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-\title{Investigation of Melt Pool Geometry Control in Additive Manufacturing Using Hybrid Modeling }
-\author{Sudeepta Mondal 1,2, Daniel Gwynn 1, Asok Ray 1,2(1) and Amrita Basak 1,*\\
-1 Department of Mechanical Engineering, Pennsylvania State University, University Park, PA 16802, USA;\\
-sbm5423@psu.edu (S.M.); dug221@psu.edu (D.G.); axr2@psu.edu (A.R.)\\
-2 Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA\\
-* Correspondence: aub1526@psu.edu; Tel.: +1-814-863-1323}
-\date{}
-\begin{document}
-\maketitle
-Article
-Received: 4 April 2020; Accepted: 18 May 2020; Published: 22 May 2020
-\begin{abstract}
-Metal additive manufacturing (AM) works on the principle of consolidating feedstock material in layers towards the fabrication of complex objects through localized melting and resolidification using high-power energy sources. Powder bed fusion and directed energy deposition are two widespread metal AM processes that are currently in use. During layer-by-layer fabrication, as the components continue to gain thermal energy, the melt pool geometry undergoes substantial changes if the process parameters are not appropriately adjusted on-the-fly. Although control of melt pool geometry via feedback or feedforward methods is a possibility, the time needed for changes in process parameters to translate into adjustments in melt pool geometry is of critical concern. A second option is to implement multi-physics simulation models that can provide estimates of temporal process parameter evolution. However, such models are computationally near intractable when they are coupled with an optimization framework for finding process parameters that can retain the desired melt pool geometry as a function of time. To address these challenges, a hybrid framework involving machine learning-assisted process modeling and optimization for controlling the melt pool geometry during the build process is developed and validated using experimental observations. A widely used 3D analytical model capable of predicting the thermal distribution in a moving melt pool is implemented and, thereafter, a nonparametric Bayesian, namely, Gaussian Process (GP), model is used for the prediction of time-dependent melt pool geometry (e.g., dimensions) at different values of the process parameters with excellent accuracy along with uncertainty quantification at the prediction points. Finally, a surrogate-assisted statistical learning and optimization architecture involving GP-based modeling and Bayesian Optimization (BO) is employed for predicting the optimal set of process parameters as the scan progresses to keep the melt pool dimensions at desired values. The results demonstrate that a model-based optimization can be significantly accelerated using tools of machine learning in a data-driven setting and reliable a priori estimates of process parameter evolution can be generated to obtain desired melt pool dimensions for the entire build process.
-\end{abstract}
-Keywords: additive manufacturing; melt pool dimension control; machine learning; Gaussian process modeling; Bayesian Optimization; surrogate-assisted modeling
-\section*{1. Introduction}
-Metal additive manufacturing (AM) facilitates direct fabrication of near-net-shape metallic components, prototypes, or both under rapid solidification conditions [1]. AM is currently used in manufacturing a wide variety of components with increasing complexity, for example, fuel nozzles, rocket injectors, and lattice structures [2]. The concept of AM is built on the principle of incremental layer-by-layer material consolidation through localized melting and resolidification of feedstock materials by using high-power energy sources [3]. The localized heating causes the formation of\\
-a melt pool that controls the microstructure and, therefore, the properties of the manufactured component [3]. Due to the cyclic nature of the deposition process as AM components continue to gain thermal energy, the thermal gradient $(G)$ and the solidification velocity $(R)$ inside the melt pool continuously change, resulting in significant alterations in the melt pool properties (e.g., geometry, thermal profile, and flow field among others) between the initial and final layers [4,5] as illustrated in Figure 1a. Figure $1 \mathrm{~b}$ shows that in spite of fixing the $G / R$ ratio at a value meant for yielding a columnar microstructure, at the leading edge (e.g., beginning of the scan), the grains are columnar; however, at the trailing edge (e.g., towards the end of the scan), the grains become equiaxed [6] due to progressive heating. The primary reason for controlling melt pool geometry in metal AM is to allow a part to be built with consistent melt pool dimensions, even as thermal conditions change continuously [7]. Understanding the fundamental physics of the melt pool evolution is, therefore, a key requirement for AM process development, optimization, and control. Although high-fidelity computational modeling of AM processes can provide reliable estimates of the melt pool evolution during the build process, such elaborate models are nearly-intractable when coupled with an optimization code for melt pool geometry control due to the computational costs [8]. Therefore, while these models are well suited for understanding the physical phenomena, challenges exist in using them for performing process design, optimization, and control [9].
-In this respect, machine learning (ML) shows potential in assisting and automating the process of manufacturing [10] through reliable prediction of melt pool geometries [11]. For example, Neural Networks (NN) [12] are widely used as a popular choice in prediction problems by modeling nonparametric input-output relationships. Despite the simplicity of usage, most of these techniques based on complex NN architectures suffer from issues of interpretability [13]. Moreover, the applications of such methods in limited datasets are rare, and lack of data can often result in poor predictive models that lack generalizability due to overfitting [14]. Moreover, a vast majority of the ML techniques used in AM relies on point estimates of the quantities of interest, without catering for uncertainty in the predictions. In critical applications involving high stakes associated with mispredictions, the estimates of uncertainty are particularly important. An attractive alternative, therefore, is to use probabilistic ML techniques like Gaussian Processes (GPs) [15] that offer the advantages of interpretability and applicability in limited data regimes. However, their applications in surrogate-based modeling and optimization are relatively less explored in multi-physics problems in AM. An implementation of surrogate modeling through the construction of computationally efficient approximations that can be used in lieu of the original simulation model [16], therefore, holds significant promise in metal AM.
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_f3867aee40a0cd4a18c2g-02}
-\end{center}
-Figure 1. (a) Comparison between experimentally observed and computationally predicted build profile in 316 stainless steel, with constant beam power of $210 \mathrm{~W}$ and the scanning speed of $12.7 \mathrm{~mm} / \mathrm{s}$ (Reproduced from [4,5], with permissions of Elsevier, 2009 and Springer Nature, 2016). (b) Simulation results showing transition from columnar grains at the beginning of the scan to equiaxed grains towards the end of the scan in an Inconel 718 specimen with a $G / R$ ratio meant to yield columnar microstructure (Reproduced from [6], with permission of Elsevier, 2019).
-Surrogate-assisted modeling and optimization techniques are popularly used in various applications that involve expensive computational models [17-23] for function evaluations. Among the different types of surrogate models, GPs [15] are used profusely for modeling black-box functions whereby a fully Bayesian approach allows for probabilistic estimates of the target functions [24-27]. With a relatively small number of measurements, a GP surrogate can be learnt to serve as a proxy to an expensive objective function [28] (e.g., prediction of melt pool dimensions for a range of process parameters in metal AM [29]). Under the settings of a GP surrogate, a Bayesian Optimization (BO) set-up can be invoked for gradient-free global optimization of an objective function under budget limitations [30] (e.g., prediction of optimal process parameters for controlling temporal melt pool dimensions in metal AM within $N$ number of iterations; $N$ being an user input). Moreover, with nonlinearities in the objective function, a search for optimum would require significant amount of sampling in the search space, particularly in high dimensions. In such settings, BO is found to be quite successful [31].
-In the field of AM, there are very few applications of GPs as surrogate models for expensive experiments and simulations. For example, Tapia et al. [32] used experimental data to learn spatial GPs for predicting porosity in metal AM produced during the laser powder bed fusion process. In another work, Tapia at al. [16] demonstrated the usage of GPs in predicting melt pool depth as a function of different process parameters, which were used to describe regimes of operation where the process was expected to be robust. Seede et al. [33] used a GP framework to develop a calibrated surrogate model for predicting optimal process parameters for building porosity free parts with low-alloy martensitic steel AF9628. However, to the best of the authors' knowledge, no work exists in the field of AM that leverages the surrogate-based predictions and uses them as a basis for active learning strategies for optimizing a desired objective, e.g., controlling melt pool dimensions over time under computational budget constraints in laser powder bed fusion process. The design and deployment of such predictive methodologies will immensely augment the response time of feedback or feedforward control strategies as the current response times are rather long compared to the process time scales [34].
-To address this gap, this paper proposes a novel framework of controlling the melt pool geometry in laser powder bed fusion process by formulating it as an optimization problem through the integration of the tools of physics-based analytical modeling and data-driven analysis. The cardinal contribution of this work in AM is to bridge the gap in model-assisted prediction and control of melt pool geometry by using ML techniques that can potentially accelerate the process of melt pool geometry control. The results demonstrate that by using a low-cost surrogate-assisted modeling using GP and BO, it is possible to obtain an excellent estimation of process parameter evolution as a function of time in order to maintain the desired meltpool geometry (e.g., dimensions) throughout the build process. The framework consists of three critical steps: (i) evaluation of the thermal field using an experimentally validated 3D analytical melt pool evolution model which serves as a source of data for formulating a GP surrogate, (ii) development of GPs with flexible kernel structures capable of handling anisotropies in the dataset, and (iii) establishment of a BO framework involving the GP surrogate that aims to solve a global optimization problem in a gradient-free setting under a constrained budget. The computational budget is predefined in most practical problems. With an appropriate selection of initial design points and acquisition function for active learning of optimal design points, this work achieves estimates of process parameters with limited model iterations. The GP surrogates, being based on Bayesian inference, offer principled estimates of uncertainty in predictions. While the present work uses a 3D analytical model for demonstrating the efficacy of the proposed approach, the framework described can be applied to any other prediction models of users' choice.
