters on melt pool size and shape with spatter analysis. 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Progress in Additive Manufacturing 2:157-167. \\href{https://doi.org/10}{https://doi.org/10}.", "start_char_idx": 341604, "end_char_idx": 345295, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "8001956f-2292-423f-96e8-f87e39517346": {"__data__": {"id_": "8001956f-2292-423f-96e8-f87e39517346", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f20357fd-50bb-4d28-9761-f12bd097797c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0071f3ded547e8dd35a4b2c2b33a2850edb7377778e98553708bea17cb64b269", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7de88bf1-862c-45e6-90c4-a164080d0d3d", "node_type": "1", "metadata": {}, "hash": "b14f76b6bddeb5a39ac482e4c30590124949cf882f7d011e8ae54c50fd90e60f", "class_name": "RelatedNodeInfo"}}, "text": "Int J Adv Manuf Technol 61:967-974\n\n  \\item Sun J, Yang Y, Wang D (2013) Parametric optimization of selective laser melting for forming Ti6Al4V samples by Taguchi method. Opt Laser Technol 49:118-124\n\n  \\item Dilip JJS, Zhang S, Teng C et al (2017) Influence of processing parameters on the evolution of melt pool, porosity, and microstructures in Ti-6Al-4V alloy parts fabricated by selective laser melting. Progress in Additive Manufacturing 2:157-167. \\href{https://doi.org/10}{https://doi.org/10}. 1007/s40964-017-0030-2\n\n  \\item Maamoun AH, Xue YF, Elbestawi MA, Veldhuis SC (2018) Effect of SLM process parameters on the quality of $\\mathrm{Al}$ alloy parts; part II: microstructure and mechanical properties. \\href{https://doi.org/10.20944/}{https://doi.org/10.20944/} preprints201811.0026.v1\n\n  \\item Riedlbauer D, Scharowsky T, Singer RF et al (2017) Macroscopic simulation and experimental measurement of melt pool characteristics in selective electron beam melting of Ti-6Al-4V. 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Mater Des 138:119-128.", "start_char_idx": 344794, "end_char_idx": 347915, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7de88bf1-862c-45e6-90c4-a164080d0d3d": {"__data__": {"id_": "7de88bf1-862c-45e6-90c4-a164080d0d3d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8001956f-2292-423f-96e8-f87e39517346", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "55c23d7e42cf22ca49192e2d0b844dc872989a8fae2559b16738fc56f8f36eb5", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9efed813-80bd-4bb5-afe7-12fd39bd15fe", "node_type": "1", "metadata": {}, "hash": "e850ea91f8f2db60df3caff83a13266c1ec5397f4b74db9adc2e8b131756aa05", "class_name": "RelatedNodeInfo"}}, "text": "J Mater Process Technol 220:202-214. \\href{https://doi.org/10.1016/j}{https://doi.org/10.1016/j}. jmatprotec.2015.01.025\n\n  \\item AlMangour B, Grzesiak D, Borkar T, Yang J-M (2018) Densification behavior, microstructural evolution, and mechanical properties of $\\mathrm{TiC} / 316 \\mathrm{~L}$ stainless steel nanocomposites fabricated by selective laser melting. 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Superalloys 88:33-42\n\n  \\item Eiselstein H, Tillack D (1991) The invention and definition of alloy 625.", "start_char_idx": 347529, "end_char_idx": 350610, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9efed813-80bd-4bb5-afe7-12fd39bd15fe": {"__data__": {"id_": "9efed813-80bd-4bb5-afe7-12fd39bd15fe", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7de88bf1-862c-45e6-90c4-a164080d0d3d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "094d58d1b3eb10cb065cafaa8305769fe042ed31a35cdd38a4d50d0bf1cbb4bd", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a6bd4a49-2c9e-46e8-9fe7-8d1e96bc2d66", "node_type": "1", "metadata": {}, "hash": "5073a582621fcea96657222a57be7a715a2d322e0aae9ccd268231454c08b125", "class_name": "RelatedNodeInfo"}}, "text": "Addit. Manuf 13:14-36\n\n  \\item Manfredi D, Calignano F (2017) Laser powder bed fusion of aluminum, titanium and nickel based alloys: materials and design investigations. IEEE:1423-1425\n\n  \\item Gong H, Teng C, Zeng K, et al (2016) Single track of selective laser melting Ti-6Al-4V powder on support structure\n\n  \\item Dilip J, Anam MA, Pal D, Stucker B (2016) A short study on the fabrication of single track deposits in SLM and characterization\n\n  \\item Brooks J, Bridges P (1988) Metallurgical stability of Inconel alloy 718. Superalloys 88:33-42\n\n  \\item Eiselstein H, Tillack D (1991) The invention and definition of alloy 625. Superalloys 718:1-14\n\n  \\item Sharman ARC, Amarasinghe A, Ridgway K (2008) Tool life and surface integrity aspects when drilling and hole making in Inconel 718. 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J Mater Process Technol 170: 240-246. \\href{https://doi.org/10.1016/j.jmatprotec.2005.05.005}{https://doi.org/10.1016/j.jmatprotec.2005.05.005}\n\n  \\item Amato KN, Gaytan SM, Murr LE et al (2012) Microstructures and mechanical behavior of Inconel 718 fabricated by selective laser melting. Acta Mater 60:2229-2239. \\href{https://doi.org/10.1016/j}{https://doi.org/10.1016/j}. actamat.2011.12.032\n\n  \\item Pr\u00f6bstle M, Neumeier S, Hopfenm\u00fcller J et al (2016) Superior creep strength of a nickel-based superalloy produced by selective laser melting. Mater Sci Eng A 674:299-307. \\href{https://doi.org/10.1016/j}{https://doi.org/10.1016/j}. msea.2016.07.061\n\n  \\item Bean GE, Witkin DB, McLouth TD, Zaldivar RJ (2018) The effect of laser focus and process parameters on microstructure and mechanical properties of SLM Inconel 718. 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Mater Sci Eng A 735:182-190. \\href{https://doi.org/10.1016/j.msea}{https://doi.org/10.1016/j.msea}. 2018.08.037\n\n  \\item Khairallah SA, Anderson AT, Rubenchik A, King WE (2016) Laser powder-bed fusion additive manufacturing: physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones.", "start_char_idx": 349979, "end_char_idx": 352926, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a6bd4a49-2c9e-46e8-9fe7-8d1e96bc2d66": {"__data__": {"id_": "a6bd4a49-2c9e-46e8-9fe7-8d1e96bc2d66", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9efed813-80bd-4bb5-afe7-12fd39bd15fe", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "49b6de39b78a672154fe87a714f50960f93744badb786a12340d56caf47d2d52", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "472c767d-ada1-41bf-9beb-c5ab46750572", "node_type": "1", "metadata": {}, "hash": "26f0ac17cb34c87538731feead8e955f0822df5dec689ac722d3c92cb46c95ca", "class_name": "RelatedNodeInfo"}}, "text": "International Society for Optics and Photonics, p 105230Y\n\n  \\item Moussaoui K, Rubio W, Mousseigne M et al (2018) Effects of selective laser melting additive manufacturing parameters of Inconel 718 on porosity, microstructure and mechanical properties. Mater Sci Eng A 735:182-190. \\href{https://doi.org/10.1016/j.msea}{https://doi.org/10.1016/j.msea}. 2018.08.037\n\n  \\item Khairallah SA, Anderson AT, Rubenchik A, King WE (2016) Laser powder-bed fusion additive manufacturing: physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater 108:36-45\n\n  \\item Seifi M, Salem A, Beuth J et al (2016) Overview of materials qualification needs for metal additive manufacturing. Jom 68: 747-764\n\n  \\item Gong H, Rafi K, Gu H et al (2014) Analysis of defect generation in Ti-6Al-4V parts made using powder bed fusion additive manufacturing processes. Addit. Manuf 1:87-98\n\n  \\item Gorsse S, Hutchinson C, Goun\u00e9 M, Banerjee R (2017) Additive manufacturing of metals: a brief review of the characteristic microstructures and properties of steels, Ti-6Al-4V and high-entropy alloys. Sci Technol Adv Mater 18:584-610. \\href{https://doi.org/10.1080/}{https://doi.org/10.1080/} 14686996.2017.1361305\n\n  \\item Xia M, Gu D, Yu G et al (2017) Porosity evolution and its thermodynamic mechanism of randomly packed powder-bed during selective laser melting of Inconel 718 alloy. Int J Mach Tools Manuf 116: 96-106. \\href{https://doi.org/10.1016/j.ijmachtools.2017.01.005}{https://doi.org/10.1016/j.ijmachtools.2017.01.005}\n\n  \\item Sadowski M, Ladani L, Brindley W, Romano J (2016) Optimizing quality of additively manufactured Inconel 718 using powder bed laser melting process. Addit. Manuf 11:60-70. \\href{https://doi.org/10}{https://doi.org/10}. 1016/j.addma.2016.03.006\n\n  \\item Laoui T, Froyen L, Yadroitsev IA et al (2004) Balling processes during selective laser treatment of powders. Rapid Prototyp J 10: 78-87. \\href{https://doi.org/10.1108/13552540410526953}{https://doi.org/10.1108/13552540410526953}\n\n  \\item Mumtaz KA, Hopkinson N (2010) Selective laser melting of thin wall parts using pulse shaping. J Mater Process Technol 210:279287. \\href{https://doi.org/10.1016/j.jmatprotec.2009.09.011}{https://doi.org/10.1016/j.jmatprotec.2009.09.011}\n\n  \\item Kasperovich G, Haubrich J, Gussone J, Requena G (2016) Correlation between porosity and processing parameters in TiA16V4 produced by selective laser melting. Mater Des 105: 160-170. \\href{https://doi.org/10.1016/j.matdes.2016.05.070}{https://doi.org/10.1016/j.matdes.2016.05.070}\n\n  \\item Gong H, Rafi K, Karthik NV, et al (2013) The effects of processing parameters on defect regularity in Ti-6Al-4V parts fabricated by selective laser melting and electron beam melting. pp 440-453\n\n  \\item Thijs L, Verhaeghe F, Craeghs T et al (2010) A study of the microstructural evolution during selective laser melting of Ti-6Al-4V. Acta Mater 58:3303-3312.", "start_char_idx": 352353, "end_char_idx": 355295, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "472c767d-ada1-41bf-9beb-c5ab46750572": {"__data__": {"id_": "472c767d-ada1-41bf-9beb-c5ab46750572", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a6bd4a49-2c9e-46e8-9fe7-8d1e96bc2d66", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d1a7c8d173866ab6661354b77365e37c1b1ed60c77cd0100668b7c7bbef43e3f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a0f58e15-d801-4df8-9be6-8ee7cc935695", "node_type": "1", "metadata": {}, "hash": "4bba3484b40efbcd27b98aafd18220846d11b0dfeedcb605f615ed23bd91841c", "class_name": "RelatedNodeInfo"}}, "text": "Mater Des 105: 160-170. \\href{https://doi.org/10.1016/j.matdes.2016.05.070}{https://doi.org/10.1016/j.matdes.2016.05.070}\n\n  \\item Gong H, Rafi K, Karthik NV, et al (2013) The effects of processing parameters on defect regularity in Ti-6Al-4V parts fabricated by selective laser melting and electron beam melting. pp 440-453\n\n  \\item Thijs L, Verhaeghe F, Craeghs T et al (2010) A study of the microstructural evolution during selective laser melting of Ti-6Al-4V. Acta Mater 58:3303-3312. \\href{https://doi.org/10.1016/j.actamat.2010}{https://doi.org/10.1016/j.actamat.2010}. 02.004\n\n  \\item Dai D, Gu D (2014) Thermal behavior and densification mechanism during selective laser melting of copper matrix composites: simulation and experiments. Mater Des 55:482-491. \\href{https://doi}{https://doi}. org/10.1016/j.matdes.2013.10.006\n\n  \\item Pang S, Chen W, Wang W (2014) A quantitative model of keyhole instability induced porosity in laser welding of titanium alloy. Metall Mater Trans A 45:2808-2818\n\n  \\item Vilaro T, Colin C, Bartout JD (2011) As-fabricated and heat-treated microstructures of the Ti-6Al-4V alloy processed by selective laser melting. Metall Mater Trans A 42:3190-3199. \\href{https://doi.org/10}{https://doi.org/10}. 1007/s11661-011-0731-y\n\n  \\item Tan JL, Tang C, Wong CH (2018) A computational study on porosity evolution in parts produced by selective laser melting. Metall and Mat Trans A 49:3663-3673 \\href{https://doi.org/10.1007/s11661018-4697-%D1%85}{https://doi.org/10.1007/s11661018-4697-\u0445}\n\n  \\item Akram J, Chalavadi P, Pal D, Stucker B (2018) Understanding grain evolution in additive manufacturing through modeling. Addit. Manuf 21:255-268. \\href{https://doi.org/10.1016/j.addma.2018.03.021}{https://doi.org/10.1016/j.addma.2018.03.021}\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{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{Melt pool simulation for the evaluation of process parameters in selective laser melting }\n\n\n\\author{Thorsten Heeling ${ }^{a, *}$, Michael Cloots ${ }^{b}$, Konrad Wegener ${ }^{a}$\\\\\na Institute of Machine Tools and Manufacturing, ETH Zurich, 8092 Zurich, Switzerland\\\\\nb Irpd AG, 9014 St. Gallen, Switzerland}\n\\date{}", "start_char_idx": 354806, "end_char_idx": 357479, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a0f58e15-d801-4df8-9be6-8ee7cc935695": {"__data__": {"id_": "a0f58e15-d801-4df8-9be6-8ee7cc935695", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "472c767d-ada1-41bf-9beb-c5ab46750572", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9fabaacdcd5568f40586419794bdbbb9987ae596945965bc136999843e51b4ef", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "28b38328-8dd6-454d-8932-10c18014c0aa", "node_type": "1", "metadata": {}, "hash": "34612ddf0331f7fcb48613fbd3522d48a4510a29d0a5e5f956c9dd979ef5f939", "class_name": "RelatedNodeInfo"}}, "text": "\\author{Thorsten Heeling ${ }^{a, *}$, Michael Cloots ${ }^{b}$, Konrad Wegener ${ }^{a}$\\\\\na Institute of Machine Tools and Manufacturing, ETH Zurich, 8092 Zurich, Switzerland\\\\\nb Irpd AG, 9014 St. Gallen, Switzerland}\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\n\n\n\\section*{A R T I C L E I N F O}\n\\section*{Article history:}\nReceived 9 November 2016\n\nReceived in revised form 7 January 2017\n\nAccepted 8 February 2017\n\nAvailable online 16 February 2017\n\n\\section*{Keywords:}\nSelective laser melting\n\nSimulation\n\nMelt pool dynamics\n\nAdditive manufacturing\n\nPowder bed fusion\n\n\\begin{abstract}\nA B S T R A C T With increasing industrial interest and significance of the selective laser melting the importance for profound process knowledge increases so that new materials can be qualified faster. Also it is the basis for an educated evaluation of possible process innovations. Therefore a 3D numerical model for the selective laser melting process is presented that allows a detailed look into the process dynamics at comparably low calculation effort. It combines a finite difference method with a combined level set volume of fluid method for the simulation of the process and starts with a homogenized powder bed in its initial configuration. The model uses a comprehensive representation of various physical effects like dynamic laser power absorption, buoyancy effect, Marangoni effect, capillary effect, evaporation, recoil pressure and temperature dependent material properties. It is validated for different process parameters using cubic samples of stainless steel 316L and nickel-based superalloy IN738LC. The results show the significance of evaporation and its related recoil pressure for a feasible prediction of the melt pool dynamics. Furthermore a possible way to reduce the times and costs for material qualification by using the simulation model to predict possible process parameters and therefore to reduce the necessary experimental effort for material qualification to a minimum is shown.\n\\end{abstract}\n\n(C) 2017 Elsevier B.V. All rights reserved.\n\n\\section*{1. Introduction}\nAdditive manufacturing technologies are of increasing importance for many applications due to their freedom of design, possible complexity and their short lead times. The selective laser melting (SLM) process is in particular suited for industrial applications because it features nearly fully dense metal parts with a feature resolution down to about $200 \\mu \\mathrm{m}$ at almost unlimited complexity. The process is based on a metal powder bed with defined layer thickness of common values of about $20-200 \\mu \\mathrm{m}$, which is deposited and selectively irradiated in every layer until the final part height is reached. Therefore at the beginning of each layer the build plate is lowered by the layer thickness and the powder reservoir is raised by a certain amount to supply the powder deposition unit with sufficient powder material. After that, the powder deposition unit is moving along over the build plate distributing the powder and pushing the residual powder as well as particles that are too large into the powder overflow. Following that, the new powder layer is selectively irradiated by the laser beam which is deflected and focused prior to entering the process chamber. Due to the irradiation the powder material as well as previous tracks and layers are molten so that a strong bonding between the layers can be achieved leading to a near-fully dense part.", "start_char_idx": 357252, "end_char_idx": 361344, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "28b38328-8dd6-454d-8932-10c18014c0aa": {"__data__": {"id_": "28b38328-8dd6-454d-8932-10c18014c0aa", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a0f58e15-d801-4df8-9be6-8ee7cc935695", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "307baddd1f3091d7a911f9ec197eb92fd84f9de72f8a290efa708e7cfb55837b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "cd0ae212-898d-4f2e-b6f8-d35394044a27", "node_type": "1", "metadata": {}, "hash": "58776be9b676e0a246484c9cd06c221c6289930ed996c46f2ace27319cf8488c", "class_name": "RelatedNodeInfo"}}, "text": "The process is based on a metal powder bed with defined layer thickness of common values of about $20-200 \\mu \\mathrm{m}$, which is deposited and selectively irradiated in every layer until the final part height is reached. Therefore at the beginning of each layer the build plate is lowered by the layer thickness and the powder reservoir is raised by a certain amount to supply the powder deposition unit with sufficient powder material. After that, the powder deposition unit is moving along over the build plate distributing the powder and pushing the residual powder as well as particles that are too large into the powder overflow. Following that, the new powder layer is selectively irradiated by the laser beam which is deflected and focused prior to entering the process chamber. Due to the irradiation the powder material as well as previous tracks and layers are molten so that a strong bonding between the layers can be achieved leading to a near-fully dense part. Shielding gas is passing through the process chamber to minimize the influence of vaporized metal and spatter on the following tracks and layers. The process is illustrated in Fig. 1.\n\nA wide range of metal alloys like stainless steels [1,2], nickelbased superalloys [3,4], titanium alloys [5,6], aluminum alloys $[7,8]$ as well as cobalt chromium alloys [9] are available and the range is continuously expanding especially for turbine and biomedical related alloys. But the process still lacks productivity, robustness, reproducibility and quality and every new alloy needs a time consuming and costly evaluation of possible process parameter sets for a certain machine configuration. A simulation based approach seems reasonable to reduce the times and costs to predict process parameters and possible optimizations since a strong and detailed understanding of the process dynamics helps to find solutions for the restricting phenomena.\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author.\n\\end{itemize}\n\nE-mail address: \\href{mailto:heeling@iwf.mavt.ethz.ch}{heeling@iwf.mavt.ethz.ch} (T. Heeling).\n}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_4337cab3afd3e8e599dcg-02(1)}\n\\end{center}\n\nFig. 1. Illustration of the main components necessary for the SLM process.\n\n\\subsection*{1.1. Process simulation}\nSeveral simulation models have already been presented, often trying to use the simulation results for the evaluation of process parameters. Starting with purely thermal approaches, which commonly feature a moving heat source for a rough estimation of the melt pool sizes and thermal histories [10,11], there are those expanding these models by thermo-elasto-plastic modeling to get an idea of the residual stresses and distortion [12-15] and those going more into detail regarding the melt pool dynamics [16-18]. This detailed investigation of the melt pool dynamics and the resulting melt pool dimensions of single or rarely multiple line simulations offer a profound insight into the process dynamics since the SLM process is a stacking of a very high amount of single tracks. These simulations especially show the importance of evaporation and the Marangoni effect on the melt pool dynamics and therefore the achievable melt pool shape and possible indicators for pores and spatter [19]. Some models even take the powder packing into consideration to account for the randomness of the powder bed which influences the melt pool to a certain extent $[18,19]$. But the modeling of every particle leads to very high calculation times due to the necessity of a very fine grid [17]. Due to the high usability of the information taken from one single molten line this approach is presented in this paper in a newly developed simulation tool using a homogenized powder bed in its initial configuration to achieve a balance between computational effort and results' detail. The model is validated over a wider set of parameters for two different alloys, the stainless steel 316L and the nickel-based superalloy IN738LC, investigating the physical effects' influences for different parameter sets. Furthermore the validated model is used to find possible indicators for the evaluation of process parameters as a step to reduce the effort for material qualification.\n\n\\section*{2. Model description}\n\\subsection*{2.1. Concept}\nThe three-dimensional numerical model is divided into a temperature field and a fluid flow part elaborating a weak coupling.", "start_char_idx": 360368, "end_char_idx": 364822, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "cd0ae212-898d-4f2e-b6f8-d35394044a27": {"__data__": {"id_": "cd0ae212-898d-4f2e-b6f8-d35394044a27", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "28b38328-8dd6-454d-8932-10c18014c0aa", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6566d144bd82298d4e4806a7b022c6ab0c06902ce613aef0eb63473a0d5dc34d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0025c182-6634-47f1-8ead-b5ef9d99bb81", "node_type": "1", "metadata": {}, "hash": "ae5ed75c994c62a5eb0b981e41bbcf9becb8361ea8e2df116c3075675fe15aef", "class_name": "RelatedNodeInfo"}}, "text": "But the modeling of every particle leads to very high calculation times due to the necessity of a very fine grid [17]. Due to the high usability of the information taken from one single molten line this approach is presented in this paper in a newly developed simulation tool using a homogenized powder bed in its initial configuration to achieve a balance between computational effort and results' detail. The model is validated over a wider set of parameters for two different alloys, the stainless steel 316L and the nickel-based superalloy IN738LC, investigating the physical effects' influences for different parameter sets. Furthermore the validated model is used to find possible indicators for the evaluation of process parameters as a step to reduce the effort for material qualification.\n\n\\section*{2. Model description}\n\\subsection*{2.1. Concept}\nThe three-dimensional numerical model is divided into a temperature field and a fluid flow part elaborating a weak coupling. While the temperature field is calculated based on a finite difference scheme, the fluid flow calculation utilizes a combined level set volume of fluid (CLSVoF) method and a pressure implicit splitting\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_4337cab3afd3e8e599dcg-02}\n\\end{center}\n\nFig. 2. Cross section of the initial configuration showing powder bed (left), the idealized previous track (right) and idealized previous layers (bottom).\n\nof operators (PISO) solver. The numerical model consists of cubic elements. While the material properties and most state variables like temperature and pressure are fixed to the elements' center points, the melt flow velocities are placed on the elements' faces and are thus evaluated on a staggered grid. Furthermore a homogenized powder bed is elaborated, leading to an initial configuration in which every powder element is just partly but equally filled with material. Since the model is used to be compared to cubic samples, the line to be molten is located next to an already solidified line, leading to the initial configuration shown in Fig. 2. The beam is simulated to be moving along the center line.\n\nThe specific properties of non-full elements are weighted with their filling degree $F$.\n\n$\\alpha_{F}(T)=F \\cdot \\alpha(T)+(1-F) \\cdot \\alpha_{g}$\n\nWith $\\alpha(T)$ representing any temperature dependent material property and $\\alpha_{g}$ the equivalent gas property. Furthermore the thermal conductivity of the powder bed is handled separately, since multiple studies have shown that the thermal conductivity of a powder bed is significantly smaller $[20,21]$.\n\n\\subsection*{2.2. Dynamic absorption model}\nThe laser power absorption model is implemented following the absorption model proposed by Gusarov et al. [22,23]. In that the following radiation transfer equation is solved for collimated incident laser power normal to a thin powder layer.\n\n$\\mu \\frac{\\partial I(z, \\mu)}{\\partial z}=\\beta \\cdot\\left(\\frac{\\omega}{2} \\int_{-1}^{1} I\\left(z, \\mu^{\\prime}\\right) \\cdot P\\left(\\mu^{\\prime}, \\mu\\right) d \\mu^{\\prime}-I(z, \\mu)\\right)$\n\nWith $\\mu=\\cos \\theta$ and $\\theta$ being the radiation propagation angle, $\\beta$ the extinction coefficient, $\\omega$ the scattering coefficient, $I(z, \\mu)$ the depth resolved intensity and $P\\left(\\mu^{\\prime}, \\mu\\right)$ the scattering phase function. To solve the radiation transfer equation the depth resolved intensity profile is calculated considering a power density moving deeper into the powder layer $Q_{+}(z)$, a power density $Q_{-}(z)$ leaving the powder layer due to reflection as well as a diffuse part due to (multiple) scattering $S(z, \\mu)$ with $\\delta$ being the Dirac delta function [23].\n\n$I(z, \\mu)=\\frac{Q_{+}(z)}{2 \\pi} \\delta(\\mu-1)+\\frac{Q_{-}(z)}{2 \\pi} \\delta(\\mu+1)+S(z, \\mu)$\n\nElaborating the boundary conditions at the powder layer surface and substrate as well as assumptions regarding isotropic scattering and the two-flux method within the framework of geometrical optics, which can be found in detail in the publications of Gusarov et al. [22,23], the depth resolved absorbed power can be calculated as follows.", "start_char_idx": 363840, "end_char_idx": 367993, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0025c182-6634-47f1-8ead-b5ef9d99bb81": {"__data__": {"id_": "0025c182-6634-47f1-8ead-b5ef9d99bb81", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "cd0ae212-898d-4f2e-b6f8-d35394044a27", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7b7b0249cc3b1d93af5cf6fe076d9f07078fe0dc1ee28a8937dd45f54439b208", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c8d8288d-34bd-42e7-b98c-6187585bb873", "node_type": "1", "metadata": {}, "hash": "19aa9c99987dff8ce963f588ac8c2f9765156b75a02d6cbb8c650fa9ae11c58a", "class_name": "RelatedNodeInfo"}}, "text": "$I(z, \\mu)=\\frac{Q_{+}(z)}{2 \\pi} \\delta(\\mu-1)+\\frac{Q_{-}(z)}{2 \\pi} \\delta(\\mu+1)+S(z, \\mu)$\n\nElaborating the boundary conditions at the powder layer surface and substrate as well as assumptions regarding isotropic scattering and the two-flux method within the framework of geometrical optics, which can be found in detail in the publications of Gusarov et al. [22,23], the depth resolved absorbed power can be calculated as follows.\n\n\n\\begin{align*}\n& P_{a b s}(\\xi)=P_{0} \\cdot\\left\\{\\frac{r a}{(4 r-3) D}\\left[\\left(1-r^{2}\\right) e^{-\\lambda}\\left[(1-r) e^{-2 a \\xi}+(1+a) e^{2 a \\xi}\\right)\\right]-\\left(3-r e^{-2 \\lambda}\\right) .\\right. \\\\\n& \\left.\\left.\\left[(1+a+r(1-a)) e^{2 a(\\lambda-\\xi)}+(1-a-r(1+a)) e^{2 a(\\xi-\\lambda)}\\right]\\right]-\\frac{3(1-r)\\left(e^{-\\xi}-r e^{\\xi-2 \\lambda}\\right)}{4 r-3}\\right\\} \\tag{4}\n\\end{align*}\n\n\nIn which $P_{0}$ is the total input power at the surface, $\\xi=\\beta \\cdot z$ is the dimensionless depth and $a$ and $D$ are values derived from the hemispherical reflectivity $r$ and optical thickness $\\lambda=\\beta \\cdot h_{p l}[23]$.\n\n$a=\\sqrt{1-r}$\n\n$\\beta=\\frac{3}{2} \\cdot \\frac{\\rho_{p l}}{1-\\rho_{p l}} \\cdot \\frac{1}{d_{p p}}$\n\n$D=(1-a)[1-a-r \\cdot(1+a)] e^{-2 a \\lambda}-(1+a)[1+a-r \\cdot(1-a)] e^{2 a \\lambda}$\n\nHere $\\rho_{p l}$ is the relative powder layer density, $h_{p l}$ the powder layer height and $d_{p p}$ the powder particle diameter. So this modeling equation considers multiple reflection due Eq. (3) and depth resolved power input based on simple powder material data. But it does not handle melt consolidation and evaporation, so that some adjustments are necessary for accuracy improvements. Therefore, the calculation of the relative powder layer density, the powder layer height and the optical thickness for every stack of elements in every time step based on the current configuration is proposed. So the relative powder density is calculated as the mean value of the filling degree of all non-empty and non-full elements per stack from the top to the first completely filled element assuming that the first full element indicates consolidated melt. The powder layer height results as the difference of the uppermost non-empty element and the uppermost completely filled element. Fig. 3 illustrates this approach.\n\nThese values are then used to calculate the optical thickness and the extinction coefficient for every element stack. Furthermore the absorbing element length is weighted by the ratio of element filling degree to the stack's relative powder density (average stack filling degree). This is necessary to prevent elements with a filling degree far lower than the average from artificial overheating. Considering these adjustments to the Gusarov absorption model, it is possible to realize a differentiation between powder, consolidating melt as\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_4337cab3afd3e8e599dcg-03}\n\\end{center}\n\nFig. 3. Illustration of the dynamic evaluation of average filling degree and powder layer height for the adjusted absorption model in a longitudinal section. Gray indicates solid/fluid material, white gas/gaseous phase. well as already consolidated melt and solid material on the scale of element resolution.\n\n\\subsection*{2.3. Heat flow}\nAdditionally to the absorption model, thermal conduction, convection and radiation as well as melting, freezing and evaporation of material and heat exchange due to melt flow are considered to calculate the temperature field. Since the time step size is very small due to the needs of the melt flow simulation an explicit finite difference scheme is used to solve the three-dimensional inhomogeneous heat conduction equation. Therefore, the conductive heat flow in $x$-direction $\\dot{Q}_{x, i, j, k}$ is exemplarily discretized as follows [24].", "start_char_idx": 367557, "end_char_idx": 371380, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c8d8288d-34bd-42e7-b98c-6187585bb873": {"__data__": {"id_": "c8d8288d-34bd-42e7-b98c-6187585bb873", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0025c182-6634-47f1-8ead-b5ef9d99bb81", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "bfe27c2615893e65340953d39143d95b394433a36ef660070e619ef1911434a2", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7dd3aa5e-7a2f-4994-b78b-cf5f743ce652", "node_type": "1", "metadata": {}, "hash": "b8b7f287dc684e3fc68cc8ad1ba3ffa5928cd49a5397d558ff448eb37da28761", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{gather*}\n\\dot{Q}_{x, i, j, k}=\\frac{2}{\\Delta x^{2}} \\cdot \\frac{\\lambda_{i, j, k} \\cdot \\lambda_{i+1, j, k}}{\\lambda_{i, j, k}+\\lambda_{i+1, j, k}} \\cdot\\left(T_{i+1, j, k}-T_{i, j, k}\\right) \\\\\n+\\frac{2}{\\Delta x^{2}} \\cdot \\frac{\\lambda_{i, j, k} \\cdot \\lambda_{i-1, j, k}}{\\lambda_{i, j, k}+\\lambda_{i-1, j, k}} \\cdot\\left(T_{i-1, j, k}-T_{i, j, k}\\right) \\tag{8}\n\\end{gather*}\n\n\nIn which $\\lambda_{i, j, k}$ is the temperature dependent thermal conductivity of element $(i, j, k)$. The boundary conditions are set so that heat is allowed to flow out of the model at the sides and bottom while being insulated to the top. Using this discretization and considering radiation $\\dot{Q}_{r a d}$, convection $\\dot{Q}_{c o n v}$ and heat flow due to melt flow $\\dot{Q}_{\\text {flow }}$ an element's temperature of time step $n$ can be predicted as follows\n\n$T_{\\text {pred }}^{n}=T^{n-1}+\\frac{P_{\\text {abs }}+\\dot{Q}_{x}+\\dot{Q}_{y}+\\dot{Q}_{z}+\\dot{Q}_{\\text {rad }}+\\dot{Q}_{\\text {conv }}+\\dot{Q}_{\\text {flow }}}{\\rho \\cdot c_{p} \\cdot V} \\cdot \\Delta t$.\n\nWith $\\Delta t$ being the time step size, $\\rho$ the material's density and $c_{p}$ the specific heat capacity. The predicted temperature is then used to check for melting, freezing or evaporation of the element and thus possibly corrected afterwards. The latent heat of fusion is considered as an additional heat sink/source between solidus and liquidus temperature while the latent heat of evaporation is considered using the evaporation model which is explained later on.\n\n\\subsection*{2.4. Evaporation and recoil pressure}\nEvaporation usually is an important factor within laser based processes because the material is subject to high powers which are induced within a small spot size. Due to the resulting rapid heating to high temperatures molten material soon starts evaporating, inducing a recoil pressure to the melt pool. Different approaches for the modeling of the recoil pressure are known, either more detailed ones which include a modeling of the Knudsen layer [25,26], or experimentally supported ones [19,27]. But all of them lead to quiet similar models based on the Clausius-Clapeyron equation for the calculation of the saturated vapor pressure, which is weighted by a coefficient that accounts for the backward flux of evaporated material [19,26,27].\n\n$p_{\\text {rec }}=0.54 \\cdot p_{0} \\cdot e^{\\frac{\\text { Levap } \\cdot M_{\\text {mol }}}{R}} \\cdot\\left(\\frac{1}{T_{0}}-\\frac{1}{T}\\right)$\n\nIn this equation $p_{0}$ and $T_{0}$ are the known pressure and temperature at which evaporation occurs while $p_{\\text {rec }}$ is the approximated recoil pressure at another temperature value $T$. $L_{\\text {evap }}$ is the heat of evaporation, $M_{m o l}$ the molar mass and $R$ the universal gas constant. To approximate the heat and mass loss of the melt pool due to evaporation as well, a return mapping for temperature and pressure within the Clausius-Clapeyron equation is employed. Starting\\\\\nwith a prediction of the new temperature at the recoil pressure of the previous time step $p_{r e c}^{n-1}$ the recoil pressure of the current time step $p_{\\text {rec }}^{n}$ is calculated.", "start_char_idx": 371383, "end_char_idx": 374559, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7dd3aa5e-7a2f-4994-b78b-cf5f743ce652": {"__data__": {"id_": "7dd3aa5e-7a2f-4994-b78b-cf5f743ce652", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c8d8288d-34bd-42e7-b98c-6187585bb873", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c9e3c128ed0b516dbe6290d19b58ba47221a01c564a950a7cf061b5958ee92a2", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2f999d21-3ab3-4714-81e1-d9f549839d98", "node_type": "1", "metadata": {}, "hash": "8215620aaa8204f82e977decb201723159609f4a8023986ff23fa4d5842577ad", "class_name": "RelatedNodeInfo"}}, "text": "$L_{\\text {evap }}$ is the heat of evaporation, $M_{m o l}$ the molar mass and $R$ the universal gas constant. To approximate the heat and mass loss of the melt pool due to evaporation as well, a return mapping for temperature and pressure within the Clausius-Clapeyron equation is employed. Starting\\\\\nwith a prediction of the new temperature at the recoil pressure of the previous time step $p_{r e c}^{n-1}$ the recoil pressure of the current time step $p_{\\text {rec }}^{n}$ is calculated.\n\n$p_{\\text {rec }}^{n}=0.54 \\cdot p_{0} \\cdot e^{\\frac{L_{\\text {evap }} \\cdot M_{\\text {mol }}}{R} \\cdot\\left(\\frac{1}{T_{0}}-\\frac{1}{T_{\\text {pred }}^{n}}\\right)}$\n\nThis new recoil pressure is used to map the temperature of the current time step $T^{n}$ back to the saturated vapor pressure curve.\n\n$T^{n}=\\left(\\frac{1}{T_{0}}-\\frac{\\ln \\left(\\frac{p_{\\text {rec }}^{n}}{p_{0}}\\right) \\cdot R}{L_{\\text {evap }} \\cdot M_{\\text {mol }}}\\right)^{-1}$\n\nThe temperature difference of predicted temperature and actual temperature is then used to calculate the evaporated volume of this time step $\\Delta V^{n}$, guaranteeing the conservation of energy within the melt pool.\n\n$\\Delta V^{n}=\\frac{\\left(T^{n}-T_{\\text {pred }}^{n}\\right) \\cdot c_{p} \\cdot V}{L_{\\text {evap }}}$\n\nThe temperature and pressure increase is done incrementally to minimize errors due to the non-linearity of the saturated vapor pressure curve.\n\n\\subsection*{2.5. Melt pool dynamics}\nThe combined level set volume of fluid (CLSVoF) method is elaborated for the calculation of the melt flow and was widely adopted from the publications of Son et al. [28-30]. It uses the volume of fluids function $F$ (equals the filling degree) as a surface identifier and to calculate the current material configuration based on the surface normals. In its original form any not completely filled element is considered a surface element. But since every powder element is taken as just partly filled in its initial configuration of the proposed approach, the criterion for the surface identification has to be changed for the presented model. So considering any element as a surface element if it has an empty neighboring element, seems to be a more fitting criterion for the presented approach. This coarsens the resolution for the identification of pores within the melt pool but allows the use of this method for the initial configuration of a homogeneous powder bed.\n\nThe surface normals are calculated using the level set function $\\phi$ which is negative for the gaseous phase, positive for the melt pool and zero on the surface.\n\n$\\mathbf{n}=\\frac{\\nabla \\phi}{|\\nabla \\phi|}$\n\nThe equation is discretized using a central differencing scheme. Based on the information gained from the volume of fluid and level set function the advection of material from one element to another can be calculated for a known fluid flow velocity field $\\mathbf{u}[28]$.\n\n$\\frac{\\partial F}{\\partial t}+\\nabla \\cdot \\mathbf{u} F=F \\nabla \\cdot \\mathbf{u}$\n\nTo reach a higher accuracy the advection is calculated subsequently for $x$-, $y$ - and $z$-direction with reconstruction steps in between while the order in the sequence of directions is changed with every time step. The right side part of the equations is used to guarantee continuity. For a sequence starting with $\\mathrm{x}$-direction the advected material can be calculated as follows [29].", "start_char_idx": 374066, "end_char_idx": 377460, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2f999d21-3ab3-4714-81e1-d9f549839d98": {"__data__": {"id_": "2f999d21-3ab3-4714-81e1-d9f549839d98", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7dd3aa5e-7a2f-4994-b78b-cf5f743ce652", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e4dd4412fa520ab42a9392335a695eb9d18aa646a9e2ae21515154dc090d9150", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d86751ea-3a44-4a54-accc-f6647d3365e2", "node_type": "1", "metadata": {}, "hash": "e3b81e8c44644294c15bffea07b18ce03f8f8325307bbe61b96f28a793d2214f", "class_name": "RelatedNodeInfo"}}, "text": "$\\mathbf{n}=\\frac{\\nabla \\phi}{|\\nabla \\phi|}$\n\nThe equation is discretized using a central differencing scheme. Based on the information gained from the volume of fluid and level set function the advection of material from one element to another can be calculated for a known fluid flow velocity field $\\mathbf{u}[28]$.\n\n$\\frac{\\partial F}{\\partial t}+\\nabla \\cdot \\mathbf{u} F=F \\nabla \\cdot \\mathbf{u}$\n\nTo reach a higher accuracy the advection is calculated subsequently for $x$-, $y$ - and $z$-direction with reconstruction steps in between while the order in the sequence of directions is changed with every time step. The right side part of the equations is used to guarantee continuity. For a sequence starting with $\\mathrm{x}$-direction the advected material can be calculated as follows [29].\n\n$\\frac{F^{*}-F^{n-1}}{\\partial t}+\\frac{\\Delta u F^{n-1}}{\\partial x}=F^{*} \\frac{\\partial u}{\\partial x}$\n\n$\\frac{F^{* *}-F^{*}}{\\partial t}+\\frac{\\Delta v F^{*}}{\\partial y}=F^{*} \\frac{\\partial v}{\\partial y}$ $\\frac{F^{n}-F^{* *}}{\\partial t}+\\frac{\\Delta w F^{* *}}{\\partial z}=F^{*} \\frac{\\partial w}{\\partial z}$\n\nThe necessary melt flow field is calculated based on the current material configuration using a pressure implicit splitting of operators (PISO) scheme, as proposed by Issa [31], for solving the continuity and momentum equation (also known as Navier-Stokes equation).\n\n$\\nabla \\cdot \\mathbf{u}=0$\n\n$\\rho\\left(\\frac{\\partial \\mathbf{u}}{\\partial t}+\\mathbf{u} \\cdot \\nabla \\mathbf{u}\\right)=-\\nabla p+\\nabla \\cdot \\eta \\nabla \\mathbf{u}+\\frac{\\mathbf{b}}{V}$\n\nHere $\\eta$ is the dynamic viscosity, $p$ the pressure and $\\mathbf{b}$ the vector of forces. The momentum equation is solved discretizing it as a generalized transport problem and splitting the calculation of the fluid flow and pressure field [32]. In a prediction step the fluid flow velocities (here $x$-direction) are calculated using\n\n$a_{i, j, k}^{u} u_{i, j, k}^{*}=\\sum_{n b} a_{n b}^{u} u_{n b}^{*}+\\left(p_{i-1, j, k}^{*}-p_{i, j k}^{*}\\right) \\cdot A_{i, j, k}+b_{i, j, k}$\n\nin which $a_{i, j, k}^{u}$ and $a_{n b}^{u}$ are coefficients to the fluid flow velocities due to the discretization of the momentum equation, $u_{i, j, k}^{*}$ and $u_{n b}^{*}$ the predicted fluid flow velocities at element face $(i, j, k)$ and it's neighboring faces, $p^{*}$ the pressure in a first guess, $A$ the area and $F$ the forces at that face. The predicted velocities are then used to correct the pressure field [32].\n\n$p^{* *}=p^{*}+p^{\\prime}$\n\n$a_{i, j, k}^{p} p^{\\prime}{ }_{i, j, k}=\\sum_{n b} a_{n b}^{p} p^{\\prime}{ }_{n b}+c^{\\prime}{ }_{i, j, k}$\n\nHere $p^{\\prime}$ are the pressure correction values, $p^{* *}$ the corrected pressure value, $a^{p}$ are coefficients to the pressure field due to the discretization of the momentum equation and $c^{\\prime}$ is the correction of the error in continuity due to the predicted fluid flow velocities. After correcting the pressure field the velocity field can be corrected as well to reach a smaller error in continuity. In x-direction it can be achieved as follows [32].", "start_char_idx": 376657, "end_char_idx": 379765, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d86751ea-3a44-4a54-accc-f6647d3365e2": {"__data__": {"id_": "d86751ea-3a44-4a54-accc-f6647d3365e2", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2f999d21-3ab3-4714-81e1-d9f549839d98", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8c51c6c02f3e16a6f0d322f35f974294be551bf88c1c258ef617723404ca6cb8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "050af402-0229-4c39-913e-56586158718f", "node_type": "1", "metadata": {}, "hash": "51911b564fd475fe0e4d180aa814c7b1338039079fa78a12be80f1f7cc7ea23b", "class_name": "RelatedNodeInfo"}}, "text": "The predicted velocities are then used to correct the pressure field [32].\n\n$p^{* *}=p^{*}+p^{\\prime}$\n\n$a_{i, j, k}^{p} p^{\\prime}{ }_{i, j, k}=\\sum_{n b} a_{n b}^{p} p^{\\prime}{ }_{n b}+c^{\\prime}{ }_{i, j, k}$\n\nHere $p^{\\prime}$ are the pressure correction values, $p^{* *}$ the corrected pressure value, $a^{p}$ are coefficients to the pressure field due to the discretization of the momentum equation and $c^{\\prime}$ is the correction of the error in continuity due to the predicted fluid flow velocities. After correcting the pressure field the velocity field can be corrected as well to reach a smaller error in continuity. In x-direction it can be achieved as follows [32].\n\n$u_{i, j, k}^{* *}=u_{i, j, k}^{*}+\\frac{A_{i, j, k}}{a_{i, j, k}^{u *}}\\left(p^{\\prime}{ }_{i-1, j, k}-p^{\\prime}{ }_{i, j, k}\\right)$\n\nWithin the PISO scheme this correction is repeated once more to reach a higher level of continuity. Therefore while being an implicit method, it usually converges after only one iteration for sufficiently small time steps due to its double correction procedure.\n\nThe presented model considers the forces induced by the buoyancy effect $\\mathbf{b}_{b o u}$ and the forces due to the capillary effect for minimization of the surface energy $\\mathbf{b}_{\\text {cap }}$, the Marangoni effect $\\mathbf{b}_{\\text {mar }}$ and the force due to recoil pressure $\\mathbf{b}_{\\text {rec }}$ as driving forces. The latter three effects are restricted to surface elements, represented by the $\\delta(\\Phi)$-function which is zero for all non-surface elements. The forces which are considered in the fluid flow momentum equation are calculated using the following equations.