-The paper is organized in five sections including the current one. Section 2 describes the development of a hybrid modeling framework consisting of the 3D analytical model and its validation against experimental data. Section 3 presents the results and discusses the significant findings. The paper is summarized and concluded in Section 4 along with recommendations for future research.
-Supplemental information in Appendix A provides the mathematical background for ML aspects of modeling and optimization.
-\section*{2. Development of a Hybrid Modeling Framework}
-\subsection*{2.1. Simulation Model}
-A well-known analytical model developed by Eagar and Tsai [35] that solves for the 3-dimensional temperature field produced by a traveling distributed heat source on a semi-infinite plate is used in the present work. This model has been previously used by several different researchers for evaluating melt pool evolution in laser powder bed fusion (L-PBF) [33] and directed energy deposition (DED) [36] AM processes when extensive evaluation of process parameter space is required. It is a distributed heat source modification of the Rosenthal's $[37,38]$ solution for the temperature distribution produced by a traveling point heat source. As compared to Rosenthal's solution, Eagar-Tsai's model provides a significant improvement in prediction of temperature in the near heat source regions. Figure 2 explains the coordinate system used in the model. The heat source is traveling with a uniform speed of $v$ in the $X$-direction, and is assumed to be a 2D surface Gaussian:
-\begin{equation*}
-Q(x, y)=\frac{P}{2 \pi \sigma^{2}} e^{-\frac{\left(x^{2}+y^{2}\right)}{2 \sigma^{2}}} \tag{1}
-\end{equation*}
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_f3867aee40a0cd4a18c2g-04}
-\end{center}
-Figure 2. Schematic illustrating the coordinate system of the analytical model.
-Here, $Q(x, y)$ is the power distribution per unit area on the $X-Y$ plane of the specimen produced by the Gaussian beam of peak power $P$ with a distribution parameter $\sigma$. According to Eagar-Tsai's model, the temperature $T(x, y, z, t)$, at a particular location $(x, y, z)$ and time $t$, with the initial temperature of the substrate being $T_{0}$, is denoted as
-\begin{equation*}
-T(x, y, z, t)-T_{0}=\frac{\alpha_{L} P}{\pi \rho c(4 \pi a)^{1 / 2}} \int_{0}^{t} \frac{d t^{\prime}\left(t-t^{\prime}\right)^{-1 / 2}}{2 a\left(t-t^{\prime}\right)+\sigma^{2}} e^{-\frac{\left(x-v t^{\prime}\right)^{2}+y^{2}}{4 a\left(t-t^{\prime}\right)+2 \sigma^{2}}-\frac{z^{2}}{4 a\left(t-t^{\prime}\right)}} \tag{2}
-\end{equation*}
-Here, $\alpha_{L}$ is the absorptivity of the laser beam, $a \triangleq \frac{k}{\rho c}$ is the thermal diffusivity, $\rho$ is the density, and $c$ is the specific heat capacity of the material of the specimen. The primary assumptions of the model include the following.
-\begin{enumerate}
-  \item Convective and radiative heat transfer from the substrate to the environment are ignored. As the process deals with metals which are good conductors, heat transfer through radiation is negligible [39] as compared to that due to conduction.
-  \item The temperature dependence of the thermo-physical properties is not taken into account.
-  \item The substrate is semi-infinite, therefore the increase in the surface temperature $T_{0}$ with time is negligible.
-  \item Phase change of the material is not taken into consideration.
-\end{enumerate}
-Eagar-Tsai's model, despite its limitations (e.g., its inability to model keyholing effect [33]), is widely used in literature for parameter space exploration through design of experiments ( $\mathrm{DoE}$ )-based approaches. Given the wide range of process parameters in metal AM machines (e.g., L-PBF has over 130 parameters that can affect the final part quality [40]), such a DoE approach would require an exponential number of samples in the dimension of the parameter space to fully explore the design space. This makes it prohibitively expensive to explore the design space for building complex parts through experimentation or high-fidelity simulations. Computationally efficient surrogates can reduce the computational burden by a significant amount. Eagar-Tsai's model, when appropriately calibrated, provides one such alternative as a low-cost simulation model that are extensively used by several researchers in recent times [33,41,42]. This model especially works well for single-track and single-layer AM depositions. Owing to these characteristics, the validation and control experiments outlined in this paper are all single-track and single-layer.
-\subsection*{2.2. Experimental Validation of the Simulation Model}
-Eagar-Tsai presented experimental validation of their model with a range of process parameters in welding carbon steel plates [35]. Other researchers validated this model for a range of different materials such as nickel- [43], iron- [33], and titanium-based [44] alloys among others to obtain satisfactory accuracy with the experimental data across a range of AM processes, e.g., L-PBF and DED [45], in recent times. However, most of the experimental validation of this model, so far, has been performed under steady state conditions. Being a transient model, Eagar-Tsai's formulation can potentially be used to simulate the melt pool dimensions as a function of time as well. In this section, both steady and unsteady state validation of the Eagar-Tsai's formulation are presented.
-\subsection*{2.2.1. Steady-State Experimental Validation}
-For the steady-state model validation, the melt pool dimensions calculated by Eagar-Tsai's model are compared with those obtained using finite-element simulations and experiments for a popular nickel-based superalloy CMSX-4 ${ }^{\circledR}$ reported by Wang \href{http://et.al}{et.al} [36]. This alloy was processed by several different researchers using L-PBF [46,47], electron beam powder bed fusion (E-PBF) [48], and DED [49], and therefore a considerable amount of experimental data is available in the open literature. The thermo-physical properties of CMSX-4 ${ }^{\circledR}$ chosen in this work are those reported by Gäumann et al. [50]: $k=22 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K}), \rho=8700 \mathrm{~kg} / \mathrm{m}^{3}, c=690 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K})$, and the liquidus temperature $T_{L}=1660 \mathrm{~K}$. Three surface melting experiments were reported by Wang et al. under different processing parameters, as enlisted in Table $1 . \mathrm{A} \mathrm{CO}_{2}$ laser beam with radius $\mathrm{W}$ was used in their work.
-Table 1. Processing parameters as reported in Wang et al. [36].
-\begin{center}
-\begin{tabular}{cccc}
-\hline
-Specimen & A & B & C \\
-\hline
-$T_{0}(K)$ & 300 & 300 & 300 \\
-$P(\mathrm{~W})$ & 900 & 900 & 450 \\
-$v(\mathrm{~mm} / \mathrm{s})$ & 2 & 6 & 6 \\
-$\mathrm{~W}(\mathrm{~mm})$ & 0.39 & 0.39 & 0.20 \\
-$\alpha_{L}$ & 0.114 & 0.114 & 0.114 \\
-\end{tabular}
-\end{center}
-Figure 3 shows the comparison between the current work with those obtained experimentally and using finite element simulations by Wang et al. [36] showing excellent agreement. Figure 4 shows a transverse cross section $(Y-Z$ plane, with $x=0)$ of the analytically calculated melt pool geometry juxtaposed on the fusion zone produced by the process parameters in the CMSX-4 ${ }^{\circledR}$ Specimen A, as reported by Wang et al. [36]. Similar agreements are also observed for the other two specimens (i.e., B and C), as evident from the results reported in Figure 3. Cross-sectional images for specimens B and $\mathrm{C}$ are omitted for brevity.
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_f3867aee40a0cd4a18c2g-06}
-\end{center}
-Figure 3. Comparison of experimentally measured melt pool dimensions with simulations results provided by Wang et al. (blue markers) [36] and the present work (red markers). Squares correspond to Specimen A, circles to Specimen B, and Diamonds to Specimen C. The filled markers indicate the melt pool depths and the unfilled ones indicate the melt pool width.
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_f3867aee40a0cd4a18c2g-06(2)}
-\end{center}
-Figure 4. Comparison of experimental and calculated melt pools for the CMSX-4 ${ }^{\circledR}$ Specimen A of Wang et al [36] (Reproduced from [36], with permission of Elsevier, 2017.). L corresponds to the liquid zone of the melt pool and s corresponds to the solid substrate.