\n\n$\\mathbf{b}_{\\text {bou }}=\\mathbf{g} \\cdot \\rho \\cdot V$\n\n$\\mathbf{b}_{\\text {cap }}=-\\mathbf{n} \\cdot \\sigma \\cdot \\kappa \\cdot A \\cdot \\delta(\\Phi)$\n\n$\\mathbf{b}_{\\text {mar }}=[(\\mathbf{I}-\\mathrm{n} \\otimes \\mathrm{n}) \\cdot \\nabla] \\cdot \\sigma \\cdot A \\cdot \\delta(\\Phi)$\n\n$\\mathbf{b}_{r e c}=\\mathbf{n} \\cdot p_{r e c} \\cdot A \\cdot \\delta(\\Phi)$\n\nIn these $\\mathbf{g}$ is the gravitational acceleration, $\\sigma$ the surface tension and $\\kappa$ the surface curvature.\n\nTable 1\n\nOverview of SS316L material data used in the numerical model [33,34]. Solidus temperature is at $1400^{\\circ} \\mathrm{C}$, liquidus at $1450^{\\circ} \\mathrm{C}$ and evaporation temperature at $2800^{\\circ} \\mathrm{C}$.", "start_char_idx": 379083, "end_char_idx": 381473, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "050af402-0229-4c39-913e-56586158718f": {"__data__": {"id_": "050af402-0229-4c39-913e-56586158718f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d86751ea-3a44-4a54-accc-f6647d3365e2", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "5ab6fb17afa448b7f3fecced229c99b9a94e609013889a0dc89fd61210bacdfb", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "534006e7-b01a-4a40-aaa0-7e9b5a84125b", "node_type": "1", "metadata": {}, "hash": "cf1197512e399d46f9952313fa276a5fa067feb3daaa48bbea99576758f3fb53", "class_name": "RelatedNodeInfo"}}, "text": "Table 1\n\nOverview of SS316L material data used in the numerical model [33,34]. Solidus temperature is at $1400^{\\circ} \\mathrm{C}$, liquidus at $1450^{\\circ} \\mathrm{C}$ and evaporation temperature at $2800^{\\circ} \\mathrm{C}$.\n\n\\begin{center}\n\\begin{tabular}{llllll}\n\\hline\nParameter & $25^{\\circ} \\mathrm{C}$ & $1400^{\\circ} \\mathrm{C}$ & $1450^{\\circ} \\mathrm{C}$ & $2800^{\\circ} \\mathrm{C}$ & Constant \\\\\n\\hline\nSpecific heat $[\\mathrm{J} / \\mathrm{kg} \\mathrm{K}]$ & 450 & 700 & 707 & 900 &  \\\\\nThermal conductivity [W/m K] & 13.3 & 33.8 & 18.1 & 22.2 &  \\\\\nSurface tension [N/m] &  &  & 1.76 & 0.41 &  \\\\\nDynamic viscosity [Pa s] &  &  & 0.0059 & 0.0014 &  \\\\\nHeat of fusion [J/kg] &  &  &  &  & 270,000 \\\\\nHeat of evaporation [J/kg] &  &  &  &  & $7,450,000$ \\\\\nHemispherical reflectance &  &  &  &  & 0.64 \\\\\n\\end{tabular}\n\\end{center}\n\nTable 2\n\nOverview of IN738LC material data used in the numerical model [35-38]. Solidus temperature is at $1250^{\\circ} \\mathrm{C}$, liquidus at $1350^{\\circ} \\mathrm{C}$ and evaporation temperature at $2950^{\\circ} \\mathrm{C}$.\n\n\\begin{center}\n\\begin{tabular}{llllll}\n\\hline\nParameter & $25^{\\circ} \\mathrm{C}$ & $1250{ }^{\\circ} \\mathrm{C}$ & $1350^{\\circ} \\mathrm{C}$ & $2950^{\\circ} \\mathrm{C}$ & constant \\\\\n\\hline\nSpecific heat [J/kg K] & 450 & 694 & 700 & 793 &  \\\\\nThermal conductivity [W/m K] & 9.8 & 26.5 & 26.95 & 27.0 &  \\\\\nSurface tension [N/m] &  &  & 1.85 & 0.15 &  \\\\\nDynamic viscosity [Pa s] &  &  & 0.0096 & 0.0024 &  \\\\\nHeat of fusion [J/kg] &  &  &  &  & 256,400 \\\\\nHeat of evaporation [J/kg] &  &  &  &  & $6,697,000$ \\\\\nHemispherical reflectance &  &  &  &  & 0.74 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\section*{3. Validation}\n\\subsection*{3.1. Material properties}\nThe material data which is used for the numerical model is listed in Tables 1 and 2. Both show the temperature dependent material data at room, solidus, liquidus and evaporation temperature as well as constant values. Data sets in between are taken from the listed references if available or otherwise are interpolated. Since the stainless steel 316L is already well known for good processing properties and the material data is available over a wide temperature range, the material is used as a baseline for the simulation. The material data of the nickel-based superalloy IN738LC on the other hand is not available in such detail especially within its liquid state. Therefore IN738LC is used as a material to check whether the simulation's results are as well usable to predict possible process parameters for materials with a higher uncertainty of material properties.\n\n\\subsection*{3.2. Experimental}\nThe numerical model is validated using cubic samples of stainless steel $316 \\mathrm{~L}$ as well as nickel-based superalloy IN738LC. The samples' uppermost layer is used to measure width, depth and the cross section area of multiple melt pool cross sections for every parameter set as illustrated in Fig. 4.", "start_char_idx": 381246, "end_char_idx": 384193, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "534006e7-b01a-4a40-aaa0-7e9b5a84125b": {"__data__": {"id_": "534006e7-b01a-4a40-aaa0-7e9b5a84125b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "050af402-0229-4c39-913e-56586158718f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d9e8a9c1e3c0404bfed2e2ae02b6fc5b5a3f23b4e5ffd9c5245c26879cacc71f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2c1738b7-c14c-47c2-9fcf-af6fa6386ca9", "node_type": "1", "metadata": {}, "hash": "2e2292387ac192cf94ac8fbf6bcd8e3e3beb26a17a6c8c3eb97fdd95ed2bd889", "class_name": "RelatedNodeInfo"}}, "text": "Since the stainless steel 316L is already well known for good processing properties and the material data is available over a wide temperature range, the material is used as a baseline for the simulation. The material data of the nickel-based superalloy IN738LC on the other hand is not available in such detail especially within its liquid state. Therefore IN738LC is used as a material to check whether the simulation's results are as well usable to predict possible process parameters for materials with a higher uncertainty of material properties.\n\n\\subsection*{3.2. Experimental}\nThe numerical model is validated using cubic samples of stainless steel $316 \\mathrm{~L}$ as well as nickel-based superalloy IN738LC. The samples' uppermost layer is used to measure width, depth and the cross section area of multiple melt pool cross sections for every parameter set as illustrated in Fig. 4. The depth is taken as the distance from the lowest to the highest point of the melt pool, the half width as the distance from the estimated center line to the outermost melt pool boundary, while the half melt pool cross section area is measured for the half of the melt pool which is not partly covered by the next track. The samples were manufactured on a ConceptLaser M2 utilizing a $200 \\mathrm{~W}$ continuous wave laser with a wavelength of $1070 \\mathrm{~nm}$ and Gaussian distribution. The samples were built up using layer-wise alternating scanning patterns (so that the hatching is rotated by $90^{\\circ}$ after every layer), hatch distance of $90 \\mu \\mathrm{m}$ and a layer thickness of $30 \\mu \\mathrm{m}$. For the stainless steel $316 \\mathrm{~L}$ scan speeds of $850 \\mathrm{~mm} / \\mathrm{s}, 1000 \\mathrm{~mm} / \\mathrm{s}, 1150 \\mathrm{~mm} / \\mathrm{s}, 1300 \\mathrm{~mm} / \\mathrm{s}$, $1450 \\mathrm{~mm} / \\mathrm{s}$ as well as $1600 \\mathrm{~mm} / \\mathrm{s}$ and for IN738LC scan speeds of $600 \\mathrm{~mm} / \\mathrm{s}, 750 \\mathrm{~mm} / \\mathrm{s}, 900 \\mathrm{~mm} / \\mathrm{s}, 1050 \\mathrm{~mm} / \\mathrm{s}$ as well as $1200 \\mathrm{~mm} / \\mathrm{s}$ were used.\n\nA cross section of the elaborated model is shown in Fig. 2, considering the layer thickness increase due to the powder's relative\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_4337cab3afd3e8e599dcg-05(1)}\n\\end{center}\n\nFig. 4. Illustration of the defined depth, width and cross section area measures used for validation.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_4337cab3afd3e8e599dcg-05}\n\\end{center}\n\nFig. 5. Time-resolved evolution of the absorbed laser power calculated using the described absorption model. Plotted ratios are of SS316L on the powder layer side using a scan speed of $1600 \\mathrm{~mm} / \\mathrm{s}$ and $200 \\mathrm{~W}$ laser power. The laser power which irradiates the pre-solidified track of the simulation model is not considered in this plot.\n\ndensity as well as an already consolidated line. The half width, depth and half cross section area data is extracted from the simulation model just on the side of the already consolidated line and therefore exactly like in the case of the experimental data.\n\n\\section*{4. Results and discussion}\n\\subsection*{4.1. Absorption characteristics}\nThe absorption model takes a crucial role in the numerical model. It directly influences the amount and distribution of the input energy and can thereby influence the melt pool dimensions as well as its dynamics. Therefore the absorption model is checked for reasonable behavior and magnitude of absorptance by monitoring the energy input along the simulated line. The regions of energy input are categorized into the parts of consolidated melt, non-consolidated melt which is defined by a powder like material configuration, the powder itself and the previous layer. Considering these categories, Fig.", "start_char_idx": 383300, "end_char_idx": 387148, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2c1738b7-c14c-47c2-9fcf-af6fa6386ca9": {"__data__": {"id_": "2c1738b7-c14c-47c2-9fcf-af6fa6386ca9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "534006e7-b01a-4a40-aaa0-7e9b5a84125b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2f1401492c4df625b8dcae232753287bc194cd1d1d0321497171e0e802dfc7cf", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "aae9544f-5c6f-4ebe-b167-15adb46d1de5", "node_type": "1", "metadata": {}, "hash": "31a18761cb1680108e83766b7a51733282414a99fa8088aea62c019e2944742f", "class_name": "RelatedNodeInfo"}}, "text": "density as well as an already consolidated line. The half width, depth and half cross section area data is extracted from the simulation model just on the side of the already consolidated line and therefore exactly like in the case of the experimental data.\n\n\\section*{4. Results and discussion}\n\\subsection*{4.1. Absorption characteristics}\nThe absorption model takes a crucial role in the numerical model. It directly influences the amount and distribution of the input energy and can thereby influence the melt pool dimensions as well as its dynamics. Therefore the absorption model is checked for reasonable behavior and magnitude of absorptance by monitoring the energy input along the simulated line. The regions of energy input are categorized into the parts of consolidated melt, non-consolidated melt which is defined by a powder like material configuration, the powder itself and the previous layer. Considering these categories, Fig. 5 exemplarily shows a reasonable time evolution of the calculated ratios of absorbed power on the powder layer side for a scan speed of $1600 \\mathrm{~mm} / \\mathrm{s}$ using the previously described absorption model. The absorbed powers are calculated relative to the input laser power. The different areas in which the power is absorbed are distinguished by temperature and material configuration. Previous layer and powder are defined by a tempera-\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_4337cab3afd3e8e599dcg-06}\n\\end{center}\n\nFig. 6. Overview of simulated average absorbed powers for different scan speeds and alloys.\n\nture below liquidus temperature. While the previous layer consists of completely filled elements, the powder elements are just partly filled. The melt is defined by a temperature above or equal the liquidus temperature and consolidated melt is indicated by completely filled elements below. Therefore, non-consolidated melt is defined by molten elements with a powder like material configuration in which elements below are just partly filled.\n\nAs the figure shows, starting from a powder covered solid material the melt pool evolves step by step. The irradiated area is continuously divided into a consolidated and non-consolidated melt as well as the powder part. In the beginning of this evolution the upper powder particle surfaces are irradiated and molten, keeping a more or less powder like structure and are therefore increasing the part of non-consolidated melt. With increasing time steps the amount of melt increases and consolidates into a melt pool so that the part of non-consolidated melt is restricted to the front of the moving laser spot. During these effects the amount of irradiated powder decreases because it is shrouded by the melt. Therefore the absorption ratios evolve significantly until a quasisteady state of the offset of melt pool front to focal spot center point is reached. These effects are represented in detail by the shown absorption ratio evolution indicating this distinct early stage of melt pool evolution. The total absorptance starts at its maximum because the laser irradiates solely powder which is characterized by its increased absorptance due to multiple reflections into the powder bed. The melting of the particle surfaces is represented by an increase of the non-consolidated melt ratio until it decreases to a steady state when the melt pool is consolidated. The absorption ratio of the consolidated melt is therefore continuously increasing while the total, powder's as well as the previous layer's absorption ratio is decreasing until the steady state is reached.\n\nThis distinct evolution of the absorption ratios can be observed for all simulated parameter sets of both alloys. But there are differ- ent magnitudes of absorption ratios as well as total absorptances. Fig. 6 shows these differences between the scan speeds and alloys.\n\nThe deviations between behaviors under different scan speeds need a closer look, while the magnitude of the averaged ratios can simply be explained by different values of the hemispherical reflectivity which are used in the absorption model. Both alloys show the same trends for increasing scan speeds. While the absorption ratio of consolidated melt decreases, the total, the powder's as well as the non-consolidated melt absorption ratios increase. Assuming a similar time of irradiation which is needed to melt the powder particles for a defined power input the offset from the front of the consolidated melt pool to the front of the focal spot increases. The higher offset leads to a larger area of irradiated powder and non-consolidated melt. The increase of powder's as well as non-consolidated melt's absorption ratio is higher than the decrease of the one of the consolidated melt because both powder and non-consolidated melt are characterized by a higher absorptance caused by multiple reflection and absorption. Considering these aspects the increase of the total absorptance with increasing scan speeds is reasonable as well.", "start_char_idx": 386204, "end_char_idx": 391227, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "aae9544f-5c6f-4ebe-b167-15adb46d1de5": {"__data__": {"id_": "aae9544f-5c6f-4ebe-b167-15adb46d1de5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2c1738b7-c14c-47c2-9fcf-af6fa6386ca9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7575724710fd3bf0111e40ced7c696b090baf7c85069d204add737dc478c80c7", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "8fa37669-000e-4385-88cb-ebb81931ffb1", "node_type": "1", "metadata": {}, "hash": "eb77beca734d014de7996f2e93c9529417907ba8479c0a570087b517ef529eb5", "class_name": "RelatedNodeInfo"}}, "text": "Both alloys show the same trends for increasing scan speeds. While the absorption ratio of consolidated melt decreases, the total, the powder's as well as the non-consolidated melt absorption ratios increase. Assuming a similar time of irradiation which is needed to melt the powder particles for a defined power input the offset from the front of the consolidated melt pool to the front of the focal spot increases. The higher offset leads to a larger area of irradiated powder and non-consolidated melt. The increase of powder's as well as non-consolidated melt's absorption ratio is higher than the decrease of the one of the consolidated melt because both powder and non-consolidated melt are characterized by a higher absorptance caused by multiple reflection and absorption. Considering these aspects the increase of the total absorptance with increasing scan speeds is reasonable as well. The simulation results of stainless steel 316L furthermore show a distinct drop of the melt pool absorption between scan speeds of $1000 \\mathrm{~mm} / \\mathrm{s}$ and $1150 \\mathrm{~mm} / \\mathrm{s}$ which disrupts the continuous increase of total absorption ratio. This drop can be explained by taking a deeper look into the melting behavior. While at $1000 \\mathrm{~mm} / \\mathrm{s}$ a deep-penetration welding-like mode can be observed, at $1150 \\mathrm{~mm} / \\mathrm{s}$ the mode changed to a more conduction driven mode, which shows less deep flanks of the recoil pressure driven cavity and therefore less multiple reflections and a lower absorption coefficient.\n\n\\subsection*{4.2. Melt pool dynamics}\nWhile high scan speeds result in flat and lens-like melt pools, lower scan speeds show an increasing tendency towards deeppenetration welding-like characteristics. Fig. 7 illustrates the differences in melt pool evolution as it shows the simulated data of SS316L with scan speeds of $850 \\mathrm{~mm} / \\mathrm{s}$ and $1600 \\mathrm{~mm} / \\mathrm{s}$ in comparison.\n\nThe low scan speed shows the development of a distinct cavity as the laser focal spot passes by. The evolution of the cavity even starts before the beam's center point reaches the cross section as soon as a small melt pool cross section is established. In the beginning it is supported by the melt consolidation on the powder side because the melt fills the void between the powder particles. The recoil pressure then increases as the surface temperature rises, so that the cavity grows and pushes the melt downwards as well as in radial directions. The maximum extent of the cavity is reached shortly after the beam's center point passed the cross section because the surface is first heated to the pressure dependent evaporation temperature and then the recoil pressure is maintained for a while by the decreasing energy input. The downward convection takes heat from the melt pool surface to the mushy zone at the melt pool bottom and therefore increases the rate of melting. Furthermore the laser energy is absorbed near to the solid material because of the cavity which leaves a small band of melt between the surrounding atmosphere and the solid material. After the laser beam passes, the recoil pressure drops due to the missing heat input and, as a result, the cavity in the cross section closes. So the melt which was pushed in radial directions fills the cavity, mainly driven by surface tension related effects as well as material is pushed backwards from the front of the melt pool. While the upper melt pool regions still melt some of the surrounding solid and powder material due to heat conduction, the lower regions of the melt pool start solidifying. A deeper look into the longitudinal sections of these two scan speeds in Fig. 8 shows that for $850 \\mathrm{~mm} / \\mathrm{s}$ the front of the melt pool is strongly influenced by the recoil pressure and there-\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_4337cab3afd3e8e599dcg-07(1)}\n\\end{center}\n\nFig. 7. Simulated evolution of melt pool geometry and surface distortion due to recoil pressure for a melt pool with deep-penetration welding tendencies $(850 \\mathrm{~mm} / \\mathrm{s})$ and a lens-like melt pool $(1600 \\mathrm{~mm} / \\mathrm{s})$ starting at room temperature. The laser beam is moving from the back towards the reader while $\\Delta x$ is the location difference between the laser beam's center point and the shown cross section. $d_{B}$ is equivalent to a $\\mathrm{D} 4 \\sigma$ beam diameter of $90 \\mu \\mathrm{m}$.", "start_char_idx": 390332, "end_char_idx": 394826, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "8fa37669-000e-4385-88cb-ebb81931ffb1": {"__data__": {"id_": "8fa37669-000e-4385-88cb-ebb81931ffb1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "aae9544f-5c6f-4ebe-b167-15adb46d1de5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7a9cb1fd6f89b57155f286ecfcb72cdac321b2c625b9d7dd16f27fde3f6de636", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5642b326-ae47-428a-a76d-449e98d4be78", "node_type": "1", "metadata": {}, "hash": "67420c4d0cfb6077e4bb3b9a4955538c3445fc4c572c12ac285cc4d6efb5aac7", "class_name": "RelatedNodeInfo"}}, "text": "7. Simulated evolution of melt pool geometry and surface distortion due to recoil pressure for a melt pool with deep-penetration welding tendencies $(850 \\mathrm{~mm} / \\mathrm{s})$ and a lens-like melt pool $(1600 \\mathrm{~mm} / \\mathrm{s})$ starting at room temperature. The laser beam is moving from the back towards the reader while $\\Delta x$ is the location difference between the laser beam's center point and the shown cross section. $d_{B}$ is equivalent to a $\\mathrm{D} 4 \\sigma$ beam diameter of $90 \\mu \\mathrm{m}$.\n\nfore suppressing the effect of the Marangoni convection. Therefore, the deep cavity develops and a small clockwise vortex to the back as well as vortices to the sides of the melt pool are established. Just behind the clockwise vortex another large counter clockwise vortex establishes due to the Marangoni convection leading from the outer regions of the cavity to the melt pool tail. The faster scan speed misses this strong suppression of the Marangoni convection in the melt pool front leading to the velocity configuration shown in Fig. 8 which therefore shows the difference between the welding modes.\n\nTherefore, the melt pool of the high scan speed misses this distinct cavity evolution. Thereby a shallow lens-like melt pool is formed. Naturally the energy input is lower due to the higher scan speed but the melt pool geometry and surface distortion in particular indicate the difference of the welding mode. The melt pool that is formed under high recoil pressures shows steeper flanks and a beginning differentiation of melt pool areas, meaning a deep and steep part in the line's center and a flat conduction driven outer area as it is typical for deep welding [39]. So the reduction of the energy density by $47 \\%$ due to the change of scan speeds from $1600 \\mathrm{~mm} / \\mathrm{s}$ to $850 \\mathrm{~mm} / \\mathrm{s}$ leads to a decrease of melt pool depth by $58 \\%$ and of cross section area by $57 \\%$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_4337cab3afd3e8e599dcg-07}\n\\end{center}\n\nFig. 8. Longitudinal sections of the simulated melt pool front and velocity distributions for $(850 \\mathrm{~mm} / \\mathrm{s})$ and $(1600 \\mathrm{~mm} / \\mathrm{s})$ for an incident laser beam moving from left to right.\n\n\\subsection*{4.3. Melt pool dimensions}\nEvaluating the results concerning the melt pool dimensions shown in Fig. 9, a good accordance of the simulation model to the experimental data can be noticed for the depth and width values over a wide set of scan speeds, while the area data deviates stronger.\n\nIn case of the SS316L all but one value of the depth and width data lay in the area of the standard deviation. The relative deviations of the simulation in comparison to the experimental average are all smaller than $20 \\%$, in most cases smaller than $10 \\%$. The values of the cross section area are deviating increasingly for lower scan speeds of SS316L. This is because of the simulation's starting temperatures which were set to room temperature. Therefore, they differ from the actual boundary conditions in the process. Considering that the energy input increases for lower scan speeds, it is obvious that the residual heat, which is the starting point for every new scanned line and layer, is as well higher for lower scan speeds. Thus it explains the increasing deviation of the cross section area for lower scan speeds.\n\nIn case of IN738LC the simulated melt pool depth deviates increasingly from the experimental ones for high scan speeds while the width matches the experimental data well. A mean deviation from the average values of $27.8 \\%$ in depth and of $6 \\%$ in width can be observed. But considering that the material data has a higher uncertainty due to inter- and extrapolation within its liquid state a still useful similarity to the experimental data with an overall average error in depth, width and area of $19.6 \\%$ can be achieved. Concerning the cross section area the same increasing deviation for slower scan speeds can be observed. Although there is a not explainable inverted trend from $750 \\mathrm{~mm} / \\mathrm{s}$ to $600 \\mathrm{~mm} / \\mathrm{s}$, it supports the explanation of different starting temperatures.\n\nTherefore, the series of process parameters for SS316L was recalculated with higher starting temperatures.", "start_char_idx": 394298, "end_char_idx": 398640, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5642b326-ae47-428a-a76d-449e98d4be78": {"__data__": {"id_": "5642b326-ae47-428a-a76d-449e98d4be78", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8fa37669-000e-4385-88cb-ebb81931ffb1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f135b7b218da6d02c9d1b3eaa025f2595142fb5c5bebefc989826a1428d267bc", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "721aae23-94ec-408e-b24a-06958fc9efda", "node_type": "1", "metadata": {}, "hash": "b4aea935b3e637c14fcb2d01a38a2c1c519c32e1fbd78d0ca423a788cdd02b48", "class_name": "RelatedNodeInfo"}}, "text": "In case of IN738LC the simulated melt pool depth deviates increasingly from the experimental ones for high scan speeds while the width matches the experimental data well. A mean deviation from the average values of $27.8 \\%$ in depth and of $6 \\%$ in width can be observed. But considering that the material data has a higher uncertainty due to inter- and extrapolation within its liquid state a still useful similarity to the experimental data with an overall average error in depth, width and area of $19.6 \\%$ can be achieved. Concerning the cross section area the same increasing deviation for slower scan speeds can be observed. Although there is a not explainable inverted trend from $750 \\mathrm{~mm} / \\mathrm{s}$ to $600 \\mathrm{~mm} / \\mathrm{s}$, it supports the explanation of different starting temperatures.\n\nTherefore, the series of process parameters for SS316L was recalculated with higher starting temperatures. For an illustration of this effect the starting temperatures were assumed as shown in Fig. 10 since the calculation of the remaining track temperature\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_4337cab3afd3e8e599dcg-08(2)}\\\\\nd)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_4337cab3afd3e8e599dcg-08(3)}\n\nFig. 9. Summary of the model validation results showing experimental average values and standard deviations in comparison to the simulated values of melt pool depth, width and cross section area of SS316L (a, c and e) and IN738LC (b, d and f).\n\n\\begin{center}\n\\begin{tabular}{c|cccccc}\n\\multicolumn{7}{c}{$\\mathrm{SS} 316 \\mathrm{~L}$} \\\\\n$\\mathrm{v}[\\mathrm{mm} / \\mathrm{s}]$ & 850 & 1000 & 1150 & 1300 & 1450 & 1600 \\\\\n\\hline\n$\\mathrm{T}_{0}\\left[{ }^{\\circ} \\mathrm{C}\\right]$ & 500 & 400 & 300 & 200 & 100 & 25 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_4337cab3afd3e8e599dcg-08}\\\\\nb)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_4337cab3afd3e8e599dcg-08(1)}\n\n$[\\mathrm{mm} / \\mathrm{s}]$\n\nexperimental\n\naverage\n\nstandard\n\ndeviation\n\n\\begin{itemize}\n  \\item simulation\n\\end{itemize}\n\nFig. 10. Comparison of simulated and experimental values for the melt pool depth (a), width (b) and cross section area (c) considering the sample temperature as an additional boundary condition for the stainless steel $316 \\mathrm{~L}$. is another challenge. As Fig. 10 shows, a far better accordance of the depth and cross section area values is achieved by considering the higher temperatures in the upper layers of the cubic samples. But the width deviations are slightly increased. By considering the higher temperatures as additional boundary conditions the overall mean error of the three considered dimensions for SS316L is reduced from $15.2 \\%$ to $12.8 \\%$. Since the simulated depth and width data for the elevated temperature series is similar or slightly higher than the experimental data, the difference of the cross section area needs to be explained by the melt pool geometry.\n\nBut the well matching values of the melt pool depth for high as well as low energy densities are remarkable, since most current models fail to achieve the experimentally observed depths. This supports the elaborated absorption and evaporation model because of the depths' strong dependence on the welding mode. The deviations in case of melt pool width are assumed to be mainly due to the fact that a dynamic contact angle of the melt to the previous layer is not yet implemented and therefore no typical spherical melt pool establishes which leads to more melting of powder due to heat conduction in the contact with the upper melt pool regions.\n\n\\subsection*{4.4. Evaluation of process parameters}\nThe key indicator for the evaluation of process parameters of the SLM process is the part density. To simulate the density as itself a high number of multiple track simulations would be necessary. But a rough prediction based on the simulated melt pool dimensions is possible as well.", "start_char_idx": 397711, "end_char_idx": 401711, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "721aae23-94ec-408e-b24a-06958fc9efda": {"__data__": {"id_": "721aae23-94ec-408e-b24a-06958fc9efda", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5642b326-ae47-428a-a76d-449e98d4be78", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "fa98d97f052d1d1a0f098569c7692f993b7d15b431facfa3e1ce44d69d48461f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6b8a7209-197b-4f1f-b495-5131a5fc1a7c", "node_type": "1", "metadata": {}, "hash": "50324b555065516f38d33c2d4c9a03ea980e2d36bcf2d53b5ef963348b7836e4", "class_name": "RelatedNodeInfo"}}, "text": "But the well matching values of the melt pool depth for high as well as low energy densities are remarkable, since most current models fail to achieve the experimentally observed depths. This supports the elaborated absorption and evaporation model because of the depths' strong dependence on the welding mode. The deviations in case of melt pool width are assumed to be mainly due to the fact that a dynamic contact angle of the melt to the previous layer is not yet implemented and therefore no typical spherical melt pool establishes which leads to more melting of powder due to heat conduction in the contact with the upper melt pool regions.\n\n\\subsection*{4.4. Evaluation of process parameters}\nThe key indicator for the evaluation of process parameters of the SLM process is the part density. To simulate the density as itself a high number of multiple track simulations would be necessary. But a rough prediction based on the simulated melt pool dimensions is possible as well. Considering that the porosity within a single melt pool is neglectable as long as no extensive deeppenetration welding occurs, the main reason for porosity in SLM are interlayer defects due to insufficient melting or melt pool overlapping. Therefore the simulated melt pool dimensions are well suited for a first evaluation, since the simulated maximum melt pool depth and width match the experimental results quite well even though a coarse mesh is used. Especially the remelted depth and width might be used for the evaluation. Both cannot be exactly measured from polished cross sections but from the simulation model. A remelted width lower than the hatch distance indicates a high risk for increasing porosity. Even more an overlap of both melt pools is necessary to assure that no powder remains unmolten within the layer. Furthermore experience shows that a remelting of more than 1.5 previous layers increases the chance of dense samples significantly. Elaborating these two criteria of hatch distance and remelted depth, a rough first approximation whether the parameter set leads to a nearly fully dense part or not is possible. Fig. 11 shows the simulated remelted depth and half width comparing them to the hatch distance and layer height and showing the relation to the achieved density of both investigated alloys.\n\nThe figure shows that both indicators are quite well suited as a first criterion to evaluate the usability of the process parameters to manufacture nearly fully dense parts since the porosity significantly increases as soon as the predicted values are less than the anticipated values. But in most cases just a residual porosity of $0.5 \\%$ is accepted so that both indicators are overrating the usability of the evaluated parameter set. Taking these indicators as a basis, the simulation results offer a chance to set several of the simulated melt pool measures into relation. The ratio of remelted depth to half remelted width shows the most promising correlation to the density. As Fig. 12 shows the porosity significantly increases if the remelted depth to half remelted width ratio drops below 1. Furthermore this value corresponds remarkably well to the usually defined value of $0.5 \\%$ residual porosity for the usability of manufactured parts even for IN738LC for which more uncertain material data had to be used.\n\nThis ratio as well has a melt pool shape related meaning since it represents the geometry of the shape of the remelted material.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_4337cab3afd3e8e599dcg-09}\n\nFig. 11. Comparison of simulated remelted depth and width to the indicators of hatch distance and 1.5 times layer height as well as the measured part porosity of SS316L and IN738LC.\n\nWhile a value smaller than 1 implies that the remelted part takes on a shallow elliptical shape, a value greater than 1 means a deep melt pool with a trend to a keyhole like shape for higher values. Considering the relation of this value to the achieved density it can be shown that the most productive way to form dense parts with a Gaussian beam is right on the edge of heat conduction melting and a starting keyhole supported melting process. For higher scan speeds the density decreases rapidly because of the decrease of remelted width and depth that lead to an increase in interlayer defects due to insufficient melting. Slower scan speeds only offer very low density increases because of a higher rate of remelting and therefore a higher chance to remove defects by following tracks and layers. But by using slower scan speeds the evaporation of material increases significantly. Furthermore the intensity of deep-penetration welding is increased, resulting in a higher possibility for porosity within the melt pool due to the collapse of the keyhole.", "start_char_idx": 400727, "end_char_idx": 405524, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "6b8a7209-197b-4f1f-b495-5131a5fc1a7c": {"__data__": {"id_": "6b8a7209-197b-4f1f-b495-5131a5fc1a7c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "721aae23-94ec-408e-b24a-06958fc9efda", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e69d1925d4e38a44fd0a70a34e6ec8c33d4b41719f20654a87bc35f4e3f68c87", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "567be920-ee12-41f7-a700-8a7a027b6b67", "node_type": "1", "metadata": {}, "hash": "c12de36392820e87e187e8820ca34843dc0b31aec328d6de4b3263343c75d8e6", "class_name": "RelatedNodeInfo"}}, "text": "Considering the relation of this value to the achieved density it can be shown that the most productive way to form dense parts with a Gaussian beam is right on the edge of heat conduction melting and a starting keyhole supported melting process. For higher scan speeds the density decreases rapidly because of the decrease of remelted width and depth that lead to an increase in interlayer defects due to insufficient melting. Slower scan speeds only offer very low density increases because of a higher rate of remelting and therefore a higher chance to remove defects by following tracks and layers. But by using slower scan speeds the evaporation of material increases significantly. Furthermore the intensity of deep-penetration welding is increased, resulting in a higher possibility for porosity within the melt pool due to the collapse of the keyhole. Considering these effects as well as the common uncertainty of the SLM process it is preferable to stay on the deep-penetration welding-like side rather than right on the edge to conduction welding. So a small drop in heat input due to spatter or evaporated material will not drastically increase the chance for interlayer defects. For a general applicability this indicator first has to be evaluated for more alloys and different machine configurations but it works well for the presented parameters.\n\n\\section*{5. Conclusion}\nThe SLM process is in need for increases in productivity and part quality. Instead of using extensive designs of experiment to\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_4337cab3afd3e8e599dcg-09(1)}\n\nFig. 12. Comparison of the ratio of remelted depth to half remelted width to the measured porosity as an indicator of parameter usability.\n\nfind parameter sets for dense material, simulation offers a chance to save time and money when changing to a new material or when changing the machine set-up, like to higher laser powers or higher layer thicknesses. This paper shows what is necessary to include in such a simulation model to get a good agreement with experimental data and why. First a detailed energy absorption model is necessary which distinguishes between powder, melt and solid material to get to a reasonable heat input and therefore a reasonable temperature field. The temperature field directly influences the second main aspect which is the representation of melt flow driven by capillary forces, Marangoni convection and the recoil pressure. Especially the recoil pressure is of high importance due to its high influence on the melt pool dynamics. The last not necessary but recommendable aspect is a reliable representation of the powder bed that offers a detailed representation of the consolidation mechanism at low calculation effort. The presented model includes all of these aspects and leads to a good accordance of simulated and experimental data at comparably low calculation effort for a wide range of scan speeds and two different materials. Although the powder bed is homogenized and a quite coarse mesh is used compared to current high fidelity simulations, all significant effects can be observed within the presented simulation results. Furthermore it is shown that the simulated data is well suited to easily evaluate the processing parameters regarding density and productivity based on remelted depth and width and therefore to effectively narrowing down the necessary experimental effort to get to dense and productive processing parameters even when using more uncertain material data.\n\n\\section*{6. Outlook}\nFurther on, the numerical model will be validated for other processing parameters like higher laser powers and higher layer thicknesses. Furthermore the validated model is used to evaluate new and innovative strategies to influence the melt pool dynamics by tailoring the intensity profiles of one or more beams. Both aspects are already underway and are offering promising results.\n\n\\section*{Acknowledgement}\nThe authors gratefully acknowledge the financial support of the Bosch Research Foundation.\n\n\\section*{References}\n[1] M. Rombouts, J.P. Kruth, L. Froyen, P. Mercelis, Fundamentals of selective laser melting of alloyed steel powders, CIRP Ann. Manuf. Technol. 55 (2006) 187-192, \\href{http://dx.doi.org/10.1016/S0007-8506(07)60395-3}{http://dx.doi.org/10.1016/S0007-8506(07)60395-3}.\n\n[2] R. Morgan, C.J. Sutcliffe, W. O\u2019Neill, Density analysis of direct metal laser re-melted 316L stainless steel cubic primitives, J. Mater. Sci.", "start_char_idx": 404665, "end_char_idx": 409156, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "567be920-ee12-41f7-a700-8a7a027b6b67": {"__data__": {"id_": "567be920-ee12-41f7-a700-8a7a027b6b67", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "6b8a7209-197b-4f1f-b495-5131a5fc1a7c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ca9d28a0e91f177a07c407a0521038b24ed3fd500560b50dea816cf96919aa4d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a1ef293c-5471-4ea8-9aa1-1a278d7a75e9", "node_type": "1", "metadata": {}, "hash": "adc33496fb92772ea28d9eb25af897f1e24f223ac03201fd574366b05b7a6baa", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{Acknowledgement}\nThe authors gratefully acknowledge the financial support of the Bosch Research Foundation.\n\n\\section*{References}\n[1] M. Rombouts, J.P. Kruth, L. Froyen, P. Mercelis, Fundamentals of selective laser melting of alloyed steel powders, CIRP Ann. Manuf. Technol. 55 (2006) 187-192, \\href{http://dx.doi.org/10.1016/S0007-8506(07)60395-3}{http://dx.doi.org/10.1016/S0007-8506(07)60395-3}.\n\n[2] R. Morgan, C.J. Sutcliffe, W. O\u2019Neill, Density analysis of direct metal laser re-melted 316L stainless steel cubic primitives, J. Mater. Sci. 39 (2004) 1195-1205, \\href{http://dx.doi.org/10.1023/B:JMSC.0000013875.62536.fa}{http://dx.doi.org/10.1023/B:JMSC.0000013875.62536.fa}.\n\n[3] L. Rickenbacher, T. Etter, S. H\u00f6vel, K. Wegener, High temperature material properties of IN738LC processed by selective laser melting (SLM) technology, Rapid Prototyp. J. 19 (2013) 282-290, \\href{http://dx.doi.org/10.1108/}{http://dx.doi.org/10.1108/} 13552541311323281\n\n[4] Z. Wang, K. Guan, M. Gao, X. Li, X. Chen, X. Zeng, The microstructure and mechanical properties of deposited-IN718 by selective laser melting, J. 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Des. 34 (2012) 159-169, \\href{http://dx.doi.org/10.1016/j.matdes.2011.07.067}{http://dx.doi.org/10.1016/j.matdes.2011.07.067}.\n\n[9] F.S.", "start_char_idx": 408600, "end_char_idx": 411109, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a1ef293c-5471-4ea8-9aa1-1a278d7a75e9": {"__data__": {"id_": "a1ef293c-5471-4ea8-9aa1-1a278d7a75e9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "567be920-ee12-41f7-a700-8a7a027b6b67", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d06a4ba2c171a2fdd79e72a1c4c20af81c809ae4908712cfc2abb07458f2cc14", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "19336133-9aeb-4e6a-b5ce-6ae1a21ce829", "node_type": "1", "metadata": {}, "hash": "93edd2919ff569871df6b188dea45ce7598607c07d869e170132dc690386e272", "class_name": "RelatedNodeInfo"}}, "text": "Process. 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Technol. 214 (2014) 2915-2925, \\href{http://dx.doi.org/10.1016/j.jmatprotec.2014.06.005}{http://dx.doi.org/10.1016/j.jmatprotec.2014.06.005}.\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{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{multirow}\n\n\\title{Determination of melt pool dimensions using DOE-FEM and RSM with process window during SLM of Ti6Al4V powder }\n\n\\author{}\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 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"hash": "1cd24a2f7beadd0de07acea3cc2aca1d6982fae73022ffd21d7f8c797b5d8609", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1129b598-535d-4559-9281-95ef0f5a50ed", "node_type": "1", "metadata": {}, "hash": "62f27e772bbd3a84f24b9aa2518b62f14fdcacdde80ee2c472fc8fc605dc26c6", "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\\textbackslash author\\{\\\\\nJyun-Rong Zhuang a, Yee-Ting Lee ${ }^{b}$, Wen-Hsin Hsieh ${ }^{c}$, An-Shik Yang b,*\n\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-01} \\\\\n ${ }^{\\mathrm{b}}$ Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 106, Taiwan, ROC \\\\\n 'Department of Mechanical Engineering, National Chung-Cheng University, Chiayi 621, Taiwan, ROC\\\\\n\\}\n\n\\section*{A R T I C L E I N F O}\n\\section*{Article history:}\nReceived 1 May 2017\n\nReceived in revised form 21 November 2017 Accepted 5 January 2018\n\nAvailable online 12 January 2018\n\n\\section*{Keywords:}\nSelective laser melting (SLM)\n\nDesign of experiment (DOE)\n\nResponse Surface Method (RSM)\n\nMelt pool dimensions\n\nProcess window\n\nTitanium alloy\n\n\\begin{abstract}\nA B S T R A C $T$ Selective laser melting (SLM) shows a positive prospect as an additive manufacturing (AM) technique for fabrication of 3D parts with complicated structures. A transient thermal model was developed by the finite element method (FEM) to simulate the thermal behavior for predicting the time evolution of temperature field and melt pool dimensions of Ti6Al4V powder during SLM. The FEM predictions were then compared with published experimental measurements and calculation results for model validation. This study applied the design of experiment (DOE) scheme together with the response surface method (RSM) to conduct the regression analysis based on four processing parameters (exactly, the laser power, scanning speed, preheating temperature and hatch space) for predicting the dimensions of the melt pool in SLM. The preliminary RSM results were used to quantify the effects of those parameters on the melt pool size. The process window was further implemented via two criteria of the width and depth of the molten pool to screen impractical conditions of four parameters for including the practical ranges of processing parameters. The FEM simulations confirmed the good accuracy of the critical RSM models in the predictions of melt pool dimensions for three typical SLM working scenarios.\n\\end{abstract}\n\n\u0e51C 2018 Elsevier Ltd. All rights reserved.\n\n\\section*{1. Introduction}\nTitanium alloys have very high tensile strength, light weight, good biocompatibility and superior corrosion resistance at even extreme temperatures $[1,2]$. For applications, titanium alloys have been broadly used in various fields such as aerospace, biomedical and automotive industries in recent years. However, titanium alloys are difficult-to-machine materials due to their high strength, low thermal conductivity and high chemical reactivity. Additionally, the slow solidification rates would produce the coarsened microstructures and the large degrees of segregation during the conventional casting processes [3]. As a result, further processing technologies are needed to maintain titanium components with great performance.\n\nAdditive manufacturing (AM), also known as three-dimensional (3D) printing, is the process of direct fabrication for 3D objects in a layer-by-layer fashion.", "start_char_idx": 420426, "end_char_idx": 424200, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1129b598-535d-4559-9281-95ef0f5a50ed": {"__data__": {"id_": "1129b598-535d-4559-9281-95ef0f5a50ed", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1eefb9eb-150d-4efc-8b36-ef62891c1f55", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9bde7f8934415e6a47992c2df13d48419044518012c9d297e8e734d39b07b8e6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "4b179417-a95d-4f28-a82d-694b2300d7b1", "node_type": "1", "metadata": {}, "hash": "a4681cbd34c2e07f695c4f1b98d319a6e10998fa91a6f770d757b8eefab2ef6a", "class_name": "RelatedNodeInfo"}}, "text": "\\end{abstract}\n\n\u0e51C 2018 Elsevier Ltd. All rights reserved.\n\n\\section*{1. Introduction}\nTitanium alloys have very high tensile strength, light weight, good biocompatibility and superior corrosion resistance at even extreme temperatures $[1,2]$. For applications, titanium alloys have been broadly used in various fields such as aerospace, biomedical and automotive industries in recent years. However, titanium alloys are difficult-to-machine materials due to their high strength, low thermal conductivity and high chemical reactivity. Additionally, the slow solidification rates would produce the coarsened microstructures and the large degrees of segregation during the conventional casting processes [3]. As a result, further processing technologies are needed to maintain titanium components with great performance.\n\nAdditive manufacturing (AM), also known as three-dimensional (3D) printing, is the process of direct fabrication for 3D objects in a layer-by-layer fashion. Selective laser melting (SLM) demonstrates a promising potential as a lately developed AM technique for fab-\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author at: Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, 1, Sec. 3, ChungHsiao E. Rd., Taipei 106, Taiwan, ROC.\n\\end{itemize}\n\nE-mail address: \\href{mailto:asyang@ntut.edu.tw}{asyang@ntut.edu.tw} (A.-S. Yang).\n}\n\nrication of 3D parts with complex structures [4-7]. The SLM process can be also applied to precision part manufacturing $[3,8]$. In practice, SLM technology applied a high energy laser beam to selectively scan thin loose powder layers to generate melting and consolidation from a CAD model within milliseconds. As a result, the powders can be melted with higher-density parts formed by SLM, and thereby shape a final model with high mechanical properties [9]. SLM is usually performed in a neutral gas, nitrogen or argon gas, to protect the molten pool from oxidation. Considering as the concerned issues involving the operations of SLM, relocating a high energy density of laser beam on a powder bed can produce elevated thermal gradients, which may result in the undesired shrinkage variations, non-homogeneous thermal cracks and residual stresses distributed within consolidated layers [10].\n\nThe laser based SLM technique involves a complex process of heat and mass transfer including conduction, convection and radiation. Significant efforts were made to explore the thermal behavior and laser melting operational characteristics in the SLM process. Hussein et al. [11] and Craeghs et al. [12] analyzed the process parameters such as the laser power, scan velocity, preheating temperature and layer thickness affecting the formation of melt pool size as well as the dimension accuracy control and final features of SLM parts.", "start_char_idx": 423224, "end_char_idx": 426070, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "4b179417-a95d-4f28-a82d-694b2300d7b1": {"__data__": {"id_": "4b179417-a95d-4f28-a82d-694b2300d7b1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1129b598-535d-4559-9281-95ef0f5a50ed", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a1caa6a8e695b829761eb620aac306e44dc11a7b2ee5f664d73c688f30281f0f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fd8cf096-0a14-475a-9f62-dff4acff37df", "node_type": "1", "metadata": {}, "hash": "a039c45c0578e6f0b98f53c3b963bb1de90a351723e85beefe06c2f348492ea7", "class_name": "RelatedNodeInfo"}}, "text": "SLM is usually performed in a neutral gas, nitrogen or argon gas, to protect the molten pool from oxidation. Considering as the concerned issues involving the operations of SLM, relocating a high energy density of laser beam on a powder bed can produce elevated thermal gradients, which may result in the undesired shrinkage variations, non-homogeneous thermal cracks and residual stresses distributed within consolidated layers [10].\n\nThe laser based SLM technique involves a complex process of heat and mass transfer including conduction, convection and radiation. Significant efforts were made to explore the thermal behavior and laser melting operational characteristics in the SLM process. Hussein et al. [11] and Craeghs et al. [12] analyzed the process parameters such as the laser power, scan velocity, preheating temperature and layer thickness affecting the formation of melt pool size as well as the dimension accuracy control and final features of SLM parts. The former found an increase in the\n\n\\section*{Nomenclature}\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline\n$A$ & laser energy absorptance of a material & $R a_{L}$ & Rayleigh number \\\\\n\\hline\nc & specific heat, J/kg K & $R$ & radius of the Gaussian heat source \\\\\n\\hline\n$D_{P}$ & average diameter of the powder particles, $m$ &  & beam, $\\mathrm{m}$ \\\\\n\\hline\n$F_{0}$ & view factor & $T_{m}$ & melting temperature, $\\mathrm{K}$ \\\\\n\\hline\n$G_{r}$ & Grashof numbers & $T_{o}$ & preheating temperature, $\\mathrm{K}$ \\\\\n\\hline\n$H$ & enthalpy, $\\mathrm{J} / \\mathrm{m}^{3}$ & $T_{P}$ & temperature of powder particles, $\\mathrm{K}$ \\\\\n\\hline\n$h$ & convective heat transfer coefficient, $\\mathrm{W} / \\mathrm{m}^{2} \\mathrm{~K}$ & $T_{\\infty}$ & ambient temperature, $/{ }^{\\circ} \\mathrm{C}$ \\\\\n\\hline\n$k_{f}$ & thermal conductivity of atmosphere, $\\mathrm{W} / \\mathrm{m} \\mathrm{K}$ & $x, y, z$ & Coordinates \\\\\n\\hline\n$k_{r}$ & thermal conductivity due to radiation, $\\mathrm{W} / \\mathrm{m} \\mathrm{K}$ & $\\beta_{f}$ & volumetric expansivity, $/{ }^{\\circ} \\mathrm{C}$ \\\\\n\\hline\n$k_{s}$ & thermal conductivity of solid, $\\mathrm{W} / \\mathrm{m} \\mathrm{K}$ & $\\rho$ & material density, $\\mathrm{kg} / \\mathrm{m}^{3}$ \\\\\n\\hline\n$l$ & length of scanning track, $m$ & $\\rho_{f}$ & fluid density, $\\mathrm{kg} / \\mathrm{m}^{3}$ \\\\\n\\hline\n$L$ & moving distance, $\\mathrm{m}$ & $\\rho_{s}$ & solid density, $\\mathrm{kg} / \\mathrm{m}^{3}$ \\\\\n\\hline\n$N_{t}$ & number of track & $\\rho_{p}$ & powder density \\\\\n\\hline\n$q$ & input heat flux, $\\mathrm{W} / \\mathrm{m}^{2}$ &  & $\\left.\\mathrm{~m}^{2} \\mathrm{~K}^{4}\\right)$ \\\\\n\\hline\n$q_{c o n}$ & convection heat flux, $\\mathrm{W} / \\mathrm{m}^{2}$ &  &  \\\\\n\\hline\n$q_{\\text {rad }}$ & heat radiation heat flux, $\\mathrm{W} / \\mathrm{m}^{2}$ &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\npredicted length of the melt pool at higher scan speed with both width and depth of the melt pool decreased. High VonMises stresses were also noted in the consolidated layers due to the cyclic melting and cooling rates in the scanned tracks. With the use of static processing parameters at downfacing planes, the latter observed bad surface quality at these planes on account of the outsized melt pool. Childs et al.", "start_char_idx": 425100, "end_char_idx": 428315, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fd8cf096-0a14-475a-9f62-dff4acff37df": {"__data__": {"id_": "fd8cf096-0a14-475a-9f62-dff4acff37df", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "4b179417-a95d-4f28-a82d-694b2300d7b1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b5b3011312615bd8a25b62c2058a1bbb5d1ebeda4fdd01f5e54a16b24402ff11", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "de8617e6-0700-40f5-9e1d-c0133d8c5f4b", "node_type": "1", "metadata": {}, "hash": "5f0644672e51641a25571d46c15bacedaff52877e58c5c648faef8cb002662e9", "class_name": "RelatedNodeInfo"}}, "text": "High VonMises stresses were also noted in the consolidated layers due to the cyclic melting and cooling rates in the scanned tracks. With the use of static processing parameters at downfacing planes, the latter observed bad surface quality at these planes on account of the outsized melt pool. Childs et al. [13] investigated the relationship of the processing parameters with molten mass for a $\\mathrm{CO}_{2}$ laser beam focused to $0.55 \\mathrm{~mm}$ and $1.1 \\mathrm{~mm}$ diameters, scanning over those beds made from M2 and $\\mathrm{H} 13$ tool steel and 314S-HC stainless steel powders in the SLM development. It was noted that the structure of the powder bed and size of particles could affect penetration of radiation into the bed and the consequent densification in the partial melting regime. Zaeh and Branner [14] described that those SLM parts (using tool steel 1.2709, X3NiCoMoTi18-9-5 alloy) with a thinner layer thickness were susceptible to deformation because of elevated temperature variations. The initial platform temperature was identified to be the major influence on the occurring deformations of the shaped cantilever. The scanning strategy and the layer size were indicated as a minor impact with larger layer sizes of $70 \\mu \\mathrm{m}$ produced additionally reduced deformations. The layer-based detail model was found to be an essential requirement for determining the deformations and residual stresses with an augmented precision. Mumtaz and Hopkinson [15] experimentally examined the selective laser melting of Inconel 625 by an Nd:YAG pulsed laser to produce thin wall parts with minimum top surface and side surface roughness. Higher peak powers tended to reduce both top surface roughness and side roughness as recoil pressures flatten out the melt pool and ease balling formation by increasing wettability of the melt. Nevertheless, higher repetition rate and lower scan speed reduced top surface roughness but increased side roughness. Using a two-dimensional (2D) formulation, Ilin et al. [16] adopted the Goldak's heat source model to predict the melt pool size and the temperature distribution of the 316L-steel bulk and powder materials. The increasing width of the melt pool near the border was perceived by the local increasing of the powder amount in the vicinity of the fusing zone. The further numerical analysis also showed the attainment of decreasing the melt pool width via increasing the scanning speed for stabilizing the laser beam melting process and enhancing the accuracy of the sample dimensions. From the predictions of unsteady temperature field for TiAl6V4 powder layers during the additive layer manufacturing (ALM) process, Roberts et al. [17] indicated rapid thermal cycles with commensurate thermal stress cycles occurred at laser heated regions.\n\nIn fact, the experimental measurements of SLM practice are considered to be difficult since it involves many details of localized laser heating, superfast melting and solidification. Numerical simulation has become a powerful tool to comprehend the underlying mechanisms behind the phenomena of SLM. The finite element method is the widely used computational method for predicting temperature and stress fields in the SLM procedure. Using a 3D finite element model to resolve the temperature field, Dai and Shaw [18] investigated the effect of the volume shrinkage due to transformation from a powder compact to dense liquid on the temperature field, size and shape of laser-densified dental porcelain bodies. Different criteria were proposed to judge the state of element by considering the possible occurrence of volume shrinkage associated with the powder conversion process during laser densification. Germain et al. [19] carried out the finite element method (FEM)-based thermal numerical simulations by Abaqus/Standard ${ }^{\\circledR}$ to resolve the shape and size of heat affected zone (HAZ) in two metals (100Cr6/AISI52100 and Ti6Al4V) all over moving laser irradiation. It was observed that the surface roughness was not affected by the laser power. Yang et al. [20] presented a 3D FEM model to predict the HAZ in the Ti6Al4V plate work piece by a moving Gaussian laser beam. The size of the HAZ was found to be closely related to the laser power, speed, and spot size. Foroozmehr et al. [21] conducted the FEM computations to simulate laser melting of a single layer of stainless steel 316L on a thick powder bed at scan speeds of 80,100 , and $150 \\mathrm{~mm} / \\mathrm{s}$.", "start_char_idx": 428008, "end_char_idx": 432510, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "de8617e6-0700-40f5-9e1d-c0133d8c5f4b": {"__data__": {"id_": "de8617e6-0700-40f5-9e1d-c0133d8c5f4b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fd8cf096-0a14-475a-9f62-dff4acff37df", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "33ea2ec37bc37fad99f46d5eae7a9ca7ce7d42f49331054956a6f984ed12ffc5", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0d957139-e7c3-4bbd-9207-c5fe2e7cec96", "node_type": "1", "metadata": {}, "hash": "97e9fa77e63278eedb356424f425bea3a95eef033bd29f22c9ac888779d70d93", "class_name": "RelatedNodeInfo"}}, "text": "It was observed that the surface roughness was not affected by the laser power. Yang et al. [20] presented a 3D FEM model to predict the HAZ in the Ti6Al4V plate work piece by a moving Gaussian laser beam. The size of the HAZ was found to be closely related to the laser power, speed, and spot size. Foroozmehr et al. [21] conducted the FEM computations to simulate laser melting of a single layer of stainless steel 316L on a thick powder bed at scan speeds of 80,100 , and $150 \\mathrm{~mm} / \\mathrm{s}$. The results showed that the melt pool dimensions reached a steady condition after\\\\\nthe third track. The melt pool depth of each track also stayed nearly constant after around $2 \\mathrm{~mm}$ from the beginning of the track. Though past studies indicated that the processing characteristics including the design and operational variables can substantially affect the structure of melt pool change, the study of employing the design of experiment (DOE) scheme along with the response surface method (RSM) for modeling of the process parameters in SLM machining applications has not been done before. In this research, a computational DOE-FEM approach based on a timedependent analysis was developed to characterize the thermal behavior of TiAl6V4 powder bed over the laser melting course, which is validated by the preceding computational and experimental results. The purpose of this study is to explore the effects of important processing parameters consisting of the laser power, scanning speed, preheating temperature and hatch space between two neighboring tracks on the predicted time sequences of temperature distribution and melt pool dimensions of Ti6Al4V powder during SLM. RSM was then used to quantify the relationship between the input processing parameters (including the laser power, scanning speed, preheating temperature and hatch space) and the response factors (i.e., the length, width and depth of melt pool) with the preliminary RSM correlations produced by the multiple regression method. The analysis of variance (ANOVA) was also employed to explore the significance of the developed regression model and each processing parameter in SLM. We further proposed the process window procedures to verify the ranges of the input processing parameters with the quality criteria, and thus preclude the improper setting of parameters for achieving practical combinations. In the end, we incorporated the justified processing parameters from the process window into the critical RSM responses to realize the accurate predictions of the melt pool extent of Ti6Al4V powder during SLM.\n\n\\section*{2. Theoretical formulation}\n\\subsection*{2.1. Physical description of SLM}\nFig. 1 shows a schematic of the thermal behavior between laser radiation and powder bed disposed on the dense substrate during\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-03(1)}\n\\end{center}\n\nFig. 1. Schematic of the thermal behavior between laser radiation and powder bed during SLM process.\\\\\nSLM process. The environment is full of inert gas (i.e. Argon (Ar) in this case) to evade corrosion. When the laser beam irradiates the surface of a powder bed, a small fraction of the laser energy can be reflected and dissipated by radiation and convection. The remainder of laser energy is absorbed by the powder layers and thereby results in rapid heating and localized melting with the formation of a molten pool. After the moving laser heat source leaves with swift consolidation occurred, the metallurgical bonding is developed between the neighboring tracks and the lower layers. Furthermore, the inherent complexities of thermal transport within the powder beds, the thermal heat losses caused by convection and radiation within the heat transfer mechanism of SLM process should also be considered for properly characterizing the thermal behavior.\n\n\\subsection*{2.2. Finite element analysis}\nThis research used the FEM software package ANSYS ${ }^{\\circledR}$ (Workbench v16.0) to conduct the thermo-mechanical coupling analysis for exploring the thermal essentials of laser melting development. A 3D FEM model, including all detailed structure parts, was constructed using ANSYS ${ }^{\\circledR}$ for the predictions of the time-varying temperature field and associated phenomena such as deformation, temperature gradients and metallurgical defects during the SLM process. Fig.", "start_char_idx": 432003, "end_char_idx": 436418, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0d957139-e7c3-4bbd-9207-c5fe2e7cec96": {"__data__": {"id_": "0d957139-e7c3-4bbd-9207-c5fe2e7cec96", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "de8617e6-0700-40f5-9e1d-c0133d8c5f4b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c6f6377f2e37b541da57d8763e7de6d251077358645be964fb76a4e90c0e9716", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0e2b876c-c641-4ee2-936d-528842b799a0", "node_type": "1", "metadata": {}, "hash": "b14af579f630e20ab8a8938614690b8f7b96162197ee866cb514d6958f64a4a0", "class_name": "RelatedNodeInfo"}}, "text": "After the moving laser heat source leaves with swift consolidation occurred, the metallurgical bonding is developed between the neighboring tracks and the lower layers. Furthermore, the inherent complexities of thermal transport within the powder beds, the thermal heat losses caused by convection and radiation within the heat transfer mechanism of SLM process should also be considered for properly characterizing the thermal behavior.\n\n\\subsection*{2.2. Finite element analysis}\nThis research used the FEM software package ANSYS ${ }^{\\circledR}$ (Workbench v16.0) to conduct the thermo-mechanical coupling analysis for exploring the thermal essentials of laser melting development. A 3D FEM model, including all detailed structure parts, was constructed using ANSYS ${ }^{\\circledR}$ for the predictions of the time-varying temperature field and associated phenomena such as deformation, temperature gradients and metallurgical defects during the SLM process. Fig. 2 illustrates the schematics depicting (a) the established 3D FEM model and (b) the laser scan strategy during SLM\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-03(2)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-03}\n\\end{center}\n\n(b)\n\nFig. 2. Schematic depicting (a) established 3D FEM model and (b) laser scan strategy during SLM process.\\\\\nprocess. A TiAl6V4 powder layer with the dimensions of $3 \\mathrm{~mm} \\times 3$ $\\mathrm{mm} \\times 0.03 \\mathrm{~mm}$ were placed on a dense substrate with the size of $3 \\mathrm{~mm} \\times 3 \\mathrm{~mm} \\times 1 \\mathrm{~mm}$ depicted in Fig. 2(a). In practice, the layer was processed progressively in the pattern of five scanning tracks as depicted in Fig. 2(b). The heat flux from a mobile laser beam with the Gaussian distribution was applied on the top surface of powder layer, moving along the axial axis with a constant velocity. The laser beam travels one element once with the duration time at a spot defined by the element size and scanning speed for the simulations of the scenarios for continual movement of a heat source [19]. During simulations, the materials of elements can be assessed by monitoring the temperature field. The laser processing parameters in the SLM process are listed in Table 1.\n\n\\subsection*{2.3. Governing equations}\nA thermal-structure model built in the ANSYS ${ }^{\\circledR}$ software was developed to effectively simulate the thermal behavior for predicting the transient temperature field associated with SLM progression. In practice, the laser beam produces the localized heating of the powder bed, causing the transfer of heat energy to the material governed by conductive heat transfer. The transient 3D heat conduction equation in the domain $D$ can be expressed as below [22].\n\n$\\rho c \\frac{\\partial T}{\\partial t}=\\frac{\\partial}{\\partial x}\\left(k \\frac{\\partial T}{\\partial x}\\right)+\\frac{\\partial}{\\partial y}\\left(k \\frac{\\partial T}{\\partial y}\\right)+\\frac{\\partial}{\\partial z}\\left(k \\frac{\\partial T}{\\partial z}\\right)+\\dot{Q}$,\n\nwhere $(x, y, z)$ are the spatial coordinates. The symbols $\\rho, c, T, t, k$ and $Q$ denote the material density, specific heat capacity, temperature of the powder system, interaction time between the laser beam and powder bed, thermal conductivity and heat generated per volume within the component, respectively. The initial temperature distribution in the powder beds at $t=0$ can be defined as follows.\n\n$\\left.T(x, y, z, t)\\right|_{t=0}=T_{o}, \\quad(x, y, z) \\in D$,\n\nwhere $T_{o}$ is the preheating temperature ( $T_{\\text {preheating }}$ ) or the ambient temperature $\\left(T_{\\infty}\\right)$ of $20^{\\circ} \\mathrm{C}$ in agreement with the test conditions.\n\nThe following expression is employed to specify the thermal boundary conditions for powder, liquid and solid [19].", "start_char_idx": 435450, "end_char_idx": 439342, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0e2b876c-c641-4ee2-936d-528842b799a0": {"__data__": {"id_": "0e2b876c-c641-4ee2-936d-528842b799a0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0d957139-e7c3-4bbd-9207-c5fe2e7cec96", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f608ee528e86a2225780a8108328c744e5eaa9af6b03ae1919e0716c958fcebb", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3445349e-983c-41fb-a79c-cc1437e85e43", "node_type": "1", "metadata": {}, "hash": "fd4bf66b3ffedf6b807a688d3d3878bc4ee7d0e2fda20fafaf82e17c93d3c1cc", "class_name": "RelatedNodeInfo"}}, "text": "The symbols $\\rho, c, T, t, k$ and $Q$ denote the material density, specific heat capacity, temperature of the powder system, interaction time between the laser beam and powder bed, thermal conductivity and heat generated per volume within the component, respectively. The initial temperature distribution in the powder beds at $t=0$ can be defined as follows.\n\n$\\left.T(x, y, z, t)\\right|_{t=0}=T_{o}, \\quad(x, y, z) \\in D$,\n\nwhere $T_{o}$ is the preheating temperature ( $T_{\\text {preheating }}$ ) or the ambient temperature $\\left(T_{\\infty}\\right)$ of $20^{\\circ} \\mathrm{C}$ in agreement with the test conditions.\n\nThe following expression is employed to specify the thermal boundary conditions for powder, liquid and solid [19].\n\n$k \\frac{\\partial T}{\\partial n}-q+q_{c}+q_{r}=0, \\quad(x, y, z) \\in S$,\n\nwhere $S$ represents the surfaces attached to imposed heat fluxes (convection and radiation), $n$ is the normal vector of $S, q$ is the input heat flux from the laser energy source with a full description of $q$ given later and $q_{c}$ is the heat loss because of natural convection of the fluid around the powder bed, as defined below.\n\n$q_{c}=h\\left(T-T_{\\infty}\\right)$,\n\nwhere $h$ is the convective heat transfer coefficient, and can be expressed as:\n\nTable 1\n\nLaser processing parameters of SLM process.\n\n\\begin{center}\n\\begin{tabular}{ll}\n\\hline\nParameter & Value \\\\\n\\hline\nLaser power, $P$ & $120 \\mathrm{~W}$ \\\\\nScan speed, $V$ & $220 \\mathrm{~mm} / \\mathrm{s}$ \\\\\nLaser spot radius, $\\omega$ & $0.05 \\mathrm{~mm}$ \\\\\nTrack length, $l$ & $0.85 \\mathrm{~mm}$ \\\\\nTrack number, $N t$ & 5 \\\\\nHatch spacing, $d$ & $0.05 \\mathrm{~mm}$ \\\\\nLaser absorptivity of powder, $A$ & 0.3 \\\\\nPowder layer thickness, $\\delta$ & $30 \\mu \\mathrm{m}$ \\\\\nInitial porosity of powder, $\\varphi_{0}$ & 0.646 \\\\\nDensity of dense material, $\\rho_{\\text {dense }}$ & $4420 \\mathrm{~kg} / \\mathrm{m}^{3}$ \\\\\nTotal heat transfer coefficient, $h$ & $80 \\mathrm{~W} / \\mathrm{m}^{2} \\mathrm{~K}$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n$h=\\frac{N u k_{f}}{L}$\n\nwhere $L$ is the characteristic length of the specimen, $N u$ is the Nusselt number and $k_{f}$ is the thermal conductivity of the fluid in the atmosphere (for example, $\\mathrm{Ar}$ is used as the protective atmosphere of SLM process: $k_{f}=0.016 \\mathrm{~W} / \\mathrm{m} /{ }^{\\circ} \\mathrm{C}$ ). Considering the molten pool, formed during laser scanning, as a hot horizontal plate [23], $\\mathrm{Nu}$ can be then calculated as:\n\n$\\overline{N u_{L}}=0.54 R a_{L}^{1 / 4}, \\quad\\left(10^{4} \\leqslant R a_{L} \\leqslant 10^{7}\\right)$\n\nwhere $R a_{L}$ is the Rayleigh number, which is the product of the Prandtl (Pr) and Grashof ( $G r$ ) numbers (i.e., $R a_{L}=G r P r$ ), as revealed below.\n\n$G r=\\frac{g \\rho_{f}^{2} \\beta_{f}\\left(T_{s}-T_{\\infty}\\right) L^{3}}{\\mu_{f}^{2}}$,\n\n$\\operatorname{Pr}=\\frac{c_{f} \\mu_{f}}{k_{f}}$,\n\nwhere $g$ is the acceleration of gravity.", "start_char_idx": 438607, "end_char_idx": 441530, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3445349e-983c-41fb-a79c-cc1437e85e43": {"__data__": {"id_": "3445349e-983c-41fb-a79c-cc1437e85e43", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0e2b876c-c641-4ee2-936d-528842b799a0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "aa58608697938523c90a95ce9005a8a8cefce15ea6d76854c6aec1371ba164a0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c603eb6c-4181-46d5-bc33-dcac7e453db8", "node_type": "1", "metadata": {}, "hash": "2deef8c106fb296d2c5b2befbe40690775ccee0733aa7fb1ee9a853b945a37aa", "class_name": "RelatedNodeInfo"}}, "text": "$G r=\\frac{g \\rho_{f}^{2} \\beta_{f}\\left(T_{s}-T_{\\infty}\\right) L^{3}}{\\mu_{f}^{2}}$,\n\n$\\operatorname{Pr}=\\frac{c_{f} \\mu_{f}}{k_{f}}$,\n\nwhere $g$ is the acceleration of gravity. The signs $\\rho_{f}, \\beta_{f}, \\mu_{f}$ and $c_{f}$ correspond to the density, volumetric expansivity, viscosity and specific heat of the fluid, respectively. Besides, the heat loss $q_{r}$ owing to radiation of the powder bed is expressed as below.\n\n$q_{r}=\\sigma \\varepsilon\\left(T^{4}-T_{\\infty}^{4}\\right)$,\n\nwhere $\\sigma$ is the Stefan-Boltzmann constant $\\left(5.67 \\times 10^{-8} \\mathrm{~W} / \\mathrm{m}^{2} \\mathrm{~K}^{4}\\right)$, and $\\varepsilon$ is the emissivity of Ti6Al4V powder, taken as 0.7 from Ref. $[25]$.\n\n\\subsection*{2.4. Moving Gaussian heat source model}\nThe thermal energy from the laser beam was treated as a moving Gaussian distributed source term to yield the localized heating of the powder bed during SLM. The distribution of the laser beam intensity follows nearly a Gaussian relationship, as mathematically presented in the following [25].\n\n$q=\\frac{2 A P}{\\pi R^{2}} \\exp \\left(-\\frac{2 r^{2}}{R^{2}}\\right)$,\n\nwhere $A$ is the laser energy absorptivity of Ti6Al4V powder as listed in Table 1, $P$ is the laser power, $R$ designates the radius of the Gaussian heat source, indicating the distance from the center of laser beam to the point at which the energy reduced to its $1 / e^{2}$, and $r$ is the radial distance from a point on the powder beds surface to the center of the laser spot. In this study, the latent heat for phase change cannot be neglected owing to the occurrence of the melting phenomena occurred during SLM. The relationship between enthalpy and specific heat was expressed as a function of temperature according to\n\n$H=\\int \\rho c d T$\n\nwhere $H$ is the enthalpy, $\\rho$ is the material density, $c$ is the specific heat capacity and $T$ is the temperature of the molten pool formed in the powder bed. As the temperature of the material exceeded the melting point, the latent heat of fusion should be considered. In this model, the enthalpy change caused by specific heat increase is utilized to calculate the latent heat of fusion at the melting point as below [26].\n\n$\\Delta H=\\rho T_{m}(\\Delta c)$,\n\nwhere $\\Delta H$ is the enthalpy change, $\\Delta c$ is the specific heat capacity change and $T_{m}$ is the melting point.\n\n\\subsection*{2.5. Thermal-physical properties}\nThe effective thermal conductivity of loose metallic powders is dominated by gas in the pores determining the accuracy of SLM simulation results. Rombouts et al. [27] found that the effective thermal conductivity of a powder bed is essentially independent of material but depends on the size and morphology of particles, void fraction, and thermal conductivity of the gas. The effective thermal conductivity of the powder bed, $k_{\\text {eff, }}$, is determined as follows [28].\n\n\n\\begin{align*}\n\\frac{k_{e f f}}{k_{f}}= & (1-\\sqrt{1-\\phi})\\left(1+\\frac{\\phi k_{r}}{k_{f}}\\right) \\\\\n& +\\sqrt{1-\\phi}\\left[\\frac{2}{1-\\frac{k_{f}}{k_{s}}}\\left(\\frac{1}{1-\\frac{k_{f}}{k_{s}}} \\ln \\left(\\frac{k_{s}}{k_{f}}\\right)-1\\right)+\\frac{k_{r}}{k_{f}}\\right] \\tag{13}\n\\end{align*}", "start_char_idx": 441351, "end_char_idx": 444533, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c603eb6c-4181-46d5-bc33-dcac7e453db8": {"__data__": {"id_": "c603eb6c-4181-46d5-bc33-dcac7e453db8", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3445349e-983c-41fb-a79c-cc1437e85e43", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "833135ce6c7a0d8e9a9d9f914178e1fc624ddfb5d1d3573b81f0cdc0a5160886", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3d1b02a3-7369-4840-b0bb-bb7476e63c91", "node_type": "1", "metadata": {}, "hash": "b44fb3666048ecb545dbfa55740c1246450a19b6ebd5ae411819375a4fe34cc8", "class_name": "RelatedNodeInfo"}}, "text": "The effective thermal conductivity of the powder bed, $k_{\\text {eff, }}$, is determined as follows [28].\n\n\n\\begin{align*}\n\\frac{k_{e f f}}{k_{f}}= & (1-\\sqrt{1-\\phi})\\left(1+\\frac{\\phi k_{r}}{k_{f}}\\right) \\\\\n& +\\sqrt{1-\\phi}\\left[\\frac{2}{1-\\frac{k_{f}}{k_{s}}}\\left(\\frac{1}{1-\\frac{k_{f}}{k_{s}}} \\ln \\left(\\frac{k_{s}}{k_{f}}\\right)-1\\right)+\\frac{k_{r}}{k_{f}}\\right] \\tag{13}\n\\end{align*}\n\n\nwhere $\\phi$ is the porosity of the powder bed which can be written as\n\n$\\phi=\\frac{\\rho_{s}-\\rho_{p}}{\\rho_{s}}$,\n\nwhere the signs $\\rho_{s}$ and $\\rho_{p}$ are the density of the dense solid and powder materials, respectively. The symbols $k_{f}, k_{s}$ and $k_{r}$ correspond to the thermal conductivity of the fluid (i.e. argon in this case) enfolding the powder and substrate, thermal conductivity of the dense solid and thermal conductivity portion resulting from the radiation among powder particles, as shown below.\n\n$k_{r}=4 F_{0} \\sigma T_{p}^{3} D_{p}$,\n\nwhere $F_{0}$ is a view factor estimated as $1 / 3, T_{P}$ is the temperature of powder particles and $D_{P}$ is the average diameter of the powder particles. The thermal physical properties of TiAl6V4 are illustrated in Table 2 [29,30], where the sudden changes of thermal physical properties can be clearly observed due to the transition from $\\alpha$ phase to $\\beta$ phase at $950{ }^{\\circ} \\mathrm{C}$ and the melting point of $1660{ }^{\\circ} \\mathrm{C}$ (1933 K).\n\nTable 2\n\nVariation of thermo-physical properties for TiAl6V4 with temperature $[29,30]$.\n\n\\begin{center}\n\\begin{tabular}{llll}\n\\hline\nTemp. $\\left[{ }^{\\circ} \\mathrm{C}\\right]$ & Density $\\left[\\mathrm{kg} / \\mathrm{m}^{3}\\right]$ & Specific heat $[\\mathrm{J} / \\mathrm{kg} \\mathrm{K}]$ & \\begin{tabular}{l}\nThermal \\\\\nconductivity $[\\mathrm{W} / \\mathrm{m} \\mathrm{K}]$ \\\\\n\\end{tabular} \\\\\n\\hline\n25 & 4420 & 546 & 7 \\\\\n100 & 4406 & 562 & 7.45 \\\\\n200 & 4395 & 584 & 8.75 \\\\\n300 & 4381 & 606 & 10.15 \\\\\n400 & 4366 & 629 & 11.35 \\\\\n500 & 4350 & 651 & 12.6 \\\\\n600 & 4336 & 673 & 14.2 \\\\\n700 & 4324 & 694 & 15.5 \\\\\n800 & 4309 & 714 & 17.8 \\\\\n900 & 4294 & 734 & 20.2 \\\\\n994 & 4282 & 753 & 22.7 \\\\\n996 & 4282 & 693 & 19.3 \\\\\n1100 & 4267 & 660 & 21 \\\\\n1200 & 4252 & 678 & 22.9 \\\\\n1300 & 4240 & 696 & 23.7 \\\\\n1400 & 4225 & 714 & 24.6 \\\\\n1500 & 4205 & 732 & 25.8 \\\\\n1600 & 4198 & 750 & 27 \\\\\n1649 & 4189 & 759 & 28.4 \\\\\n1651 & 3920 & 1007 & 83.5 \\\\\n1700 & 3886 & 831 & 83.5 \\\\\n1800 & 3818 & 831 & 83.5 \\\\\n1900 & 3750 & 831 & 83.5 \\\\\n\\hline\n &  &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\section*{3. Computational analysis}\n\\subsection*{3.1.", "start_char_idx": 444138, "end_char_idx": 446710, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3d1b02a3-7369-4840-b0bb-bb7476e63c91": {"__data__": {"id_": "3d1b02a3-7369-4840-b0bb-bb7476e63c91", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c603eb6c-4181-46d5-bc33-dcac7e453db8", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "5e4a88d50f9ec102176892cc02edfd0e6f9505c0392ef6a6658b7b9027cb2998", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5c914285-f1a4-4b46-b21e-fc3289080316", "node_type": "1", "metadata": {}, "hash": "913684886a3e6db811cda1ed4ccc20a8d38a9f343e13eae53b312fb3a39bea43", "class_name": "RelatedNodeInfo"}}, "text": "Computational analysis}\n\\subsection*{3.1. Design of experiment}\nDesign of experiments (DOE) is a tool to study the individual effects and interactions of a group of factors on a complex system. In the simulation-based DOE, planned changes of each input variable require a new run of finite element calculations to investigate the thermal effects of the input variables on the thermal responses during SLM. In this paper, simulations of achieving accurate predictions of melt pool size in laser melting of Ti6Al4V powder layer were carried out by the deterministic method in DOE. The information from the FEM results could be fitted as response surfaces to develop three explicit approximation functions of all selected input variables. The customized design points were adopted in accordance with the common operating conditions of SLM. The DOEFEM results were thus used to analyze and determine the most suitable correlations between the factors and the length, width and depth of molten pool as well as to estimate the relative importance of each specific factor on three dimensions of melt pool for identifying the most influential variables. The ranges in terms of the lower/upper bounds and initial setting were prescribed to perform the analysis for choosing the significant factors. Referring to the earlier results of laser assisted machining of Ti6Al4V alloy $[24,26]$, the input variables corresponding to those processing parameters consist of the laser power $(P)$, scanning speed $(V)$, preheating temperature $(T)$ and hatch spacing $(H)$ between two neighboring tracks, whereas the response variables were the dimensions (i.e. the length, width and depth) of melt pool. Table 3 illustrates the ranges for those input variables and their levels. The output data of response parameters were three dimensions of melt pool during SLM. To conduct the DOE-FEM simulations, we utilized a four-factor and a seven-level central composite design to achieve the high-quality of the fitted second-order polynomial model equation for attaining 49 design points (involving 1 center point, 16 axial points and 32 factorial points) at a reasonable computational cost.\n\n\\subsection*{3.2. Screening of input variables}\nThe central composite design (CCD) can be the most broadly used experimental design uniting one center point, the points along the axis of the input variables and the points settled by a fractional factorial design to develop the design space of three dimensions of melt pool over the powder layer. Fundamentally, the CCD scheme locates the sampling points such that the space of random input variables is investigated in the most efficient way, increasing the accuracy of the response surfaces derived from the calculated results of sampling points. This study performed the simulations using ANSYS ${ }^{\\circledR}$ with the CCD scheme to generate the results, which were further processed by a response surface methodology with MATLAB ${ }^{\\circledR}$ software to develop 3D response surface plots for screening of input variables. The coefficient of determination $R^{2}$ (defined as $1-S S_{\\text {residual }} / S S_{\\text {total }}$ with $S S_{\\text {residual }}$ and $S S_{\\text {total }}$ corresponding to the residual sum of squares and the total sum of squares) and adjusted $R^{2}$ values can statistically judge the quality of the fitted second-order polynomial model equation, and thus generate the 3D surface plots to resolve the relationship between the responses and visualize the interactions between the variables used in the study $[31,32]$.\n\n\\subsection*{3.3. Evaluation procedure and analysis of data}\nThe FEM simulated results were fitted to a quadratic polynomial model with regression coefficients acquired. The generalized\n\nTable 3\n\nRanges of input variables and their levels.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline\n\\multirow[t]{2}{*}{Input Variables} & \\multicolumn{7}{|c|}{Factors Level} \\\\\n\\hline\n & -1 & -0.5 & -0.25 & 0 & 0.25 & 0.5 & 1 \\\\\n\\hline\nPower (w) & 40 & 67.5 & 81.25 & 95 & 108.75 & 122.5 & 150 \\\\\n\\hline\nScan speed $(\\mathrm{mm} / \\mathrm{s})$ & 20 & 115 & 162.5 & 210 & 257.5 & 305 & 400 \\\\\n\\hline\nPreheat temp.", "start_char_idx": 446669, "end_char_idx": 450858, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5c914285-f1a4-4b46-b21e-fc3289080316": {"__data__": {"id_": "5c914285-f1a4-4b46-b21e-fc3289080316", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3d1b02a3-7369-4840-b0bb-bb7476e63c91", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "64f45f8784392d7aae94aa2f7c0aa395726cb95f8c93e95a0046dc5b31f4a16d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d1884080-0f39-4926-9160-492a74c6be12", "node_type": "1", "metadata": {}, "hash": "78e9281c1df0cb38384d7f91c2162768d050550c14adb11399b1456fd6098db7", "class_name": "RelatedNodeInfo"}}, "text": "The generalized\n\nTable 3\n\nRanges of input variables and their levels.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline\n\\multirow[t]{2}{*}{Input Variables} & \\multicolumn{7}{|c|}{Factors Level} \\\\\n\\hline\n & -1 & -0.5 & -0.25 & 0 & 0.25 & 0.5 & 1 \\\\\n\\hline\nPower (w) & 40 & 67.5 & 81.25 & 95 & 108.75 & 122.5 & 150 \\\\\n\\hline\nScan speed $(\\mathrm{mm} / \\mathrm{s})$ & 20 & 115 & 162.5 & 210 & 257.5 & 305 & 400 \\\\\n\\hline\nPreheat temp. $\\left({ }^{\\circ} \\mathrm{C}\\right)$ & 20 & 65 & 87.5 & 110 & 132.5 & 155 & 200 \\\\\n\\hline\nHatch space $(\\mathrm{mm})$ & 0.05 & 0.0625 & 0.06875 & 0.075 & 0.08125 & 0.0875 & 0.1 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nsecond-order polynomial model used in the response surface analysis was as below:\n\n$Y=\\beta_{0}+\\sum_{i=1}^{k} \\beta_{i} X_{i}+\\sum_{i=1}^{k} \\beta_{i i} X_{i}^{2}+\\sum \\sum_{i<j=1}^{k} \\beta_{i j} X_{i} X_{j}$.\n\nHere $Y$ indicates the response function, whereas $X_{i}$ and $X_{j}$ represent the independent variables. The signs $\\beta_{0}, \\beta_{i}, \\beta_{i i}$ and $\\beta_{i j}$ are the regression coefficients for intercept, linear, quadratic and interaction terms, respectively. The response surfaces and contour plots were generated using MATLAB ${ }^{\\circledR}$ software while retaining a variable constant in the fitted second-order polynomial equation. Hence, the relationship between the response and experimental levels of each factor can be visualized with the response surfaces deduced. Fig. 3 illustrates the flowchart of the evaluation procedure. The first step is to define the desirable input parameters (with the ranges) and response factors. In this study, we intend to evaluate the influences of process parameters on the performance of final parts. Hence, a performance evaluation criterion is selected to quantify the response results. In practice, DOE coupled with the response surface analysis is more advantageous than the traditional single parameter variation study due to time efficiency and cost saving. This type of DOE was to recognize the groups of input variables and discriminate those most significant factors for each response variable during the process. The second-order CCD is one of the most popular and useful DOE method among the categories of RSM. This study set up the ranges for all selected input variables and produced the test matrix for DOE in conjunction with CCD. FEM calculations were then performed according to the design matrix generated by DOE and CCD to obtain the preliminary responses with ANOVA conducted for statistically analyzing the results. After that, the quality of fit was checked using the adjusted coefficient ( $\\operatorname{Adj} \\mathrm{R}^{2}$ ) and $\\mathrm{p}$ value. In general, the value of $R^{2}$ spans from 0 to 1 with a $R^{2}$ value closer to 1 showing a higher quality of the response model. Then the factor with the $\\mathrm{p}$ value less than 0.01 was considered having significant effect on the response. If the quality of fit is unsatisfactory, the design matrix will be reconstructed by adding more design points. The development of strict quality criteria is necessitated to ensure successful operations in SLM. Therefore, the process window was implemented as a filter to remove the ineffectual and impractical conditions of input variables, and then apply the narrower ranges of the processing parameters to establish the critical RSM models with ANOVA made for accurately determining three dimensions of melt pool. The comparison of the critical RSM predictions of three dimensions of melt pool with the FEM simulated results was completed to validate the critical regression models.\n\n\\section*{4.", "start_char_idx": 450418, "end_char_idx": 454069, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d1884080-0f39-4926-9160-492a74c6be12": {"__data__": {"id_": "d1884080-0f39-4926-9160-492a74c6be12", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5c914285-f1a4-4b46-b21e-fc3289080316", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "86053e46da41f229fbde354de8bbd74a31b2de9b297a6baa7e5351fa0d4faa1d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5e32f8b1-5014-4cf4-aad9-52de3e341887", "node_type": "1", "metadata": {}, "hash": "bd9568c4e66b8da6d270f67692a56bdc0ab7e4a06a4a0bcd2f13ee9f627eaeea", "class_name": "RelatedNodeInfo"}}, "text": "In general, the value of $R^{2}$ spans from 0 to 1 with a $R^{2}$ value closer to 1 showing a higher quality of the response model. Then the factor with the $\\mathrm{p}$ value less than 0.01 was considered having significant effect on the response. If the quality of fit is unsatisfactory, the design matrix will be reconstructed by adding more design points. The development of strict quality criteria is necessitated to ensure successful operations in SLM. Therefore, the process window was implemented as a filter to remove the ineffectual and impractical conditions of input variables, and then apply the narrower ranges of the processing parameters to establish the critical RSM models with ANOVA made for accurately determining three dimensions of melt pool. The comparison of the critical RSM predictions of three dimensions of melt pool with the FEM simulated results was completed to validate the critical regression models.