-\subsection*{2.2.2. Transient Experimental Validation}
-After obtaining excellent agreement with the steady-state results, the analytical model is further validated using transient melt pool results available in the open literature [51]. Figure 5 shows the longitudinal cross section of an L-PBF-processed CMSX-4 ${ }^{\circledR}$ specimen. This specimen is fabricated by consolidating a powder layer thickness of $1.4 \mathrm{~mm}$ on a CMSX-4 ${ }^{\circledR}$ substrate having dimensions of $35.56 \mathrm{~mm}$ (length) $\times 6.86 \mathrm{~mm}$ (width) $\times 2.54 \mathrm{~mm}$ (thickness). The process parameters reported are $750 \mathrm{~W}$ laser power, $12.7 \mu \mathrm{m}$ raster scan spacing, and $600 \mathrm{~mm} / \mathrm{s}$ raster scan speed. The raster scanning speed $\left(v_{R}\right)$ is related to the linear velocity ( $\left.\mathrm{v}\right)$ of the laser in the $X$ direction by $v=\frac{\text { scan spacing } \times v_{R}}{2 \times \text { width }}$.
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_f3867aee40a0cd4a18c2g-06(1)}
-\end{center}
-Figure 5. Longitudinal cross section of a CMSX-4 ${ }^{\circledR}$ specimen fabricated with $750 \mathrm{~W}$ laser power and scan speed of $600 \mathrm{~mm} / \mathrm{s}$ showing increase in melt pool depth along the length of the specimen (Reproduced with permission from the authors of [51].).
-Figure 6 shows the comparison between the analytically calculated and experimentally observed melt pool depth for the CMSX-4 ${ }^{\circledR}$ specimen as illustrated in Figure 5. The maximum absolute relative error between the experimental and analytical melt pool depths is $\sim 8 \%$ at the start of the scan period, with the mean absolute error during the $30 \mathrm{~s}$ period being $2.71 \%$. The results also show the transient\\
-nature of the melt pool, with the depth continuously increasing as a function of time with a fixed set of process parameters.
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_f3867aee40a0cd4a18c2g-07}
-\end{center}
-Figure 6. Comparison of analytically calculated transient melt pool evolution with experimental data.
-\subsection*{2.3. Hybrid Model}
-The validation results show that Eagar-Tsai's model can provide excellent low-cost estimates of melt pool dimensions for single-track and single-layer AM depositions. The goal of this work is to obtain model-based estimates of the required temporal variations in process parameters for achieving target melt pool dimensions during the build process. In order to achieve this, an optimization problem that finds process parameters as a function of time is solved with an objective of minimizing the deviation from the desired melt pool dimensions. As the true functional form that relates the process parameters to the melt pool dimensions is unknown, the information regarding gradients is not readily accessible, therefore the optimization problem is in a black-box setting. Several such black-box optimization techniques are well-studied by different researchers [52], e.g., stochastic process-based approaches (kriging methods) [53], evolutionary algorithms [54], trust-region based algorithms [55], and random search [56]. These approaches typically involve iterative sampling of the objective function in the search space. Such sampling often proves to be prohibitively expensive, particularly in high dimensions, when the involved process model is computationally very expensive.
-To address this challenge, in the present work, an application of gradient-free optimization under budget limitations is implemented by solving the melt pool geometry control problem using BO that employs computationally inexpensive GP surrogate models learnt via sparse sampling of the space of process parameters (e.g., $P$ and $v$ ). The details of the mathematical formulations of GP and BO can be found in Appendix A. Although all optimization demonstrations in this paper involve the Eagar-Tsai's model as the process model, it can very well be replaced by any other process models of users' choice, without any fundamental change in the optimization algorithm.
-\section*{3. Results and Discussion}
-This section presents the results and discusses the significant findings therefrom.
-\subsection*{3.1. Prediction of Melt Pool Dimensions Using GP}
-The melt pool dimensions in the L-PBF AM process continuously increase due to progressive heating of the specimen caused by the layer-wise fabrication as evinced by simulation results [57] as well as experimental observation [47]. Figure 7 shows the variation in melt pool dimensions as a function of time for a CMSX-4 ${ }^{\circledR}$ specimen fabricated using a laser power of $900 \mathrm{~W}$ and linear scan velocity of $0.25 \mathrm{~mm} / \mathrm{s}$. The melt pool depth increases from $1.814 \mathrm{~mm}$ at $t=1 \mathrm{~s}$ to $3 \mathrm{~mm}$ at $t=20 \mathrm{~s}$, while the melt pool width increases from $3.82 \mathrm{~mm}$ to $6.11 \mathrm{~mm}$. The percentage increase in melt pool\\
-depth is $\sim 65 \%$, and the increase in width is $\sim 59 \%$. The melt pool reaches a steady state at $\sim 20 \mathrm{~s}$. If the melt pool dimensions need to be maintained at desired values, the process parameters should be adjusted during this transience period. However, performing simulations for a range of process parameters over the entire deposition process is computationally expensive when coupled with an optimization framework.\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_f3867aee40a0cd4a18c2g-08}
-Figure 7. Temporal variation of melt pool dimensions for a CMSX-4 ${ }^{\circledR}$ specimen fabricated using $P=900 \mathrm{~W}$ and $v=0.25 \mathrm{~mm} / \mathrm{s}$ : (a) longitudinal cross section with the liquidus isotherm showing the variation in melt pool dimensions with time and $(\mathbf{b})$ variation of melt pool depth and width with time.
-In applications where data is scarce, particularly when each simulation can be potentially computationally expensive, it is often infeasible to have a large number of training points. Moreover, inherent uncertainties in the physical process and the simulation models (e.g., uncertainties in the thermophysical properties of the material) mandate the need of uncertainty quantification with the predictions $[33,58]$. Surrogates, like GPs, can be very useful in such cases in order to have probabilistic estimates of the quantity of interest with limited datasets, whereby the posterior mean and variance can not only be informative for prediction at unknown input locations, but the information can also be used for budget-constrained optimization, as described in the following subsection. A surrogate modeling and optimization technique as discussed in Appendix A is adopted in this work to find the model-based estimates of the process parameters required for controlling the melt pool dimensions.
-In order to build the surrogate using GPs, two-hundred (200) Latin hypercube sampling (LHS) simulations are performed to obtain the values of melt pool depth and width at each time instant for combinations of $P$ and $v$ in the range of 300 to $1200 \mathrm{~W}$ and 0.5 to $2.5 \mathrm{~mm} / \mathrm{s}$, respectively. This parameter range is chosen to avoid any keyhole mode of melt pool formation in CMSX-4 ${ }^{\circledR}$ where the Eagar-Tsai's model shows limited accuracy $[59,60]$. The cross section of melt pools created in conduction mode is generally semicircular, as predicted by Eagar and Tsai's conduction mode model [35]. LHS is selected as this is one of the most commonly used statistical methods for DoE. It allows for a good spread of the initial DoE over the design region with limited iterations due to its high sampling efficiency [61]. For every time instant under consideration, each DoE point comprises a combination of process parameters $(P, v)$ and its corresponding melt pool depth and width values.
-The effect of training data size on the regression performance of the GP surrogate in predicting melt pool depth and width is of critical interest. Out of the 200 initial LHS points, a test set of randomly selected 100 points is set aside for testing the regression performance of the GP models. Different GPs are trained at different time instants with randomly selected samples from the training set. The training data size is varied from 10 to 100 , in steps of 10 samples. Ten random selections of the training data is chosen for each training size, in order to find the average behavior of the regression performance for each training size. The prediction performances are tested on the set aside 100 samples for each trained GP model.
-The metric for gauging the prediction performance is chosen as the Relative Squared Error (RSE) $\triangleq \frac{\left\|\hat{y}-y^{*}\right\|^{2}}{\left\|y^{*}\right\|^{2}}$, where $\hat{y}$ is the prediction and $y^{*}$ is the true value (i.e., ground truth as obtained by the Eagar-Tsai's model). A lower RSE suggests that the most likely prediction (mean of the predicted posterior Gaussian distribution) of the depth/width in the test set matches closely with the true value. Figure 8 shows that the RSE is quite low for all the time steps, while there is a slight increase in RSE from $2 \mathrm{~s}$ to $20 \mathrm{~s}$ for both depth and width. RSEs for the melt pool depth and width prediction show a sharp drop from training size of 10 to 20 samples, after which the RSE saturates for almost all the higher training sizes. This indicates that a training size of at least 20 LHS DoE points is in general sufficient for a satisfactory prediction of the melt pool depth and width in the selected process parameter space. This provides an estimate of the number initial DoE points required for learning the surrogate model for the subsequent $\mathrm{BO}$ steps at each time instant.\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_f3867aee40a0cd4a18c2g-09}
-Figure 8. Relative Squared Error in prediction of melt pool depth and width at (a) $t=2 \mathrm{~s}$, (b) $t=5 \mathrm{~s}$, (c) $t=10 \mathrm{~s}$, and (d) $t=20 \mathrm{~s}$.