\n\n\\section*{4. Results and discussion}\nThe transient thermal analysis was conducted to solve the time sequences of temperature distribution during SLM. Fig. 4(a) presents the numerical grids for reproducing the laser heating of a powder bed in SLM simulations. The mesh setup consisted of two sections: the powder layer and dense substrate. Essentially, finer grids have been arranged in the areas near the scanning region of powder layer to describe the prompt variations of temperature field. In view of the numerical accuracy and computation efficiency, an ANSYS ${ }^{\\circledR}$ Solid 70 hexahedral element was used in the powder bed while tetrahedral elements were utilized in the substrate. Hence, the 3D FEM model was meshed into 51,996 elements (with the nodes of 61,600 ) for the powder layer and 24,532 elements (with the nodes of 35,475) for the substrate layer, respectively. The grid-independence inspection was conducted on the total grids of $37,750,76,528$ and 142,819 points at the laser power of $120 \\mathrm{~W}$ and scanning speed of $220 \\mathrm{~mm} / \\mathrm{s}$ with a time step of $2 \\times 10^{-5} \\mathrm{~s}$ in the laser melting of Ti6Al4V powder layers. Fig. 4(b) illustrates the predicted length, width and depth of the melt pool at the end of the fifth track for different grids. The differences of the predictions of length, width and depth of the melt pool between the grids of 37,750 and 142,819 were $6.5 \\%, 8.2 \\%$ and $6.2 \\%$. Alternatively, for the meshes of 76,528 and 142,819 grids, the discrepancies of calculated length, width and depth of melt pool were substantially reduced to $1.1 \\%, 1.7 \\%$ and $1.9 \\%$, respectively. Furthermore, the time step-independence of the solutions was checked using three different time steps of $4 \\times 10^{-6} \\mathrm{~s}, 2 \\times 10^{-5} \\mathrm{~s}$ and $10^{-4} \\mathrm{~s}$. Two groups of time steps, specifically $4 \\times 10^{-6} \\mathrm{~s}$ and $10^{-4}$ $\\mathrm{s}$ as well as $4 \\times 10^{-6} \\mathrm{~s}$ and $2 \\times 10^{-5} \\mathrm{~s}$, in simulations indicated $4.3 \\%, 4.6 \\%$ and $5.4 \\%$ together with $1.4 \\%, 2.2 \\%$ and $2.6 \\%$, respectively, for the variations of predicted length, width and depth of the melt pool. Since more computational resources are needed in response to an increase in total grids or decrease of time step, the FEM computations of time-dependent temperature distributions at different grids and time steps indicated satisfactory grid and time step independence for the following simulations attained by a mesh setup of 76,528 grids with a time step of $2 \\times 10^{-5} \\mathrm{~s}$. It usually required around $65 \\mathrm{~min}$ of central processing unit (CPU) time on an Intel ${ }^{\\circledR}$ Xeon $^{\\circledR}$ E5-2670v3-2.3 GHz $\\times 2$ (192 GB RAM) high-performance workstation to achieve a solution for one single simulation.\n\n\\subsection*{4.1.", "start_char_idx": 453122, "end_char_idx": 456945, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5e32f8b1-5014-4cf4-aad9-52de3e341887": {"__data__": {"id_": "5e32f8b1-5014-4cf4-aad9-52de3e341887", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d1884080-0f39-4926-9160-492a74c6be12", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9cb654838727e73f9c79206d6566638c1e36fe6bd58ae177b933e0dfb463e1c0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d41cd70b-115a-45b6-9221-46156fcf4f3d", "node_type": "1", "metadata": {}, "hash": "93ce65522c07acd0bb9fce7458120750b7e9cb3e72854de795d7678320c17990", "class_name": "RelatedNodeInfo"}}, "text": "Since more computational resources are needed in response to an increase in total grids or decrease of time step, the FEM computations of time-dependent temperature distributions at different grids and time steps indicated satisfactory grid and time step independence for the following simulations attained by a mesh setup of 76,528 grids with a time step of $2 \\times 10^{-5} \\mathrm{~s}$. It usually required around $65 \\mathrm{~min}$ of central processing unit (CPU) time on an Intel ${ }^{\\circledR}$ Xeon $^{\\circledR}$ E5-2670v3-2.3 GHz $\\times 2$ (192 GB RAM) high-performance workstation to achieve a solution for one single simulation.\n\n\\subsection*{4.1. Measurement validation}\nTwo simulation cases were conducted to validate the computational model by comparing the calculated results with the experimental results [33] and the predictions [26,34], respectively. The details of test conditions for those two cases are given in Tables 4 and 5. Fischer et al. [31] scanned the pure titanium powder layer with a Nd:YAG laser beam and observed the peak skin temperature in the sintering process by a Raytheon infrared camera. Kolossov et al. [32] conducted the 3D FEM analysis to characterize the temperature changes during the selective sintering process. Fig. 5 illustrates a comparison of (a) the calculated surface temperature contours after $0.75 \\mathrm{~s}$ with (b) the visualized infrared image [31] and (c) the predictions [26] during SLM. The calculated peak surface temperature of $2650 \\mathrm{~K}$ agreed reasonably well with the thermal image in Fig. 5(b) representing elevated temperatures of $2678 \\pm 200 \\mathrm{~K}$, (Region a with a red color in Ref. [34]) over the powder bed because of the direct laser exposure. Considering the melting temperature of $1933 \\mathrm{~K}$ for Ti6Al4V, the simulated melt pool dimensions of $209.68 \\mu \\mathrm{m}$ long, $156.67 \\mu \\mathrm{m}$ wide and $63.6 \\mu \\mathrm{m}$ deep were in good agreement with the predictions of $219.6 \\mu \\mathrm{m} \\times 162.5$ $\\mu \\mathrm{m} \\times 67.8 \\mu \\mathrm{m}$ in Ref. [34]. Fig. 6 shows a comparison of (a) the calculated temperature distribution in the $x$-axis at $y=2.5 \\mathrm{~mm}$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-07}\n\\end{center}\n\nFig. 3. Flowchart of the evaluation procedure.\n\nand $z=2.0 \\mathrm{~mm}$ with (b) the measured temperature profile and the predictions [34]. The computed temperature profile along the axial direction reached its highest temperature of $2537.1 \\mathrm{~K}$ at around $x=1.8 \\mathrm{~mm}$ on the top surface, and matched well with the measured data and predicted results. In general, the validation shows that the present FEM model is accurate enough to predict the transient temperature distribution and melt pool dimensions during SLM process.\n\n\\subsection*{4.2. Thermal characteristics during SLM}\nFig. 7 shows the time sequences of predicted temperature contours on the top surface of 3D melt pool at various locations including the start of the first track (Point 1), the center of the third track (Point 2) and the end of the fifth track (Point 3) for the laser power of $120 \\mathrm{~W}$ and scanning speed of $220 \\mathrm{~mm} / \\mathrm{s}$ during SLM of TiAl6V4 powder: (a) top view and (b) side view. The dotted line on the charts denoted the isotherm curve of melting temperature of Ti6Al4V (i.e. $1933 \\mathrm{~K}$ ) on the top surface. Accordingly, the region within this specific contour line was in a liquid state due to its temperature above the melting point, and thereby formed a melt pool characterized by a series of ellipses. Asymmetry of temperature contours was noted along the laser scanning direction.", "start_char_idx": 456282, "end_char_idx": 460008, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d41cd70b-115a-45b6-9221-46156fcf4f3d": {"__data__": {"id_": "d41cd70b-115a-45b6-9221-46156fcf4f3d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5e32f8b1-5014-4cf4-aad9-52de3e341887", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "80493c3241a3ae60f08e2d5b3d7af095c02ab7cdf6843e3d0794c9a0708d0018", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d2b400a1-21b8-4eb3-9c56-96c48847fbcd", "node_type": "1", "metadata": {}, "hash": "66f648a16da67d38d97014aa5bf1c9a9008a8241c14974f10213294b2d68bedc", "class_name": "RelatedNodeInfo"}}, "text": "The dotted line on the charts denoted the isotherm curve of melting temperature of Ti6Al4V (i.e. $1933 \\mathrm{~K}$ ) on the top surface. Accordingly, the region within this specific contour line was in a liquid state due to its temperature above the melting point, and thereby formed a melt pool characterized by a series of ellipses. Asymmetry of temperature contours was noted along the laser scanning direction. The combined effects of higher thermal conductivity of the scanned part and the thermal accumulation resulted in more intensive isothermal contours of front ellipses as compared to those at the back side. As the laser spot located at the start of the first track (Point 1, Fig. 7(a)), the predicted maximum temperature of the powder layer was $4650.3 \\mathrm{~K}$ due to low conductivity of material in the region under laser irradiation, exceeding the Ti6Al4V melting point of $1933 \\mathrm{~K}$ and boiling point of $3808 \\mathrm{~K}$ to cause the occurrence of localized melting and even potential vaporization of powder. However, it was found that the extent of the vaporization region was approximately $32.3 \\mu \\mathrm{m} \\times 29.2 \\mu \\mathrm{m} \\times 1.1 \\mu \\mathrm{m}$ with the laser exposure time duration less than $13.6 \\mathrm{~ms}$. Consequently, the effect of material loss may be reasonably ignored in the analysis on account of a truly small evaporated zone in size over a very short time period. In the meantime, this peak temperature notably dropped with increasing move distance of laser spot because of the heat conduction into the dense substrate layer with a high conductivity. The melt pool size was around $109.85 \\mu \\mathrm{m}$ long, $105.15 \\mu \\mathrm{m}$ wide and $13.13 \\mu \\mathrm{m}$ deep, respectively. When the laser beam\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-08}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-08(2)}\n\\end{center}\n\n(b)\n\nFig. 4. (a) Numerical grids for reproducing laser heating of a powder bed in SLM simulations; (b) predicted length, width and depth of melt pool at the end of the fifth track for different grids.\n\nTable 4\n\nExperimental details of Fischer et al. [33].\n\n\\begin{center}\n\\begin{tabular}{ll}\n\\hline\nParameter & Value \\\\\n\\hline\nLaser power & $3 \\mathrm{~W}$ \\\\\nLaser beam radius & $0.05 \\mathrm{~mm}$ \\\\\nScanning speed & $1 \\mathrm{~mm} / \\mathrm{s}$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 5\n\nSimulation details of Kolossov et al. [34].\n\n\\begin{center}\n\\begin{tabular}{ll}\n\\hline\nParameter & Value \\\\\n\\hline\nLaser power & $2 \\mathrm{~W}$ \\\\\nLaser beam radius & $0.025 \\mathrm{~mm}$ \\\\\nScanning speed & $1 \\mathrm{~mm} / \\mathrm{s}$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nreached the center of the third scan track (point 2, Fig. 7(b)), the center temperature of the melt pool decreased from $4650.3 \\mathrm{~K}$ to 2662.3 K. In addition, the melt pool dimensions of $196.4 \\mu \\mathrm{m} \\times$ $156.48 \\mu \\mathrm{m} \\times 61.9 \\mu \\mathrm{m}$ increased significantly as compared to the pool formed at the start point of first track. When the laser spot further moved to the end of the fifth track (Point 3, Fig.", "start_char_idx": 459593, "end_char_idx": 462808, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d2b400a1-21b8-4eb3-9c56-96c48847fbcd": {"__data__": {"id_": "d2b400a1-21b8-4eb3-9c56-96c48847fbcd", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d41cd70b-115a-45b6-9221-46156fcf4f3d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3f536729e1c16a870db478de2da340f36d566153e26aab81c693fd0aedf1b55f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "33e75c4b-2270-45a5-9907-a929acd9e934", "node_type": "1", "metadata": {}, "hash": "28fb41bdb31b03c3dba33e110895999ca82f458396e37efbb67eeb7f7dea60f3", "class_name": "RelatedNodeInfo"}}, "text": "7(b)), the center temperature of the melt pool decreased from $4650.3 \\mathrm{~K}$ to 2662.3 K. In addition, the melt pool dimensions of $196.4 \\mu \\mathrm{m} \\times$ $156.48 \\mu \\mathrm{m} \\times 61.9 \\mu \\mathrm{m}$ increased significantly as compared to the pool formed at the start point of first track. When the laser spot further moved to the end of the fifth track (Point 3, Fig. 7(c)), the temperature contours were visualized to be more intense at the front side than those at the back side of the ellipses with an increase in the maximum temperature of the powder bed to 2673.2 K. The melt pool dimensions of $209.68 \\mu \\mathrm{m} \\times 156.67 \\mu \\mathrm{m}$ $\\times 63.6 \\mu \\mathrm{m}$ were relatively larger than those cases at Point 1 and\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-08(4)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-08(3)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-08(1)}\n\\end{center}\n\n(c)\n\nFig. 5. Comparison of (a) calculated surface temperature contours after $0.75 \\mathrm{~s}$ with (b) Visualized infrared images [33] and (c) predictions [26] during SLM.\n\nPoint 2. The reason was that heat produced in the past track had an influence on the temperature field of the next track, resulting in a heat accumulation outcome during SLM. Thus, the combined results of greater heat accumulation and a longer interaction time\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-09(1)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-09}\n\\end{center}\n\n(b)\n\nFig. 6. Comparison of (a) calculated temperature distribution along the $x$ direction at $y=2.5 \\mathrm{~mm}$ and $z=2.0 \\mathrm{~mm}$ with (b) measured temperature profile and the predictions [34] during SLM.\n\nof the laser beam with the powder bed produced a higher temperature for the last track.\n\nFig. 8 exhibits the time evolution of top surface temperature of the powder bed at the center of the third track (point 2) for the laser power of $120 \\mathrm{~W}$ and scan speed of $220 \\mathrm{~mm} / \\mathrm{s}$. In essence, the temperature profile showed five large fluctuations. From the simulated results, each peak indicated the arrival of the laser beam at the center of each scan track with the greatest temperature of $2664 \\mathrm{~K}$ observed at the third peak $(t=9.6 \\mathrm{~ms})$. For the first three waves, the corresponding peak temperatures gradually increased and this was because each subsequent scanning could affect and reheat the previous track for the laser spot approaching the monitoring point. The cyclic melting/heating processes continued in all five tracks over the surface of a deposited powder layer. Besides, a remelting phenomenon occurred along the prior scan track, leading to the development of excessive molten metal with a significant heat accumulation effect. When the laser beam passed over the center of the third track and arrived at the end of the last track $(t=19.2 \\mathrm{~ms})$, the peak temperatures tended to lessen with the last peak temperature of $1934.8 \\mathrm{~K}$ at the monitoring point slightly over the melting point of TiAl6V4. However, the high temperature gradients around the molten pool can result in substantial solidification rates and melt unstably.", "start_char_idx": 462422, "end_char_idx": 465892, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "33e75c4b-2270-45a5-9907-a929acd9e934": {"__data__": {"id_": "33e75c4b-2270-45a5-9907-a929acd9e934", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d2b400a1-21b8-4eb3-9c56-96c48847fbcd", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b5bc9859f9e17495c225e58fe330ba90ddbd4eb9e15a081dca459d00f6f2373e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fc8d12a4-bda7-4d19-8a09-79776eecad0b", "node_type": "1", "metadata": {}, "hash": "e4951bc0b38cd2cbede94d97759050c3b2343a4668ae746e8114ee582a96afef", "class_name": "RelatedNodeInfo"}}, "text": "For the first three waves, the corresponding peak temperatures gradually increased and this was because each subsequent scanning could affect and reheat the previous track for the laser spot approaching the monitoring point. The cyclic melting/heating processes continued in all five tracks over the surface of a deposited powder layer. Besides, a remelting phenomenon occurred along the prior scan track, leading to the development of excessive molten metal with a significant heat accumulation effect. When the laser beam passed over the center of the third track and arrived at the end of the last track $(t=19.2 \\mathrm{~ms})$, the peak temperatures tended to lessen with the last peak temperature of $1934.8 \\mathrm{~K}$ at the monitoring point slightly over the melting point of TiAl6V4. However, the high temperature gradients around the molten pool can result in substantial solidification rates and melt unstably. Therefore, the residual stress could generate deformation or crack in laser-processed components, and in turn reduced the bonding ability between the adjacent layers and decreased the final densification of SLM parts [5].\\\\\nFig. 9 shows the predicted interfacial temperature profiles between the powder bed and substrate layer at the center of the first scanning track for the laser powers of $40 \\mathrm{~W}, 67.5 \\mathrm{~W}, 120 \\mathrm{~W}$ and $150 \\mathrm{~W}$ with the fixed scanning speeds of (a) $80 \\mathrm{~mm} / \\mathrm{s}$ and (b) $305 \\mathrm{~mm} / \\mathrm{s}$. The temperatures were monitored during the travel of laser beam along the first pathway. The simulations clearly indicated apparent temperature waves at the monitoring point. During laser heating, the temperature profiles for various laser powers nearly attained their highest temperatures concurrently at a relatively low scanning speed of $80 \\mathrm{~mm} / \\mathrm{s}$. The monitoring temperatures escalated from the preheating temperature of $383 \\mathrm{~K}$ to those peak temperatures as a result of the heat accumulation effect. For a relatively low power of $40 \\mathrm{~W}$, the maximum operating temperature was just $1647 \\mathrm{~K}$ at $t=5.5 \\mathrm{~ms}$, causing the melting failure of TiAl6V4 powder because of an inadequate energy supplied by the laser beam. As the laser power was increased to $150 \\mathrm{~W}$, the maximum interfacial temperature noticeably escalated up to $2360 \\mathrm{~K}$, which exceeded the melting point of $1933 \\mathrm{~K}$. Accordingly, the melting phenomenon occurred to form a relatively larger high-temperature molten pool as a result of the sufficient energy penetration of the laser beam into the titanium alloy powder. The associated melting times required for heat penetration through the powder layer were 3.2, 2.7 and $2.3 \\mathrm{~ms}$ for the laser powers of $67.5,120$ and $150 \\mathrm{~W}$, respectively, suggesting that a stronger laser power can shorten the penetration time for laser heating to the interface of powder depth. In addition, an augmented laser power led to a higher melting temperature thanks to a greater laser energy input, and thereby produced a resultant bigger and deeper molten pool with a longer liquid lifetime. On the other hand, when the applied scanning speed increased to $305 \\mathrm{~mm} / \\mathrm{s}$, the time periods for lower laser powers to achieve their peak temperatures were delayed, revealing more time through the laser penetration depth to the substrate. A relatively less irradiation time influenced a reduction in the amount of energy transfer to the powder layer during laser heating, resulting in the difficulties of melting TiAl6V4 powder along the scanning track and ensuring reliable bonds of neighboring tracks for the conditions of 40 and $67.5 \\mathrm{~W}$. However, those increased laser powers of 120 and $150 \\mathrm{~W}$ could melt the powder layer as a result of much shorter melting times (i.e. 0.44 and $0.43 \\mathrm{~ms}$ ) as compared to the total scanning time of $2.8 \\mathrm{~ms}$.\n\n\\subsection*{4.3. Development of preliminary RSM}\nFig.", "start_char_idx": 464970, "end_char_idx": 469031, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fc8d12a4-bda7-4d19-8a09-79776eecad0b": {"__data__": {"id_": "fc8d12a4-bda7-4d19-8a09-79776eecad0b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "33e75c4b-2270-45a5-9907-a929acd9e934", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "59430d5695cf88457a40a4a27d7effd22b678452160748de61e61d201eeecb3d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bef1becb-3f78-4381-8ef3-3bd4e74fcc28", "node_type": "1", "metadata": {}, "hash": "14cf1e8e29e628cab4c04489ec3bcd87973ca5cadb228361673e8c7859f35f2e", "class_name": "RelatedNodeInfo"}}, "text": "A relatively less irradiation time influenced a reduction in the amount of energy transfer to the powder layer during laser heating, resulting in the difficulties of melting TiAl6V4 powder along the scanning track and ensuring reliable bonds of neighboring tracks for the conditions of 40 and $67.5 \\mathrm{~W}$. However, those increased laser powers of 120 and $150 \\mathrm{~W}$ could melt the powder layer as a result of much shorter melting times (i.e. 0.44 and $0.43 \\mathrm{~ms}$ ) as compared to the total scanning time of $2.8 \\mathrm{~ms}$.\n\n\\subsection*{4.3. Development of preliminary RSM}\nFig. 10 illustrates the predictions of length, width and depth of the melt pool during SLM of TiAl6V4 powder with different processing parameters: (a) laser power of $40-150 \\mathrm{~W}(v=210 \\mathrm{~mm} / \\mathrm{s}$, $T=110{ }^{\\circ} \\mathrm{C}$ and $H=0.075 \\mathrm{~mm}$.); (b) scanning speed of $20-400$ $\\mathrm{mm} / \\mathrm{s}\\left(P=95 \\mathrm{~W}, T=110^{\\circ} \\mathrm{C}\\right.$ and $H=0.075 \\mathrm{~mm}$.); (c) preheating temperature of $20-200{ }^{\\circ} \\mathrm{C}(P=95 \\mathrm{~W}, v=210 \\mathrm{~mm} / \\mathrm{s}$ and $H=0.075$ $\\mathrm{mm}$.$) and (d) hatch space 0.05-0.075 \\mathrm{~mm}(P=95 \\mathrm{~W}, v=210 \\mathrm{~mm} /$ $\\mathrm{s}$ and $T=110^{\\circ} \\mathrm{C}$.) Essentially, the length, width and depth of the melt pool was found to increase with the laser power on the powder layer due to more energy transferred into the heat affected zone. The applied power elevated from 40 to $150 \\mathrm{~W}$ at a scanning speed of $220 \\mathrm{~mm} / \\mathrm{s}$ led to significant enlargement on the melt pool size. It was observed that the associated dimensions of length, width and depth increased from $101.2 \\mu \\mathrm{m} \\times 81.7 \\mu \\mathrm{m} \\times 21.8 \\mu \\mathrm{m}$ to $245.5 \\mu \\mathrm{m} \\times 187.7 \\mu \\mathrm{m} \\times 84 \\mu \\mathrm{m}$ in Fig. 10(a). Since the amount of liquid formation of melt pool mainly depends on the operating temperature of the SLM process, increasing laser power can produce a high temperature rise of the powder layer, and in turn expand the melt pool extent. In contrast, the simulated results in Fig. 10(b) evidently indicated the decline of three dimensions of the melt pool with the increment of the applied scan speeds.", "start_char_idx": 468427, "end_char_idx": 470727, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bef1becb-3f78-4381-8ef3-3bd4e74fcc28": {"__data__": {"id_": "bef1becb-3f78-4381-8ef3-3bd4e74fcc28", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fc8d12a4-bda7-4d19-8a09-79776eecad0b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "016fd15fa9824393ef2b894e728cb9832d276b23696ddea1ebc5b310b4b04ba9", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "349af34d-5529-4d50-8df4-2745a84cd686", "node_type": "1", "metadata": {}, "hash": "dbe40d0b9049b6cd5e571bd082b33e8d83a39aad19056bda23e6c54922ba7499", "class_name": "RelatedNodeInfo"}}, "text": "It was observed that the associated dimensions of length, width and depth increased from $101.2 \\mu \\mathrm{m} \\times 81.7 \\mu \\mathrm{m} \\times 21.8 \\mu \\mathrm{m}$ to $245.5 \\mu \\mathrm{m} \\times 187.7 \\mu \\mathrm{m} \\times 84 \\mu \\mathrm{m}$ in Fig. 10(a). Since the amount of liquid formation of melt pool mainly depends on the operating temperature of the SLM process, increasing laser power can produce a high temperature rise of the powder layer, and in turn expand the melt pool extent. In contrast, the simulated results in Fig. 10(b) evidently indicated the decline of three dimensions of the melt pool with the increment of the applied scan speeds. When the scanning speed was increased from 20 to $400 \\mathrm{~mm} / \\mathrm{s}$ at a fixed\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-10}\n\\end{center}\n\nTrack 1\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_28c7c9a63c5801f46eefg-10(1)}\n\nScan direction\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_28c7c9a63c5801f46eefg-10(2)}\n\n$4650.3 K$\n\n4175.1\n\n3699.8\n\n3224.6\n\n2749.4\n\n2274.1\n\n1798.9\n\n1323.6\n\n848.39\n\n373.15\n\n$2662.3 K$\n\n2408\n\n2153.6\n\n1899.3\n\n1644.9\n\n1390.6\n\n1136.2\n\n881.85\n\n627.5\n\n373.15\n\n$2673.2 K$\n\n2417.7\n\n2162.1\n\n1906.5\n\n1651\n\n1395.4\n\n1139.8\n\n884.28\n\n628.72\n\n373.15\n\n(a)\n\n(b)\n\nFig. 7. Time sequences of predicted temperature contours on the top surface of 3D melt pool at various locations including the start of the first track (Point 1 ), the center of the third track (Point 2) and the end of the fifth track (Point 3) for laser power of $120 \\mathrm{~W}$ and scanning speed of $220 \\mathrm{~mm} / \\mathrm{s}$ during SLM of TiAl6V4 powder: (a) top view and (b) side view.\n\nlaser power of $95 \\mathrm{~W}$, the length of the melt pool decreased from 220.6 to $158 \\mu \\mathrm{m}$. In addition, the associated width /depth reduced from $187.7 / 92.2 \\mu \\mathrm{m}$ to $106.1 / 37.4 \\mu \\mathrm{m}$, respectively. Under higher scan speed conditions ( $20-400 \\mathrm{~mm} / \\mathrm{s}$ ), there was no sufficient time for the event of melting process to produce a long thin melt pool over the track, causing a substantial splash of melted materials with the region still remained in a state of non-melted powder. The computed results in Fig. 10(c) and (d) indicated insignificant variations of three dimensions of the melt pool over the ranges of preheating temperature of $20-400^{\\circ} \\mathrm{C}$ and hatching space of\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-11}\n\\end{center}\n\nFig. 8. Time evolution of the top surface temperature of powder bed at the center of the third track (point 2) for the laser power of $120 \\mathrm{~W}$ and scan speed of $220 \\mathrm{~mm} / \\mathrm{s}$.", "start_char_idx": 470068, "end_char_idx": 472841, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "349af34d-5529-4d50-8df4-2745a84cd686": {"__data__": {"id_": "349af34d-5529-4d50-8df4-2745a84cd686", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bef1becb-3f78-4381-8ef3-3bd4e74fcc28", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d3b0e7ce0cb171cb8587483ab120d1cb3c2fdcd76fb0c42925360811c389483f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1c5c9186-196b-4583-bb38-bd61118d1045", "node_type": "1", "metadata": {}, "hash": "a783cf1246760701d15c5b29818b7c1bf538888f4b218c6f01415765e32b7220", "class_name": "RelatedNodeInfo"}}, "text": "The computed results in Fig. 10(c) and (d) indicated insignificant variations of three dimensions of the melt pool over the ranges of preheating temperature of $20-400^{\\circ} \\mathrm{C}$ and hatching space of\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-11}\n\\end{center}\n\nFig. 8. Time evolution of the top surface temperature of powder bed at the center of the third track (point 2) for the laser power of $120 \\mathrm{~W}$ and scan speed of $220 \\mathrm{~mm} / \\mathrm{s}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-11(1)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-11(2)}\n\\end{center}\n\n(b)\n\nFig. 9. Predicted interfacial temperature profiles between powder bed and substrate layer at the center of the first scanning track for the laser powers of 40 $\\mathrm{W}, 67.5 \\mathrm{~W}, 120 \\mathrm{~W}$ and $150 \\mathrm{~W}$ with the fixed scan speeds of (a) $80 \\mathrm{~mm} / \\mathrm{s}$ and (b) 305 $\\mathrm{mm} / \\mathrm{s}$.\n\n$0.075-0.1 \\mathrm{~mm}$. Nevertheless, the preheating temperature can be closely related to the densification of SLM-processed parts, which affect the dimensional accuracy of finished products [35]. Besides, due to the overlapping between ensuing tracks depending on the hatching space distance, some sections were exposed to multiple scans and melted repetitively to firmly bond adjacent tracks for forming a dense layer. Hence, it can be useful to produce a uniform distribution of energy for attaining a fully melting condition with a short hatching space. In general, the laser power and scanning speed were identified as the most important laser processing parameters influencing the melt pool size.\n\nIn this study, the boundary conditions affecting three dimensions of the melt pool were examined to accurately predict the melt pool extent. Table 6 illustrates the test matrix for DOE with 49 simulation runs completed and results obtained, corresponding to the combined effect of those 4 input variables in their specific ranges. These results were then analyzed using MATLAB ${ }^{\\circledR}$ software to obtain the second order regression model. The preliminary RSM models are expressed by Eqs. (17)-(19)\n\n\n\\begin{align*}\n\\text { Length }= & 9.2+1.663 P-0.2175 V+0.165 T+1300 H \\\\\n& -0.000683 P \\times P+0.000364 V \\times V-0.000509 T \\\\\n& \\times T-8265 H \\times H-0.000875 P \\times V+0.000128 P \\\\\n& \\times T+0.26 P \\times H+0.000263 V \\times T-0.365 V \\times H \\\\\n& -0.93 T \\times H \\tag{17}\n\\end{align*}\n\n\n\n\\begin{align*}\n\\text { Width }= & 53.9+1.628 P-0.2509 V+0.028 T-41 H \\\\\n& -0.001947 P * P+0.000396 V * V+0.000121 T \\\\\n& * T+214 H * H-0.001298 P * V+0.000320 P * T \\\\\n& -0.56 P * H+0.000071 V * T+0.552 V * H \\\\\n& -0.89 T * H \\tag{18}\n\\end{align*}", "start_char_idx": 472323, "end_char_idx": 475171, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1c5c9186-196b-4583-bb38-bd61118d1045": {"__data__": {"id_": "1c5c9186-196b-4583-bb38-bd61118d1045", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "349af34d-5529-4d50-8df4-2745a84cd686", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c9b564e4cc0e399fffc2d91eb388f5725ceb1325baddf4f3c237ffe01d733b14", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6ee9940f-9ea8-4cee-9ef3-78a17dc4863c", "node_type": "1", "metadata": {}, "hash": "4de20581e348ef704de9e32dd568816a98d44e916d8e51b8b4d6cb6d27e9c5fd", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{align*}\n\\text { Width }= & 53.9+1.628 P-0.2509 V+0.028 T-41 H \\\\\n& -0.001947 P * P+0.000396 V * V+0.000121 T \\\\\n& * T+214 H * H-0.001298 P * V+0.000320 P * T \\\\\n& -0.56 P * H+0.000071 V * T+0.552 V * H \\\\\n& -0.89 T * H \\tag{18}\n\\end{align*}\n\n\n\n\\begin{align*}\n\\text { Depth }=3.5 & +0.863 P-0.0969 V-0.014 T-148 H \\\\\n& +0.000348 P * P+0.000354 V * V+0.000080 T * T \\\\\n& +1106 H * H-0.001455 P * V+0.000297 P * T \\\\\n& -0.05 P * H-0.000032 V * T-0.119 V * H+0.02 T * H \\tag{19}\n\\end{align*}\n\n\nThe P-values were used as a tool to indicate the interactions between those variables for investigating the significance of each coefficient. In fact, the corresponding coefficients with smaller $\\mathrm{P}$ values were more significant than those with relatively larger $P$ values. Table 7 exhibits the ANOVA test results for preliminary quadratic regression models of three dimensions of melt pool at the end of the fifth track, revealing the significance at a level of $1 \\%(P<0.01)$ for three preliminary quadric regression models. Table 8 illustrates the summary of preliminary quadric regression coefficients. For the regression correlations of length/width/depth of the melt pool, the determination coefficients $\\left(R^{2}=98.91 \\% /\\right.$ 98.77\\%/96.94\\%) and the adjusted determination coefficients (Adj. $\\mathrm{R}^{2}=98.47 \\% / 98.27 \\% / 95.68 \\%$ ) confirmed that the models were highly significant. The models were found to be sufficient for accurate forecasts of three dimensions of melt pool within the ranges of input variables. In this study, the linear coefficients $(P, V)$ were most significant terms in preliminary model at greater than the $95 \\%$ confidence level, whereas other coefficients were not significant. The laser power and scanning speed were designated as the primary effects since those have a vital influence on the melt pool dimensions. Then the equations were completed to determine 3D response surfaces for predicting the relationships between the independent variables (laser power and scan speed) and the dependent variables (the length, width and depth of melt pool), while the other two variables were held constant at their respective center values of the testing ranges $\\left(T=110{ }^{\\circ} \\mathrm{C}\\right.$ and $H=0.075$ $\\mathrm{mm}$ ), as depicted in Fig. 11.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-12(1)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-12(2)}\n\\end{center}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-12}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-12(3)}\n\\end{center}\n\n(d)\n\nFig. 10. Predictions of length, width and depth of the melt pool during SLM of TiAl6V4 powder with different processing parameters: (a) laser power of $40-150 \\mathrm{~W}$ ( $v=210$ $\\mathrm{mm} / \\mathrm{s}, T=110^{\\circ} \\mathrm{C}$ and $H=0.075 \\mathrm{~mm}$.", "start_char_idx": 474924, "end_char_idx": 477954, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "6ee9940f-9ea8-4cee-9ef3-78a17dc4863c": {"__data__": {"id_": "6ee9940f-9ea8-4cee-9ef3-78a17dc4863c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1c5c9186-196b-4583-bb38-bd61118d1045", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "dae27c08ebb4fa6b5a972975297cb5e1daea456bfecd713dc936a6922a4beab6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "79185e9f-cf18-4e79-bd59-8b253788fe4d", "node_type": "1", "metadata": {}, "hash": "ee5ffe6a20f92c796cde814987fda33d316665d681c5f750eccb26024bf068a4", "class_name": "RelatedNodeInfo"}}, "text": "10. Predictions of length, width and depth of the melt pool during SLM of TiAl6V4 powder with different processing parameters: (a) laser power of $40-150 \\mathrm{~W}$ ( $v=210$ $\\mathrm{mm} / \\mathrm{s}, T=110^{\\circ} \\mathrm{C}$ and $H=0.075 \\mathrm{~mm}$.); (b) scanning speed of $20-400 \\mathrm{~mm} / \\mathrm{s}\\left(P=95 \\mathrm{~W}, T=110^{\\circ} \\mathrm{C}\\right.$ and $H=0.075 \\mathrm{~mm}$.); (c) preheating temperature of $20-200{ }^{\\circ} \\mathrm{C}(P=95 \\mathrm{~W}, v=$ $210 \\mathrm{~mm} / \\mathrm{s}$ and $H=0.075 \\mathrm{~mm}$.) and (d) hatch space $0.05-0.075 \\mathrm{~mm}\\left(P=95 \\mathrm{~W}, v=210 \\mathrm{~mm} / \\mathrm{s}\\right.$ and $T=110^{\\circ} \\mathrm{C}$. ) Hold values of $P=95 \\mathrm{~W}, v=210 \\mathrm{~mm} / \\mathrm{s}, T=110{ }^{\\circ} \\mathrm{C}$ and $H=0.075$ $\\mathrm{mm}$.\n\nTable 6\n\nTest matrix for DOE with 49 simulation runs completed and results obtained.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline\nNo. & $\\mathrm{X} 1$, power $(\\mathrm{W})$ & X2, scan speed $(\\mathrm{mm} / \\mathrm{s})$ & $\\mathrm{X} 3$, preheat temp. $\\left({ }^{\\circ} \\mathrm{C}\\right)$ & X4, hatch space $(\\mathrm{mm})$ & Length (mm) & Width (mm) & Depth (mm) \\\\\n\\hline\n1 & 0 & 0 & 0 & 0 & 0.169 & 0.137 & 0.053 \\\\\n\\hline\n2 & -1 & 0 & 0 & 0 & 0.101 & 0.082 & 0.022 \\\\\n\\hline\n3 & -0.5 & 0 & 0 & 0 & 0.133 & 0.105 & 0.033 \\\\\n\\hline\n4 & 1 & 0 & 0 & 0 & 0.246 & 0.181 & 0.084 \\\\\n\\hline\n5 & 0.5 & 0 & 0 & 0 & 0.211 & 0.159 & 0.066 \\\\\n\\hline\n6 & 0 & -1 & 0 & 0 & 0.221 & 0.188 & 0.092 \\\\\n\\hline\n7 & 0 & -0.5 & 0 & 0 & 0.184 & 0.149 & 0.062 \\\\\n\\hline\n8 & 0 & 1 & 0 & 0 & 0.158 & 0.116 & 0.037 \\\\\n\\hline\n9 & 0 & 0.5 & 0 & 0 & 0.161 & 0.126 & 0.041 \\\\\n\\hline\n10 & 0 & 0 & -1 & 0 & 0.169 & 0.135 & 0.049 \\\\\n\\hline\n11 & 0 & 0 & -0.5 & 0 & 0.169 & 0.137 & 0.051 \\\\\n\\hline\n12 & 0 & 0 & 1 & 0 & 0.174 & 0.140 & 0.055 \\\\\n\\hline\n13 & 0 & 0 & 0.5 & 0 & 0.172 & 0.138 & 0.053 \\\\\n\\hline\n14 & 0 & 0 & 0 & -1 & 0.170 & 0.140 & 0.052 \\\\\n\\hline\n15 & 0 & 0 & 0 & -0.5 & 0.170 & 0.134 & 0.", "start_char_idx": 477697, "end_char_idx": 479690, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "79185e9f-cf18-4e79-bd59-8b253788fe4d": {"__data__": {"id_": "79185e9f-cf18-4e79-bd59-8b253788fe4d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "6ee9940f-9ea8-4cee-9ef3-78a17dc4863c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8d7b74db6793c5fa3ee956d881bc59c59cf91c7434af1f5626c98b3d0dff7b95", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ddcd607e-72bd-47be-87fd-588c1c5ef01a", "node_type": "1", "metadata": {}, "hash": "7d136ff89133807d5ab976e73f42a383bb402eca9bafc12a57cdc4ff9ae0134c", "class_name": "RelatedNodeInfo"}}, "text": "169 & 0.135 & 0.049 \\\\\n\\hline\n11 & 0 & 0 & -0.5 & 0 & 0.169 & 0.137 & 0.051 \\\\\n\\hline\n12 & 0 & 0 & 1 & 0 & 0.174 & 0.140 & 0.055 \\\\\n\\hline\n13 & 0 & 0 & 0.5 & 0 & 0.172 & 0.138 & 0.053 \\\\\n\\hline\n14 & 0 & 0 & 0 & -1 & 0.170 & 0.140 & 0.052 \\\\\n\\hline\n15 & 0 & 0 & 0 & -0.5 & 0.170 & 0.134 & 0.052 \\\\\n\\hline\n16 & 0 & 0 & 0 & 1 & 0.171 & 0.135 & 0.052 \\\\\n\\hline\n17 & 0 & 0 & 0 & 0.5 & 0.170 & 0.134 & 0.052 \\\\\n\\hline\n18 & -0.5 & -0.5 & -0.5 & -0.5 & 0.143 & 0.116 & 0.037 \\\\\n\\hline\n19 & -0.25 & -0.25 & -0.25 & -0.25 & 0.162 & 0.129 & 0.042 \\\\\n\\hline\n20 & 0.5 & -0.5 & -0.5 & -0.5 & 0.228 & 0.184 & 0.081 \\\\\n\\hline\n21 & 0.25 & -0.25 & -0.25 & -0.25 & 0.194 & 0.153 & 0.064 \\\\\n\\hline\n22 & -0.5 & 0.5 & -0.5 & -0.5 & 0.122 & 0.096 & 0.030 \\\\\n\\hline\n23 & -0.25 & 0.25 & -0.25 & -0.25 & 0.146 & 0.116 & 0.037 \\\\\n\\hline\n24 & 0.5 & 0.5 & -0.5 & -0.5 & 0.190 & 0.142 & 0.058 \\\\\n\\hline\n25 & 0.25 & 0.25 & -0.25 & -0.25 & 0.189 & 0.139 & 0.057 \\\\\n\\hline\n26 & -0.5 & -0.5 & 0.5 & -0.5 & 0.146 & 0.122 & 0.039 \\\\\n\\hline\n27 & -0.25 & -0.25 & 0.25 & -0.25 & 0.165 & 0.130 & 0.043 \\\\\n\\hline\n28 & 0.5 & -0.5 & 0.5 & -0.5 & 0.228 & 0.184 & 0.084 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 6 (continued)\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline\nNo. & $\\mathrm{X} 1$, power $(\\mathrm{W})$ & $\\mathrm{X} 2$, scan speed $(\\mathrm{mm} / \\mathrm{s})$ & $\\mathrm{X} 3$, preheat temp.", "start_char_idx": 479400, "end_char_idx": 480773, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ddcd607e-72bd-47be-87fd-588c1c5ef01a": {"__data__": {"id_": "ddcd607e-72bd-47be-87fd-588c1c5ef01a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "79185e9f-cf18-4e79-bd59-8b253788fe4d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d85b41eeb40091f59e9e03ac51f671887dc19287cdfe94304f93961b94bf4136", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6d0b1195-f22a-4055-b955-8f839d6d7453", "node_type": "1", "metadata": {}, "hash": "a9754baf2a7fe43029b1459e9afd19e63c05ce2a1c632d96658929bfca6cb68c", "class_name": "RelatedNodeInfo"}}, "text": "122 & 0.039 \\\\\n\\hline\n27 & -0.25 & -0.25 & 0.25 & -0.25 & 0.165 & 0.130 & 0.043 \\\\\n\\hline\n28 & 0.5 & -0.5 & 0.5 & -0.5 & 0.228 & 0.184 & 0.084 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 6 (continued)\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline\nNo. & $\\mathrm{X} 1$, power $(\\mathrm{W})$ & $\\mathrm{X} 2$, scan speed $(\\mathrm{mm} / \\mathrm{s})$ & $\\mathrm{X} 3$, preheat temp. $\\left({ }^{\\circ} \\mathrm{C}\\right)$ & X4, hatch space (mm) & Length (mm) & Width (mm) & Depth (mm) \\\\\n\\hline\n29 & 0.25 & -0.25 & 0.25 & -0.25 & 0.212 & 0.158 & 0.064 \\\\\n\\hline\n30 & -0.5 & 0.5 & 0.5 & -0.5 & 0.128 & 0.097 & 0.031 \\\\\n\\hline\n31 & -0.25 & 0.25 & 0.25 & -0.25 & 0.152 & 0.118 & 0.038 \\\\\n\\hline\n32 & 0.5 & 0.5 & 0.5 & -0.5 & 0.202 & 0.151 & 0.061 \\\\\n\\hline\n33 & 0.25 & 0.25 & 0.25 & -0.25 & 0.186 & 0.142 & 0.058 \\\\\n\\hline\n34 & -0.5 & -0.5 & -0.5 & 0.5 & 0.142 & 0.117 & 0.037 \\\\\n\\hline\n35 & -0.25 & -0.25 & -0.25 & 0.25 & 0.161 & 0.132 & 0.042 \\\\\n\\hline\n36 & 0.5 & -0.5 & -0.5 & 0.5 & 0.224 & 0.180 & 0.081 \\\\\n\\hline\n37 & 0.25 & -0.25 & -0.25 & 0.25 & 0.196 & 0.153 & 0.063 \\\\\n\\hline\n38 & -0.5 & 0.5 & -0.5 & 0.5 & 0.118 & 0.097 & 0.029 \\\\\n\\hline\n39 & -0.25 & 0.25 & -0.25 & 0.25 & 0.141 & 0.112 & 0.036 \\\\\n\\hline\n40 & 0.5 & 0.5 & -0.5 & 0.5 & 0.190 & 0.146 & 0.058 \\\\\n\\hline\n41 & 0.25 & 0.25 & -0.25 & 0.25 & 0.186 & 0.140 & 0.056 \\\\\n\\hline\n42 & -0.5 & -0.5 & 0.5 & 0.5 & 0.144 & 0.119 & 0.039 \\\\\n\\hline\n43 & -0.25 & -0.25 & 0.25 & 0.25 & 0.164 & 0.130 & 0.043 \\\\\n\\hline\n44 & 0.5 & -0.5 & 0.5 & 0.5 & 0.226 & 0.182 & 0.085 \\\\\n\\hline\n45 & 0.25 & -0.25 & 0.25 & 0.25 & 0.196 & 0.156 & 0.064 \\\\\n\\hline\n46 & -0.5 & 0.5 & 0.5 & 0.5 & 0.122 & 0.098 & 0.031 \\\\\n\\hline\n47 & -0.25 & 0.25 & 0.25 & 0.25 & 0.149 & 0.119 & 0.037 \\\\\n\\hline\n48 & 0.5 & 0.5 & 0.5 & 0.5 & 0.196 & 0.149 & 0.060 \\\\\n\\hline\n49 & 0.25 & 0.25 & 0.25 & 0.25 & 0.188 & 0.141 & 0.057 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 7\n\nANOVA test results for preliminary quadric regression model three dimensions of melt pool at the end of the fifth track.", "start_char_idx": 480382, "end_char_idx": 482399, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "6d0b1195-f22a-4055-b955-8f839d6d7453": {"__data__": {"id_": "6d0b1195-f22a-4055-b955-8f839d6d7453", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ddcd607e-72bd-47be-87fd-588c1c5ef01a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1ddb71bcd17899eab821cacb0417038ff492cc0a64eb7c677eb4ed65fb3955d5", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "66cf42ef-788e-4bbf-9a1f-2fd0fbecaec0", "node_type": "1", "metadata": {}, "hash": "588a7ea6759486fcbfb960755cc308f37a8595180d163c1d9b5bb480b72365d1", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\nSource & DF &  &  & Adj SS &  &  & Adj MS &  &  & F-Value &  &  & P-Value \\\\\n\\hline\n\\multicolumn{14}{|c|}{(a) ANOVA for the length of melt pool} \\\\\n\\hline\nModel & 14 &  &  & 50016.3 &  &  & 3572.6 &  &  & 221.25 &  &  & .000 \\\\\n\\hline\nLinear & 4 &  &  & 49433.1 &  &  & 12358.3 &  &  & 765.36 &  &  & .000 \\\\\n\\hline\nSquare & 4 &  &  & 468 &  &  & 117 &  &  & 7.25 &  &  & .000 \\\\\n\\hline\n2-Way Interaction & 6 &  &  & 118.5 &  &  & 19.8 &  &  & 1.22 &  &  & .319 \\\\\n\\hline\nError & 34 &  &  & 549 &  &  & 16.1 &  &  &  &  &  &  \\\\\n\\hline\nTotal & 48 &  &  & 50565.3 &  &  &  &  &  &  &  &  &  \\\\\n\\hline\n\\multicolumn{14}{|c|}{(b) ANOVA for the width of melt pool} \\\\\n\\hline\nModel & 14 & 29306.8 &  &  & 2093.3 &  &  & 195.72 &  &  & .000 &  &  \\\\\n\\hline\nLinear & 4 & 28596.9 &  &  & 7149.2 &  &  & 668.44 &  &  & .000 &  &  \\\\\n\\hline\nSquare & 4 & 502.2 &  &  & 125.5 &  &  & 11.74 &  &  & .000 &  &  \\\\\n\\hline\n2-Way Interaction & 6 & 211.6 &  &  & 35.3 &  &  & 3.3 &  &  & .011 &  &  \\\\\n\\hline\nError & 34 & 363.6 &  &  & 10.7 &  &  &  &  &  &  &  &  \\\\\n\\hline\nTotal & 48 & 29670.5 &  &  &  &  &  &  &  &  &  &  &  \\\\\n\\hline\n\\multicolumn{14}{|c|}{(c) ANOVA for the depth of melt pool} \\\\\n\\hline\nModel & 14 &  & 12908.3 &  &  & 922.02 &  &  & 76.98 &  &  & .000 &  \\\\\n\\hline\nLinear & 4 &  & 12330.3 &  &  & 3082.56 &  &  & 257.35 &  &  & .000 &  \\\\\n\\hline\nSquare & 4 &  & 332.3 &  &  & 83.07 &  &  & 6.94 &  &  & .000 &  \\\\\n\\hline\n2-Way Interaction & 6 &  & 248.3 &  &  & 41.38 &  &  & 3.45 &  &  & .009 &  \\\\\n\\hline\nError & 34 &  & 407.3 &  &  & 11.98 &  &  &  &  &  &  &  \\\\\n\\hline\nTotal & 48 &  & 13315.6 &  &  &  &  &  &  &  &  &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\subsection*{4.4. Process window}\nThe process window of SLM technical is specified by the laser power and scan speed.", "start_char_idx": 482401, "end_char_idx": 484257, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "66cf42ef-788e-4bbf-9a1f-2fd0fbecaec0": {"__data__": {"id_": "66cf42ef-788e-4bbf-9a1f-2fd0fbecaec0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "6d0b1195-f22a-4055-b955-8f839d6d7453", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4e93dd829742502cab318528f2986f23ffd4df5d3dc4c25f38f7cc9214311162", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "96d12b70-bf65-41ea-9cf9-014228eb7e89", "node_type": "1", "metadata": {}, "hash": "1811daef5646b8c022f99e38fd9a47e015c9cd66fa7058c6e6004a2d363fa901", "class_name": "RelatedNodeInfo"}}, "text": "Process window}\nThe process window of SLM technical is specified by the laser power and scan speed. To enable the detailed observations of the better heat affected zone and surface smoothness under SLM procedures, it is thus necessary to develop strict quality criteria. The laser power and scan speed were constrained by two criteria of the width and depth of the molten pool. For the cases with the melt pool width less than the hatch space, the TiAl6V4 powder bed cannot be completely melted with residue left, leading to the failure of SLM operation. Alternatively, as the melt pool width is two times greater than the hatch space, the over-concentrated laser energy tends to produce excessive re-melting and overheating between or even beyond the neighboring tracks with the occurrence of splashes and balling for causing the poor surface quality. Another criterion is that the depth of molten pool must be exceeding the single layer thickness of TiAl6V4 powder to ensure the direct bonding formation of powder layer with the dense substrate.\\\\\nFrom the aforementioned criteria, the process window can effectively realize practical combinations for the predictions of the molten pool size during SLM, as illustrated in Fig. 12.\n\n\\subsection*{4.5. Development and validation of critical RSM with FEM predictions}\nAs indicated above, the process window can be used as a filter to remove the ineffectual and impractical conditions of input variables, and then apply the screened combinations (i.e. narrower ranges of those processing parameters) to fit a full quadratic regression model with regression coefficients obtained for accurately determining three dimensions of melt pool. As described in Table 9, the critical regression models indicated the corresponding adjusted determination coefficients (Adj. $\\mathrm{R}^{2}$ ) were 97.89\\%/98.03\\%/97.57\\%, indicating that only less than $2.11 \\% / 1.97 \\% / 2.43 \\%$ of the total variations were not explained by the models. Besides, the significance of each coefficient was determined using P-value. It could be seen that two independent variables $(P, V)$ and two quadratic\n\nTable 8\n\nSummary of preliminary quadric regression coefficients:\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\n\\begin{tabular}{l}\nModel summary \\\\\nTerm \\\\\n\\end{tabular} & \\begin{tabular}{l}\nRsqr \\\\\n$98.91 \\%$ \\\\\nCoef \\\\\n\\end{tabular} & \\begin{tabular}{l}\nAdj Rsqr \\\\\n$98.47 \\%$ \\\\\nSE Coef \\\\\n\\end{tabular} & \\begin{tabular}{l}\nStandard Error of Estimate \\\\\n4.0183 \\\\\nT-Value \\\\\n\\end{tabular} & P-Value \\\\\n\\hline\n\\multicolumn{5}{|c|}{(a) Regression coefficients for the length of melt pool} \\\\\n\\hline\nConstant & 9.2 & 41.4 & 0.22 & .825 \\\\\n\\hline\nP & 1.663 & 0.302 & 5.51 & .000 \\\\\n\\hline\nV & -0.2175 & 0.0826 & -2.63 & .013 \\\\\n\\hline\n$\\mathrm{T}$ & 0.165 & 0.176 & 0.94 & .354 \\\\\n\\hline\n$\\mathrm{H}$ & 1300 & 775 & 1.68 & .103 \\\\\n\\hline\nP*P & -0.0007 & 0.0009 & -0.73 & .469 \\\\\n\\hline\n$\\mathrm{V} * \\mathrm{~V}$ & 0.0004 & 0.0001 & 4.65 & .000 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{~T}$ & -0.0005 & 0.0003 & -1.46 & .153 \\\\\n\\hline\n$\\mathrm{H}^{*} \\mathrm{H}$ & -8265 & 4515 & -1.83 & .076 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~V}$ & -0.0009 & 0.0004 & -2.34 & .025 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~T}$ & 0.0001 & 0.0008 & 0.16 & .", "start_char_idx": 484158, "end_char_idx": 487420, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "96d12b70-bf65-41ea-9cf9-014228eb7e89": {"__data__": {"id_": "96d12b70-bf65-41ea-9cf9-014228eb7e89", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "66cf42ef-788e-4bbf-9a1f-2fd0fbecaec0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "da0b5a229a69896254c03c21bd758120dd9b7402cf64ebb5a1592080823433e8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ac833560-4742-437a-807a-b7e8f16d2ba8", "node_type": "1", "metadata": {}, "hash": "b34191950e26769fcc15d8d5ce4dcd7a8e41d063c2d3b45ec86eab0c28c677e7", "class_name": "RelatedNodeInfo"}}, "text": "0009 & -0.73 & .469 \\\\\n\\hline\n$\\mathrm{V} * \\mathrm{~V}$ & 0.0004 & 0.0001 & 4.65 & .000 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{~T}$ & -0.0005 & 0.0003 & -1.46 & .153 \\\\\n\\hline\n$\\mathrm{H}^{*} \\mathrm{H}$ & -8265 & 4515 & -1.83 & .076 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~V}$ & -0.0009 & 0.0004 & -2.34 & .025 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~T}$ & 0.0001 & 0.0008 & 0.16 & .872 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{H}$ & 0.26 & 2.84 & 0.09 & .926 \\\\\n\\hline\n$\\mathrm{V} * \\mathrm{~T}$ & 0.0003 & 0.0002 & 1.15 & .257 \\\\\n\\hline\nV* $\\mathrm{H}$ & -0.365 & 0.821 & -0.45 & .659 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{H}$ & -0.93 & 1.73 & -0.53 & .596 \\\\\n\\hline\n\\multirow[t]{2}{*}{Model Summary} & Rsqr & Adj Rsqr & Standard Error of Estimate &  \\\\\n\\hline\n & $98.77 \\%$ & $98.27 \\%$ & 3.27038 &  \\\\\n\\hline\nTerm & Coef & SE Coef & T-Value & P-Value \\\\\n\\hline\n\\multicolumn{5}{|c|}{(b) Regression coefficients for the width of melt pool} \\\\\n\\hline\nConstant & 53.9 & 33.7 & 1.6 & .119 \\\\\n\\hline\n$\\mathrm{P}$ & 1.628 & 0.245 & 6.63 & .000 \\\\\n\\hline\nV & -0.2509 & 0.0672 & -3.73 & .001 \\\\\n\\hline\n$\\mathrm{T}$ & 0.028 & 0.143 & 0.2 & .845 \\\\\n\\hline\n$\\mathrm{H}$ & -41 & 631 & -0.07 & .948 \\\\\n\\hline\n$\\mathrm{P} * \\mathrm{P}$ & -0.00195 & 0.000759 & -2.56 & .015 \\\\\n\\hline\n$\\mathrm{V} * \\mathrm{~V}$ & 0.000396 & 0.000064 & 6.22 & .000 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{~T}$ & 0.000121 & 0.000284 & 0.43 & .672 \\\\\n\\hline\n$\\mathrm{H}^{*} \\mathrm{H}$ & 214 & 3675 & 0.06 & .954 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~V}$ & -0.0013 & 0.000304 & -4.27 & .000 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~T}$ & 0.00032 & 0.000641 & 0.5 & 0.621 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{H}$ & -0.56 & 2.31 & -0.24 & .809 \\\\\n\\hline\n$\\mathrm{V} * \\mathrm{~T}$ & 0.000071 & 0.000186 & 0.38 & .706 \\\\\n\\hline\n$\\mathrm{V}^{*} \\mathrm{H}$ & 0.552 & 0.668 & 0.83 & .415 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{H}$ & -0.89 & 1.41 & -0.63 & .533 \\\\\n\\hline\n\\multirow[t]{2}{*}{Model Summary} & Rsqr & Adj Rsqr & Standard Error of Estimate &  \\\\\n\\hline\n & $96.94 \\%$ & $95.", "start_char_idx": 487050, "end_char_idx": 489051, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ac833560-4742-437a-807a-b7e8f16d2ba8": {"__data__": {"id_": "ac833560-4742-437a-807a-b7e8f16d2ba8", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "96d12b70-bf65-41ea-9cf9-014228eb7e89", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "95a796b8a94aaf202d8e42bf92b0c1f696a3773c26a434cf90faba8d26f26398", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a459c375-99ca-47c7-9835-df90bf83d1fe", "node_type": "1", "metadata": {}, "hash": "2cee84739968df3b1e3cbbc9f97f8eaf9bc1f7b28d6669b98363e93a6cafa1c6", "class_name": "RelatedNodeInfo"}}, "text": "5 & 0.621 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{H}$ & -0.56 & 2.31 & -0.24 & .809 \\\\\n\\hline\n$\\mathrm{V} * \\mathrm{~T}$ & 0.000071 & 0.000186 & 0.38 & .706 \\\\\n\\hline\n$\\mathrm{V}^{*} \\mathrm{H}$ & 0.552 & 0.668 & 0.83 & .415 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{H}$ & -0.89 & 1.41 & -0.63 & .533 \\\\\n\\hline\n\\multirow[t]{2}{*}{Model Summary} & Rsqr & Adj Rsqr & Standard Error of Estimate &  \\\\\n\\hline\n & $96.94 \\%$ & $95.68 \\%$ & 3.4609 &  \\\\\n\\hline\nTerm & Coef & SE Coef & T-Value & P-Value \\\\\n\\hline\n\\multicolumn{5}{|c|}{(c) Regression coefficients for the depth of melt pool} \\\\\n\\hline\nConstant & 3.5 & 35.6 & 0.1 & .923 \\\\\n\\hline\n$\\mathrm{P}$ & 0.863 & 0.26 & 3.32 & .002 \\\\\n\\hline\nV & -0.0969 & 0.0711 & -1.36 & .182 \\\\\n\\hline\n$\\mathrm{T}$ & -0.014 & 0.151 & -0.09 & .926 \\\\\n\\hline\n$\\mathrm{H}$ & -148 & 668 & -0.22 & .826 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{P}$ & 0.000348 & 0.000803 & 0.43 & .668 \\\\\n\\hline\n$\\mathrm{V} * \\mathrm{~V}$ & 0.000354 & 0.000067 & 5.26 & .000 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{~T}$ & 0.00008 & 0.0003 & 0.27 & .792 \\\\\n\\hline\n$\\mathrm{H}^{*} \\mathrm{H}$ & 1106 & 3889 & 0.28 & .778 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~V}$ & -0.00146 & 0.000321 & -4.53 & .000 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~T}$ & 0.000297 & 0.000678 & 0.44 & .664 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{H}$ & -0.05 & 2.44 & -0.02 & .985 \\\\\n\\hline\n$\\mathrm{V}^{*} \\mathrm{~T}$ & $-3.2 \\mathrm{E}-05$ & 0.000196 & -0.16 & .87 \\\\\n\\hline\n$\\mathrm{V}^{*} \\mathrm{H}$ & -0.119 & 0.707 & -0.17 & .867 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{H}$ & 0.02 & 1.49 & 0.02 & .988 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nterms $\\left(P^{2}\\right.$ and $\\left.V^{2}\\right)$ were the most significant terms of three dimensions of melt pool in terms of the overall results. The critical regression models were obtained by the coefficients, as shown below.\n\n\n\\begin{align*}\n\\text { Length }= & -9.9+2.855 P-0.323 V+0.159 T+605 H \\\\\n& -0.01066 P * P+0.000104 V * V-0.000392 T * T \\\\\n& -6744 H * H+0.00164 P * V-0.00348 P * T  \\tag{20}\\\\\n& +6.49 P * H+0.001118 V * T-1.48 V * H+0.79 T * H\n\\end{align*}", "start_char_idx": 488640, "end_char_idx": 490697, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a459c375-99ca-47c7-9835-df90bf83d1fe": {"__data__": {"id_": "a459c375-99ca-47c7-9835-df90bf83d1fe", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ac833560-4742-437a-807a-b7e8f16d2ba8", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ea38454a9a9dae038fb7afee4646e7ab26d732fa726fc3a7a4516622ba8299ed", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "854f9fc0-95dd-4e88-8aa6-c5194d658f32", "node_type": "1", "metadata": {}, "hash": "dcee011d2f73ea6f10af2584a6cc2a56f16418c73c771b264e1708a47235f4a1", "class_name": "RelatedNodeInfo"}}, "text": "988 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nterms $\\left(P^{2}\\right.$ and $\\left.V^{2}\\right)$ were the most significant terms of three dimensions of melt pool in terms of the overall results. The critical regression models were obtained by the coefficients, as shown below.\n\n\n\\begin{align*}\n\\text { Length }= & -9.9+2.855 P-0.323 V+0.159 T+605 H \\\\\n& -0.01066 P * P+0.000104 V * V-0.000392 T * T \\\\\n& -6744 H * H+0.00164 P * V-0.00348 P * T  \\tag{20}\\\\\n& +6.49 P * H+0.001118 V * T-1.48 V * H+0.79 T * H\n\\end{align*}\n\n\nWidth $=13.1+2.792 P-0.348 V+0.114 T-256 H$\n\n$$\n\\begin{aligned}\n& -0.01011 P * P+0.00007 V * V+0.000179 T * T \\\\\n& +960 H * H+0.000858 P * V-0.00172 P * T \\\\\n& +0.31 P * H+0.000529 V * T+0.780 V * H \\\\\n& -0.92 T * H\n\\end{aligned}\n$$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-15(3)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-15(1)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-15}\n\\end{center}\n\n(c)\n\nFig. 11. Preliminary response surfaces of (a) length, (b) width and (c) depth of molten pool.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-15(2)}\n\\end{center}\n\nFig. 12. Process window for SLM of Ti6Al4V powder at $T=110^{\\circ} \\mathrm{C}$ and $H=0.075 \\mathrm{~mm}$ for improper (red cross points) and appropriate (blue circle points) settings of laser power and scan speed. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)\n\n\n\\begin{align*}\n\\text { Depth }= & -14.5+0.715 P+0.0610 V+0.0094 T-85 H \\\\\n& +0.00363 P * P+0.000185 V * V+0.000146 T * T \\\\\n& +1967 H * H-0.002587 P * V+0.000507 P * T \\\\\n& -1.51 P * H-0.000003 V * T-0.021 V * H-0.78 T * H \\tag{21}\n\\end{align*}\n\n\nTherefore, the critical response surfaces were developed by the regression models, as depicted in Fig. 13. The verification of the validity of critical response surfaces was conducted via comparing the predictions by the critical regression models with the FEM simulated results. Table 10 shows the ANOVA test results for critical quadratic regression models of three dimensions of melt pool at the end of the fifth track. The significance was specified at a level of $1 \\%(P<0.01)$. The smaller was the value of $P$, the more significant was the corresponding coefficient. Moreover, the analysis of variance (ANOVA) in Table 10 revealed that the linear and square models of three critical regression models significantly affected the melt pool size with the resultant regression correlations being significant at greater than the $99.9 \\%$ confidence level.", "start_char_idx": 490181, "end_char_idx": 492927, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "854f9fc0-95dd-4e88-8aa6-c5194d658f32": {"__data__": {"id_": "854f9fc0-95dd-4e88-8aa6-c5194d658f32", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a459c375-99ca-47c7-9835-df90bf83d1fe", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "22b86df1ed3239afe2160cea15c688e58f3999ab4a33628f5716bd6075ff8309", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "49634cbd-1d7b-460a-a989-76b14acfb762", "node_type": "1", "metadata": {}, "hash": "32c116e4b76ed21d8b8cfcd5d1611277459ed9063fffb750547a12b14fc4bde2", "class_name": "RelatedNodeInfo"}}, "text": "Therefore, the critical response surfaces were developed by the regression models, as depicted in Fig. 13. The verification of the validity of critical response surfaces was conducted via comparing the predictions by the critical regression models with the FEM simulated results. Table 10 shows the ANOVA test results for critical quadratic regression models of three dimensions of melt pool at the end of the fifth track. The significance was specified at a level of $1 \\%(P<0.01)$. The smaller was the value of $P$, the more significant was the corresponding coefficient. Moreover, the analysis of variance (ANOVA) in Table 10 revealed that the linear and square models of three critical regression models significantly affected the melt pool size with the resultant regression correlations being significant at greater than the $99.9 \\%$ confidence level. The comparison in Table 11 indicated that the greatest differences of three dimensions of melt pool between the critical RSM predictions and the FEM simulated results were $3.6 \\%, 2.2 \\%$ and $2.0 \\%$, respectively, for three typical working scenarios of SLM. The predicted three dimensions of melt pool by the critical RSM models agreed well with the FEM simulations, suggesting accurate prediction capabilities of the critical regression models.\n\n\\section*{5. Conclusions}\nA dynamic DOE-FEM analysis was formulated to simulate the thermal characteristics of TiAl6V4 powder for accurately resolving the time progression of temperature distribution and melt pool extent during SLM. The predictions of the length, width and depth of melt pool were in good agreement with previous computational results and experimental measurements in the literature. We then implemented the RSM technique to characterize the relationship of the input processing parameters of the laser power, scanning speed, preheating temperature and hatch space with the response factors of the length, width and depth of the melt pool for establishing the regression correlations in SLM. The preliminary RSM results indicated that the length, width and depth of the melt pool\n\nTable 9\n\nSummary of critical quadric regression coefficients:\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\n\\begin{tabular}{l}\nModel Summary \\\\\nTerm \\\\\n\\end{tabular} & \\begin{tabular}{l}\nRsqr \\\\\n$98.79 \\%$ \\\\\nCoef \\\\\n\\end{tabular} & \\begin{tabular}{l}\nAdj Rsqr \\\\\n$97.89 \\%$ \\\\\nSE Coef \\\\\n\\end{tabular} & \\begin{tabular}{l}\nStandard Error of Estimate \\\\\n2.8163 \\\\\nT-Value \\\\\n\\end{tabular} & P-Value \\\\\n\\hline\n\\multicolumn{5}{|c|}{(a) Regression coefficients for the length of melt pool} \\\\\n\\hline\nConstant & -9.9 & 38.8 & -0.26 & .801 \\\\\n\\hline\nP & 2.855 & 0.64 & 4.46 & .000 \\\\\n\\hline\nV & -0.323 & 0.15 & -2.16 & .044 \\\\\n\\hline\n$\\mathrm{T}$ & 0.159 & 0.169 & 0.94 & .358 \\\\\n\\hline\n$\\mathrm{H}$ & 605 & 661 & 0.92 & .371 \\\\\n\\hline\nP*P & -0.01066 & 0.00371 & -2.87 & .01 \\\\\n\\hline\n$\\mathrm{V} * \\mathrm{~V}$ & 0.000104 & 0.000114 & 0.91 & .374 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{~T}$ & -0.00039 & 0.000271 & -1.45 & .165 \\\\\n\\hline\n$\\mathrm{H}^{*} \\mathrm{H}$ & -6744 & 3515 & -1.92 & .07 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~V}$ & 0.00164 & 0.00122 & 1.34 & .196 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~T}$ & -0.00348 & 0.00179 & -1.94 & .067 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{H}$ & 6.49 & 3.96 & 1.64 & .", "start_char_idx": 492069, "end_char_idx": 495378, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "49634cbd-1d7b-460a-a989-76b14acfb762": {"__data__": {"id_": "49634cbd-1d7b-460a-a989-76b14acfb762", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "854f9fc0-95dd-4e88-8aa6-c5194d658f32", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "dd6296130730dbcabef5bc3e8c238f4e19be2389c0ada9474b49edc670734f51", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2053dda6-01fc-4bc9-a58d-81e453a4cf60", "node_type": "1", "metadata": {}, "hash": "07d9f4b5c976ecf4f8c48ff3b4e13b58cc11473359b1aa18aa1e4b54fd81112b", "class_name": "RelatedNodeInfo"}}, "text": "000114 & 0.91 & .374 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{~T}$ & -0.00039 & 0.000271 & -1.45 & .165 \\\\\n\\hline\n$\\mathrm{H}^{*} \\mathrm{H}$ & -6744 & 3515 & -1.92 & .07 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~V}$ & 0.00164 & 0.00122 & 1.34 & .196 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~T}$ & -0.00348 & 0.00179 & -1.94 & .067 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{H}$ & 6.49 & 3.96 & 1.64 & .118 \\\\\n\\hline\n$\\mathrm{V}^{*} \\mathrm{~T}$ & 0.001118 & 0.000502 & 2.23 & .038 \\\\\n\\hline\nV* $\\mathrm{H}$ & -1.48 & 1 & -1.48 & .156 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{H}$ & 0.79 & 1.93 & 0.41 & .686 \\\\\n\\hline\n\\multirow[t]{2}{*}{Model Summary} & Rsqr & Adj Rsqr & Standard Error of Estimate &  \\\\\n\\hline\n & $98.87 \\%$ & $98.03 \\%$ & 3.27038 &  \\\\\n\\hline\nTerm & Coef & SE Coef & T-Value & P-Value \\\\\n\\hline\n\\multicolumn{5}{|c|}{(b) Regression coefficients for the width of melt pool} \\\\\n\\hline\nConstant & 13.1 & 26.6 & 0.49 & .628 \\\\\n\\hline\n$\\mathrm{P}$ & 2.792 & 0.439 & 6.35 & .000 \\\\\n\\hline\nV & -0.348 & 0.103 & -3.39 & .003 \\\\\n\\hline\n$\\mathrm{T}$ & 0.114 & 0.116 & 0.99 & .337 \\\\\n\\hline\n$\\mathrm{H}$ & -256 & 453 & -0.56 & .579 \\\\\n\\hline\n$\\mathrm{P} * \\mathrm{P}$ & -0.01011 & 0.00255 & -3.97 & .001 \\\\\n\\hline\n$\\mathrm{V} * \\mathrm{~V}$ & 0.00007 & 0.000078 & 0.89 & .383 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{~T}$ & 0.000179 & 0.000186 & 0.96 & .349 \\\\\n\\hline\n$\\mathrm{H}^{*} \\mathrm{H}$ & 960 & 2412 & 0.4 & .695 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~V}$ & 0.000858 & 0.000839 & 1.02 & .319 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~T}$ & -0.00172 & 0.00123 & -1.4 & .178 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{H}$ & 0.31 & 2.72 & 0.11 & .911 \\\\\n\\hline\n$\\mathrm{V} * \\mathrm{~T}$ & 0.000529 & 0.000345 & 1.53 & .141 \\\\\n\\hline\n$\\mathrm{V}^{*} \\mathrm{H}$ & 0.78 & 0.688 & 1.13 & .271 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{H}$ & -0.92 & 1.33 & -0.7 & .495 \\\\\n\\hline\n\\multirow[t]{2}{*}{Model Summary} & Rsqr & Adj Rsqr & Standard Error of Estimate &  \\\\\n\\hline\n & $98.60 \\%$ & $97.57 \\%$ & 1.", "start_char_idx": 495004, "end_char_idx": 496947, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2053dda6-01fc-4bc9-a58d-81e453a4cf60": {"__data__": {"id_": 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"2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "49634cbd-1d7b-460a-a989-76b14acfb762", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b7b90bf6622cbf9f23cecbe06b24216dae2e9b78c0f90bc777c4b893870f01c8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1338d703-b041-4628-9948-c56bcd9bac34", "node_type": "1", "metadata": {}, "hash": "cf4894cea651b48da8deb18fb46eba23d65924244b08975b987bb668bfd20dbd", "class_name": "RelatedNodeInfo"}}, "text": "178 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{H}$ & 0.31 & 2.72 & 0.11 & .911 \\\\\n\\hline\n$\\mathrm{V} * \\mathrm{~T}$ & 0.000529 & 0.000345 & 1.53 & .141 \\\\\n\\hline\n$\\mathrm{V}^{*} \\mathrm{H}$ & 0.78 & 0.688 & 1.13 & .271 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{H}$ & -0.92 & 1.33 & -0.7 & .495 \\\\\n\\hline\n\\multirow[t]{2}{*}{Model Summary} & Rsqr & Adj Rsqr & Standard Error of Estimate &  \\\\\n\\hline\n & $98.60 \\%$ & $97.57 \\%$ & 1.4851 &  \\\\\n\\hline\nTerm & Coef & SE Coef & T-Value & P-Value \\\\\n\\hline\n\\multicolumn{5}{|c|}{(c) Regression coefficients for the depth of melt pool} \\\\\n\\hline\nConstant & -14.5 & 20.5 & -0.71 & .486 \\\\\n\\hline\n$\\mathrm{P}$ & 0.715 & 0.337 & 2.12 & .048 \\\\\n\\hline\nV & 0.061 & 0.0789 & 0.77 & .449 \\\\\n\\hline\n$\\mathrm{T}$ & 0.0094 & 0.0889 & 0.11 & .917 \\\\\n\\hline\n$\\mathrm{H}$ & -85 & 348 & -0.24 & .81 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{P}$ & 0.00363 & 0.00195 & 1.86 & .078 \\\\\n\\hline\n$\\mathrm{V} * \\mathrm{~V}$ & 0.000185 & 0.00006 & 3.08 & .006 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{~T}$ & 0.000146 & 0.000143 & 1.02 & .319 \\\\\n\\hline\n$\\mathrm{H}^{*} \\mathrm{H}$ & 1967 & 1851 & 1.06 & .301 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~V}$ & -0.00259 & 0.000644 & -4.02 & 0.001 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{~T}$ & 0.000507 & 0.000945 & 0.54 & 0.598 \\\\\n\\hline\n$\\mathrm{P}^{*} \\mathrm{H}$ & -1.51 & 2.09 & -0.72 & 0.478 \\\\\n\\hline\n$\\mathrm{V}^{*} \\mathrm{~T}$ & $-3 E-06$ & 0.000265 & -0.01 & 0.992 \\\\\n\\hline\n$\\mathrm{V}^{*} \\mathrm{H}$ & -0.021 & 0.528 & -0.04 & 0.969 \\\\\n\\hline\n$\\mathrm{T}^{*} \\mathrm{H}$ & -0.78 & 1.02 & -0.77 & 0.453 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nwere found to increase with the laser power on the powder layer, whereas escalating scan speeds led to the reduction of three dimensions of the melt pool. Furthermore, the preheating temperature and hatching space were insignificant to the melt pool extent. The adjusted determination coefficients (Adj. $R^{2}$ ) for the regression correlations of length/width/depth of melt pool were $98.47 \\% / 98.27 \\% / 95.68 \\%$, respectively. To screen out ineffectual and impractical conditions, the process window was applied using the quality criteria to realize critical response surfaces for enveloping the practical ranges of processing parameters. For the critical RSM results, the adjusted determination coefficients (Adj. $\\mathrm{R}^{2}$ ) were improved to $97.89 \\% / 98.03 \\% / 97.57 \\%$ for the regression correlations of length/ width/depth of melt pool.", "start_char_idx": 496535, "end_char_idx": 498965, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1338d703-b041-4628-9948-c56bcd9bac34": {"__data__": {"id_": "1338d703-b041-4628-9948-c56bcd9bac34", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2053dda6-01fc-4bc9-a58d-81e453a4cf60", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "06e44699fe9cfa83f9304f14e8a4894cd04aaf265a7ab8e07f802d5003cdf946", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "53159190-c272-409f-9881-5ff5e142d59d", "node_type": "1", "metadata": {}, "hash": "ae3a3fa5a353e35b4582ccb2fd44f1db5f55ad268644dffd74b0b1f49f6713ce", "class_name": "RelatedNodeInfo"}}, "text": "whereas escalating scan speeds led to the reduction of three dimensions of the melt pool. Furthermore, the preheating temperature and hatching space were insignificant to the melt pool extent. The adjusted determination coefficients (Adj. $R^{2}$ ) for the regression correlations of length/width/depth of melt pool were $98.47 \\% / 98.27 \\% / 95.68 \\%$, respectively. To screen out ineffectual and impractical conditions, the process window was applied using the quality criteria to realize critical response surfaces for enveloping the practical ranges of processing parameters. For the critical RSM results, the adjusted determination coefficients (Adj. $\\mathrm{R}^{2}$ ) were improved to $97.89 \\% / 98.03 \\% / 97.57 \\%$ for the regression correlations of length/ width/depth of melt pool. In view of three typical SLM working scenarios, the comparison indicated that the greatest differences of the critical RSM predictions with FEM simulations were $3.6 \\%, 2.2 \\%$ and $2.0 \\%$ for three dimensions of the melt pool. Accurate predictions of the melt pool dimensions can be helpful to smooth the homogeneity of liquid zone size during SLM, and thereby improve the quality of produced parts. Based on the screened results, the ranges of laser power and scanning speed were modified to $67.5-122.5 \\mathrm{~W}$ and $115-400 \\mathrm{~mm} / \\mathrm{s}$, which can effectively realize practical combinations to predict the melt pool dimensions\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-17}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-17(1)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_28c7c9a63c5801f46eefg-17(2)}\n\\end{center}\n\n(c)\n\nFig. 13. Critical response surfaces of (a) length, (b) width and (c) depth of molten pool.", "start_char_idx": 498171, "end_char_idx": 500044, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "53159190-c272-409f-9881-5ff5e142d59d": {"__data__": {"id_": "53159190-c272-409f-9881-5ff5e142d59d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1338d703-b041-4628-9948-c56bcd9bac34", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "567a0e6ec8ad8cd6701f688347242a752b6484499d076405edd04ba1abc92c76", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c59c139c-b3db-4b18-bc49-3ac1256b3bc5", "node_type": "1", "metadata": {}, "hash": "7b360f6040c58a2a32bc76ca60c097092ed22bfea5a38001df09936ffcb3405d", "class_name": "RelatedNodeInfo"}}, "text": "13. Critical response surfaces of (a) length, (b) width and (c) depth of molten pool.\n\nTable 10\n\nANOVA test results for critical quadric regression model three dimensions of melt pool at the end of the fifth track:\n\n\\begin{center}\n\\begin{tabular}{llllll}\n\\hline\nSource & DF & Adj SS & Adj MS & F-Value & P-Value \\\\\n\\hline\n(a) ANOVA for the length of melt pool &  &  &  &  &  \\\\\nModel & 14 & 12231.6 & 873.68 & 110.6 & .000 \\\\\nLinear & 4 & 8712 & 2178.01 & 275.71 & .000 \\\\\nSquare & 4 & 152.7 & 38.17 & 4.83 & .007 \\\\\n2-Way Interaction & 6 & 67.2 & 11.2 & 1.42 & .259 \\\\\nError & 19 & 150.1 & 7.9 &  &  \\\\\nTotal & 33 & 12381.6 &  &  &  \\\\\n(b) ANOVA for the width of melt pool &  &  &  &  &  \\\\\nModel & 14 & 6174.56 & 441.04 & 118.57 & .000 \\\\\nLinear & 4 & 3926.85 & 981.71 & 263.93 & .000 \\\\\nSquare & 4 & 93.94 & 23.49 & 6.31 & .002 \\\\\n2-Way Interaction & 6 & 20.21 & 3.37 & 0.91 & .512 \\\\\nError & 19 & 70.67 & 3.72 &  &  \\\\\nTotal & 33 & 6245.23 &  &  &  \\\\\n(c) ANOVA for the depth of melt pool &  &  &  &  &  \\\\\nModel & 14 & 2939.59 & 209.97 & 95.79 & .000 \\\\\nLinear & 4 & 2158.46 & 539.62 & 246.19 & .000 \\\\\nSquare & 4 & 22.95 & 5.74 & 2.62 & .068 \\\\\n2-Way Interaction & 6 & 80.66 & 13.44 & 6.13 & .001 \\\\\nError & 19 & 41.65 & 2.19 &  &  \\\\\nTotal & 33 & 2981.23 &  &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nwithout necessitating the changes of SLM machine or the design of manufactured parts. It is thus suggested that the RSM technique in conjunction with the process window to filter those unsuitable processing parameters can be a more effective way to achieve a good accuracy of the predictions for melt pool dimensions during SLM. The evaluation procedure established in this investigation can be also suitable for other additive manufacturing techniques.\\\\\nTable 11\n\nComparison of predictions from the critical RSM with simulated results.", "start_char_idx": 499959, "end_char_idx": 501805, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c59c139c-b3db-4b18-bc49-3ac1256b3bc5": {"__data__": {"id_": "c59c139c-b3db-4b18-bc49-3ac1256b3bc5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "53159190-c272-409f-9881-5ff5e142d59d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "da9ec815aac2810b10c9708dfe1a3a4eed0a2aca8e61e70c438f2fa59d246928", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fae511f5-173e-41f2-b7ce-0f12f0488986", "node_type": "1", "metadata": {}, "hash": "f677de6f38659b735452438f33c5b434cbc3f34698cb7df1ebe1f9208effdfb3", "class_name": "RelatedNodeInfo"}}, "text": "It is thus suggested that the RSM technique in conjunction with the process window to filter those unsuitable processing parameters can be a more effective way to achieve a good accuracy of the predictions for melt pool dimensions during SLM. The evaluation procedure established in this investigation can be also suitable for other additive manufacturing techniques.\\\\\nTable 11\n\nComparison of predictions from the critical RSM with simulated results.\n\n\\begin{center}\n\\begin{tabular}{lccl}\n\\hline\n\\begin{tabular}{l}\nMelt pool \\\\\ndimensions \\\\\n\\end{tabular} & \\begin{tabular}{l}\nSimulated results \\\\\n$(\\mathrm{mm})$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nPredicted model \\\\\n$(\\mathrm{mm})$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nDiscrepancy \\\\\n$(\\%)$ \\\\\n\\end{tabular} \\\\\n\\hline\n$P=70 \\mathrm{w}, V=270 \\mathrm{~mm} / \\mathrm{s}, T=110^{\\circ} \\mathrm{C}$ and $H=0.075 \\mathrm{~mm}$ &  &  &  \\\\\n\\begin{tabular}{l}\nLength \\\\\n\\end{tabular} & 128.57 & 126.3 &  \\\\\nWidth & 100.12 & 99.57 & 1.29 \\\\\nDepth & 32.38 & 30.92 & 1.09 \\\\\n$P=80 \\mathrm{w}, V=200 \\mathrm{~mm} / \\mathrm{s}, T=110^{\\circ} \\mathrm{C}$ and $H=0.075 \\mathrm{~mm}$ & 3.58 &  &  \\\\\nLength & 155.26 & 153.49 &  \\\\\nWidth & 121.02 & 122.06 & 0.77 \\\\\nDepth & 39.6 & 40.22 & 0.46 \\\\\n$P=90 \\mathrm{w}, V=350 \\mathrm{~mm} / \\mathrm{s}, T=110^{\\circ} \\mathrm{C}$ and $H=0.075 \\mathrm{~mm}$ & 2.18 &  &  \\\\\nLength & 156.25 & 152.31 &  \\\\\nWidth & 115.36 & 115.51 & 0.43 \\\\\nDepth & 37.26 & 36.99 & 0.34 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\section*{Acknowledgment}\nThis paper represents part of the results obtained under the support of the Ministry of Science and Technology, Taiwan, ROC (Contract No. MOST105-2218-E-194-004; 105-2622- E-194-004CC2).\n\n\\section*{References}\n[1] D.K. 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Romano, H.P.", "start_char_idx": 506167, "end_char_idx": 509134, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a234e5dc-8be8-4345-898a-cef842a64326": {"__data__": {"id_": "a234e5dc-8be8-4345-898a-cef842a64326", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0c73bb00-3f59-4646-85a3-6e85813ea4bc", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "baa50758dfc05ea29150f1143c04c61d1d572b4556f24d4b38e2b723b198c70e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "46a5ccce-20d5-4e39-8a71-2b5ccb333eb7", "node_type": "1", "metadata": {}, "hash": "c018843c286589072f6a4736c850c00dfbb5bba009294102ece4c0cf54fda42a", "class_name": "RelatedNodeInfo"}}, "text": "Mater. Sci. 50 (2011) 2124-2134.\n\n[30] K.C. Mills, Recommended Values of Thermophysical Properties for Selected Commercial, Woodhead Publishing (2002)\n\n[31] J.L. Devore, Probability and Statistics for Engineering and the Sciences, 8th Edition., Cengage Learning, Boston, MA, 2011.\n\n[32] B. Davoodi, B. Eskandari, Tool wear mechanisms and multi-response optimization of tool life and volume of material removed in turning of $\\mathrm{N}$ 155 iron-nickel-base superalloy using RSM, Measurement. 68 (2015) 286 294.\n\n[33] P. Fischer, M. Locher, V. Romano, H.P. Weber, S. Kolossov, R. Glardon, Temperature measurements during selective laser sintering of titanium powder, Int. J. Mach. Tools Manuf. 44 (2004) 1293-1296.\n\n[34] S. Kolossov, E. Boillat, R. Glardon, P. Fischer, M. Locher, 3D FE simulation for temperature evolution in the selective laser sintering process, Int. J. Mach. Tools Manuf. 44 (2004) 117-123.\n\n[35] W.E. King, A.T. Anderson, R.M. Ferencz, N.E. Hodge, C. Kamath, S.A. Khairallah, A.M. Rubenchik, Laser powder bed fusion additive manufacturing of metals; physics, computational, and materials challenges, Appl. Phys. Rev. 2 (2015) 041304 .\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{A novel heat source model for analysis of melt Pool evolution in selective laser melting process }\n\n\n\\author{Kang-Hyun. Lee ${ }^{\\mathrm{a}}$, Gun Jin Yun ${ }^{\\mathrm{b}, \\mathrm{a}, *}$\\\\\na Department of Mechanical \\& Aerospace Engineering, Seoul National University, Gwanak-gu Gwanak-ro 1, Seoul, 08826, Republic of Korea\\\\\n${ }^{\\mathrm{b}}$ Institute of Advanced Aerospace Technology, Seoul National University, Gwanak-gu Gwanak-ro 1, Seoul, 08826, Republic of Korea}\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": 508578, "end_char_idx": 511331, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "46a5ccce-20d5-4e39-8a71-2b5ccb333eb7": {"__data__": {"id_": "46a5ccce-20d5-4e39-8a71-2b5ccb333eb7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a234e5dc-8be8-4345-898a-cef842a64326", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "952452783fa5a2e5c4ee235f6bbd619da69f2b2be047080ce0186aeb6085883a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b5e787f5-8d06-4556-bee9-83315db6b1ef", "node_type": "1", "metadata": {}, "hash": "daa0faf9307e641d6f032b564387889b994a27171f7c84835f3ce092ee40d901", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{A R T I C L E I N F O}\n\\section*{Keywords:}\nSelective laser melting\n\nMelt pool\n\nFinite element analysis\n\nAdditive manufacturing\n\nMelting mode\n\n\\begin{abstract}\nA B S T R A C T In this paper, a novel hybrid heat source model is developed considering the different absorption mechanisms for porous and dense state materials, and an effective absorptivity is adapted to the proposed model to analyze the melting mode transition. The proposed model can predict the melt pool characteristics including the melt pool dimensions and the melting modes in the selective laser melting (SLM) process. The problem is formulated using the heat transfer equation considering the phase transition and the degree of consolidation based on the phasefield approach. The single-track scans of $316 \\mathrm{~L}$ stainless steel for both the non-powder case and the powder case are simulated to validate the model and the obtained results are in good agreement with the experimentally measured melt pool dimensions (mean error within 6\\%). Furthermore, the melting modes (conduction and keyhole) can be distinguished based on the predicted melt pool morphology and the degree of vaporization with the proposed model, which provides insight to define the optimized process boundary. It is also found that the keyhole mode melting is more sensitive to the change of the process parameter than the conduction mode melting.\n\\end{abstract}\n\n\\section*{1. Introduction}\nAdditive manufacturing (AM) technologies have been rapidly developed in the last few years as they enable the fabrication of complexshaped functional parts for various applications [1-4]. Among the proposed AM technologies, SLM is one of the powder bed-based AM processes that uses a high energy laser beam and metallic powder to build a part in a layer by layer fashion. During the SLM process, a thin layer of powder material is deposited with predefined thickness and a laser beam selectively melts the loose powder on the solid substrate. The consolidation and densification then take place after the full melting of the powder, which leads to high-density parts compared to other AM technologies such as selective laser sintering (SLS) [5,6]. The high material utilization and the flexibility of materials being processed also make the SLM process take a special position within the various AM processes [7-9].\n\nHowever, SLM printed parts suffer from various manufacturing defects including porosity, residual stress, and part distortion as the process involves the consolidation of powder material with rapid cooling [10-13]. The generated melt pool with a high-temperature gradient due to the concentrated heat flux is also crucial for defect formation, part quality, and microstructure evolution in the SLM process [14-17]. The process optimization for managing the foregoing defects requires investigation of various process parameters including laser power, scanning velocity, and layer thickness. Gong et al. [18] investigated the porosity distribution of SLM and electron beam melting (EBM) printed parts using the Archimedes method. The authors then introduced a process window with classifications considering the effect of process parameters on the degree of melting and heating. Dilip et al. [19] proposed an experimental study about melt pool evolutions and morphologies from single-track deposits. They concluded that the optimal setting of laser power and scanning speed leads to a well-defined bowl-shaped melt pool. Kasperovich et al. [20] presented an optimization strategy for porosity reduction in SLM printed specimens based on a correlation study between the process parameters and the void fraction. They also discussed the different formation mechanisms for the keyhole pores and the lack-of-fusion pores caused by excessive or insufficient energy density, respectively.\n\nFor saving a considerable amount of cost and time to optimize the process window with try-and-error experiments, numerical methods have been widely developed and used in recent years. The majority of previous literature shows that the phase transition and consolidation during the SLM process are crucial components for computing the temperature distribution during the process [21-24]. The released or\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author.\n\\end{itemize}\n\nE-mail address: \\href{mailto:gunjin.yun@snu.ac.kr}{gunjin.yun@snu.ac.kr} (G.J. Yun).\n}\nabsorbed latent heat of fusion and vaporization significantly affect the temperature field and enthalpy changes at each material point. The variation of the thermophysical material properties due to the change of material state with extreme temperature fluctuation also makes the problem highly non-linear [25,26].", "start_char_idx": 511334, "end_char_idx": 516065, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b5e787f5-8d06-4556-bee9-83315db6b1ef": {"__data__": {"id_": "b5e787f5-8d06-4556-bee9-83315db6b1ef", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "46a5ccce-20d5-4e39-8a71-2b5ccb333eb7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a6cfb1cef08ca29013eab46c1923844eba83f136cdb3a7f1bae9266612f64a68", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a2d86993-2fb3-48a2-b7d6-0b17da2fe541", "node_type": "1", "metadata": {}, "hash": "8b2e578ceb5620eb008f636e43d1f2ffff677096a83566a623b052109bf95319", "class_name": "RelatedNodeInfo"}}, "text": "For saving a considerable amount of cost and time to optimize the process window with try-and-error experiments, numerical methods have been widely developed and used in recent years. The majority of previous literature shows that the phase transition and consolidation during the SLM process are crucial components for computing the temperature distribution during the process [21-24]. The released or\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author.\n\\end{itemize}\n\nE-mail address: \\href{mailto:gunjin.yun@snu.ac.kr}{gunjin.yun@snu.ac.kr} (G.J. Yun).\n}\nabsorbed latent heat of fusion and vaporization significantly affect the temperature field and enthalpy changes at each material point. The variation of the thermophysical material properties due to the change of material state with extreme temperature fluctuation also makes the problem highly non-linear [25,26].\n\nIn recent years, high-fidelity numerical simulations based on computational fluid dynamics (CFD) have been utilized to study the physical phenomena in the SLM process. Khairallah et al. [27] proposed a numerical model which included a Marangoni effect with the recoil pressure. The authors emphasized the effect of the dynamical melt flow with the defect formation mechanisms and investigated the evolution of the melt pool in detail. Wu et al. [28] developed a simulation framework employing the volume of fluid (VOF) method [29] and studied the effect of material evaporation on the melt pool profile. Their study showed that the melt pool was in the keyhole mode melting as evaporation occurred with the narrow and deep melt penetration. Bayat et al. [30] also proposed a mesoscale model to investigate the formation of lack-of-fusion pores during the multi-track and multi-layer laser melting process. However, these methods often demand high computational resources which are not feasible for obtaining multiple analysis results with several sets of process parameters. For example, a threedimensional powder-scale multi-physics model using the finite volume method (FVM) took 140 hours for only $4 \\mathrm{~ms}$ simulations of the selective melting process with an Intel Core i7-2600 CPU [31]. Furthermore, if the laser spot size and the penetration depth get bigger, larger geometry needs to be modeled which significantly increases the total computation time.\n\nAlternatively, there have been some effective models of SLM process developed to provide reliable analysis results with reasonable computation cost considering typical physical phenomena in the process such as volume shrinkage, material evaporation, and thermocapillary convection (or Marangoni convection) using numerical techniques. Li et al. [32] developed a sequentially coupled thermo-mechanical analysis framework for the SLM process considering volume shrinkage of the powder layer and vaporization. The framework is then used to predict the temperature field, melt pool shape, and residual stress distribution in the multiple layers. Loh et al. [33] proposed an effective model of the SLM process to investigate the temperature history as well as the melt pool dimensions considering the shrinkage and material removal. Ladani et al. [34] applied the effective liquid conductivity in the SLM process simulation to obtain more realistic melt pool dimensions and temperature profiles considering the Marangoni effect. Zhang et al. [35] proposed a three-dimensional numerical model of laser powder-bed fusion (LPBF) process with the anisotropically enhanced thermal conductivity to effectively incorporate the fluid dynamics including the mass convection. They also showed that the melt pool simulation without enhanced conductivity and varied absorptivity significantly underestimates the depth of the melt pool.\n\nFor the continuum-based simulation of the SLM process, proper models for effective material properties are required to improve the accuracy of analysis results. For example, the thermal properties including the conductivity and the specific heat capacity of the powder material can be approximated by the volume averaging method with the phase functions [22,36]. However, the properties related to the laser irradiation such as the absorptivity and the extinction coefficient are more dependent on the powder packing geometry, the surface morphology, and the flat-surface absorptivity. Boley et al. [37] used the powder-scale simulation with different powder packing geometries and the direct calorimetric measurement to determine the absorptivity values of several metals in the powder state. They also found out that the effective absorptivity of the powder material is highly dependent on the flat-surface absorptivity. Moser et al. [38] investigated the geometrical effects including the powder particle size distribution on the laser absorptivity and the laser extinction using the particle model with the raytracing algorithm.", "start_char_idx": 515186, "end_char_idx": 520088, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a2d86993-2fb3-48a2-b7d6-0b17da2fe541": {"__data__": {"id_": "a2d86993-2fb3-48a2-b7d6-0b17da2fe541", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b5e787f5-8d06-4556-bee9-83315db6b1ef", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9b970c6cd295dd702ac3e1fc59edfabecb9d3ff587c802b77853019c9d48407e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9dbb9bca-ce00-4e5c-a896-6db0a103a3cc", "node_type": "1", "metadata": {}, "hash": "32052b3e35a0ec1400d41eb27161e22a597e3ac02f6dc467ddfd64b25119e843", "class_name": "RelatedNodeInfo"}}, "text": "For example, the thermal properties including the conductivity and the specific heat capacity of the powder material can be approximated by the volume averaging method with the phase functions [22,36]. However, the properties related to the laser irradiation such as the absorptivity and the extinction coefficient are more dependent on the powder packing geometry, the surface morphology, and the flat-surface absorptivity. Boley et al. [37] used the powder-scale simulation with different powder packing geometries and the direct calorimetric measurement to determine the absorptivity values of several metals in the powder state. They also found out that the effective absorptivity of the powder material is highly dependent on the flat-surface absorptivity. Moser et al. [38] investigated the geometrical effects including the powder particle size distribution on the laser absorptivity and the laser extinction using the particle model with the raytracing algorithm. The authors also derived the correlation equations of effective absorptivity and extinction coefficient of powder material based on the numerical model with the non-dimensional radius of particle with uncertainty estimates. Trapp et al. [39] also found out that the keyhole formation due to the high laser energy can enhance the light absorption with multiple light scattering. Their results show that the effective absorptivity of bulk solid $316 \\mathrm{~L}$ stainless steel increases from 0.3 and saturates at 0.78 where the depth of the melt pool reaches $300 \\mu \\mathrm{m}$.