-Figure 9 shows the regression performance (on the test dataset of 100 samples) in predicting the melt pool depth and width at $2 \mathrm{~s}$ with a training set size of 20. Sample numbers in Figure 9a,c refer to the test samples, which are different $(P, v)$ combinations. The test samples are arranged in an ascending order of their true depth values. The $2 \sigma$-band coverage percentage is the proportion of test points for which the true amplitude lies within $\pm 2 \sigma$ of the predicted mean, which corresponds to the $95 \%$ confidence interval, as the output distribution is a Gaussian. The parity plots in Figure 9b,d show the comparison of the predicted means with the true values. The high $R^{2}$ (coefficient of determination) scores for the depth (0.96) and width (0.99) predictions at 2 s indicate high reliability of the GP model in predicting the melt pool dimensions. Similar results are shown in Figure 10 for the melt pool depth and width predictions at $20 \mathrm{~s}$, with a training set size of 20 samples. The $R^{2}$ score decreases to 0.82 for depth prediction and 0.88 for width prediction, which is also explained by the higher RSE in prediction at $20 \mathrm{~s}$ (Figure 8). The variability in the predicted values from the true values is explained by the\\
-wider $\pm 2 \sigma$ band at the test locations. The lower $R^{2}$ score at $20 \mathrm{~s}$ as compared to $2 \mathrm{~s}$ can be attributed to the higher variability in the steady state values of depth and width as compared to the initial stages as a function of the process parameters. From the perspective of applicability of the surrogate predictions, GPs provide the end user with not only a computationally inexpensive way of predicting the melt pool dimensions at different operating conditions for which experiments and simulations are not performed, but also with an estimate of uncertainty quantification (UQ) for predictions from the variance associated at the query points.\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_f3867aee40a0cd4a18c2g-10(1)}
-Figure 9. Melt pool depth and width prediction performance at $2 \mathrm{~s}$ with a training set size of 20 samples. $(\mathbf{a}, \mathbf{b})$ Probabilistic prediction of depth and corresponding parity plot. (c,d) Probabilistic prediction of width and corresponding parity plot. Samples arranged in ascending order of the true values in panels $(\mathbf{a}, \mathbf{c})$. Predicted values at the points of query are represented as follows; GP mean by blue dots and $\pm 2 \sigma$ bands by vertical bars, where $\sigma$ is the standard deviation of the GP's posterior prediction at a query point. Red stars indicate the true value of the melt pool depth at those points.\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_f3867aee40a0cd4a18c2g-10}
-Figure 10. Cont.\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_f3867aee40a0cd4a18c2g-11}
-Figure 10. Melt pool depth and width prediction performance at $20 \mathrm{~s}$ with a training set size of 20 samples. (a,b) Probabilistic prediction of depth and corresponding parity plot. (c,d) Probabilistic prediction of width and corresponding parity plot. Samples arranged in ascending order of the true values in panels $(\mathbf{a}, \mathbf{c})$. Predicted values at the points of query are represented as follows; GP mean by blue dots and $\pm 2 \sigma$ bands by vertical bars, where $\sigma$ is the standard deviation of the GP's posterior prediction at a query point. Red stars indicate the true value of the melt pool depth at those points.
-\subsection*{3.2. Optimization of Process Parameters for Melt Pool Dimension Control: Objective Function}
-As discussed in Sections 1 and 2, appropriate control of the process parameters, e.g., $P$ and $v$ are required for maintaining desired melt pool dimensions during the deposition process. The goal of controlling the melt pool dimensions is formulated as an objective function that needs to be maximized in the setting of BO, as described in Appendix A.3. In order to pose the melt pool control problem in an optimization setting, an appropriately defined objective function $(J)$ is to be maximized at every discrete time instant of control,
-\begin{equation*}
-J \triangleq-\left(c_{1} \frac{\left|d-d^{*}\right|}{\left|d^{*}\right|}+c_{2} \frac{\left|w-w^{*}\right|}{\left|w^{*}\right|}+c_{3} \frac{\left|P-P_{\min }\right|}{\left|P_{\max }-P_{\min }\right|}\right) \tag{3}
-\end{equation*}
-where $d$ and $\mathrm{W}$ denote the depth and width, respectively, at a particular time instant, whereas $d^{*}$ and $w^{*}$ represent the desired depth and width, respectively, during the deposition process. $P$ indicates the power at time instants of control, whereas $P_{\max }$ and $P_{\min }$ denote the maximum and minimum values of the range of laser power in the space of process parameters. Therefore, $\frac{\left|P-P_{\min }\right|}{\left|P_{\max }-P_{\min }\right|}$ denotes the normalized power input at a particular time instant, and incorporating it into the objective functional serves as a penalty term for high power values. This is introduced since it is desired to achieve the controlled process along with avoiding processing conditions involving very high levels of power.
-$c_{1}, c_{2}$, and $c_{3}$ in Equation (3) denote the relative weights of the components of the objective function that controls the depth, width, and power, respectively. By varying the relative values of $c_{1}, c_{2}$, and $c_{3}$, it is possible to preferentially weigh the objective function to meet the requirements. Formulating the objective functional $J$ is a key step in the optimization process, and the optimization routine should be designed in such a way that undesirable process parameters result in low values of objectives. This formulation conforms to the mathematical characteristics of the Matern covariance function [15] used in this work, which assumes local smoothness of the inputs, so that input process parameters that are close together in the $(P, v)$ space are expected to have similar objective values. As undesirable parameter combinations have low objectives, points in the close vicinity of them will have low acquisition potential (see Appendix A) during the optimization steps, and therefore will have lower priority for the incumbent selection.
-\subsection*{3.3. Optimization Routine}
-A sequential global-local optimization thread [62] is employed in this work for the selection of process parameters for controlling the melt pool geometry. The terms "global" and "local" correspond to the search spaces with respect to which BO is performed. In the global optimization thread, a potential optimal process parameter combination is selected, around which a refinement is made during the local optimization thread for the final selection of the optimal process parameter combination. The outline of the process is described in the flowchart as depicted in Figure 11. Details of the optimization algorithm can be found in Appendix B. Entities capped with "tilde" $(\sim)$ correspond to parameters of the local optimization thread.
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_f3867aee40a0cd4a18c2g-12}
-\end{center}
-Figure 11. Flowchart depicting the global-local optimization process.
-The control problem is designed to maintain the melt pool depth $\left(d^{*}\right)$ at $2.5 \mathrm{~mm}$ and width $\left(w^{*}\right)$ at $5.0 \mathrm{~mm}$. The initial global GPs are learnt with $20 N_{\text {init }}$ LHS points in the $(P, v)$ space, with $P \in[300,1200] \mathrm{W}$ and $v \in[0.5,2.5] \mathrm{mm} / \mathrm{s}$. The ranges of the process parameters and the controlled geometrical parameters chosen in this problem are often dictated by the experimental requirements and constraints, and can be modified as needed. The optimization problem over the entire duration of the L-PBF process can be considered as a sequence of optimization problems performed at some discrete intervals of time, which motivates the choice of learning separate surrogates for each discrete time instant for which the melt pool needs to be controlled.
-With the initial trained GP from 20 LHS samples for each time instant, low-cost surrogate predictions are made over the large global search space $X_{\text {star }}$, consisting of 2000 uniformly chosen points. This methodology forms the key to the surrogate-based optimization processes: predictions are made over an extensive search space by employing a low-cost surrogate by avoiding functional evaluations (physics-based simulations in this case) at the search points. Based on the mean-variance trade-off of the GP's posterior predictive distribution, the acquisition function EI (See Appendix A) guides the search iteratively to subsequent optimization points until the computational budget is depleted. $N_{\text {GlobalIter }}=10$ optimization steps are chosen for the global thread, after which the optimal process parameter combination with the highest objective value is selected.
-For all the time instants of control, it was possible to obtain optimal process parameters within the global thread that can yield the melt pool depth and width close to the desired values.
-However, for finer adjustments in $P$ and $v$ values in order to achieve the micron-level control in the melt pool geometry, the local optimization thread is executed. Here, the local search space $\tilde{X}_{\text {star }}$ is built around $\tilde{\mathbf{x}}^{*}$, the optimum with the highest objective value from the global thread, in the following way; $P$ is varied within $\pm 20 \mathrm{~W}$ and $v$ within $\pm 0.15 \mathrm{~mm} / \mathrm{s}$ of the corresponding values in $\tilde{\mathbf{x}}^{*} .20 \tilde{\mathrm{N}}_{\text {init }}$ LHS points are chosen within the limits of $\tilde{X}_{\text {star }}$, the optimization routine is performed within this local search space for $\tilde{N}_{\text {Locallter }}=10$ steps. This yields the refinement of the process parameter values that result in melt pool dimensions very close to the ones desired. The number of optimization iterations in both the local and global threads (i.e., $N_{\text {Globaliter }}$ and $\tilde{N}_{\text {Localtter }}$ ) are kept as design parameters in this paper, which are expected to be driven by computational budget for practical applications. The scaling factors for the objective function components are chosen as $c_{1}=1, c_{2}=0.1$, and $c_{3}=0.1$, which are based on the greater relative importance of maintaining the depth as close to $d^{*}$ as possible during the build process, so that a uniform deposit is maintained.