\n\nThe previous works for effective modeling of SLM focused on the reflection of typical mechanisms in the SLM process including the phase transition, the volume shrinkage, and the material removal. Various numerical techniques such as element deactivation and the effective material properties have been used to enhance the simulation accuracy. However, simulation without considering the important phenomena such as variation of the material interface and different light absorption mechanisms for powder and dense solid material can lead to unrealistic results even though the target output such as the melt pool dimension gets closer to the experimental results. Furthermore, there has been no previous study proposed with an effective model of the SLM process considering the transition of melting mode in the simulation. In this study, an effective model of the SLM process with a novel hybrid heat source model considering the different laser absorption mechanisms for powder and dense solid material is proposed. The proposed model combines both of the volumetric and the surface heat source models considering the different optical thicknesses for the powder state and the dense state material. An effective algorithm to track the interface where the laser interacts with the material is proposed based on the states of material points in clustered element columns. Furthermore, the melt pool depth-dependent absorptivity is applied to analyze the keyhole mode melting. To the best knowledge of the authors, there has been no attempt to consider the varying effective absorptivity with the melt pool geometry in the thermal analysis of the SLM process. For validation of the model, the predicted melt pool depth and width are compared to the experimental results for both the case with the powder layer and the case without the powder layer. The simulations with a range of process parameters that involve the conduction mode and the keyhole mode melting are conducted and the results are discussed for evaluation of the process. For the implementation of the proposed model in numerical analysis, the commercial FEA software ABAQUS is used with multiple user-subroutines. The detailed processes of modeling and implementation are also provided in this research.\n\n\\section*{2. Modeling approach}\nThe schematic diagram of the SLM process and its numerical model in the Cartesian coordinate system $(x, y, z)$ is as shown in Fig. 1. In the SLM process, a laser beam scans the predefined scanning track on the powder bed with the layer thickness $d_{p}$. The material is then melted forming a thin molten track, which is called the melt pool in general. For high density and good bonding of the track to the substrate, the generated melt pool should completely wet the substrate before solidification [40,41]. Thus, the dimensions and shape of the melt pool are important characteristics to control the quality of the process.\n\nTo track the temperature evolution and the melt pool formation in the SLM process, a thermal problem can be constructed considering the important mechanisms in the process. The laser beam can be modeled as moving heat flux in the numerical model with the given initial state of the material. Furthermore, the thermal behavior of material must be modeled properly considering the intense fluctuation of temperature including the variation of material state to obtain a reliable solution. This section introduces the proposed numerical modeling methods and the required backgrounds to build an effective analysis model of the SLM process.", "start_char_idx": 519117, "end_char_idx": 524238, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9dbb9bca-ce00-4e5c-a896-6db0a103a3cc": {"__data__": {"id_": "9dbb9bca-ce00-4e5c-a896-6db0a103a3cc", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a2d86993-2fb3-48a2-b7d6-0b17da2fe541", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e9f6461f56539d6a80cfd2a4c67028636b214a5e12629301bb9bf936f787bd9f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2da92154-b315-4dab-a4b3-d20b6c84891c", "node_type": "1", "metadata": {}, "hash": "f6687e9f75b28516cc49fe2ffdbf5b7769f6e0aa9507d2933dd34c40629038d8", "class_name": "RelatedNodeInfo"}}, "text": "The material is then melted forming a thin molten track, which is called the melt pool in general. For high density and good bonding of the track to the substrate, the generated melt pool should completely wet the substrate before solidification [40,41]. Thus, the dimensions and shape of the melt pool are important characteristics to control the quality of the process.\n\nTo track the temperature evolution and the melt pool formation in the SLM process, a thermal problem can be constructed considering the important mechanisms in the process. The laser beam can be modeled as moving heat flux in the numerical model with the given initial state of the material. Furthermore, the thermal behavior of material must be modeled properly considering the intense fluctuation of temperature including the variation of material state to obtain a reliable solution. This section introduces the proposed numerical modeling methods and the required backgrounds to build an effective analysis model of the SLM process.\n\n\\subsection*{2.1. Energy balance equation}\nIn this research, the thermodynamically-consistent phase field\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-03}\n\\end{center}\n\nFig. 1. Schematic diagram of the SLM process with a cross-section view of temperature distribution (gray color denotes $\\boldsymbol{T}>\\boldsymbol{T}_{\\boldsymbol{m}}$ ).\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-03(1)}\n\\end{center}\n\nFig. 2. Temperature dependent volumetric heat capacity and conductivity of dense state $316 \\mathrm{~L}$ stainless steel used in the proposed model.\n\napproach is adapted to deal with the problems of phase transition and the degree of consolidation [22,42]. Also, the latent heat of vaporization is added to the governing equation with the corresponding interpolation function of the state variable. The governing equation used for the analysis is as follows\n\n$\\frac{d H}{d t}=\\nabla \\cdot \\boldsymbol{q}(\\boldsymbol{r}, t)+Q(x, y, z, t)$, in $\\Omega$\n\n$\\boldsymbol{q}=-k \\nabla T$\n\nwhere $H$ is the enthalpy, $\\mathbf{q}$ is the heat flux vector, $Q$ is the heat source term, $T$ is the temperature, and the $t$ denotes the time. The enthalpy is expressed in terms of the temperature and the state variables as follows\n\n$H=C_{s}(\\psi) T+p\\left(\\phi_{m}\\right)\\left\\{L_{m}+\\left[C_{l}-C_{s}(\\psi)\\right]\\left(T-T_{m}\\right)\\right\\}+L_{v} p\\left(\\phi_{v}\\right)$\n\n$p(\\phi)=\\phi^{3}\\left(10-15 \\phi+6 \\phi^{2}\\right)$\n\nwhere $C_{s}$ and $C_{l}$ are the volumetric heat capacity in a solid-state and liquid state, $L_{m}$ and $L_{v}$ are the latent heat of melting and vaporization, $T_{m}$ is the melting temperature which is the average value of the liquidus temperature $T_{l}$ and the solidus temperature $T_{s}$. The function $p(\\phi)$ is the interpolation function of phase parameter $\\phi$ which satisfies the local minima condition of free energy density for each material state [42]. The phase parameters $\\phi_{m}$ and $\\phi_{v}$ are defined as follows\n\n$\\phi_{m}=\\frac{1}{2}\\left\\{\\tan \\left[\\frac{A\\left(T-T_{m}\\right)}{T_{l}-T_{s}}\\right]+1\\right\\}, \\phi_{v}=\\frac{1}{2}\\left\\{\\tan \\left[\\frac{A\\left(T-T_{v}\\right)}{T_{v p}-T_{v l}}\\right]+1\\right\\}$\n\nwhere $\\mathrm{A}$ is the parameter for smooth phase transition which is set to 5.0 in this study, $T_{v p}$ is the vaporized temperature, $T_{v l}$ is the temperature at the start of vaporization, and $T_{v}$ is the average vaporization temperature.", "start_char_idx": 523229, "end_char_idx": 526744, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2da92154-b315-4dab-a4b3-d20b6c84891c": {"__data__": {"id_": "2da92154-b315-4dab-a4b3-d20b6c84891c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9dbb9bca-ce00-4e5c-a896-6db0a103a3cc", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "bb7e2c824e83d50c5f8cf808c80d472accdc3c404538a0097c27cd41dfe8df41", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3308ad58-90f3-4af0-90ff-ba1754a53c66", "node_type": "1", "metadata": {}, "hash": "fe380c852ede6873d81fb00f43764362ba73207fa39c9aed1a416d63ed8af097", "class_name": "RelatedNodeInfo"}}, "text": "The phase parameters $\\phi_{m}$ and $\\phi_{v}$ are defined as follows\n\n$\\phi_{m}=\\frac{1}{2}\\left\\{\\tan \\left[\\frac{A\\left(T-T_{m}\\right)}{T_{l}-T_{s}}\\right]+1\\right\\}, \\phi_{v}=\\frac{1}{2}\\left\\{\\tan \\left[\\frac{A\\left(T-T_{v}\\right)}{T_{v p}-T_{v l}}\\right]+1\\right\\}$\n\nwhere $\\mathrm{A}$ is the parameter for smooth phase transition which is set to 5.0 in this study, $T_{v p}$ is the vaporized temperature, $T_{v l}$ is the temperature at the start of vaporization, and $T_{v}$ is the average vaporization temperature. The thermal properties including conductivity and heat capacity are determined by the consolidation parameter $\\psi$, which holds the maximum value of $\\phi_{m}$ to characterize thermal history at each material point defined as follows [22]\n\n$\\psi(\\boldsymbol{r}, t)=\\max \\left[\\phi\\left(\\boldsymbol{r}, t^{\\prime}\\right), \\psi(\\boldsymbol{r}, t)\\right], 0 \\leq t^{\\prime} \\leq t$\n\n$\\varepsilon=\\varepsilon_{0}(1-\\psi)$\n\n$C_{S}(\\psi)=(1-\\varepsilon) C_{d}$\n\n$k(\\psi)=(1-\\psi) k_{p}+\\psi k_{d}$\n\nwhere $\\varepsilon$ is the porosity, $\\varepsilon_{0}$ is the initial porosity of the powder bed, $C_{d}$ is the volumetric heat capacity of the dense material, $k_{p}$ is the thermal conductivity of the powder material which is set to $0.3 \\mathrm{~W} / \\mathrm{mK}$ considering the powder particle size $(10-50 \\mu \\mathrm{m})$ and the gas in the pores [36] near melting point, and $k_{d}$ is the thermal conductivity of the dense material. It is worth noting that the thermal conductivity of gas actually increases with temperature increment [43]. The constant conductivity of $0.3 \\mathrm{~W} / \\mathrm{mK}$ is chosen because the value is still much lower than that of the thermal conductivity of the dense solid. We consider $316 \\mathrm{~L}$ stainless steel with the temperature dependent material properties in dense states as shown in Fig. 2. The material properties over the melting temperature are estimated as constant values $\\left(C_{l}=5.95 \\times 10^{6} \\mathrm{~J} / \\mathrm{m}^{3}, k_{d}=32 \\mathrm{~W} / \\mathrm{mK}\\right)$ [36,44]. The other thermophysical properties of $316 \\mathrm{~L}$ stainless steel used in this study are as shown in Table 1 and the variation of enthalpy for different initial states is as shown in Fig. 3.\n\nDuring the SLM process, the melt pool convection due to the thermocapillary force and the buoyancy effect can influence the heat transfer. According to Ladani et al. [34], the buoyancy effect can be neglected due to the small Bond (Bo) number of materials including $316 \\mathrm{~L}$ stainless steel, Ti6Al4V, and In718 which are commonly used materials in SLM process. On the other hand, the anisotropically or isotropically enhanced thermal heat conductivity has been widely used to consider the thermocapillary effect in the thermal FEA for improved accuracy $[35,45-50]$. The use of enhanced conductivity also requires a careful calibration process between the independent and the dependent variables with a proper shape of function. The anisotropically enhanced thermal conductivities in $x, y$, and $z$ directions can be expressed as follows\n\nTable 1\n\nProperties of 316 L stainless steel [36,52-54].", "start_char_idx": 526221, "end_char_idx": 529395, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3308ad58-90f3-4af0-90ff-ba1754a53c66": {"__data__": {"id_": "3308ad58-90f3-4af0-90ff-ba1754a53c66", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2da92154-b315-4dab-a4b3-d20b6c84891c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "044d939233d74b7773bdb2d5091a1a598e3ffb64357f015e5667a22ba5ef4f44", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7352ac8b-9599-4056-893a-1fd1afcf633a", "node_type": "1", "metadata": {}, "hash": "41dacb683038a8a6ed53cf348d75936c816170384fd64e0c553515b4e6eb11c6", "class_name": "RelatedNodeInfo"}}, "text": "According to Ladani et al. [34], the buoyancy effect can be neglected due to the small Bond (Bo) number of materials including $316 \\mathrm{~L}$ stainless steel, Ti6Al4V, and In718 which are commonly used materials in SLM process. On the other hand, the anisotropically or isotropically enhanced thermal heat conductivity has been widely used to consider the thermocapillary effect in the thermal FEA for improved accuracy $[35,45-50]$. The use of enhanced conductivity also requires a careful calibration process between the independent and the dependent variables with a proper shape of function. The anisotropically enhanced thermal conductivities in $x, y$, and $z$ directions can be expressed as follows\n\nTable 1\n\nProperties of 316 L stainless steel [36,52-54].\n\n\\begin{center}\n\\begin{tabular}{ll}\n\\hline\nDescriptions & Values \\\\\n\\hline\nSolidus temperature $[\\mathrm{K}]$ & 1680 \\\\\nLiquidus temperature $[\\mathrm{K}]$ & 1720 \\\\\nLatent heat of fusion/melting $\\left[\\mathrm{kJ} / \\mathrm{m}^{3}\\right]$ & $L_{m}=2.18 \\times 10^{6}$ \\\\\nLiquidus temperature $[\\mathrm{K}]$ & 3030 \\\\\n(Liquid $\\rightarrow$ vapor) & 3070 \\\\\nVaporized temperature $[\\mathrm{K}]$ & $L_{v}=44.7 \\times 10^{6}$ \\\\\nLatent heat of vaporization $\\left[\\mathrm{kJ} / \\mathrm{m}^{3}\\right]$ &  \\\\\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-04}\n\\end{center}\n\nFig. 3. Variation of enthalpy versus temperature with different initial states of materials.\n\n$\\boldsymbol{q}=-\\left[\\begin{array}{ccc}k_{x} & 0 & 0 \\\\ 0 & k_{y} & 0 \\\\ 0 & 0 & k_{z}\\end{array}\\right] \\nabla T$\n\n$k_{x}=\\lambda_{x} k, k_{y}=\\lambda_{y} k, k_{z}=\\lambda_{z} k$\n\nwhere $\\lambda_{x}, \\lambda_{y}$ and $\\lambda_{z}$ are the anisotropically enhanced factors of thermal conductivity, which are usually set to 1 when $T<T_{m}$, and set to 2-30 when $T \\geq T_{m}[34,35,49]$. The enhanced factors are determined based on trial and error comparing the predicted values with the experimental results. The enhanced factor also can be applied as a function rather than a constant. Zhang et al. [35] used a linear approximation of anisotropic enhanced conductivity $\\lambda_{z}$ based on the fact that the experimentally measured melt pool depth is proportional to $P / \\sqrt{v}$ where the laser power $P$ is the laser power, and $v$ is the scanning velocity. However, the high fixed enhanced conductivity for the entire time of the analysis with given process parameters $(P$ and $v)$ can attenuate the concentrated heat flux and the high temperature gradient at the beginning of the laser interaction. Thus, based on the fact that the enhanced factor $\\lambda_{z}$ directly affects the predicted melt pool depth, a linear approximation is used in this study as follows\n\n$\\lambda_{z}=p_{1} \\cdot d_{m}+p_{2}$\n\nwhere $d_{m}$ is the varying melt pool depth during the process, $p_{1}$ and $p_{2}$ are the empirically determined fitting parameters. On the other hand, the constant enhanced factors $\\lambda_{x}$ and $\\lambda_{y}$ are used for simplification considering their smaller values compared to $\\lambda_{z}$ when deep melt penetration is formed. In this study, the enhanced factors $\\lambda_{x}, \\lambda_{y}$ and $p_{2}$, which is the initial value of $\\lambda_{z}$, are assumed as the constant value of 2.5 [51].\n\nAlthough enhanced thermal conductivity in previous studies has been treated as a useful tool to predict the melt pool geometry, the overestimated conductivity to obtain the deep melt pool depth can lead to an excessively large heat flux which is unrealistic.", "start_char_idx": 528629, "end_char_idx": 532216, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7352ac8b-9599-4056-893a-1fd1afcf633a": {"__data__": {"id_": "7352ac8b-9599-4056-893a-1fd1afcf633a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3308ad58-90f3-4af0-90ff-ba1754a53c66", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "873fc167306f74b6fddf892ff68d54783fdf56ba734a82de44da6e2f5a1bd5dd", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0606a48f-1479-4660-9995-8f6c0092c23b", "node_type": "1", "metadata": {}, "hash": "1011c98c993fc401d9d3b14cf71ebe010e293bdc657ca9cd1419a5abce1df144", "class_name": "RelatedNodeInfo"}}, "text": "On the other hand, the constant enhanced factors $\\lambda_{x}$ and $\\lambda_{y}$ are used for simplification considering their smaller values compared to $\\lambda_{z}$ when deep melt penetration is formed. In this study, the enhanced factors $\\lambda_{x}, \\lambda_{y}$ and $p_{2}$, which is the initial value of $\\lambda_{z}$, are assumed as the constant value of 2.5 [51].\n\nAlthough enhanced thermal conductivity in previous studies has been treated as a useful tool to predict the melt pool geometry, the overestimated conductivity to obtain the deep melt pool depth can lead to an excessively large heat flux which is unrealistic. Moreover, the high thermal conductivity can lead to suppression of material vaporization which is the dominant physical phenomenon in the keyhole mode. Thus, the enhanced thermal conductivity must be used carefully considering the mechanism of deep laser penetration and the material vaporization to get realistic results. To deal with this problem, an effective model incorporating the material removal, the powder volume shrinkage, and the newly proposed hybrid heat source model with effective absorptivity is proposed in this study.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-04(1)}\n\\end{center}\n\nFig. 4. Volume shrinkage due to the initial porosity of powder layer and material removal due to evaporation.\n\n\\subsection*{2.2. Powder volume shrinkage and material removal}\nDuring the melting process of SLM, a certain amount of volume shrinks due to the void fraction of the powder layer. The location of the surface then gets lower after the void is filled by the molten material. This volume shrinkage affects the morphology of the generated melt pool because it affects the heat conduction in the surrounding powder layer. Furthermore, the applied heat flux for each material point changes due to the variation of the distance from the center of the laser beam. The proportion of volume shrinkage of the powder layer is generally equivalent to the initial porosity of powder [33]. In this study, the initial porosity of the powder $\\varnothing$ is estimated as 0.4 [24,55]. To consider the volume shrinkage in the simulation, a simplified method is used in this study which is deactivating the shrunk element. After the powder layer is molten ( $T>T_{m}$ ), the shrunk volume (shown in Fig. 4) is treated as an empty space with zero conductivity in the simulation. In addition, the empty space can be simulated by element removal function provided by ABAQUS/Standard [56] ramping down the heat fluxes to zero during the removal step. In this way, the removed elements with zero heat flux can be reactivated with the defined initial state in the following analysis step with newly deposited powder material for simulation of multi-layer deposition.\n\nAs the material vaporization is considered in the governing Eq. (3), the vaporization can be detected when the temperature exceeds the vaporized temperature. Then, the vaporized volume is treated as the same as the shrunk volume to consider material removal. A problem that arises with this method is the deep penetration depth caused by high laser energy density cannot be detected well due to the removed material and the fixed height of the center of the numerical heat flux. To overcome this matter, a model of heat flux with a moving interface is proposed in this study and the detailed explanation is in Section 3.2.\n\n\\section*{3. Hybrid heat source model for the SLM process}\n\\subsection*{3.1. Surface and volumetric heat source models}\nIn the SLM process, the interaction between the laser and the material works very differently depending on the material state. For a dense state of the material, the optical penetration depth is known to be very small which is of the order of tens of nanometers [57,58]. This means most of the laser energy acts on the surface and cannot penetrates deep into the material.", "start_char_idx": 531583, "end_char_idx": 535533, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0606a48f-1479-4660-9995-8f6c0092c23b": {"__data__": {"id_": "0606a48f-1479-4660-9995-8f6c0092c23b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7352ac8b-9599-4056-893a-1fd1afcf633a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3361037456b6f752b5ed1479cf876f3a8ee144be5c41135bc442c30bddbb99b8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "722811b3-0962-4aad-a95a-95e43ad12ff8", "node_type": "1", "metadata": {}, "hash": "a0a9f192656c27b69a96c5c9c906cdeb039caaa73fad4f699094d7854e5a6bf9", "class_name": "RelatedNodeInfo"}}, "text": "A problem that arises with this method is the deep penetration depth caused by high laser energy density cannot be detected well due to the removed material and the fixed height of the center of the numerical heat flux. To overcome this matter, a model of heat flux with a moving interface is proposed in this study and the detailed explanation is in Section 3.2.\n\n\\section*{3. Hybrid heat source model for the SLM process}\n\\subsection*{3.1. Surface and volumetric heat source models}\nIn the SLM process, the interaction between the laser and the material works very differently depending on the material state. For a dense state of the material, the optical penetration depth is known to be very small which is of the order of tens of nanometers [57,58]. This means most of the laser energy acts on the surface and cannot penetrates deep into the material. In this case, the surface heat source model with Gaussian distribution is usually adopted as follows [24,59]\\\\\n$Q_{s}(x, y, t)=\\alpha I_{0} \\exp \\left(-2 \\frac{\\left.\\left(x-x_{c}\\right)^{2}+\\left(y-y_{c}\\right)^{2}\\right)}{r^{2}}\\right)$\n\n$I_{0}=\\frac{2 P}{\\left(\\pi r^{2}\\right)}$\n\nwhere $\\alpha$ is the optical absorptivity, $I_{0}$ is the maximum beam intensity, and $r$ is the effective radius of the beam where $I=I_{0} e^{-2}, x_{c}$ and $y_{c}$ are the positions of the beam center in $x$ and $y$ directions.\n\nOn the other hand, the laser irradiation onto the porous powder layer involves multiple reflections with deep penetration due to the pores between the powder particles. In this case, the volumetric heat sources are often used to consider the distributed heat flux in threedimensional space. The volumetric heat source model considering the progressive attenuation of laser beam intensity is as follows [60]\n\n$Q_{v}(x, y, z, t)=\\alpha \\beta I_{0} \\exp \\left[-2 \\frac{\\left.\\left(x-x_{c}\\right)^{2}+\\left(y-y_{c}\\right)^{2}\\right)}{r^{2}}-\\beta\\left(z_{c}-z\\right)\\right]$\n\nwhere $\\beta$ is the optical extinction coefficient and $z_{c}$ is the position of the beam center in $z$ direction. To determine the effective absorptivity and the extinction coefficient of the powder layer, Moser et al. [38] derived following correlation equations based on the simulation results from the particle-scale models with the ray-tracing algorithm\n\n$\\alpha_{e f f}=0.053+1.37 \\alpha_{s}-1.04 \\alpha_{s}^{2}+0.399 \\alpha_{s}^{3}$\n\n$\\beta R=0.325+1.03 \\alpha-1.22 \\alpha^{2}+0.587 \\alpha^{3}$\n\nwhere $\\alpha_{e f f}$ is the effective optical absorptivity of the powder material, $\\alpha_{s}$ is the optical absorptivity ranges from 0.1 to 0.9 of the bulk solid metal, and $R$ is the average radius of the powder particles. Using the Eq.s (13) - (17), the different heat flux equations for dense state material and porous material can be calculated with the readily available material properties and given process parameters.\n\n\\subsection*{3.2. Combination of two heat source models with interface tracking}\nTo apply different heat source models to a certain material point considering the material state, we propose a novel hybrid heat source model with both of the surface and the volumetric heat flux Eq.s (13) and (15). The schematic diagram of the proposed model is as shown in Fig. 5. At the beginning of the process, the material on the solid substrate is a porous state $(\\psi=0)$ for the entire powder layer and the laser can penetrate through the pores. Thus, the volumetric heat flux is applied in this case with the determined effective optical absorptivity and the extinction coefficient of the powder material. When sufficient energy is applied to the powder material by the moving heat flux, the material turns into a liquid state and becomes a solid-state after cooling. The liquid state and bulk solid-state are both treated as a dense state $(\\psi=1)$.", "start_char_idx": 534676, "end_char_idx": 538504, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "722811b3-0962-4aad-a95a-95e43ad12ff8": {"__data__": {"id_": "722811b3-0962-4aad-a95a-95e43ad12ff8", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0606a48f-1479-4660-9995-8f6c0092c23b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b2188c61216183b49b481f7af5dbc59b917bd37b9e30773a306e88185696301f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "cb274bab-b8e5-4b40-8cce-a17e35dcaa54", "node_type": "1", "metadata": {}, "hash": "f31ed5c6edb5e0d8a9fcaeeb5ca4cea51f5209932d8f28181420ac9d13372ce8", "class_name": "RelatedNodeInfo"}}, "text": "Combination of two heat source models with interface tracking}\nTo apply different heat source models to a certain material point considering the material state, we propose a novel hybrid heat source model with both of the surface and the volumetric heat flux Eq.s (13) and (15). The schematic diagram of the proposed model is as shown in Fig. 5. At the beginning of the process, the material on the solid substrate is a porous state $(\\psi=0)$ for the entire powder layer and the laser can penetrate through the pores. Thus, the volumetric heat flux is applied in this case with the determined effective optical absorptivity and the extinction coefficient of the powder material. When sufficient energy is applied to the powder material by the moving heat flux, the material turns into a liquid state and becomes a solid-state after cooling. The liquid state and bulk solid-state are both treated as a dense state $(\\psi=1)$. In this case, the laser cannot penetrate deep into the material and most of the laser energy is applied on the material surface.\n\nHowever, applying different heat flux with the captured interfaces where the laser and the material interact is very complicated in the SLM process due to the powder volume shrinkage and the material vaporization. Also, the laser interaction mechanism in the SLM process shows that the material state of the upper material affects the applied heat flux to the material below. Thus, an effective method to capture the interface based on the generated space during the simulation (Section 2.2) is proposed in this study. First, the whole finite elements are classified into numbers of columns in $z$ direction as shown in Fig. 6a. The elements in each column share the material state information and the number of empty elements $\\left(N_{0}\\right)$ is computed at every time increment. Also, the number of shrunk elements, molten elements, and vaporized elements can be computed for each element column in the same way.\n\nThe proposed hybrid heat source model is applied to the following algorithm. First, if there is powder material in a column, then the applied heat flux model for all the elements in the column is the volumetric heat source with progressive attenuation (15). After a certain time is passed and if all of the powder material is melted in the element column, the surface heat source model is applied to the captured interface as shown in Fig. 6b. The interface can be lower as more material is vaporized with intense heating. The governing equation to apply the surface heat flux with a varying interface is as follows\n\n$\\frac{d H}{d t}=\\nabla \\cdot \\boldsymbol{q}(\\boldsymbol{r}, t)+2\\left[Q_{s}(x, y, t)-h\\left(T-T_{\\infty}\\right)-\\sigma \\zeta\\left(T^{4}-T_{\\infty}^{4}\\right)\\right]|\\nabla \\varphi|$\n\nwhere $h$ is the convection coefficient, $\\sigma$ is the Stephan-Boltzmann constant, $\\zeta$ is the emissivity, $T_{\\infty}$ is the ambient temperature, $\\varphi$ is the value of the material fraction $(\\varphi=1$ when the material is present (porous or dense) and $\\varphi=0$ for empty space) and $|\\nabla \\varphi|$ is the interface delta function. Using this method, the heat flux model and the boundary conditions can be adaptively applied to the elements in each column considering the variation of the material state.\n\nIn addition, the denudation of metallic powder due to the vaporization during the SLM process has been reported in the previous studies [61,62]. It is worth noting that the denudation effect affects the formation of the consolidated track since the interface where the laser strikes varies due to the removed powder particles. In particular, Mattews et al. [61] studied the degree of denudation (dimensions of the denudated zone) as a function of laser parameters and gas pressure. If\\\\\nGaussian distributed heat flux $Q_{v}$ (volumetric)\\\\\nGaussian distributed heat flux $Q_{v}+Q_{s}(\\mathrm{~W} /$ interface delta function $)$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_bd6e034633d8b3d1d1d5g-05}\n\nFig. 5.", "start_char_idx": 537579, "end_char_idx": 541603, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "cb274bab-b8e5-4b40-8cce-a17e35dcaa54": {"__data__": {"id_": "cb274bab-b8e5-4b40-8cce-a17e35dcaa54", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "722811b3-0962-4aad-a95a-95e43ad12ff8", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e211ac95f5e0cce57736fdaae03f7a9a9ce9d7c8d33802864c8a0ffba15f9503", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "462d2355-0ce8-423a-b08d-a28f9accb296", "node_type": "1", "metadata": {}, "hash": "02320972f850524f26505b7fb749396fc3a3b47aad3c0d857963d40ffdfab55e", "class_name": "RelatedNodeInfo"}}, "text": "In addition, the denudation of metallic powder due to the vaporization during the SLM process has been reported in the previous studies [61,62]. It is worth noting that the denudation effect affects the formation of the consolidated track since the interface where the laser strikes varies due to the removed powder particles. In particular, Mattews et al. [61] studied the degree of denudation (dimensions of the denudated zone) as a function of laser parameters and gas pressure. If\\\\\nGaussian distributed heat flux $Q_{v}$ (volumetric)\\\\\nGaussian distributed heat flux $Q_{v}+Q_{s}(\\mathrm{~W} /$ interface delta function $)$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_bd6e034633d8b3d1d1d5g-05}\n\nFig. 5. The schematic diagram of the hybrid heat source model of the SLM process.\\\\\na)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-06}\n\\end{center}\n\nb)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-06(2)}\n\\end{center}\n\nFig. 6. a) Management of empty space in each column of elements, b) material states dependent laser penetration in the melt pool.\n\nthe approximate denudated volume is known, the corresponding volume can be converted to empty space just before the laser interacts or from the beginning of the analysis considering the small effect (low conductivity) of the powder material to incorporates the denudation effect. This effect is not considered in this study since the degree of the denudation is not known but consideration of this effect is suggested for future work.\n\n\\subsection*{3.3. Effective absorptivity with deep melt penetration}\nIn particular, the multiple reflections on keyhole walls can lead to a significant increase in energy absorption in the real SLM process [63]. Trapp et al. [39] found out that the effective optical absorptivity of material increases as the keyhole traps the light with the surface depression of the melt pool. They also measured the variation of the effective laser absorptivity of bulk solid 316 L stainless steel with the variation of the melt pool dimensions and the laser power. The graph in Fig. 7 and Fig. 8 show that as the melt pool depth increases, which means more possibility of keyhole mode, the effective absorptivity of dense state $316 \\mathrm{~L}$ stainless steel increases from 0.3 and saturates at 0.78 . To consider this phenomenon in the simulation, we applied the melt pool depth-dependent optical absorptivity of the dense state material with the surface heat flux model after the full melting of the powder material. We assumed the effective absorptivity for dense state material\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-06(1)}\n\\end{center}\n\nFig. 7. Effective absorptivity for dense state $316 \\mathrm{~L}$ stainless steel versus melt pool depth [39] with the fitted curve.\\\\\nEffective absorptivity for dense state material $\\left(\\alpha_{d}\\right)$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-06(3)}\n\\end{center}\n\nMelt pool depth (d)\n\nFig. 8. Melt pool depth-dependent effective absorptivity of dense state material.\n\nfollows the experimental result proposed by Trapp et al. [39]. The data is then fitted to be applied in the numerical analysis for convenience as follows\n\n\\[\n\\left\\{\\begin{array}{c}\n\\alpha_{d}=0.3(d<50)  \\tag{19}\\\\\n\\alpha_{d}=c_{1} d^{3}+c_{2} d^{2}+c_{3} d+c_{4}(50 \\leq d \\leq 300) \\\\\n\\alpha_{d}=0.78(300<d)\n\\end{array}\\right.", "start_char_idx": 540880, "end_char_idx": 544398, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "462d2355-0ce8-423a-b08d-a28f9accb296": {"__data__": {"id_": "462d2355-0ce8-423a-b08d-a28f9accb296", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "cb274bab-b8e5-4b40-8cce-a17e35dcaa54", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3f2bb82ac7f8be298ece1284060f25b546e4765d7e21a2390d636500b0c269db", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "79cb3b25-0f5e-4dc0-8fd8-3ec95bb831b7", "node_type": "1", "metadata": {}, "hash": "089d5712e09381a64656824fdb705d5561f44e6e29a9791dc2ea9afac4218869", "class_name": "RelatedNodeInfo"}}, "text": "8. Melt pool depth-dependent effective absorptivity of dense state material.\n\nfollows the experimental result proposed by Trapp et al. [39]. The data is then fitted to be applied in the numerical analysis for convenience as follows\n\n\\[\n\\left\\{\\begin{array}{c}\n\\alpha_{d}=0.3(d<50)  \\tag{19}\\\\\n\\alpha_{d}=c_{1} d^{3}+c_{2} d^{2}+c_{3} d+c_{4}(50 \\leq d \\leq 300) \\\\\n\\alpha_{d}=0.78(300<d)\n\\end{array}\\right.\n\\]\n\nwhere $\\quad c_{1}=1.037 \\times 10^{-7}, c_{2}=-6.916 \\times 10^{-5}, c_{3}=0.01485 \\quad$ and $c_{4}=-0.3133$. Although the data was obtained after the end of the process measuring the melt penetration $d$, we used the melt pool depthdependent absorptivity assuming $d=d_{m}$. The varying melt pool depth $d_{m}$ can be computed using the material states in $z$ direction at every time increment as explained in Section 3.2.\n\nThe measured effective absorptivity is affected by various physical phenomena including the surface depression due to the recoil pressure and the multiple laser scatterings. Even though the complex fluid dynamics and the light scattering are not directly modeled, we assumed that the varying effective absorptivity can enhance the accuracy of the melt pool simulation with the proposed effective model. Moreover, the value may need to be calibrated for improved accuracy of the model likes some other effective properties. It is also worth noting that further\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-07}\n\\end{center}\n\nFig. 9. Schematic of simulation domain with boundary conditions.\n\ncalibration will be required according to the type of materials used and the processing conditions. In this study, however, the fitted curve from the experimental results is applied directly to the model to analyze its effect on the results. The development of proper calibration methods and the study of underlying physics will be addressed in future works.\n\n\\section*{4. Numerical implementation with FEA}\nTo build the proposed effective model of the SLM process, the builtin heat transfer analysis step in commercial FEA tool ABAQUS/ Standard is used to calculate the transient temperature field. The important physical phenomena of the SLM process explained in the previous sections are effectively modeled using multiple user subroutines called for different purposes [56]. The mesh design and the boundary conditions of the half-symmetric model with respect to $x-z$ plane is shown in Fig. 9. The flowchart for the implementation of the effective model in ABAQUS is as shown in Fig. 10. As defined in Section 3.2, the elements must be classified into several columns to define the heat flux with the varying interface. To sort the elements according to its position, the information of the element and the node in the ABAQUS input\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-07(1)}\n\\end{center}\n\nFig. 10. Flowchart of the proposed effective model of SLM process in ABAQUS with multiple user subroutines. file is first pre-processed by a custom MATLAB script to assign a column number to each element. Thereafter, the assigned column number is imported into ABAQUS using a UEXTERNALDB subroutine which is called at the beginning of the analysis. Moreover, the initial state of each material point needs to be varied according to the determined layer thickness. Therefore, the initial values of material state variables for each material point are defined according to their positions using an SDVINI subroutine. After the initial conditions are defined, the problem is solved based on the governing equation with the defined material behavior and the boundary conditions. To define the thermal material behavior considering the consolidation and the phase transitions (1)(3), a UMATHT subroutine is developed to update the enthalpy of each material point and the heat flux vector according to the governing equation and the material properties. Therefore, the material state can be defined by the state variables in eq. (5) and (6) with the corresponding temperature history.", "start_char_idx": 543992, "end_char_idx": 548086, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "79cb3b25-0f5e-4dc0-8fd8-3ec95bb831b7": {"__data__": {"id_": "79cb3b25-0f5e-4dc0-8fd8-3ec95bb831b7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "462d2355-0ce8-423a-b08d-a28f9accb296", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "053d0b861bec90e287da1ec2d7eb11dfb1445efd260078c88f1d0d61d77e8e5b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9af82bfb-006d-4972-943c-83619f95782a", "node_type": "1", "metadata": {}, "hash": "ed3962f853a39bea57e24b3a45fc197aece9ab95012f0ce990fd60310cd75d33", "class_name": "RelatedNodeInfo"}}, "text": "Thereafter, the assigned column number is imported into ABAQUS using a UEXTERNALDB subroutine which is called at the beginning of the analysis. Moreover, the initial state of each material point needs to be varied according to the determined layer thickness. Therefore, the initial values of material state variables for each material point are defined according to their positions using an SDVINI subroutine. After the initial conditions are defined, the problem is solved based on the governing equation with the defined material behavior and the boundary conditions. To define the thermal material behavior considering the consolidation and the phase transitions (1)(3), a UMATHT subroutine is developed to update the enthalpy of each material point and the heat flux vector according to the governing equation and the material properties. Therefore, the material state can be defined by the state variables in eq. (5) and (6) with the corresponding temperature history. The variation of the enthalpy and the heat flux are also computed analytically with the temperature increment for convergence in the implicit method. Furthermore, a USDFLD subroutine is developed to manage the material states and transfer them to a DFLUX subroutine, which is used to define the non-uniform distributed heat flux with thermal boundary conditions. For convenience, the material state is defined by one discrete numeric value with the following four conditions: -1 for powder state, 0 for dense solid-state, 1 for the liquid state, and 2 for the empty state. It is worth noting that the amount of applied heat flux is not only dependent on the state of the material point itself but also dependent on the states of the materials in the build direction. Therefore, the common block provided in FORTRAN is used to access and share important information such as the material states of the other material points through multiple user subroutines. The obtained material states of the whole elements are used to define the interface where the laser interacts at every time increment using UEXTERNALDB. The interface and the melt pool depth $d_{m}$ are computed explicitly with a reasonably small maximum time increment of $10^{-6} \\mathrm{~s}$ because both of them are determined based on the states of the whole elements in the analysis domain. Based on the computed interface, the hybrid heat source model with both of the surface heat flux (13) and the volumetric heat flux (15) can be adaptively applied to the material point using the DFLUX subroutine.\n\n\\section*{5. Results and discussion}\n\\subsection*{5.1. Single-track laser scan without powder bed}\nA single-track laser scan without powder material is simulated first to validate the proposed effective model using the experimentally measured melt pool dimensions with different melting modes [39]. In the simulation, a $316 \\mathrm{~L}$ stainless steel without powder layer is subjected to a single laser scan where the spot dimeter is $60 \\mu m$. The process parameters used are as shown in Table 2. The laser power is varied widely from $32 \\mathrm{~W}$ to $223 \\mathrm{~W}$ with the constant scanning velocity of $500 \\mathrm{~mm} / \\mathrm{s}$ to analyze the melting mode transition. It is worth noting that only the surface heat flux is used in this case because there is no porous material in the analysis domain as explained in Section 3.2. After several trial-and-error attempts and the comparison with the experimental results, the value of $p_{1}$ in (12) is determined as 0.1757 for improved prediction of the melt pool depth. This value is also adopted for the case with a powder bed in section 5.2 since the melt penetration\n\nTable 2\n\nProcess parameters for the non-powder material case.\n\n\\begin{center}\n\\begin{tabular}{ll}\n\\hline\nDescriptions & Values \\\\\n\\hline\nLaser power $[\\mathrm{W}]$ & $P=32,48,65,83,99,117,134,178,223$ \\\\\nLaser scanning speed $[\\mathrm{mm} / \\mathrm{s}]$ & $v_{x}=500$ \\\\\nLaser spot diameter $[\\mu \\mathrm{m}]$ & $D=60$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-08(1)}\n\\end{center}\n\nFig. 11. Predicted melt pool dimensions and the experimental results for single-track scan without powder material.\n\nis measured from the level of the solid substrate surface.", "start_char_idx": 547113, "end_char_idx": 551434, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9af82bfb-006d-4972-943c-83619f95782a": {"__data__": {"id_": "9af82bfb-006d-4972-943c-83619f95782a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "79cb3b25-0f5e-4dc0-8fd8-3ec95bb831b7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0ad46bc7fd4287bdcc5f4f138a040ad18eed2e71e2bb535c2cfb3768384d0076", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "775f4eae-be59-4422-af05-ba64a0d0f727", "node_type": "1", "metadata": {}, "hash": "8a2236846802e1f3ed0faecca2fdfcbf8d79f4c15c0f23a422f56b9289434634", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\begin{tabular}{ll}\n\\hline\nDescriptions & Values \\\\\n\\hline\nLaser power $[\\mathrm{W}]$ & $P=32,48,65,83,99,117,134,178,223$ \\\\\nLaser scanning speed $[\\mathrm{mm} / \\mathrm{s}]$ & $v_{x}=500$ \\\\\nLaser spot diameter $[\\mu \\mathrm{m}]$ & $D=60$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-08(1)}\n\\end{center}\n\nFig. 11. Predicted melt pool dimensions and the experimental results for single-track scan without powder material.\n\nis measured from the level of the solid substrate surface.\n\nThe predicted melt pool dimensions using the proposed model and the experimental results are shown in Fig. 11. The result shows that both the melt pool width and depth increase as more laser power is applied. The predicted results are also in good agreement with the experimental results. The varying melt pool width and depth about $20 \\mu \\mathrm{m}$ to $270 \\mu \\mathrm{m}$ are predicted and the proposed model has the mean errors for both the depth and the width within 6\\% as seen in Table 3. In particular, the predicted melt pool width shows larger error than the predicted melt pool depth because the calibrated linear approximation is used for the enhanced factor $\\lambda_{z}$ whereas the constant value is used for the enhanced factor $\\lambda_{y}$ which is related to the melt pool width for simplification of the calibration process. The errors may also occur due to the measuring error and potential differences between the applied thermo-physical properties and the real material properties.