-Figure 12 shows the performance of the surrogate based optimization method. Figure 12a,b shows the variation of the controlled melt pool depth and width from the desired $d^{*}$ and $w^{*}$ values as a function of time. It is seen that the maximum variation in the meltpool depth is $1.1 \mu \mathrm{m}$ which is $0.04 \%$ of the desired depth, while that for width is $173 \mu \mathrm{m}$, which is $3.46 \%$ of the desired width. The process parameters change from $P=948.07 \mathrm{~W}, v=0.40 \mathrm{~mm} / \mathrm{s}$ at $t=2 \mathrm{~s}$ to $P=737.81 \mathrm{~W}, v=0.37 \mathrm{~mm} / \mathrm{s}$ at $t=20 \mathrm{~s}$ (Figure 12c,d). It is to be noted that penalization of $P$ in the objective function allows us to have a smoothly variation of $P$ over $20 \mathrm{~s}$ with lower $P$ values, which changes by $\sim 22 \%$ of the starting value at $t=2 \mathrm{~s}$. The maximum change in $v$ is $\sim 27 \%$. It is possible to have process parameters with higher $P$ values (and higher $v$ values) that control the melt pool, but those conditions are avoided by $P$ penalization in the objective function. Similar formulation of the objective function can be pursued by $v$ penalization, if smother $v$ transition is desired.\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_f3867aee40a0cd4a18c2g-13}
-Figure 12. Time-varying control of process parameters at intervals of $2 \mathrm{~s}$ for maintaining $d^{*}=2.5 \mathrm{~mm}$ and $w^{*}=5.0 \mathrm{~mm}$ : (a) variation in melt pool depth $\left(d-d^{*}\right)$ at the control steps, (b) variation in melt pool width $\left(w-w^{*}\right)$ at the control steps, (c) optimal laser power, and (d) optimal laser velocity.
-\subsection*{3.4. Validation with Experimental Results of Melt Pool Depth Control}
-The model-based control strategy is validated with experimental results reported in the open literature [63]. Figure 13a shows the longitudinal cross section of an L-PBF processed René 80 specimen fabricated using a powder layer thickness of $1.4 \mathrm{~mm}$ on a substrate of dimensions $35.56 \mathrm{~mm} \times 6.86 \mathrm{~mm} \times 2.54 \mathrm{~mm}$. The experiment was carried out with the raster scanning speed of $450 \mathrm{~mm} / \mathrm{s}$ and scan spacing of $25.4 \mu \mathrm{m}$. In reality, experiments are extremely challenging to perform with melt pool depth as a controlled variable as there exists no easy way of measuring the melt pool depth in situ. During the conduction mode, the surface temperature control of melt pools was found to correlate well with the melt pool depth experimentally by Bansal et al. [63]. The observation was also made by Raghavan et al. in E-PBF of Incone ${ }^{\circledR} 718$ [64]. The mean value of the melt pool depth during the control period is around $1200 \mu \mathrm{m}$ from experiments. Accordingly, $d^{*}$ is set at $1200 \mu \mathrm{m}$ for the surrogate-based optimization routine involving only $P$ as outlined in the experiments.
-The melt pool simulation is performed by employing the Eagar-Tsai's model, with the thermo-physical properties of solid René $80: k=24.56 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K}), \rho=7604 \mathrm{~kg} / \mathrm{m}^{3}, c=600 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K})$, and the liquidus temperature $T_{L}=1607 \mathrm{~K}$ obtained using the software JMatPro ${ }^{\circledR}$ [65], with the alloy composition of René 80 provided by the vacuum alloy product catalog of Cannon Muskegon [66]. The objective function involves two components in this case:
-\begin{equation*}
-J \triangleq-\left(c_{1} \frac{\left|d-d^{*}\right|}{\left|d^{*}\right|}+c_{2} \frac{\left|P-P_{\min }\right|}{\left|P_{\max }-P_{\min }\right|}\right) \tag{4}
-\end{equation*}
-with $c_{1}=1$ and $c_{2}=0.1$.
-Figure 13 shows that the predicted melt pool depth with the surrogate assisted control scheme remains very close to the desired $d^{*}$. A variation of $\sim 200 \mu \mathrm{m}$ is observed in the experimental results, whereby the melt pool depth shows a slightly increasing trend towards the end of the control process, reflected by the slight increase in power input from $10 \mathrm{~s}$ till $14 \mathrm{~s}$. The trend of the surrogate predicted controlled power input matches closely with the experimental results till $8 \mathrm{~s}$, which is explained by the fact that for a constant laser speed, the power input should decrease as a function of time in order to maintain a constant melt pool depth as the specimen gains thermal energy continuously. Nonetheless, the validation results indicate the efficacy of the surrogate-based optimization routine in predicting process parameters as a function of time for achieving melt pool dimension control during the deposition process.
-(a)\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_f3867aee40a0cd4a18c2g-14}
-Figure 13. (a) Longitudinal cross section showing a René 80 specimen fabricated using an adaptive control scheme (Reproduced from [63], with permission of the author). (b) Melt pool depth as a function of time. (c) Controlled laser power as a function of time, obtained by the adaptive control scheme of Bansal [63], compared with the results from surrogate based optimization method. The black markers in $(\mathbf{b}, \mathbf{c})$ show the variation in the melt pool depth and laser power as a function of time during the time of control. The red markers in $(\mathbf{b}, \mathbf{c})$ show the variation in the melt pool depth and laser power obtained by the BO routine.
-\section*{4. Summary and Conclusions}
-This paper develops a novel hybrid methodology for control of melt pool geometry in AM in the framework of ML-assisted modeling and optimization. The continuous changes in the melt pool geometry are predicted by a low-cost GP surrogate developed using an experimentally validated analytical 3D model. The uncertainties in the predictions for the melt pool geometry are quantified using GPs. Reliable estimates of the optimal process parameter evolution are obtained through active learning via BO by devising appropriate objective functions that quantify the control requirements. The methodology provides an estimation of process parameter variation during the AM deposition process in order to maintain a desired melt pool geometry under continuously varying thermal conditions.
-Being data-driven, the reliability of the optimized process parameters obtained from the algorithm is based on the accuracy of the underlying physical model in predicting the melt pool geometry in the range of process parameters considered. However, with a high-fidelity model, the computational cost involved in the optimization process can be significantly high. For example, the cost of running a Netfabb ${ }^{\circledR}$ [67] DED model for a single-track and single-layer process on a CMSX-4 ${ }^{\circledR}$ specimen as described in this paper is $\sim 10$ times as expensive as Eagar-Tsai's model at $t=2 \mathrm{~s}$, and $\sim 150$ times at $t=10 \mathrm{~s}$. Although such high-cost simulation is prohibitive in practical applications, in the future, the methodology will be enhanced by using information from different fidelities [68] of AM computational models to develop a multifidelity modeling and optimization framework for prediction and control of melt pool geometries. For example, a Netfabb ${ }^{\circledR}$ model can be combined with inexpensive observations from Eagar-Tsai's model to develop a two-fidelity GP that can be used for melt pool geometry prediction and optimization with an expected reduction in computational cost. Additional investigations are also planned as summarized below.
-\begin{enumerate}
-  \item Usage of process parameters (other than $P$ and $v$ ) such as scan spacing (i.e., hatch spacing), scan pattern (i.e., hatch pattern), build plate temperature, and powder layer thickness (for powder bed AM) and powder feed rate (for directed energy AM) as control inputs.
-  \item Incorporation of design constraints in the surrogate assisted modeling framework, e.g., tackling harder problems whereby a melt pool geometry needs to be controlled, along with the final microstructure such as columnar grains in CMSX-4 ${ }^{\circledR}$.
-  \item Development of heterogeneous design spaces in formulating multifidelity modeling framework, which can be useful in catering to optimization problems where the varied levels of fidelities have different input spaces. As an example, a HF L-PBF process model can have several process parameters, such as powder distribution properties, hatch spacing, scan strategy, etc., apart from $P$ and $v$ of the laser (which are the only process parameters for a LF model like the Eagr-Tsai's model), which can potentially affect the build characteristics. Optimization in such a framework can be possible via heterogeneous transfer learning [69] to learn from a common subspace of the inputs.
-  \item Integration of the surrogate modeling framework developed in this work with microstructure prediction framework using an open source SPPARKS code [70] to optimize the process parameters for obtaining a desired microstructure.
-  \item Implementation of the surrogate modeling framework for checking its efficacy towards mitigating unintended melt pool behavior such as keyholing effect. However, in such a case, the computational model needs to be a high fidelity one capable of predicting such a behavior.
-\end{enumerate}
-It is envisioned that the newly developed framework can be implemented in developing feedback strategies for melt pool control during AM processes with shorter response time due to improved prediction capability [71].
-Author Contributions: Conceptualization, S.M. and A.B.; methodology, S.M.; software, S.M. and D.G.; validation, S.M., A.B. and D.G.; formal analysis, S.M.; investigation, S.M. and A.B.; resources, A.B. and A.R.; writing-original draft preparation, S.M. and A.B.; writing-review and editing, A.B., S.M. and A.R.; visualization, S.M.; supervision, A.B. and A.R.; funding acquisition, A.R. and A.B. All authors have read and agreed to the published version of the manuscript.
-Funding: This research was funded in part by U.S. Air Force Office of Scientific Research (AFOSR) under Grant \# FA9550-15-1-0400 in the area of dynamic data-driven application systems (DDDAS). Any opinions, findings, and conclusions in this paper are those of the authors and do not necessarily reflect the views of the sponsoring agencies.
-Conflicts of Interest: The authors declare no conflict of interest.
-\section*{Appendix A. Mathematical Background}
-This section provides the mathematical background for machine learning (ML)-assisted modeling and optimization of additive manufacturing (AM) processes. While the details are available in standard literature (see, e.g., in [72,73]), the following three subsections succinctly present the core concepts of ML for completeness of the paper.
-\section*{Appendix A.1. Surrogate Modeling: Gaussian Processes}
-This subsection provides a brief overview of the surrogate modeling technique using Gaussian Processes (GPs), which is the foundation of the Bayesian Optimization (BO) framework used in this work for control of melt pool geometry. Salient properties of GPs modeling are delineated below.
-\begin{enumerate}
-  \item GPs belong to a class of stochastic processes based on the assumption of a multivariate jointly Gaussian distribution for any finite collection of random variables.
-  \item GPs are nonparametric models that do not assume a predefined functional relationship between the inputs and outputs (unlike polynomial regression models [73], for example).
-  \item GPs are flexible for modeling nonlinear functions. As the underlying concept is fully Bayesian, the predictions are made via a posterior probability distribution, which is a normal distribution in case of GPs, completely specified by its mean and covariance.
-\end{enumerate}
-Remark A1. The main advantage in having a probabilistic prediction method is that it naturally provides a measure of uncertainty quantification (UQ) associated with these predictions through the variance of the distribution. Moreover, having a probabilistic estimate instead of a fixed estimate provides the end user with a confidence level of the predictions.
-For a finite subcollection $\left\{\mathbf{x}_{1}, \mathbf{x}_{2}, \cdots, \mathbf{x}_{N}\right\}$ of the random input $\mathbf{x}$, the corresponding objective values
-$$
-\left\{f\left(\mathbf{x}_{1}\right), f\left(\mathbf{x}_{2}\right), \ldots, f\left(\mathbf{x}_{N}\right)\right\}
-$$
-are assumed to have a multivariate jointly Gaussian distribution:
-\[
-\left[\begin{array}{c}
-f\left(\mathbf{x}_{1}\right)  \tag{A1}\\
-\vdots \\
-f\left(\mathbf{x}_{N}\right)
-\end{array}\right] \sim \mathcal{N}\left(\left[\begin{array}{c}
-m\left(\mathbf{x}_{1}\right) \\
-\vdots \\
-m\left(\mathbf{x}_{N}\right)
-\end{array}\right],\left[\begin{array}{c}
-k\left(\mathbf{x}_{1}, \mathbf{x}_{1}\right) \cdots k\left(\mathbf{x}_{1}, \mathbf{x}_{N}\right) \\
-\vdots \\
-k\left(\mathbf{x}_{N}, \mathbf{x}_{1}\right) \cdots k\left(\mathbf{x}_{N}, \mathbf{x}_{N}\right)
-\end{array}\right]\right)
-\]
-where the mean $m(\mathbf{x}) \triangleq E[f(\mathbf{x})]$ and the covariance $k\left(\mathbf{x}, \mathbf{x}^{\prime}\right) \triangleq E\left[(f(\mathbf{x})-m(\mathbf{x}))\left(f\left(\mathbf{x}^{\prime}\right)-m\left(\mathbf{x}^{\prime}\right)\right)\right]$, and $E(\cdot)$ indicates the expectation of a random variable.
-Let $D^{t r n}=\left\{\left(\mathbf{x}_{i}^{t r n}, y_{i}^{t r n}\right)\right\}, i=1, \cdots, N$, be the training set that are available for model formulation. For a noisy regression model, it is assumed that
-\begin{equation*}
-y_{i}^{t r n}=f\left(\mathbf{x}_{i}^{t r n}\right)+\varepsilon_{i} \tag{A2}
-\end{equation*}
-where the additive noise $\varepsilon_{i}$ are independent and identically distributed (iid) zero-mean Gaussian random variables, i.e., $\varepsilon_{i} \sim \mathcal{N}\left(0, \sigma^{2}\right)$. By incorporating the noise term, the joint distribution of the observed values and the functional values at the test locations are
-\[
-\left[\begin{array}{l}
-\mathbf{y}^{t r n}  \tag{A3}\\
-\mathbf{y}^{t s t}
-\end{array}\right] \sim \mathcal{N}\left(\mathbf{0},\left[\begin{array}{cc}
-k\left(\mathbf{x}^{t r n}, \mathbf{x}^{t r n}\right)+\sigma^{2} I & k\left(\mathbf{x}^{t r n}, \mathbf{x}^{t s t}\right) \\
-k\left(\mathbf{x}^{t s t}, \mathbf{x}^{t r n}\right) & k\left(\mathbf{x}^{t s t}, \mathbf{x}^{t s t}\right)
-\end{array}\right]\right)
-\]
-where $D^{t s t}=\left\{\left(\mathbf{x}^{t s t}, y^{t s t}\right)\right\}$ is the test set in which $y^{t s t}$ is online observed data and $\mathbf{x}^{t s t}$ is the unknown variables to be estimated. Therefore, by the property of multivariate normal distributions, the conditional distribution of the function values at the test location is Gaussian [72]. In particular,
-\begin{equation*}
-\mathbf{y}^{t s t} \mid \mathbf{y}^{t r n}, \mathbf{x}^{t r n}, \mathbf{x}^{t s t} \sim \mathcal{N}\left(\mu^{t s t}, \Sigma^{t s t}\right) \tag{A4}
-\end{equation*}
-where
-\[
-\begin{array}{r}
-\mu^{t s t}=K\left(\mathbf{x}^{t s t}, \mathbf{x}^{t r n}\right)\left[K\left(\mathbf{x}^{t r n}, \mathbf{x}^{t r n}\right)+\sigma^{2} I\right]^{-1} \mathbf{y}^{t r n} \\
-\Sigma^{t s t}=K\left(\mathbf{x}^{t s t}, \mathbf{x}^{t s t}\right)-K\left(\mathbf{x}^{t s t}, \mathbf{x}^{t r n}\right)\left[K\left(\mathbf{x}^{t r n}, \mathbf{x}^{t r n}\right)\right. \\
-\left.+\sigma^{2} I\right]^{-1} K\left(\mathbf{x}^{t r n}, \mathbf{x}^{t s t}\right) \tag{A6}
-\end{array}
-\]
-Thus, the algorithm predicts the mean and covariance for the posterior distribution that models the output at every test data point.
-\section*{Appendix A.2. Kernel Function}
-The choice of the covariance function is one of the most critical aspects of the model selection process in GP-based surrogates. It is assumed that the objective function is locally smooth and that the GP priors belong to the class of automatic relevance determination (ARD) Matérn covariance functions [15]. The ARD formulation facilitates learning a length-scale for each input dimension to deal with directional anisotropies in the data set. The Matern class of covariance functions has a shape parameter that can be tuned in order to control the smoothness of the correlation function in the input space. In this work, a Matérn shape parameter of $5 / 2$ is used, which results in the form $k\left(\mathbf{x}, \mathbf{x}^{\prime} ; \boldsymbol{\theta}\right)=\sigma_{f}^{2}\left(1+\sqrt{5} r+\frac{5}{3} r^{2}\right) \exp (-\sqrt{5} r)$, where $r=\sqrt{\sum_{m=1}^{D} \frac{\left(x_{k}-x_{k}^{\prime}\right)^{2}}{\sigma_{m}^{2}}}$. The hyperparameters in the kernel are $\boldsymbol{\theta}=\left[\sigma_{f}^{2},\left(\sigma_{m}\right)_{k=1}^{D}\right]$, where $D$ is the dimensionality of the data set, and $\sigma_{f}$ and $\sigma_{m}$ are the scaling coefficient and the characteristic length-scales, respectively.
-Instead of squared exponential kernels that are generally best suited for interpolating smooth functional relationships, Matern kernels are chosen here because length-scales associated with the latter are less prone to be affected by the presence of non-smooth regions in the data set, which might yield poor extrapolation results in the smoother regions [74].