\n\nTo facilitate the understanding of the process parameters and their effects, the ratio between the volume of vaporized material and the volume of molten material $\\eta$ is computed to evaluate the degree of the intense heating. Although the high laser power contributes to the deep melt penetration (which is preferred for stronger bonding between the molten track and the substrate in the SLM process) and wider melt width (which is preferred for minimizing the production time), the more energy can be wasted through the vaporization of the material. The increasing $\\eta$ shows that this waste gets more severe as more energy is applied. Thus, $\\eta$ should be minimized while the minimum melt pool size is ensured for enough bonding between the material and the substrate from the energy efficiency point of view. The result also shows that the vaporization does not occur for the laser power of $32 \\mathrm{~W}, 48 \\mathrm{~W}$, and $65 \\mathrm{~W}(\\eta=0)$. For these laser powers, the rate of change of the melt pool depth with the varying laser power is relatively small compared to the higher laser powers as shown in Fig. 12. The graphs from both the experimental results and the simulation show that the rate of change is below 0.5 before the vaporization occurs, and increases sharply up to 2.44 and holds the value above 1.0 after the vaporization occurs. This shows that when the applied energy is not sufficient to cause the vaporization of the material, the size of the melt pool does not fluctuate a lot according to the change of the process parameter. It can be also said that if a desired melt pool size can be achieved in the range of\n\nTable 3\n\nComparison of simulation results with experimental results.", "start_char_idx": 550857, "end_char_idx": 554169, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "775f4eae-be59-4422-af05-ba64a0d0f727": {"__data__": {"id_": "775f4eae-be59-4422-af05-ba64a0d0f727", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9af82bfb-006d-4972-943c-83619f95782a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1405b4bc5334936fea39e6b5443d94f5ea5baf392ce737fd140f4d8c8cc85cc6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2bdf15a2-3c45-4b73-86de-bdef60732d5a", "node_type": "1", "metadata": {}, "hash": "be0c210384d75f4f0b43a697fdf82627f87630c7d28c59466de68edf11431fe7", "class_name": "RelatedNodeInfo"}}, "text": "For these laser powers, the rate of change of the melt pool depth with the varying laser power is relatively small compared to the higher laser powers as shown in Fig. 12. The graphs from both the experimental results and the simulation show that the rate of change is below 0.5 before the vaporization occurs, and increases sharply up to 2.44 and holds the value above 1.0 after the vaporization occurs. This shows that when the applied energy is not sufficient to cause the vaporization of the material, the size of the melt pool does not fluctuate a lot according to the change of the process parameter. It can be also said that if a desired melt pool size can be achieved in the range of\n\nTable 3\n\nComparison of simulation results with experimental results.\n\n\\begin{center}\n\\begin{tabular}{llllll}\n\\hline\n\\begin{tabular}{l}\nMin error \\\\\n(width) [\\%] \\\\\n\\end{tabular} & \\begin{tabular}{l}\nMax error \\\\\n(width) [\\%] \\\\\n\\end{tabular} & \\begin{tabular}{l}\nMean error \\\\\n(width) [\\%] \\\\\n\\end{tabular} & \\begin{tabular}{l}\nMin error \\\\\n(depth) [\\%] \\\\\n\\end{tabular} & \\begin{tabular}{l}\nMax error \\\\\n(depth) [\\%] \\\\\n\\end{tabular} & \\begin{tabular}{l}\nMean error \\\\\n(depth) [\\%] \\\\\n\\end{tabular} \\\\\n\\hline\n0.116 & 9.67 & 5.65 & 0.114 & 8.0 & 2.64 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-08}\n\\end{center}\n\nFig. 12. Rate of change of the melt pool depth according to the laser power.\n\nparameters with lower energy density, the process can be optimized with the stable formation of the melt pool.\n\nIn the laser process of alloy, the transition between the different modes of melting due to the material vaporization involves complex physical phenomena including the surface depression induced by the recoil pressure and the multiple laser scatterings. When the laser energy exceeds a certain boundary to cause the vaporization of the material, the melt pool shape is observed to have a keyhole shape with deep melt penetration rather than a bowl shape [19]. The two distinct melting modes in laser welding have been observed in previous studies and literature [64,65]. This remarkable change of the melt pool shape from the conduction mode melting to the keyhole mode melting can be explained by the different energy absorption mechanisms. Compared to the conduction mode melting, keyhole mode melting is always associated with the vaporization of the alloy [66]. As the surface is depressed with the material vaporization, there is more chance of the light to be trapped which leads to enhanced energy absorption. The increased absorbed energy then leads to more intense vaporization and deeper laser penetration forming a keyhole-shaped melt pool. In this study, this absorption mechanism is considered using the effective absorptivity which is dependent on the melt pool depth (Section 3.3).\n\nFig. 13 illustrates the melt pool cross-section images using optical microscopy. As shown in Fig. 14, the different modes of melting can be distinguished by the predicted morphology of the melt pool (gray\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-09(2)}\n\\end{center}\n\nFig. 13. Melt pool cross-section images with varied laser power from reference [39] used under CC BY 4.0 license.\n\ndenotes the empty space, red denotes the molten region, and blue denotes the dense solid). When the laser energy is not very high (Fig. 14a and b), the melt pool width is 2-3 times as large as the melt pool depth. The material vaporization also does not occur in this case which can be classified as the conduction mode melting. If the laser power increases and the material vaporization takes place (Fig. $14 \\mathrm{c}$ and d), the melt pool depth rapidly increases with the high energy absorption. Then, a keyhole-shaped melt pool geometry is predicted and the process can be classified as the keyhole mode melting.\n\n\\subsection*{5.2.", "start_char_idx": 553408, "end_char_idx": 557349, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2bdf15a2-3c45-4b73-86de-bdef60732d5a": {"__data__": {"id_": "2bdf15a2-3c45-4b73-86de-bdef60732d5a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "775f4eae-be59-4422-af05-ba64a0d0f727", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8a2d9bdb280ee076d71e7eef8995c77010ca95e30762571ff6b6ddf12bc3f782", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fb5dc065-a93a-440d-841c-6abf3f7c3fb7", "node_type": "1", "metadata": {}, "hash": "d14731fbdb2bc99d2e4f3d0a4010552dbaca8b39f3a516e1935b01489b17603f", "class_name": "RelatedNodeInfo"}}, "text": "13. Melt pool cross-section images with varied laser power from reference [39] used under CC BY 4.0 license.\n\ndenotes the empty space, red denotes the molten region, and blue denotes the dense solid). When the laser energy is not very high (Fig. 14a and b), the melt pool width is 2-3 times as large as the melt pool depth. The material vaporization also does not occur in this case which can be classified as the conduction mode melting. If the laser power increases and the material vaporization takes place (Fig. $14 \\mathrm{c}$ and d), the melt pool depth rapidly increases with the high energy absorption. Then, a keyhole-shaped melt pool geometry is predicted and the process can be classified as the keyhole mode melting.\n\n\\subsection*{5.2. Single-track laser scan with powder bed}\nA simulation for a single-track laser scan with the powder material is conducted for melt pool analysis of the SLM process. For the validation of the proposed model, the analysis results are compared with the experimental results in the previous study [67] with the two distinct melting modes. In the simulation, a $316 \\mathrm{~L}$ stainless steel with the powder layer thickness of $75 \\mu \\mathrm{m}$ is subjected to a single path laser scan where the spot diameter is $55 \\mu \\mathrm{m}$. The two cases of the conduction mode melting with the laser power of $100 \\mathrm{~W}$ and the keyhole mode melting with the laser power of $200 \\mathrm{~W}$ are simulated with the scanning velocity of $300 \\mathrm{~mm} / \\mathrm{s}$.\n\nTo validate the performance of the proposed model, the analysis results with the conventional heat source models which are the Gaussian surface heat flux model (2-dimensional) [24,68] and the Goldak's semi-ellipsoid model (three-dimensional) [69,70] are obtained for comparative purpose. Then, the analysis results obtained by the proposed hybrid heat source model (Section 3) are discussed with the different characteristics of the melting modes. The analysis results are shown in Table 4 and Table 5 with the corresponding relative errors. The proposed interface tracking method (Section 3.2) is used for all of the analysis cases to consider the empty space caused by the volume shrinkage and the material vaporization.\n\n\\subsection*{5.2.1. Simulation with conventional heat source models}\nFor the case of the conduction mode melting $(P=100 W)$, the Gaussian surface heat flux model is used as a comparison target considering the shallow melt depth compared to the keyhole mode melting. Fig. 15a shows the predicted melt pool morphology using the Gaussian surface heating model. Due to the concentrated heat flux to the material interface from the beginning of the laser interaction, the vaporization can readily occur within the laser spot size. Furthermore, the low conductivity of the powder material intensifies the local temperature increases. As a result, the vaporization occurs in both the material in the powder layer and the material in the solid substrate. This shows that the surface heat flux model overestimates the material vaporization. As seen in Table 4, $\\eta$ is 0.531 with the surface heat flux model which means the volume of the vaporized material is extremely large. It can be said that the result is very unrealistic because the melting mode is conduction in this case.\n\nFor the case of the keyhole mode melting $(P=200 W)$, the Goldak's semi-ellipsoid model is used for comparison considering the deep laser\n\n\\section*{- - - : Experimental melt pool boundary}\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_bd6e034633d8b3d1d1d5g-09(1)}\\\\\na) $32 \\mathrm{~W}$\n\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_bd6e034633d8b3d1d1d5g-09}\\\\\nb) $65 \\mathrm{~W}$\\\\\nKeyhole mode melting\n\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_bd6e034633d8b3d1d1d5g-09(3)}\\\\\nc) $83 \\mathrm{~W}$\\\\\nd) $223 \\mathrm{~W}$\n\nFig. 14.", "start_char_idx": 556602, "end_char_idx": 560491, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fb5dc065-a93a-440d-841c-6abf3f7c3fb7": {"__data__": {"id_": "fb5dc065-a93a-440d-841c-6abf3f7c3fb7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2bdf15a2-3c45-4b73-86de-bdef60732d5a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7d58b45cd50d4ff3f4ac4b4b3402724c82e8229c278c8081a32fe42a115ff487", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9b733f29-337b-4daf-8bea-573d53a110a7", "node_type": "1", "metadata": {}, "hash": "b7e2a5a3e5264e7529d9a3a5028ee271e7b15ae5576118bc97a52defa8506837", "class_name": "RelatedNodeInfo"}}, "text": "14. Predicted melt pool morphology in the $\\boldsymbol{y}-\\boldsymbol{z}$ cross section for single-track scan without powder material a) $\\boldsymbol{P}=32 \\mathrm{~W}, \\mathrm{~b}) \\boldsymbol{P}=65 \\mathrm{~W}$, c) $\\boldsymbol{P}=83 \\mathrm{~W}$, d) $\\boldsymbol{P}=223 \\mathrm{~W}$.\n\nTable 4\n\nComparison of simulation results with experimental results (conduction mode).\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline\nSimulation method & Width $[\\mu m]$ (error \\%) & depth $[\\mu m]$ (error \\%) & $\\eta$ & Experimental width $[\\mu m]$ & Experimental depth $[\\mu m]$ \\\\\n\\hline\nSurface heat source & $80.1(22.23)$ & $84.9(63.27)$ & 0.531 & $103 \\pm 24$ & 52 \\\\\n\\hline\nHybrid heat source w/ enhanced $k$ & $101.1(1.84)$ & $51.3(1.35)$ & 0.0 &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 5\n\nComparison of simulation results with experimental results (keyhole mode).\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline\nSimulation method & Width $[\\mu m]$ (error \\%) & depth $[\\mu m]$ (error \\%) & $\\eta$ & Experimental width $[\\mu m]$ & Experimental depth $[\\mu m]$ \\\\\n\\hline\nVolumetric heat source & $134.8(3.69)$ & $260.8(1.95)$ & 0.0 & $130 \\pm 10$ & 266 \\\\\n\\hline\nHybrid heat source w/ enhanced $k$ & $135.1(3.92)$ & $263.9(0.79)$ & 0.122 &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\npenetration depth. The model can be expressed as follows\n\n$Q(x, y, z, t)=\\frac{2 \\alpha P}{\\bar{a} \\bar{b} \\bar{c} \\pi \\sqrt{\\pi}} \\exp \\left[-\\left(\\frac{\\left(x+v_{x} t\\right)^{2}}{\\bar{a}^{2}}+\\frac{(y)^{2}}{\\bar{b}^{2}}+\\frac{(z)^{2}}{\\bar{c}^{2}}\\right)\\right]$\n\nwhere $\\bar{a}, \\bar{b}$, and $\\bar{c}$ are the dimensions of the ellipsoid determined by the beam radius $R$, the laser penetration depth $\\delta$, and eccentricity $e$ as follows.\n\n$\\bar{a}=e R, \\bar{b}=R / e, \\bar{c}=\\delta$\n\nThree-dimensional heat source models are useful to predict the deep melt pool with the calibrated heat source geometry based on the\n\na) Surface heat source w/o enhanced $k$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-10(3)}\n\\end{center}\n\nC) Volumetric heat source w/o enhanced $k$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-10(2)}\n\\end{center}\n\nmeasured melt pool dimensions [35,71]. In this study, half of the measured melt pool width $(=65 \\mu \\mathrm{m})$ is used for the beam radius and the measured melt pool depth $(=266 \\mu \\mathrm{m})$ is used for the laser penetration depth. Fig. 15c shows the predicted melt pool morphology using Goldak's model. As seen in Table 5, the errors between the simulation and the experiment are within $4 \\%$ for both the width and the depth in this case. This shows that a three-dimensional heat source model can predict the melt pool dimensions with high accuracy if a calibration process is performed in advance.", "start_char_idx": 560488, "end_char_idx": 563326, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9b733f29-337b-4daf-8bea-573d53a110a7": {"__data__": {"id_": "9b733f29-337b-4daf-8bea-573d53a110a7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fb5dc065-a93a-440d-841c-6abf3f7c3fb7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "282922fed5be00a2492f59cf3b14de695a68b8d1fe99020567d57d240ca32507", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b8d22e46-e1ee-4496-b3ce-934eb3757467", "node_type": "1", "metadata": {}, "hash": "ee960cd8b81ec23c101b32ed4620ca860c54725ef7f1090f7f33324ae6008484", "class_name": "RelatedNodeInfo"}}, "text": "In this study, half of the measured melt pool width $(=65 \\mu \\mathrm{m})$ is used for the beam radius and the measured melt pool depth $(=266 \\mu \\mathrm{m})$ is used for the laser penetration depth. Fig. 15c shows the predicted melt pool morphology using Goldak's model. As seen in Table 5, the errors between the simulation and the experiment are within $4 \\%$ for both the width and the depth in this case. This shows that a three-dimensional heat source model can predict the melt pool dimensions with high accuracy if a calibration process is performed in advance. However, the result shows that vaporization does not occur $(\\eta=0)$ even though the keyhole mode melting is observed in the experiment [67]. The reason can be ascribed\n\n\\section*{b) Hybrid heat source w/ enhanced $k$}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-10(1)}\n\\end{center}\n\nd) Hybrid heat source w/ enhanced $k$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-10}\n\\end{center}\n\nFig. 15. Predicted melt pool morphology I. conduction mode melting $(\\boldsymbol{P}=100 \\mathbf{W})$ : a) surface heat source without enhanced $\\boldsymbol{k}$, b) hybrid heat source with enhanced $\\boldsymbol{k}$ II. keyhole mode melting $(\\boldsymbol{P}=200 \\mathbf{W})$ c) volumetric heat source, d) hybrid heat source with enhanced. $\\boldsymbol{k}$\\\\\na) Conduction mode $(P=100 \\mathrm{~W})$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-11}\n\\end{center}\n\nb) Keyhole mode $(P=200 \\mathrm{~W})$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-11(1)}\n\\end{center}\n\nFig. 16. Top views of the melt pool evolution at the level of the solid substrate surface with the proposed hybrid heat source models a) conduction mode melting $(\\boldsymbol{P}=100 \\mathbf{W})$, b) keyhole mode melting $(\\boldsymbol{P}=200 \\mathbf{W})$. The dotted-line circles are the projection of the laser beam.\n\nto the fact that the widely distributed energy in the three-dimensional space attenuates the concentrated energy input as well as the temperature gradient. Thus, the transition between the melting modes cannot be detected in this case.\n\n\\subsection*{5.2.2. Simulation with a hybrid heat source model}\nThe same processes in the previous section are simulated using the proposed hybrid heat source model. As seen in Table 4 and Table 5, the errors between the simulation results based on the proposed model and the experimental results are within $4 \\%$ for both the conduction mode melting and the keyhole mode melting. The melting mode also can be distinguished by the predicted melt pool morphology and the degree of vaporization as seen in Fig. 15b and d. For the conduction mode melting $(P=100 \\mathrm{~W})$, the molten region in the solid substrate is predicted to have a bowl shape without material vaporization $(\\eta=0.0)$. On the other hand, the predicted molten region in the solid substrate is a keyhole shape with material vaporization $(\\eta=0.122)$ for the keyhole mode melting $(P=200 W)$. The top views of the predicted melt pool morphology are also depicted in Fig. 16 a) and b) which show that a wider and longer melt pool is formed in keyhole mode melting.\n\nIn order to further investigate the effect of process parameters on melt pool evolution, different scanning velocities are applied in the simulation with the laser powers of $200 \\mathrm{~W}$ and $300 \\mathrm{~W}$ as shown in Fig. 17. The predicted melt pool dimensions and $\\eta$ are as shown in Table 6. It is shown that as the velocity is decreased, a deeper and wider melt pool is generated with an increased degree of vaporization.", "start_char_idx": 562756, "end_char_idx": 566480, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b8d22e46-e1ee-4496-b3ce-934eb3757467": {"__data__": {"id_": "b8d22e46-e1ee-4496-b3ce-934eb3757467", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9b733f29-337b-4daf-8bea-573d53a110a7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b88892a538a90662ccc97d2c6b15e8bf2e6dcf27894365015d5be35304799eb6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d355ba94-5666-44fd-b660-78bc3f756316", "node_type": "1", "metadata": {}, "hash": "b8a3c44e992866f37dd26213b23371ff3a076094b5ff32fd41cba2b9d4f66979", "class_name": "RelatedNodeInfo"}}, "text": "On the other hand, the predicted molten region in the solid substrate is a keyhole shape with material vaporization $(\\eta=0.122)$ for the keyhole mode melting $(P=200 W)$. The top views of the predicted melt pool morphology are also depicted in Fig. 16 a) and b) which show that a wider and longer melt pool is formed in keyhole mode melting.\n\nIn order to further investigate the effect of process parameters on melt pool evolution, different scanning velocities are applied in the simulation with the laser powers of $200 \\mathrm{~W}$ and $300 \\mathrm{~W}$ as shown in Fig. 17. The predicted melt pool dimensions and $\\eta$ are as shown in Table 6. It is shown that as the velocity is decreased, a deeper and wider melt pool is generated with an increased degree of vaporization. In particular, the mean error of the predicted melt pool width is $4.43 \\%$, and the mean error of the predicted melt pool depth is $1.92 \\%$ compared to the experimental results. Furthermore, the discrimination of melting modes from the literature [67] correlates with the value of $\\eta$ with the\n\nproposed model (zero or non-zero). In other words, the keyhole mode melting is successfully captured along with the material vaporization. It is noteworthy that this result can serve as a useful guideline for defining the process boundary with the formation of a stable melt pool. Overall, the analysis results show that the proposed model can predict the morphology of the melt pool in the SLM process considering the different characteristics of the melting modes.\n\nTo verify the obtained results by the proposed model in detail, the values of the applied heat flux to the material points are visualized as shown in Fig. 18. The center of the laser beam is moving from left to right and the volume shrinkage occurs due to the melting of the porous material as shown in Fig. 18a. It is also can be noticed that the heat flux is concentrated on the upper surface where the volume is shrunk while the more widely distributed heat flux is applied where the porous layer is still present. The graph in Fig. 18b shows the change of the applied heat flux according to the time at two different positions. It is worth noting that the applied heat flux at P1 is always higher than P2 because it is closer to the center of the laser beam in the $z$ direction. The graph shows that until $1.64 \\times 10^{-3} \\mathrm{~s}$, the heat flux is applied to both of P1 and P2 with the small difference between their values. This means the volumetric heat source is applied in this period due to the presence of the powder material. The curves in this period have several discontinuities due to the variation of the material interface with volume shrinkage while maintaining the increasing trend. Then, the applied heat flux for P1 increases sharply at a certain time and the applied heat flux for P2 changes to zero due to the transition from the volumetric heat flux to the surface heat flux. Also, the graph shows that the maximum heat flux (which means the center of the laser beam is closest to the point) occurs after this transition happens. This contributes to more realistic analysis results for the following reasons. First, the high temperature gradient due to the low conductivity of the powder can be avoided at the beginning of the laser interaction. When the volumetric heat source based on the laser absorption and extinction through the powder particles (15) is applied, the heat flux is distributed in three-dimensional space and it mitigates the concentrated heat flux. Thus, the powder material can turn into the dense state more evenly within the laser spot. Then, the surface heat flux takes place after the powder material is fully molten. Although the concentrated heat flux is applied at this time, the vaporization is suppressed because the laser energy is not very high in conduction mode melting and the conductivity of the dense state material is significantly higher than that of the powder.\n\nBesides, the applied heat flux can increase significantly due to the variation of the effective absorptivity $\\alpha_{d}$ which is dependent on the melt pool depth $d_{m}$. Fig. 19 shows the maximum applied heat flux in an element column during the laser scan process with keyhole mode melting. As shown in the graph in Fig.", "start_char_idx": 565699, "end_char_idx": 570011, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d355ba94-5666-44fd-b660-78bc3f756316": {"__data__": {"id_": "d355ba94-5666-44fd-b660-78bc3f756316", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b8d22e46-e1ee-4496-b3ce-934eb3757467", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "67f5886c1a6a1656f998e7eb9a9a3a1d4e72a2821456e5e7b2bfe7abc1ae8f09", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "000fc32f-e3ca-4204-8350-90f33b14e680", "node_type": "1", "metadata": {}, "hash": "6aee2b54eea844f45253cabda5b39e44757e4bbd1c4afc7c68a954e7c0f9ccb0", "class_name": "RelatedNodeInfo"}}, "text": "When the volumetric heat source based on the laser absorption and extinction through the powder particles (15) is applied, the heat flux is distributed in three-dimensional space and it mitigates the concentrated heat flux. Thus, the powder material can turn into the dense state more evenly within the laser spot. Then, the surface heat flux takes place after the powder material is fully molten. Although the concentrated heat flux is applied at this time, the vaporization is suppressed because the laser energy is not very high in conduction mode melting and the conductivity of the dense state material is significantly higher than that of the powder.\n\nBesides, the applied heat flux can increase significantly due to the variation of the effective absorptivity $\\alpha_{d}$ which is dependent on the melt pool depth $d_{m}$. Fig. 19 shows the maximum applied heat flux in an element column during the laser scan process with keyhole mode melting. As shown in the graph in Fig. 19b, the maximum applied heat flux increases up to $11.67 \\times 10^{6} \\mathrm{~W} / \\mathrm{mm}^{3}$ which is more than twice as large as the peak value $\\left(=4.69 \\mathrm{~W} / \\mathrm{mm}^{3}\\right)$ in the conduction mode melting in Fig. 18b. As already explained in the Section 3.3, it is worth noting that the increase of effective absorptivity is caused by a combination of multiple physical phenomena. Such complex mechanisms and physics need to be studied for a better understanding of the melt pool dynamics. In this study, however, the complex mechanisms are condensed into the effective absorptivity with the proposed model of the SLM process. This simplification may cause error between the simulation and the experiment thus, the underlying physics should be studied in more detail in the future. Meanwhile, the analysis results showed that the proposed model can predict the melt pool dimensions with reasonable errors and the variation of the melt pool morphology in different melting modes. Therefore, it can be said that the model has a certain practical guidance role for parameter selection.\n\n\\section*{6.", "start_char_idx": 569029, "end_char_idx": 571140, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "000fc32f-e3ca-4204-8350-90f33b14e680": {"__data__": {"id_": "000fc32f-e3ca-4204-8350-90f33b14e680", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d355ba94-5666-44fd-b660-78bc3f756316", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cb53c9be821d6cbad4dd0a7cd7143700758bea7ab3e9f5ed32a283c8b4c965e4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d4c3f283-a7f6-420a-9271-52ee1fd30ff4", "node_type": "1", "metadata": {}, "hash": "feeeeab94ea4cfb5dcc466074051dbcda63a9986f4f2cf1a4d2911d5e5895b3a", "class_name": "RelatedNodeInfo"}}, "text": "18b. As already explained in the Section 3.3, it is worth noting that the increase of effective absorptivity is caused by a combination of multiple physical phenomena. Such complex mechanisms and physics need to be studied for a better understanding of the melt pool dynamics. In this study, however, the complex mechanisms are condensed into the effective absorptivity with the proposed model of the SLM process. This simplification may cause error between the simulation and the experiment thus, the underlying physics should be studied in more detail in the future. Meanwhile, the analysis results showed that the proposed model can predict the melt pool dimensions with reasonable errors and the variation of the melt pool morphology in different melting modes. Therefore, it can be said that the model has a certain practical guidance role for parameter selection.\n\n\\section*{6. Conclusion}\nIn this paper, an effective model of the SLM process is developed with a novel hybrid heat source model to predict and analyze the melt\n\n$$\nP=100 \\mathrm{~W}, v=150 \\mathrm{~mm} / \\mathrm{s}\n$$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-12(4)}\n\\end{center}\n\n$$\nP=100 \\mathrm{~W}, v=200 \\mathrm{~mm} / \\mathrm{s}\n$$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-12(2)}\n\\end{center}\n\n$$\nP=200 \\mathrm{~W}, v=400 \\mathrm{~mm} / \\mathrm{s}\n$$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-12}\n\\end{center}\n\n$$\nP=200 \\mathrm{~W}, v=600 \\mathrm{~mm} / \\mathrm{s}\n$$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-12(3)}\n\\end{center}\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline\nProcess parameters: $P[\\mathrm{~W}], v[\\mathrm{~mm} / \\mathrm{s}]$ & Width $[\\mu m]$ (error \\%) & depth $[\\mu m]$ (error \\%) & $\\eta$ & Experimental width $[\\mu m]$ & Experimental depth $[\\mu m]$ & Melting mode \\\\\n\\hline\n100,150 & $132.1(8.26)$ & $155.2(3.47)$ & 0.077 & $144 \\pm 13$ & 150 & keyhole \\\\\n\\hline\n100,200 & $117.6(0.51)$ & $121.9(3.25)$ & 0.037 & $117 \\pm 7$ & 126 & keyhole \\\\\n\\hline\n100,300 & 101.1(1.84) & $51.3(1.35)$ & 0 & $103 \\pm 24$ & 52 & conduction \\\\\n\\hline\n200,300 & $135.1(3.92)$ & $263.9(0.79)$ & 0.122 & $130 \\pm 10$ & 266 & keyhole \\\\\n\\hline\n200,400 & $132.3(5.84)$ & $162.8(2.39)$ & 0.091 & $125 \\pm 16$ & 159 & keyhole \\\\\n\\hline\n200,600 & $120.0(6.19)$ & $69.8(0.29)$ & 0 & $113 \\pm 19$ & 70 & conduction \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nFig. 17. Predicted melt pool morphology with various laser powers and scanning velocities.\n\nTable 6\n\nMelt pool analysis results with various laser powers and velocities compared to the experimental results [67].\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_bd6e034633d8b3d1d1d5g-12(1)}\n\nFig. 18.", "start_char_idx": 570257, "end_char_idx": 573090, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d4c3f283-a7f6-420a-9271-52ee1fd30ff4": {"__data__": {"id_": "d4c3f283-a7f6-420a-9271-52ee1fd30ff4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "000fc32f-e3ca-4204-8350-90f33b14e680", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "36e695cbe458a90a54cb1a99f462643ca087a032a7df5f9bfc576ee94c442f0a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "52c07f49-ce5c-429c-97d3-2e61c55cabbc", "node_type": "1", "metadata": {}, "hash": "f3b3718a5c2be86ca550d115367195bfdf1feb4c43d9dd43bba14539fb0981fc", "class_name": "RelatedNodeInfo"}}, "text": "17. Predicted melt pool morphology with various laser powers and scanning velocities.\n\nTable 6\n\nMelt pool analysis results with various laser powers and velocities compared to the experimental results [67].\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_bd6e034633d8b3d1d1d5g-12(1)}\n\nFig. 18. Time versus applied heat flux amount at different positions for conduction mode melting.\n\npool characteristics. The proposed model considers the important mechanisms in the SLM process including the volume shrinkage, the material vaporization, and the variation of effective absorptivity due to the transition of the melting modes. The thermal behavior of the material with the phase transition and the consolidation is also considered in the energy balance equation using the phase-field approach. The main conclusions that can be drawn from the study are summarized as follows:\n\n1 An FEA has been performed with ABAQUS for a single-track scan of\\\\\na)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-13(1)}\n\\end{center}\n\nb)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_bd6e034633d8b3d1d1d5g-13}\n\\end{center}\n\nFig. 19. a) A column of an element in the analysis domain, b) time versus maximum applied heat flux in an element column for keyhole mode melting.\n\nthe SLM process. The multiple user-subroutines have been developed to account for the important mechanisms in the SLM process and the hybrid heat source model is applied treating the analysis domain as a cluster of element columns.\n\n2 The analysis results show that the model achieved good agreement (mean error within 6\\% for both the case without powder and the case with powder) when compared to the experimentally measured melt pool dimensions. The predicted melting modes based on the melt pool morphologies are also in good agreement with the experimental results.\n\n3 The different characteristics of the two melting modes (conduction and keyhole) are discussed in the process optimization point of view with the degree of intense heating. It is concluded that the keyhole mode melting is not preferred in terms of energy efficiency and is more sensitive to the change of the laser power.\n\n4 The performance of the proposed hybrid heat source model is also compared with the conventional heat source models. The result shows that the combination of the volumetric and the surface heat fluxes contributes to more realistic results considering the different absorption mechanisms of the porous and dense materials.\n\nIn the future, more sets of process parameters and various metal alloys should be considered to further validate the performance of the proposed model. The more detailed study about the degree of intense heating and the transition between the melting modes is also required with reliable experimental measurements. Moreover, the effects of the other process parameters including the laser spot size, layer thickness, and the hatch-distance in the multiple-track cases would be investigated. Then, the proposed model would be used as a tool to derive the simulation-based process window with the predicted melt pool characteristics.\n\n\\section*{CRediT authorship contribution statement}\nKang-Hyun. Lee: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing - original draft. Gun Jin Yun: Funding acquisition, Investigation, Project administration, Resources, Supervision, Writing review \\& editing.\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*{Acknowledgment}\nThis work was supported by the Korea Evaluation Institute of Industrial Technology (KEIT) grant funded by the Korea government\\\\\n(MOTIE) (No.20004662, Industrial Technology Innovation Program) and Institute of Engineering Research at Seoul National University. The authors are grateful for their supports.\n\n\\section*{References}\n[1] D. Gu, Laser Additive Manufacturing of High-performance Materials, Springer, 2015.\n\n[2] I. Chang, Y. Zhao, Advances in Powder Metallurgy: Properties, Processing and Applications, Elsevier, 2013.\n\n[3] M. Wong, S. Tsopanos, C.J. Sutcliffe, I. Owen, Selective laser melting of heat transfer devices, Rapid Prototyp. J. 13 (5) (2007) 291-297.\n\n[4] P. Rochus, J.-Y.", "start_char_idx": 572785, "end_char_idx": 577234, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "52c07f49-ce5c-429c-97d3-2e61c55cabbc": {"__data__": {"id_": "52c07f49-ce5c-429c-97d3-2e61c55cabbc", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d4c3f283-a7f6-420a-9271-52ee1fd30ff4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2a49fe99439288f7e796a527396a5c701ddb4543ef1c0a58dbfd27957288ced0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fee18387-4f1f-48d3-970e-dc17b4be1c12", "node_type": "1", "metadata": {}, "hash": "910187b4ddc08feaa0db28c369ca37dcbf403c909c3a83fc16033fafd90786f7", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{Acknowledgment}\nThis work was supported by the Korea Evaluation Institute of Industrial Technology (KEIT) grant funded by the Korea government\\\\\n(MOTIE) (No.20004662, Industrial Technology Innovation Program) and Institute of Engineering Research at Seoul National University. The authors are grateful for their supports.\n\n\\section*{References}\n[1] D. Gu, Laser Additive Manufacturing of High-performance Materials, Springer, 2015.\n\n[2] I. Chang, Y. Zhao, Advances in Powder Metallurgy: Properties, Processing and Applications, Elsevier, 2013.\n\n[3] M. Wong, S. Tsopanos, C.J. Sutcliffe, I. Owen, Selective laser melting of heat transfer devices, Rapid Prototyp. J. 13 (5) (2007) 291-297.\n\n[4] P. Rochus, J.-Y. Plesseria, M. Van Elsen, J.-P. Kruth, R. Carrus, T. Dormal, New applications of rapid prototyping and rapid manufacturing (RP/RM) technologies for space instrumentation, Acta Astronaut. 61 (1-6) (2007) 352-359.\n\n[5] R. Li, Y. Shi, Z. Wang, L. Wang, J. Liu, W. Jiang, Densification behavior of gas and water atomized 316L stainless steel powder during selective laser melting, Appl. Surf. Sci. 256 (13) (2010) 4350-4356.\n\n[6] J.-P. Kruth, L. Froyen, J. Van Vaerenbergh, P. Mercelis, M. Rombouts, B. 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Manuf. 1 (2014) 87-98.", "start_char_idx": 576515, "end_char_idx": 579408, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fee18387-4f1f-48d3-970e-dc17b4be1c12": {"__data__": {"id_": "fee18387-4f1f-48d3-970e-dc17b4be1c12", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "52c07f49-ce5c-429c-97d3-2e61c55cabbc", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8dd1472276506f3bf2a438905d4617b8db7f22d3a82d5b404662a50f7d57d660", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "42d87bf1-1222-492d-9e57-b08488d2f163", "node_type": "1", "metadata": {}, "hash": "bd4d328aa380a5fa933713ac1a93593b9b6c24ed2872f8e2c8f2b0fa5cbee8a0", "class_name": "RelatedNodeInfo"}}, "text": "52 (14) (2004) 4385-4398.\n\n[12] P. 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Lewandowski, Melt pool characterization for selective laser melting of Ti-6Al4V pre-alloyed powder, Solid Freeform Fabrication Symposium (2014) 256-267.\n\n[17] Y. He, C. Montgomery, J. Beuth, B. Webler, Melt pool geometry and microstructure of Ti6Al4V with B additions processed by selective laser melting additive manufacturing, Mater. Des. 183 (2019) 108126.\n\n[18] H. Gong, K. Rafi, T. Starr, B. Stucker, The effects of processing parameters on defect regularity in Ti-6Al-4V parts fabricated by selective laser melting and electron beam melting, 24th Annual International Solid Freeform Fabrication Symposium-An Additive Manufacturing Conference, Austin, TX, 2013, pp. 12-14.\n\n[19] J. Dilip, S. Zhang, C. Teng, K. Zeng, C. Robinson, D. Pal, B. Stucker, Influence of processing parameters on the evolution of melt pool, porosity, and microstructures in Ti-6Al-4V alloy parts fabricated by selective laser melting, Prog. Addit. Manuf. 2 (3) (2017) 157-167.\n\n[20] G. Kasperovich, J. 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Des. 156 (2018) 143-153.\n\n\\begin{itemize}\n  \\item \n\\end{itemize}", "start_char_idx": 588025, "end_char_idx": 590509, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "17b7490e-e47c-492c-ae74-ca535041242d": {"__data__": {"id_": "17b7490e-e47c-492c-ae74-ca535041242d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c0a03beb-0b1b-4707-9ecf-cb47e0ec40b8", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "59f1d6d264515682fa8ef2449a519b3993f7b3a33774cab0b76b699e1c0dac84", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "4d72fa23-3228-4d84-926a-4e97fcc50e52", "node_type": "1", "metadata": {}, "hash": "92c73b815fdc9bf35468b1c86e108027c3f385db14d50231e8f786bcbdd8b5d4", "class_name": "RelatedNodeInfo"}}, "text": "[69] J. Goldak, A. Chakravarti, M. Bibby, A new finite element model for welding heat sources, Metall. Trans. B 15 (2) (1984) 299-305.\n\n[70] Q. Zhang, J. Xie, Z. Gao, T. London, D. Griffiths, V. Oancea, A metallurgical phase transformation framework applied to SLM additive manufacturing processes, Mater. Des. 166 (2019) 107618.\n\n[71] C. Bruna-Rosso, A.G. Demir, B. Previtali, Selective laser melting finite element modeling: validation with high-speed imaging and lack of fusion defects prediction, Mater. Des. 156 (2018) 143-153.\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{Laser-Induced Keyhole Defect Dynamics during Metal Additive Manufacturing }\n\n\n\\author{Andrew M. Kiss, Anthony Y. Fong, Nicholas P. Calta, Vivek Thampy, Aiden A. Martin,\\\\\nPhilip J. Depond, Jenny Wang, Manyalibo J. Matthews, Ryan T. Ott,\\\\\nChristopher J. Tassone, Kevin H. Stone, Matthew J. Kramer, Anthony van Buuren,\\\\\nMichael F. Toney, and Johanna Nelson Weker*}\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\nLaser powder bed fusion (LPBF) metal additive manufacturing provides distinct advantages for aerospace and biomedical applications. However, widespread industrial adoption is limited by a lack of confidence in part properties driven by an incomplete understanding of how unique process parameters relate to defect formation and ultimately mechanical properties. To address that gap, high-speed $\\mathrm{X}$-ray imaging is used to probe subsurface melt pool dynamics and voidformation mechanisms inaccessible to other monitoring approaches. This technique directly observes the depth and dynamic behavior of the vapor depression, also known as the keyhole depression, which is formed by recoil pressure from laser-driven metal vaporization. Also, vapor bubble formation and motion due to melt pool currents is observed, including instances of bubbles splitting before solidification into clusters of smaller voids while the material rapidly cools. Other phenomena include bubbles being formed from and then recaptured by the vapor depression, leaving no voids in the final part. Such events complicate attempts to identify defect formation using surface-sensitive process-monitoring tools. Finally, once the void defects form, they cannot be repaired by simple laser scans, without introducing new defects, thus emphasizing the importance of understanding processing parameters to develop robust defect-mitigation strategies based on experimentally validated models.\n\n\\section*{1.", "start_char_idx": 589937, "end_char_idx": 593436, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "4d72fa23-3228-4d84-926a-4e97fcc50e52": {"__data__": {"id_": "4d72fa23-3228-4d84-926a-4e97fcc50e52", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "17b7490e-e47c-492c-ae74-ca535041242d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0b2ae9480f7e629b3a1a4d60be148921853d13ede5f2d8b1bae6f0f273b1b6a3", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "61159d24-c460-4462-9f58-f5fe5bdda9e9", "node_type": "1", "metadata": {}, "hash": "ffd616e108d8e6f0734e86030ab1fd9343c36f7bde2d10a44b2707a8ef237e45", "class_name": "RelatedNodeInfo"}}, "text": "This technique directly observes the depth and dynamic behavior of the vapor depression, also known as the keyhole depression, which is formed by recoil pressure from laser-driven metal vaporization. Also, vapor bubble formation and motion due to melt pool currents is observed, including instances of bubbles splitting before solidification into clusters of smaller voids while the material rapidly cools. Other phenomena include bubbles being formed from and then recaptured by the vapor depression, leaving no voids in the final part. Such events complicate attempts to identify defect formation using surface-sensitive process-monitoring tools. Finally, once the void defects form, they cannot be repaired by simple laser scans, without introducing new defects, thus emphasizing the importance of understanding processing parameters to develop robust defect-mitigation strategies based on experimentally validated models.\n\n\\section*{1. Introduction}\nAdditive manufacturing (AM) is a powerful alternative to conventional manufacturing approaches that can streamline the manufacturing process from design to final part, enable design flexibility, and reduce material waste..$^{[1-3]}$ Although several techniques have been developed, laser powder bed fusion (LPBF) is one of the most common approaches for metal AM. ${ }^{[4,5]}$ Some of the inherent advantages of the LPBF method are the excellent spatial resolution due to the laser beam that is typically focused to a diameter of less than $100 \\mu \\mathrm{m}$ and fast build times afforded by scan rates on the order of $100 \\mathrm{~s}$ to $1000 \\mathrm{~mm} \\mathrm{~s}^{-1}[6,7]$ These scan speeds lead to highly localized, rapid heating and cooling, with relevant time scales on the order of micro- to milliseconds. ${ }^{[6]}$\n\nWhile AM parts are used in industry today, ${ }^{[8-10]}$ understanding of the fundamental processes that govern final part properties is incomplete ${ }^{[6]}$ and impedes widespread adoption. A central gap in knowledge is the physical details of the link between laser parameters and defect-formation mechanisms. Without this under-\n\\footnotetext{standing, the engineering qualification of parts is through trial and error, which is time-consuming and expensive. In particular, understanding the physics in order to converge on a set of build parameters to minimize internal porosity is one of the key factors in improving the mechanical properties of a printed part, which depend in part on the size, shape, and distribution of voids. ${ }^{[11-14]}$ Systematic experimental studies relating void size and distribution to laser scan speed and power typically rely on ex situ characterization, such as two-dimensional micrographs using scanning electron microscopy (SEM), optical microscopy $(\\mathrm{OM}){ }^{[15]}$ or three-dimensional computed tomography approaches. ${ }^{[16]}$ SEM and OM are inherently surface-sensitive techniques that require destructive preparation methods such as slicing to see subsurface defects. X-ray-based microtomography has successfully been used to image voids in titanium alloy Ti-6Al-4V (Ti64) $^{[17]}$ and 316L stainless steel ${ }^{[18,19]}$ parts printed using LPBF. By sorting the voids by size and sphericity,\n\nDr. A. M. Kiss, Dr. A. Y. Fong, Dr. V. Thampy, Dr. C. ,\\\\\nDr. K. H. Stone, Dr. M. F. Toney, Dr. J. Nelson Weker\n\nStanford Synchrotron Radiation Lightsource\n\nSLAC National Accelerator Laboratory\n\nE-mail: \\href{mailto:jlnelson@slac.stanford.edu}{jlnelson@slac.stanford.edu}\n\nDr. N. P. Calta, Dr. A. A. Martin, P. J. Depond, J. Wang, Dr. M. J. Matthews, Dr. A. van Buuren\n\nPhysical and Life Sciences Directorate\n\nLawrence Livermore National Laboratory Livermore, CA 94550, USA\n\nDr. R. T. Ott, Dr. M. J. Kramer\n\nDivision of Materials Science and Engineering\n\nAmes Laboratory\n\nlowa State University\n\nAmes, IA 50011, USA\n\n(iD) The ORCID identification number(s) for the author(s) of this article can be found under \\href{https://doi.org/10.1002/adem.201900455}{https://doi.org/10.1002/adem.201900455}.