-\section*{Appendix A.3. Bayesian Optimization}
-In this work, the term optimization is used to denote maximization of a target function, without any loss of generality. A minimization problem can be posed similarly by taking the negative of the target function. Therefore, in order to optimize an objective function $f$, the following solution is sought.
-\begin{equation*}
-\mathbf{x}^{*}=\underset{\mathbf{x} \in \mathcal{X}}{\operatorname{argmax}} f(\mathbf{x}) \tag{A7}
-\end{equation*}
-If the functional form of $f$ is unknown, it may not be possible to have gradient-based optimization for solving the problem; in that case, gradient-free or black-box optimization might be suitable. $\mathrm{BO}$ is one such black-box optimization technique [31] that leverages the predictions through a surrogate model for sequential active learning (AL) to find the global optima of the objective function. The AL strategies\\
-are aimed at finding a trade-off between exploration and exploitation in possibly noisy settings [52,75,76], which facilitates a balance between global search and local optimization through acquisition functions. Usage of GPs in the surrogate modeling framework for BO often leads to closed-form analytical expressions for acquisition functions, which are inexpensive to compute.
-In the above formulation, the acquisition functions are designed in the following way. The potential of performance improvement is driven by the predicted mean function (which is in the category of exploitation), whereas the uncertainty prediction is manifested by regions of high variance (which is in the category of exploration). A trade-off between these two requirements is achieved by the acquisition functions iteratively, as a sequential optimization process.\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_f3867aee40a0cd4a18c2g-18(1)}\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_f3867aee40a0cd4a18c2g-18}
-Figure A1. Sequence of Bayesian Optimization iterations for maximizing $f(x)$. (a) Iteration \#1 : Prediction based on initial DOE of 4 points. (b) Iteration \#2. (c) Iteration \#5. (d) Iteration \#7. Filled blue circles indicate initial DOE. Filled red circles denote points selected in optimization iterations.
-One commonly used acquisition function in Bayesian optimization is Expected Improvement (EI), which is employed in this work. According to the formulation of Mockus et al. [77] and Jones et al. [52], the EI acquisition function can be written as
-\[
-E I(\mathbf{x})=\left\{\begin{array}{rr}
-\left(\mu(\mathbf{x})-f\left(\mathbf{x}^{+}\right)-\xi\right) \Phi(Z)+\sigma(\mathbf{x}) \phi(Z)  \tag{A8}\\
-0 & \text { if } \sigma(\mathbf{x})>0 \\
-\text { if } \sigma(\mathbf{x})=0
-\end{array}\right.
-\]
-where
-\[
-Z= \begin{cases}\frac{\left(\mu(\mathbf{x})-f\left(\mathbf{x}^{+}\right)-\xi\right)}{\sigma(\mathbf{x})} & \text { if } \sigma(\mathbf{x})>0  \tag{A9}\\ 0 & \text { if } \sigma(\mathbf{x})=0\end{cases}
-\]
-and $\mathbf{x}^{+}=\operatorname{argmax}_{\mathbf{x}_{i} \in \mathbf{x}_{1: k}} f\left(\mathbf{x}_{i}\right)$ is the input corresponding to the maximum functional value sampled until iteration $k$; the parameter $\xi>0$ controls the trade-off between exploration and exploitation [31]; $\mu(\mathbf{x})$ and $\sigma(\mathbf{x})$ are the mean and variance, respectively, predicted by the GPs for the an input point $\mathbf{x}$;\\
-and $\phi(\cdot)$ and $\Phi(\cdot)$ are the probability distribution function (PDF) and cumulative distribution function (CDF) of the standard normal distribution, respectively.
-If the objective function is noise corrupted, instead of using the best observation, the point with the highest expected value is defined as the incumbent, i.e., $f\left(\mathbf{x}^{+}\right)$replaced by $\mu^{+}$, which is defined as
-\begin{equation*}
-\mu^{+} \triangleq \underset{\mathbf{x}_{i} \in \mathbf{x}_{1: k}}{\operatorname{argmax}} \mu\left(\mathbf{x}_{i}\right) \tag{A10}
-\end{equation*}
-The optimization algorithm proceeds sequentially by sampling $\hat{\mathbf{x}}=\operatorname{argmax}_{\mathbf{x}} E I(\mathbf{x})$ at every step of the iteration process to add on to the dataset, after which the GP model is retrained with the new data set to predict the acquisition potential for the next iterative step. This process continues until an optimum is reached, or the computational budget is extinguished. As the acquisition potential is predicted over the entire search space by the surrogate, BO can achieve fast predictions without a lot of function calls in the search space (i.e., without having to run the simulations to obtain the objectives at all the search locations), which, otherwise, might be computationally infeasible when the search space is high-dimensional and the simulations are expensive.
-Figure A1 demonstrates the optimization process through a simple problem of maximizing a black-box function $f(x)$ in the input space of $[-2,2]$ (denoted by solid blue line). The process is started with an initial design of experiments (DoE) of 4 points (filled blue circles) chosen in the search domain by Latin hypercube sampling (LHS) [61], which allows the initial selection of points to be well-spread in the search space. Figure Ala shows the GP prediction in the initial stage, which is characterized by the mean function (red dotted line), and the variance associated with the prediction (denoted by the orange band). The variance is high globally at the initial stage, because only four points are sampled on the true function. The maximizer of the acquisition function $E I(x)$ shows the location to sample for the next point at every iteration (filled red circles). Figure A1b shows that the predicted mean of the function in Figure A1a drives the selection of the first optimization point. It is interesting to note that in Figure A1c, although the true maximizer of $f(x)$ is already sampled, $E I(x)$ points towards a region where the variance is high. This is because of the exploration-exploitation trade-off which allows the algorithm to explore the search space instead of greedily searching for the optimum, a property that helps the algorithm avoid being stuck at a local optima. Eventually after seven optimization iterations, the routine converges at the true optima, as shown in Figure A1d. Moreover, the mean function predicted at the last stage is very close to the true function, and the uncertainty band also reduces globally, which indicates that the algorithm not only finds the maximizer of the function, but in doing so it also learns a pretty accurate surrogate model of the function, which can now be used as a low-cost approximation of the true function.
-\section*{Appendix B. Optimization Algorithm}
-Algorithm A1 shows the surrogate-based optimization routine that is employed in this paper for solving the melt pool geometry control problem, which is elucidated in Section 3.3. The global thread picks up an optimal point $\tilde{\mathbf{x}}^{*}$, which is refined in the local thread to give $\mathbf{x}^{*}$, as the final optimal point chosen by the algorithm.
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_f3867aee40a0cd4a18c2g-20}
-\end{center}
-\section*{Local Thread}
-Require: Start with surrogate local GP for the objective functional $J$ with $\tilde{N}_{\text {init }}$ LHS initializations for $k=1$ to $\tilde{N}_{\text {Localiter }}$ optimization steps do
-\begin{itemize}
-  \item Use the trained local GP to predict the posterior distribution of the objective function in the local search space $\tilde{X}_{\text {star }}$
-  \item Sample the optimized process parameter from $\tilde{X}_{\text {star }}$ as $\tilde{\mathbf{x}}_{\mathbf{k}}^{*}=\operatorname{argmax}_{\tilde{\mathbf{x}}} E I(\tilde{\mathbf{x}})$
-  \item Compute the objective function $J_{k}$ at the chosen $\tilde{\mathbf{x}}_{\mathbf{k}}^{*}$
-  \item Add the pair $\left(\tilde{\mathbf{x}}_{\mathbf{k}^{\prime}}^{*} J_{k}\right)$ to the local surrogate model's input and output sets respectively
-  \item Retrain the local surrogate model
-\end{itemize}
-$$
-\text { end for }
-$$
-\begin{itemize}
-  \item Select $\mathbf{x}^{*}=\operatorname{argmax}_{\tilde{\mathbf{x}}_{k}} J$
-\end{itemize}
-\section*{References}
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-(C) 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (\href{http://creativecommons.org/licenses/by/4.0/}{http://creativecommons.org/licenses/by/4.0/}).
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-\title{High Strength Aluminium Alloys in Laser-Based Powder Bed Fusion - a Review }
-\author{Julie Langedahl Leirmo, ${ }^{\mathrm{a}, *}$\\
-${ }^{a}$ Department of Manufacturing and Civil Engineering, NTNU - Norwegian University of Science and Technology, Teknologiveien 22, 2815 Gjøvik, Norway\\
-*Corresponding author. Tel.: +47 48202281.E-mail address: julie.1.leirmo@ntnu.no}
-\date{}
-\begin{document}
-\maketitle
-\begin{abstract}
-Despite the difficulties of processing high strength aluminium alloys in laser-powder bed fusion additive manufacturing, there is a growing interest in these types of alloys. In this paper, a brief literature review is presented, aiming to give an overview of different approaches to enable laser-powder bed fusion additive manufacturing of high strength aluminium alloys in the 2xxx and 7xxx series. Relevant literature was collected and analysed. The analysis found that adjusting the scan speed is the most investigated approach for aluminium alloys in both the $2 \mathrm{xxx}$ and $7 \mathrm{xxx}$ series. Layer thickness is the least investigated approach, and never investigated for alloys in the 7xxx series.