\n\nDOI: 10.1002/adem. 201900455\n}\n\nCunningham et al.", "start_char_idx": 592497, "end_char_idx": 596588, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "61159d24-c460-4462-9f58-f5fe5bdda9e9": {"__data__": {"id_": "61159d24-c460-4462-9f58-f5fe5bdda9e9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "4d72fa23-3228-4d84-926a-4e97fcc50e52", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d7fc4351d3741eb115b8b2628f78d0a19a7701d09dc9cd51c4e6a680a78ae686", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ac5e2952-0899-4502-b1f9-ef5a1ba76812", "node_type": "1", "metadata": {}, "hash": "df737517900069163f36a97af547e15c9a9026c3217e6e03e663a9c042ea98e8", "class_name": "RelatedNodeInfo"}}, "text": "N. P. Calta, Dr. A. A. Martin, P. J. Depond, J. Wang, Dr. M. J. Matthews, Dr. A. van Buuren\n\nPhysical and Life Sciences Directorate\n\nLawrence Livermore National Laboratory Livermore, CA 94550, USA\n\nDr. R. T. Ott, Dr. M. J. Kramer\n\nDivision of Materials Science and Engineering\n\nAmes Laboratory\n\nlowa State University\n\nAmes, IA 50011, USA\n\n(iD) The ORCID identification number(s) for the author(s) of this article can be found under \\href{https://doi.org/10.1002/adem.201900455}{https://doi.org/10.1002/adem.201900455}.\n\nDOI: 10.1002/adem. 201900455\n}\n\nCunningham et al. roughly categorized void origin as lack of fusion (highly irregular, larger voids), keyholing (large, spherical voids), and precursor voids (small, spherical voids). However, as the authors note, morphology is not a definitive metric for determining void-formation mechanisms. Although computational efforts to simulate process physics provide valuable insight, they require experimental validation and are computationally expensive, which makes a high-fidelity simulation of an entire build impractical. ${ }^{[6,20]}$ Therefore, in situ monitoring is needed to fully understand the mechanisms which lead to different defect void formations during the LPBF process.\n\nSeveral in situ process monitoring techniques have been developed to examine the build process for improving process parameters and inform models. Visible-light high-speed imaging provides insight into many important phenomena including spatter, powder motion and denudation, and melt pool dynamics $^{[1,21-23]}$ Thermal imaging has also played a significant role in understanding how material thermal properties and build strategies affect the final build. ${ }^{[1,24-27]}$ In addition, commercial systems now include melt-pool monitoring using cameras and photodiodes to quantify process stability ${ }^{[1]}$ Although these techniques provide useful, real-time information, they are limited to probing the surface of the part due to their use of visible or infrared light. Acoustic measurements can indirectly probe subsurface phenomena, but the difficulty of correlating complex acoustic signals to discrete defect-creation events currently hinders their widespread adoption. ${ }^{[28,29]}$ Complimentary techniques are needed to directly probe the interior of the part and understand the underlying physics controlling the melt pool and the surrounding material.\n\nSynchrotron-based X-ray techniques provide the high X-ray flux necessary to probe the interior of the part to directly monitor the build process and material properties. ${ }^{[30-36]}$ X-ray phasecontrast imaging was used to capture melt-pool dynamics and void formation of laser butt welding with a laser scanning at $500 \\mathrm{~W}$ and $16.7 \\mathrm{~mm} \\mathrm{~s}^{-1}$, with $1 \\mathrm{kHz}$ frame rates. ${ }^{[36]}$ Although these imaging settings were sufficient to observe this system, higher frame rates are necessary for capturing the key dynamics at the micro- to millisecond timescales during these LPBF builds. Using high-speed X-ray imaging, the vapor depression, and sometime the melt-pool dynamics can be imaged directly. ${ }^{[30,32-35]}$ Recent work has used synchrotron X-ray imaging to probe how melt-pool behavior relates to spatter and meltpool dynamics ${ }^{[33]}$ in conditions approximating overhang regions, which are particularly defect-prone regions in bulk part builds. ${ }^{[34]}$ Cunningham et al. imaged the melt pool and vapor depression on bare Ti64 using synchrotron-based X-rays to study how the power and velocity of the incident laser beam affected the heat-transfer mode of the sample (i.e., conduction or keyhole mode) and its relation to laser drilling speed, vapor depression dynamics, and front keyhole wall angle. ${ }^{[35]}$ Herein, we utilize high-speed X-ray imaging to quantify subsurface-defect formation and dynamics during the LPBF process in Ti64. We span the laser-processing parameter space from the conduction regime, where the melt-pool dynamics are dominated by the conduction of heat into the solid material, into the keyhole regime, where the recoil momentum of the vaporized material exerts a force on the melted material and forms a depression, to validate the theoretically determined keyhole threshold.", "start_char_idx": 596019, "end_char_idx": 600303, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ac5e2952-0899-4502-b1f9-ef5a1ba76812": {"__data__": {"id_": "ac5e2952-0899-4502-b1f9-ef5a1ba76812", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "61159d24-c460-4462-9f58-f5fe5bdda9e9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "57e265b753140aba84517007e0c38858298791e1dd42279dfc66a3cd7a577420", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "39de9baf-1a95-4f34-9b33-5a769839ea58", "node_type": "1", "metadata": {}, "hash": "2e66c10e3436cc1d0b552ac9fb59646b54116c66c52df3d79806e0aae7b2fcdb", "class_name": "RelatedNodeInfo"}}, "text": "${ }^{[34]}$ Cunningham et al. imaged the melt pool and vapor depression on bare Ti64 using synchrotron-based X-rays to study how the power and velocity of the incident laser beam affected the heat-transfer mode of the sample (i.e., conduction or keyhole mode) and its relation to laser drilling speed, vapor depression dynamics, and front keyhole wall angle. ${ }^{[35]}$ Herein, we utilize high-speed X-ray imaging to quantify subsurface-defect formation and dynamics during the LPBF process in Ti64. We span the laser-processing parameter space from the conduction regime, where the melt-pool dynamics are dominated by the conduction of heat into the solid material, into the keyhole regime, where the recoil momentum of the vaporized material exerts a force on the melted material and forms a depression, to validate the theoretically determined keyhole threshold. ${ }^{[18]}$ We also explore strategies to repair these keyholing voids after they form. Our results reveal the complexity in repairing these voids and possible pitfalls in positively identifying defect-formation events using surface-sensitive monitoring tools without complementary in situ subsurface probes.\n\n\\section*{2. Results and Discussion}\n\\subsection*{2.1. Identifying Keyhole Regime and Void Formation}\nBy adjusting the laser power at two different speeds (146 and $455 \\mathrm{~mm} \\mathrm{~s}^{-1}$ ), we compare the frequency of void formation as the laser energy density is increased into the keyhole regime (Figure 1). For the $146 \\mathrm{~mm} \\mathrm{~s}^{-1}$ laser-speed tracks, two different runs for each laser power were averaged together. The error bars in Figure 1 show one standard deviation from the average for the $146 \\mathrm{~mm} \\mathrm{~s}^{-1}$ laser speed. The onset of void formation for both speeds is around $75 \\mathrm{~W}$. Previous studies have predicted that the transition from the conduction regime to keyhole regime occurs when the normalized enthalpy exceeds a value of $\\approx 6$, whereas experiments in stainless steel show this transition occurring closer to a normalized enthalpy of $\\approx 300^{[18,37]}$ Normalized enthalpy $\\left(\\Delta H / h_{\\mathrm{s}}\\right)$ can be written as\n\n$\\frac{\\Delta H}{h_{s}}=\\frac{A P}{\\pi \\rho C T_{m} \\sqrt{D^{3}}}$\n\nwhere $\\Delta H$ is the specific enthalpy, $h_{\\mathrm{s}}$ is the enthalpy at melting, $A$ is the absorptivity of the material (assumed here to be 0.6 under all conditions), $P$ is the laser power, $\\rho$ is the density $\\left(4.43 \\mathrm{~g} \\mathrm{~cm}^{-3}\\right.$ for Ti64), ${ }^{[38]} C$ is the specific heat capacity\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ab996ee883a125af6982g-2}\n\\end{center}\n\nFigure 1. The frequency of void defect formation within the fixed field of view $(2.048 \\mathrm{~mm})$ as the laser power is increased into the keyhole regime for two different laser scan speeds. An arrow indicating the approximate location of the transition to the keyhole regime is drawn to show the relationship between keyhole formation and the formation of voids. The faster scan speed shows a linear increase in voids with increased laser power with a slope of 0.05 voids $\\mathrm{mm}^{-1} \\mathrm{~W}^{-1}$. The slow speed shows the same linear dependence after a dramatic increase in void formation between 75 and $100 \\mathrm{~W}$. The slower scan speed is the average number of voids for two different tracks with the error bars showing one standard deviation.", "start_char_idx": 599435, "end_char_idx": 602911, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "39de9baf-1a95-4f34-9b33-5a769839ea58": {"__data__": {"id_": "39de9baf-1a95-4f34-9b33-5a769839ea58", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ac5e2952-0899-4502-b1f9-ef5a1ba76812", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "572d946d6ddf76e122be47e4f5c205d49516d995ad79ad1d976c021104074548", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f4c27c8e-def8-45eb-a53b-d4684425b6e5", "node_type": "1", "metadata": {}, "hash": "1d49ccca74e7a33f91ee85eec4ebdacf5d5f09a547a91b0f5844699918c76aec", "class_name": "RelatedNodeInfo"}}, "text": "The frequency of void defect formation within the fixed field of view $(2.048 \\mathrm{~mm})$ as the laser power is increased into the keyhole regime for two different laser scan speeds. An arrow indicating the approximate location of the transition to the keyhole regime is drawn to show the relationship between keyhole formation and the formation of voids. The faster scan speed shows a linear increase in voids with increased laser power with a slope of 0.05 voids $\\mathrm{mm}^{-1} \\mathrm{~W}^{-1}$. The slow speed shows the same linear dependence after a dramatic increase in void formation between 75 and $100 \\mathrm{~W}$. The slower scan speed is the average number of voids for two different tracks with the error bars showing one standard deviation. Error bars are not shown for the $455 \\mathrm{~mm} \\mathrm{~s}^{-1}$ laser speed because only one run was performed for each power.\\\\\n$\\left(0.83 \\mathrm{~J} \\mathrm{~g}^{-1} \\mathrm{~K}^{-1}\\right),{ }^{[38]} T_{\\mathrm{m}}$ is the melting temperature $(1923 \\mathrm{~K}),{ }^{[38]}$ $D$ is thermal diffusivity of the melt $\\left(0.086 \\mathrm{~cm}^{2} \\mathrm{~s}^{-1}\\right),{ }^{[38]} u$ is the scan speed of the laser, and $a$ is the radius of the laser beam such that $a=\\sigma \\sqrt{2}$. Normalized enthalpy is a term commonly used in laser welding literature ${ }^{[37,39]}$ and has been shown to accurately describe the transition from conduction to void formation regime under different laser scan speeds, power, and beam size. ${ }^{[18]}$ For the two laser scan speeds presented here, the onset of void formation occurs at around a normalized enthalpy of $17 \\pm 8$. This agrees well with the previous experimental estimate $(30 \\pm 4)$ made on $316 \\mathrm{~L}$ stainless steel using two different beam sizes strengthening the proposition that the normalized enthalpy is indeed an useful metric to compare selective laser melting under varying laser conditions and even across different materials.\n\nImmediately after the onset of void formation, the two laser scan speeds behave very differently. We observe that the liquidvapor interface is more stable at higher scan speeds and is therefore less likely to produce bubbles. The faster scan rate $\\left(455 \\mathrm{~mm} \\mathrm{~s}^{-1}\\right)$ shows a linear increase in the number of voids with increasing power with a slope of 0.05 voids $\\mathrm{mm}^{-1} \\mathrm{~W}^{-1}$. However, the slower scan speed $\\left(146 \\mathrm{~mm} \\mathrm{~s}^{-1}\\right)$ shows a sharp jump in the number of voids formed at $100 \\mathrm{~W}$ before a linear increase with a slope equal to that of the faster scan rate; namely 0.05 voids $\\mathrm{mm}^{-1} \\mathrm{~W}^{-1}$. This dramatic jump in voids is maintained in the slower scan speed even if considering the void formation rate (voids $\\mathrm{mm}^{-1} \\mathrm{~s}^{-1}$ ) rather than the total number of voids formed within the field of view (voids per $\\mathrm{mm}^{-1}$ ). This jump is also seen if the number of voids is plotted with respect to the normalized enthalpy (Figure S2, Supporting Information). Conversely, well into the keyhole regime where the number of voids formed changes linearly at a rate independent of scan speed, the total number of voids is scan-speed dependent. These observations suggest that the change in the rate of void formation well into the keyhole regime is adequately described with the laser scan parameters; yet, the void formation mechanism immediately after the onset of void formation cannot be fully explained.\n\n\\subsection*{2.2. Vapor Depression Dynamics}\nFrom the high-speed in situ imaging data, we can also track the vapor depression dynamics formed by the recoil pressure of the vaporized metal as the laser scans across the powder (Figure 2a). The vapor depression shape and depth are highly variable even as the laser is scanned at a constant speed.", "start_char_idx": 602151, "end_char_idx": 606017, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f4c27c8e-def8-45eb-a53b-d4684425b6e5": {"__data__": {"id_": "f4c27c8e-def8-45eb-a53b-d4684425b6e5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "39de9baf-1a95-4f34-9b33-5a769839ea58", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ffa77691fe5e5c43971f354afc79720b58f8a22136aeea0d5deb82087d88714e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "382e9894-01ea-42ea-9d81-77c6e6a16042", "node_type": "1", "metadata": {}, "hash": "c68114389a17ef35d33237d51245762dcc03867c91f1aa8dd9c1e3f25fe6bae3", "class_name": "RelatedNodeInfo"}}, "text": "This jump is also seen if the number of voids is plotted with respect to the normalized enthalpy (Figure S2, Supporting Information). Conversely, well into the keyhole regime where the number of voids formed changes linearly at a rate independent of scan speed, the total number of voids is scan-speed dependent. These observations suggest that the change in the rate of void formation well into the keyhole regime is adequately described with the laser scan parameters; yet, the void formation mechanism immediately after the onset of void formation cannot be fully explained.\n\n\\subsection*{2.2. Vapor Depression Dynamics}\nFrom the high-speed in situ imaging data, we can also track the vapor depression dynamics formed by the recoil pressure of the vaporized metal as the laser scans across the powder (Figure 2a). The vapor depression shape and depth are highly variable even as the laser is scanned at a constant speed. Dramatic changes in shape and depth of the vapor depression often result in the formation of a vapor-filled bubble forming near the base of the depression. We have tracked the vapor depression depth, distance between the top of the powder and the bottom of the vapor depression, as a function of time (Figure $2 \\mathrm{~b}$ ) and found an average depth of $262 \\mu \\mathrm{m}$ with a standard deviation of $26 \\mu \\mathrm{m}$ for a scan speed of $146 \\mathrm{~mm} \\mathrm{~s}^{-1}$ and laser power of $100 \\mathrm{~W}$.\n\nTo better understand the relationship between the vapor depression and void formation, we plotted the average vapordepression depth and average void depth distance between the top of the powder bed and the bottom of the vapor depression or center of void, respectively, as functions of power (Figure 3). For both speeds, below a laser power of $75 \\mathrm{~W}$, a vapor depression was not visible and void defects do not form. The onset of void formation is also the scan speed and power at which a vapor depression is visible. Although these phenomena occur simultaneously for the performed experiments, additional work is needed to determine the relationship between the onset of the vapor depression and generation of voids. As the power increases, the depth of both the voids and vapor depression increase. This agrees with the vapor depression results from Cunningham et al. on bare Ti64 plates, where they reported a linear relationship of vapor depression with increased power ${ }^{[35]}$ Moreover, the slower scan speed results in a higher average depth of both voids and the depression for all laser powers investigated.\n\nOn average, voids form within a standard deviation (colored error bars) of the base of the vapor depression, and typically slightly shallower. This suggests that voids form when the base of the depression is pinched off as a gas bubble, and the bubbles are not dragged significantly closer to the surface or (a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ab996ee883a125af6982g-3(1)}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ab996ee883a125af6982g-3}\n\\end{center}\n\nFigure 2. a) A series of images shows the vapor depression moving through the sample. The depth and shape of the vapor depression varies considerably in these four images. b) The vapor-depression depth can be tracked during a scan to see the variation. This scan at $146 \\mathrm{~mm} \\mathrm{~s}^{-1}$ and $100 \\mathrm{~W}$ shows an average vapor-depression depth of $262 \\mu \\mathrm{m}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ab996ee883a125af6982g-4}\n\\end{center}\n\nFigure 3. The average depth of the voids with increasing laser power tracks the average vapor-depression depth for both 146 and $455 \\mathrm{~mm} \\mathrm{~s}^{-1}$ laser scan speed. On average, voids (open symbols) form within the colored error bars, representing one standard deviation of the depth of the vapor depression, or slightly shallower. The variability in both the vapor depression and void depths increases with increased power and decreased speed.\n\ndeeper by the melt-pool currents before solidifying. This agrees with what we observe from the X-ray movies of the different prints.", "start_char_idx": 605094, "end_char_idx": 609284, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "382e9894-01ea-42ea-9d81-77c6e6a16042": {"__data__": {"id_": "382e9894-01ea-42ea-9d81-77c6e6a16042", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f4c27c8e-def8-45eb-a53b-d4684425b6e5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "55536e5a18b215e3fe6c6768cedc814966023ec782a671dbede0fa19d92778a0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b98db361-8949-4b79-b9e3-71da882d7a9c", "node_type": "1", "metadata": {}, "hash": "8ccde9d1f876c23120e18720fea722d5c7962f1b062809fb7151de9903a2dbd4", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ab996ee883a125af6982g-4}\n\\end{center}\n\nFigure 3. The average depth of the voids with increasing laser power tracks the average vapor-depression depth for both 146 and $455 \\mathrm{~mm} \\mathrm{~s}^{-1}$ laser scan speed. On average, voids (open symbols) form within the colored error bars, representing one standard deviation of the depth of the vapor depression, or slightly shallower. The variability in both the vapor depression and void depths increases with increased power and decreased speed.\n\ndeeper by the melt-pool currents before solidifying. This agrees with what we observe from the X-ray movies of the different prints. Moreover, the spread in the void depth increases considerably with higher power and slower speed as seen in the large standard deviation in the average void depth (black error bars). This large distribution agrees with our observations from the X-ray movies where we find that voids tend to form when the vapor depression depth is near an extreme, either much shallower or deeper than the average depth. Looking closer at the distribution of void depths (Figure S3 and S4, Supporting Information) it is difficult to extract a clear trend; nevertheless, it clearly does not resemble a normal distribution centered around the average vapor-depression depth.\n\nIt is also notable that the average vapor-depression depth (and therefore, void depth) is linear with normalized enthalpy for both speeds (Figure S5, Supporting Information) in the keyhole regime. Thus, normalized enthalpy appears to capture the key mechanisms for the average depth of the vapor depression and resulting voids, but does not accurately predict the number of voids formed for a given set of scan parameters. We observe from the high-speed imaging that voids are created due to instabilities in the vapor depression and develop randomly during the scan. Therefore, the frequency of these events is dependent on the instability of the vapor depression, which is related to material properties (vaporization temperature, viscosity, surface tension) as well as process parameters (surface temperature, vapor pressure above the sample, depression depth, melt-pool waves, laser-driven currents in the liquid). Next, we explore a few observed phenomena related to the dynamics of the melt-vapor interface.\n\n\\subsection*{2.3. Bubble Dynamics}\nIn addition to vapor-depression dynamics, in situ X-ray imaging reveals the dynamic behavior of vapor-filled bubbles as they move through the melt pool and are trapped by the solidifying metal. Many of the observed voids appear as expected, developing from the instability of the liquid-vapor interface and solidifying soon after creation. However, we do observe some more interesting, frequent phenomena that should be considered. For example, we frequently observe the breaking apart of single bubbles into two or more bubbles during solidification. An example is shown in Figure 4 and Movie S1, Supporting Information. In the first panel, the bottom of the vapor depression is slightly bulged suggesting a bubble may form. In the second panel of Figure 4, the bubble is first observed $\\approx 100 \\mu \\mathrm{m}$ behind the depression as the laser scans from left to right. The \" $x$ \" in each frame indicates the position of the bubble in the second frame. Notably, the bubble appears well past the depression, which only moves $\\approx 6 \\mu \\mathrm{m}$ between frames. This indicates that the laser-driven bubble motion shortly after formation for this scan is much faster than we can accurately capture with the camera frame rate used $(20 \\mathrm{kHz})$. However, we observe, for higher energy density scans, the motion of bubbles in the melt pool is much slower and is captured. Often those bubbles are observed being dragged along by the laser near the surface of the melt pool at depths around $60-100 \\mu \\mathrm{m}$ and as far as $\\approx 300 \\mu \\mathrm{m}$ behind the vapor depression (Movie S2, Supporting Information).\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ab996ee883a125af6982g-4(1)}\n\\end{center}\n\nFigure 4. Four consecutive images of the vapor depression showing the formation of a void. As the laser (approximate position shown with red line) and vapor depression moves from left to right, the void develops after the laser has passed, as seen in the second frame. An \" $x$ \" is used to mark the location of the void in that second frame.", "start_char_idx": 608586, "end_char_idx": 613079, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b98db361-8949-4b79-b9e3-71da882d7a9c": {"__data__": {"id_": "b98db361-8949-4b79-b9e3-71da882d7a9c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "382e9894-01ea-42ea-9d81-77c6e6a16042", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "48b23ece0d26e7a80b1e792ff131152943fc59428a5f8b7c77f09128bcc01cc8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c61dff0c-8a96-4a2e-a916-e49bfafe32bc", "node_type": "1", "metadata": {}, "hash": "b02359d7cd99275aec6dae726b0502c6040406c870fd6f091eaeeea9d12af918", "class_name": "RelatedNodeInfo"}}, "text": "Often those bubbles are observed being dragged along by the laser near the surface of the melt pool at depths around $60-100 \\mu \\mathrm{m}$ and as far as $\\approx 300 \\mu \\mathrm{m}$ behind the vapor depression (Movie S2, Supporting Information).\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ab996ee883a125af6982g-4(1)}\n\\end{center}\n\nFigure 4. Four consecutive images of the vapor depression showing the formation of a void. As the laser (approximate position shown with red line) and vapor depression moves from left to right, the void develops after the laser has passed, as seen in the second frame. An \" $x$ \" is used to mark the location of the void in that second frame. As the laser moves right and the melt pool begins to cool, the void is seen splitting into two voids and solidifying (yellow arrows). The scan was performed at $146 \\mathrm{~mm} \\mathrm{~s}^{-1}$ and $100 \\mathrm{~W}$. See Movie S1, Supporting Information.\n\nBased on the imaging, the bubble in Figure 4 travels at $1.3 \\mathrm{~mm} \\mathrm{~s}^{-1}$ opposite the direction of the laser scan in the $50 \\mu$ s after pinching off the vapor depression. Less than $100 \\mu \\mathrm{s}$ after forming, as the bubble slows to near zero, as it is influenced by the viscosity and currents of the melt pool, it also splits in two. By $150 \\mu \\mathrm{s}$ after formation, both bubbles are trapped as void defects with the distance between their centers at the approximate location of the bubble immediately before splitting. The behavior of the bubbles primarily depends on the complex fluid flow present in the melt pool, which has been modeled in the case of 316 AM and in laser welding of Ti alloys ${ }^{[4,40]}$ and cannot be imaged directly using our current X-ray projection imaging setup.\n\nWe found that bubble breakup is a relatively common occurrence for the processing parameters that we examined. In fact, nearly all the scans with laser power above $100 \\mathrm{~W}$ for a scan speed of $455 \\mathrm{~mm} \\mathrm{~s}^{-1}$ and above $75 \\mathrm{~W}$ for a scan speed of $146 \\mathrm{~mm} \\mathrm{~s}^{-1}$ show bubble breakup. Since the bubbles tend to form near the bottom of the vapor depression, their formation occurs close in proximity to the edge of the melt pool solid-liquid interface. ${ }^{[4,18]}$ As a bubble is carried by convective currents away from the vapor depression and depending on the direction of the current, the bottom of the bubble approaches that solid-liquid interface, and the bubble becomes pinned to that location. Marangonidriven melt-pool flow pulls on the top of the bubble and eventually overcomes surface tension to split the bubble. The frequency of this effect is likely material dependent, as the relative strength of the Marangoni-driven flow and surface tension are materialdependent properties.\n\nA second notable bubble dynamic is the recapturing of a bubble by the vapor depression (Figure S6, Movie S3, Supporting Information). In this particular case, instability in the vapor depression shape and size leads to a bubble which exists for $\\approx 100 \\mu$ s before being recaptured by the depression. The bubble is formed near the vapor depression, creating a situation where it would more likely be recaptured. This self-healing, recapturing event is less frequent than bubbles breaking apart, but also occurs more often in scans with laser power above $100 \\mathrm{~W}$ for a scan speed of $455 \\mathrm{~mm} \\mathrm{~s}^{-1}$ and above $75 \\mathrm{~W}$ for a scan speed of $146 \\mathrm{~mm} \\mathrm{~s}^{-1}$ where the vapor depression shape is rapidly changing. Bubble recapture and bubble breakup are important phenomenon that need careful consideration when developing process-monitoring tools which might detect bubble recapture as a void-formation event and give a false-positive or bubble breakup as only one void rather than a cluster of smaller ones.\n\n\\subsection*{2.4. Void Repair Strategies}\nAlthough determining the controlling mechanisms of void formation in AM processes is critical to advancing AM technologies, equally important is understanding how such defects can be removed or fixed after creation.", "start_char_idx": 612381, "end_char_idx": 616547, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c61dff0c-8a96-4a2e-a916-e49bfafe32bc": {"__data__": {"id_": "c61dff0c-8a96-4a2e-a916-e49bfafe32bc", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b98db361-8949-4b79-b9e3-71da882d7a9c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3c67766e10e87ea738376a67a2ee3d65bff7efe5b3fbcf65a3071f618ad59783", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "685fcbe7-bf35-4f58-9986-b27e9b27217a", "node_type": "1", "metadata": {}, "hash": "9ee61eca0fac6d5220182bc8480dd0557ee3540534a2e1f6b9792cf4368635ed", "class_name": "RelatedNodeInfo"}}, "text": "This self-healing, recapturing event is less frequent than bubbles breaking apart, but also occurs more often in scans with laser power above $100 \\mathrm{~W}$ for a scan speed of $455 \\mathrm{~mm} \\mathrm{~s}^{-1}$ and above $75 \\mathrm{~W}$ for a scan speed of $146 \\mathrm{~mm} \\mathrm{~s}^{-1}$ where the vapor depression shape is rapidly changing. Bubble recapture and bubble breakup are important phenomenon that need careful consideration when developing process-monitoring tools which might detect bubble recapture as a void-formation event and give a false-positive or bubble breakup as only one void rather than a cluster of smaller ones.\n\n\\subsection*{2.4. Void Repair Strategies}\nAlthough determining the controlling mechanisms of void formation in AM processes is critical to advancing AM technologies, equally important is understanding how such defects can be removed or fixed after creation. It has been proposed that scanning the laser over an already printed region can be an effective means of repairing voids. ${ }^{[41]}$ Nondestructive X-ray imaging provides an ideal approach to investigate this strategy for void repair, as it allows imaging between multiple laser passes to assess the formation and repair of voids. Herein, we directly investigated the effectiveness of using a second laser scan with variable laser power to repair keyhole void defects. Prior to laser exposure, no voids are discernable in the substrate. As expected from the work described earlier, voids result from an initial laser pass with speed of $144 \\mathrm{~mm} \\mathrm{~s}^{-1}$ and power at $100 \\mathrm{~W}$. In an attempt to repair these voids, a second laser pass was executed at a) $100 \\mathrm{~W}$, b) $150 \\mathrm{~W}$, and c) $50 \\mathrm{~W}$ using the same scan speed. Images after these passes are shown in Figure 5, where the voids created by the initial scan are colored red if they are successfully repaired by the subsequent scan, or magenta if they remain after the repair attempt. New voids formed in the second scan are blue. During the second laser pass at $100 \\mathrm{~W}$ (Figure 5a), the average vapor depression reaches the same depth within the substrate as the first pass. Thus, the melt pool is around the same depth, melting the same material as the first pass and repairing the voids formed during the original laser scan. However, the second laser scan also forms new voids at approximately the same depth, but in different locations. This suggests that void formation under these conditions primarily arises from the stochastic behavior of meltpool dynamics rather than any preexisting defect in the material itself. This void repair and reformation behavior was consistent\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_ab996ee883a125af6982g-5}\n\\end{center}\n\nFigure 5. Test of the effect of laser power on the success of repairing voids. In each of these scenarios, the first laser pass was performed at $100 \\mathrm{~W}$. a) The original voids are repaired (red) by the $100 \\mathrm{~W}$ repair track, but new voids are created (blue) at the same depth. b) The original voids are repaired (red) at $150 \\mathrm{~W}$, but new voids (blue) are created deeper in the substrate. c) The repair track was run at $50 \\mathrm{~W}$ and does not repair the existing voids (magenta). All laser passes are with a scan speed of $144 \\mathrm{~mm} \\mathrm{~s}^{-1}$. The approximate location of the surface of the sample is indicated with a dashed line.\\\\\nover three tracks treated with the same scanning and rescanning strategy. Based on these laser parameters, using a second laser scan with the same laser power does not represent a successful repair strategy for keyhole voids.\n\nWhen the laser power in the second pass is increased from 100 to $150 \\mathrm{~W}$ (Figure 5b), the melt pool extends deeper in the substrate, melting the material around the voids generated during the first pass and repairing them. However, the higher power scan also leaves behind voids deeper into the substrate, between 180 and $385 \\mu \\mathrm{m}$ below the surface, consistent with the average void depth results shown in Figure 3.", "start_char_idx": 615640, "end_char_idx": 619800, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "685fcbe7-bf35-4f58-9986-b27e9b27217a": {"__data__": {"id_": "685fcbe7-bf35-4f58-9986-b27e9b27217a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c61dff0c-8a96-4a2e-a916-e49bfafe32bc", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "bc018b81c7885427a54e3437d25c179881e2480bec9080071667d4ffd199eaf9", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2fb30cf1-9aa3-476d-818c-3287d519672f", "node_type": "1", "metadata": {}, "hash": "2049997a1800bc80470c7f44564502e3ec08f07f1795a3fd8351a5536b0cab81", "class_name": "RelatedNodeInfo"}}, "text": "All laser passes are with a scan speed of $144 \\mathrm{~mm} \\mathrm{~s}^{-1}$. The approximate location of the surface of the sample is indicated with a dashed line.\\\\\nover three tracks treated with the same scanning and rescanning strategy. Based on these laser parameters, using a second laser scan with the same laser power does not represent a successful repair strategy for keyhole voids.\n\nWhen the laser power in the second pass is increased from 100 to $150 \\mathrm{~W}$ (Figure 5b), the melt pool extends deeper in the substrate, melting the material around the voids generated during the first pass and repairing them. However, the higher power scan also leaves behind voids deeper into the substrate, between 180 and $385 \\mu \\mathrm{m}$ below the surface, consistent with the average void depth results shown in Figure 3. Since the voids are generated on average $50-100 \\mu \\mathrm{m}$ shallower than the depth of the vapor depression, a laser pass with a lower laser power may be able to repair the initial voids and form voids higher in the substrate or not form voids at all. To investigate this, a final repair attempt used a second laser power of only $50 \\mathrm{~W}$ (Figure 5c). The low power repair track produced a vapor depression that only penetrates roughly $80 \\mu \\mathrm{m}$ into the substrate and does not produce any new voids; however, the melt pool does not penetrate deep enough to remove any of the voids formed in the first pass.\n\nThis test of a void repair strategy using varying laser power demonstrates the difficulty in finding a laser power strong enough to access keyhole voids without producing new voids. However, this approach only investigates repair of keyhole porosity and it is entirely possible that such a remelting strategy could be an effective repair approach for voids formed by other mechanisms, such as lack of fusion or voids originating from the precursor powder. In any case, this study suggests that the melting of additional powder layers will not remove the voids formed at the base of the vapor depression in keyhole-mode processing. If one considers building the next layer with the second scan with an additional $50-70 \\mu \\mathrm{m}$ layer of powder on the surface, the vapor depression will not penetrate on average to the depth required to repair most of the voids created by the first pass. Thus, a voidrepair strategy using varying laser power with or without an additional powder layer added before the second laser scan, is not a workable approach.\n\n\\section*{3. Conclusions}\nIn conclusion, we have directly measured the dynamics of the vapor depression, keyhole void formation, vapor bubble dynamics, and void-repair strategies during LPBF using a high-speed in situ synchrotron X-ray-imaging technique. The measured keyhole threshold in Ti64 agrees well with the theory proposed and demonstrated in 316L stainless steel by King et al. ${ }^{[18]}$ Additionally, we found that although the average vapordepression depth and average void depth scale linearly with normalized enthalpy, the likelihood of void formation does not. Instead, the slower scan speed produced significantly more voids in the keyhole regime than expected from normalized enthalpy. We observed bubbles pinch off the vapor depression and then influenced by strong fluid flow in the melt pool, which can cause them to break into multiple bubbles during solidification or reconnect with the vapor depression. Finally, the simple voidrepair strategy using a second laser pass is not a valuable strategy for keyhole void removal even if the laser power is modified. Once a keyhole void is formed, it is extremely difficult to remove with additional laser processing. We observe that normalized enthalpy is a reliable metric to predict the build conditions and quality based on the vapor-depression depth, and therefore, an important value to monitor during the build process to minimize void defects. High-speed X-ray imaging of LPBF build processes is a valuable tool which can observe new phenomena, inform modeling and simulation efforts, and improve understanding to improve confidence in LPBF-built components.\n\n\\section*{4. Experimental Section}\nUsing high-speed X-ray imaging, void formation during the build process was nondestructively imaged at $2 \\mu \\mathrm{m}$ pixel size and up to $20 \\mathrm{kHz}$ frame rates. For these experiments, $3 \\mathrm{~mm}$ long single-layer tracks were formed in $50-70 \\mu \\mathrm{m}$ thick layers of Ti64 powder on top of a substrate of the same material.", "start_char_idx": 618968, "end_char_idx": 623509, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2fb30cf1-9aa3-476d-818c-3287d519672f": {"__data__": {"id_": "2fb30cf1-9aa3-476d-818c-3287d519672f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "685fcbe7-bf35-4f58-9986-b27e9b27217a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "300a2fdd3fac5c18616ecc8448a346e87081ba7d7b513fa9fbaff8a5c503023d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "88317475-b146-412e-b426-31e60b704e70", "node_type": "1", "metadata": {}, "hash": "003861998277eb67a47e07dc68b5f60a0d07be0812619dfc0e61ccec7b6e9b5d", "class_name": "RelatedNodeInfo"}}, "text": "We observe that normalized enthalpy is a reliable metric to predict the build conditions and quality based on the vapor-depression depth, and therefore, an important value to monitor during the build process to minimize void defects. High-speed X-ray imaging of LPBF build processes is a valuable tool which can observe new phenomena, inform modeling and simulation efforts, and improve understanding to improve confidence in LPBF-built components.\n\n\\section*{4. Experimental Section}\nUsing high-speed X-ray imaging, void formation during the build process was nondestructively imaged at $2 \\mu \\mathrm{m}$ pixel size and up to $20 \\mathrm{kHz}$ frame rates. For these experiments, $3 \\mathrm{~mm}$ long single-layer tracks were formed in $50-70 \\mu \\mathrm{m}$ thick layers of Ti64 powder on top of a substrate of the same material. Since we were interested in observing void defects formed during the build, a precursor powder with minimal voids was selected. The laser power and speed were varied from 50 to $300 \\mathrm{~W}$ and 144 to $455 \\mathrm{~mm} \\mathrm{~s}^{-1}$, respectively, with $\\mathrm{a} \\approx 50 \\mu \\mathrm{m}$ diameter (D4 $\\sigma$ ) Gaussian beam. Only the center of the $3 \\mathrm{~mm}$ tracks was imaged to ensure the laser scan speed and power had reached steady state, avoiding mirror acceleration effects and laser power spikes at the beginning of tracks. The images presented in this work represent $X$-ray absorption differences, where each frame is referenced to the initial image $\\left(t-t_{0}\\right)$. During a scan, darker regions represented a reduction in absorption (implying less material was present) and lighter regions represented an increase in absorption (implying more material was present). For the statistical analysis, void defects were identified through thresholding the averaged difference image between before and after the laser pass (Figure S1, Supporting Information). Voids below $3 \\times 3$ pixels $\\left(<36 \\mu \\mathrm{m}^{2}\\right.$ projected area which translates to an equivalent diameter of $<7 \\mu \\mathrm{m}$ ) were disregarded to avoid counting noisy pixels as voids.\n\nFurther details on the in situ chamber and the experimental setup can be found in Calta et al., ${ }^{[32]}$ as well as the Supporting Information section of this article.\n\n\\section*{Acknowledgements}\nThis material is based upon work supported by the US Department of Energy's Office of Energy Efficiency and Renewable Energy (EERE) under the Advanced Manufacturing Office, CPA agreements 32035, 32037, and 32038. Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the US Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA27344. Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. Ames Laboratory is operated for the US DOE by lowa State University under Contract No. DE-AC02-07CH11358. A.M.K. acknowledges support from the SRX beamline of the National Synchrotron Light Source II, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DE-SC0012704.\n\n\\section*{Conflict of Interest}\nThe authors declare no conflict of interest.\n\n\\section*{Keywords}\nadditive manufacturing, laser powder bed fusion, titanium, $\\mathrm{X}$-ray imaging\n\nReceived: April 24, 2019\n\nRevised: June 25, 2019\n\nPublished online:\n\n[1] S. K. Everton, M. Hirsch, P. Stravroulakis, R. K. Leach, A. T. Clare, Mater. Des. 2016, 95, 431.\n\n[2] T. Wohlers, Wohlers Report 2014 : 3D Printing and Additive Manufacturing State of the Industry Annual Worldwide Progress Report, Wohlers Associates, Fort Collins, Col. 2014.\n\n[3] W. E. Frazier, J. Mater. Eng. Perform. 2014, 23, 1917.", "start_char_idx": 622676, "end_char_idx": 626624, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "88317475-b146-412e-b426-31e60b704e70": {"__data__": {"id_": "88317475-b146-412e-b426-31e60b704e70", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "feeeb440-ee3b-492d-a6d6-1bc969903848", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d48be411bf4f37e0d82d3570d6be56713870438f4b8242a810bfdc00bef7f69b", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2fb30cf1-9aa3-476d-818c-3287d519672f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_2_to_17.txt", "file_name": "merged_2_to_17.txt", "file_type": "text/plain", "file_size": 630699, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "04afbe2f8e215aa0b4657331daa04051c4472adb62d50b2cf9f4ba7285427caf", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d9b53749-34b6-4333-8d2c-a06efcec6ae2", "node_type": "1", "metadata": {}, "hash": "bd109e2affeac82e299008a1a22c0158d1476b7f488c0e5dfe4cd03a7b1ecb03", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{Conflict of Interest}\nThe authors declare no conflict of interest.\n\n\\section*{Keywords}\nadditive manufacturing, laser powder bed fusion, titanium, $\\mathrm{X}$-ray imaging\n\nReceived: April 24, 2019\n\nRevised: June 25, 2019\n\nPublished online:\n\n[1] S. 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