-\end{abstract}
-(C) 2021 The Authors. Published by Elsevier B.V.
-This is an open access article under the CC BY-NC-ND license (\href{https://creativecommons.org/licenses/by-nc-nd/4.0}{https://creativecommons.org/licenses/by-nc-nd/4.0})
-Peer-review under responsibility of the scientific committee of the 54th CIRP Conference on Manufacturing System
-Keywords: Additive Manufacturing; Powder Bed Fusion; Aluminium
-\section*{1. Introduction}
-There has been a growing interest in additive manufacturing $(\mathrm{AM})$ of aluminium (Al) in recent years in various industries such as automotive and aerospace. Low weight combined with relatively high strength makes $\mathrm{Al}$ popular material. In combination with AM technology, parts can become even lighter while still obtaining, or even enhance the required strength and mechanical properties compared with the cast counterpart [1]. However, $\mathrm{Al}$ in $\mathrm{AM}$ and especially laserpowder bed fusion (LPBF) faces challenges due to the nature of $\mathrm{Al}$ and the LPBF technology. Al powder has high reflectivity and low laser absorption and is therefore difficult to melt with a laser, which makes it difficult to produce parts with satisfying quality [1-4].
-Several investigations have been performed regarding $\mathrm{Al}$ in LPBF, and in recent years there has been a particular interest for high strength alloys Al alloys in LPBF. In the current study, literature on the processability of high strength $\mathrm{Al}$ alloys in the $2 \mathrm{xxx}$ and $7 \mathrm{xxx}$ series has been collected and analysed. The aim is to give a brief overview of the current trends in research for the successful production of high strength Al parts with LPBF.
-A brief theoretical background is given in the next section before the methodology is described in section 3. The results are presented in section 4 and discussed thereafter. Finally, conclusions and proposed future work is presented in section 6.
-\section*{2. Theoretical background}
-\subsection*{2.1. Additive manufacturing}
-ISO/ASTM 52900:2015(E) [5] defines AM as a "process of joining materials to make parts from 3D model data, usually layer upon layer, as opposed to subtractive manufacturing and formative manufacturing methodologies." The interest in AM is predominantly due to the possibility to produce lightweight parts with complex geometries that cannot be obtained with traditional technologies $[1,6]$. The possibility to produce complex parts also enables the fabrication of parts in one piece whereas conventional technologies would yield several components to be assembled [7].
-\subsection*{2.2. Powder bed fusion}
-According to ISO/ASTM 52900:2015(E) [5], PBF is an "additive manufacturing process in which thermal energy selectively fuses regions of a powder bed". PBF is separated into subcategories that use different types of energy and is suitable for different types of materials $[8,9]$. In the remainder of this paper, the abbreviation LPBF is used to refer to laser powder bed fusion of metals only. Common for all of the PBF technologies is that a thin layer of powder is deposited onto the build surface whereas the desired areas are fused before another thin powder layer is deposited on top of the previous [10].
-\subsection*{2.3. Laser-powder bed fusion for metals}
-The build process starts with the deposition of a thin layer of the metal powder which then is scanned with a laser beam to fuse the powder particles. The process is repeated in a layerwise manner until the desired part is formed [11]. The powder in the successive layer must not only be melted but also fused into the former layer to ensure a solid part $[9,12]$. According to Ahuja, et al. [12], a melting depth of three-layer thicknesses is the most suitable.
-In LPBF, the process is conducted in a controlled atmosphere where the build chamber is filled with an inert gas, usually argon $(A r)$, to prevent oxidation [1, 9]. The metal powder particles are fused with a high-power laser beam to form near-net-shape parts that require minimal post-processing $[9,13,14]$. In addition to the possibility of complex parts with little post-processing, LPBF can produce parts with high accuracy compared to other AM techniques [15].
-\subsection*{2.4. Aluminium in additive manufacturing}
-High strength combined with low weight is one of the properties that makes $\mathrm{Al}$ favourable in industries such as automotive and aerospace $[1,16]$. Combined with the possibility of complex geometries and topology optimization, even lighter parts can be produced that still have the required strength, making the technology even more attractive [4, 7, 17]. However, at this point, only a few $\mathrm{Al}$ alloys can reliably be processed by AM [18]. Mostly Al-Si-Mg alloys and other alloys with Silicon $(\mathrm{Si})$ as the main alloying element is used in AM because they are relatively easy to melt with a laser beam due to their near-eutectic composition [11, 12]. This composition gives a short solidification range, compared with some high strength $\mathrm{Al}$ alloys $[12,19,20]$. Because $\mathrm{Si}$ is a nonmetallic element, the thermal expansion coefficient is much lower than for metals, and the addition of $\mathrm{Si}$ can reduce this effect and consequently prevent cracking [15].
-One of the factors that make it hard to additively manufacture $\mathrm{Al}$ alloys is the high reflectivity of $\mathrm{Al}$ and its low laser absorption $[1,21,22]$. The poor flowability of the $\mathrm{Al}$ alloy powder also makes it hard to process with LPBF technology [22]. Another challenge with $\mathrm{Al}$ in $\mathrm{AM}$ is that these alloys are prone to hot cracking. The main factor for hot cracking is the chemical composition of the $\mathrm{Al}$ alloy [23].
-In general, $\mathrm{Al}$ alloy parts produced by LPBF show a higher hardness than their cast counterparts. It is believed that this is due to the rapid cooling rate found in the LPBF process, which results in a microstructure refinement [24]. The ductility of the $\mathrm{Al}$ alloys produced by LPBF however, seems to decrease [25].
-\subsection*{2.5. High strength aluminium alloys}
-High strength Al alloys in the $2 \mathrm{xxx}$ and $7 \mathrm{xxx}$ series are wrought alloys intended for cold-forming processes. Consequently, they easily form defects when exposed to heat from e.g. a laser beam in the LPBF process [15].
-Some of the main issues are that these alloys are prone to solidification cracking, liquid cracking, and hot cracking. Moreover, some of the alloying elements in these alloys, such as $\mathrm{Zn}, \mathrm{Mg}$, and $\mathrm{Li}$, easily evaporate in the process and are therefore not very processable by LPBF $[22-24,26]$. Evaporation of these alloying elements can reduce metallurgical integrity [23].
-\subsection*{2.5.1. $2 x x x$ series alloys}
-The $\mathrm{Al}$ alloys in the $2 \mathrm{xxx}$ series have copper $(\mathrm{Cu})$ as the main alloying element besides Al. Al-Cu alloys in this series are not suitable for welding, hence challenging to produce by LPBF [17]. They are prone to hot cracking, which is connected to the solidification interval [17]. However, these Al-Cu alloys are ductile and therefore reduces the stress peaks which results in predicted plastic deformation rather than failure [27].
-\subsection*{2.5.2. $7 x x x$ series alloys}
-$\mathrm{Al}$ alloys in the $7 \mathrm{xxx}$ series have Zink $(\mathrm{Zn})$ as their major alloying element [28]. While all 7xxx alloys are prone to hot cracking, $\mathrm{Al} 7075$ is found to be especially susceptible when used in LPBF $[15,29]$. The 7xxx alloys are also not weldable because they are prone to liquidation cracking. This occurs due to a thin liquid film at the boundaries of the grains, which cannot follow the solidification shrinkage [26].
-\section*{3. Methodology}
-The literature was collected through searches in online search engines and databases such as Google Scholar and Web of Science. A total of 27 papers were collected in this study, 16 regarding $2 \mathrm{xxx}$ series alloys and 11 regarding $7 \mathrm{xxx}$ series alloys. The investigated approaches can be divided into three different categories as shown in Figure 1, namely additives, process parameters, and heat treatment. The category additives contain approaches where new alloying elements are added, the amount of an alloying element is increased, or where an alloy has been mixed with another alloy. The category process parameters contain approaches where process parameters have
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_392391e00aace0077bd8g-2}
-\end{center}
-Fig. 1. Approaches investigated in this study\\
-been adjusted. The category heat treatment contains different heat treatments on LPBF produced parts. Tx includes T1, T2, ..., T10 treatment [30]. Only those who explicitly said they did a Tx treatment are placed in the Tx category, while the rest is placed in the category others. Al alloys specially developed for LPBF are not included in this study, but the interested reader is referred to Aversa, et al. [22] which provides an extensive review on this topic.
-It is known that there is a significant number of papers on the topic that is published in other languages, especially in German. Due to the author's insufficient skillset in this language, they are not included in this study.
-\section*{4. Results}
-The publishing year for all the collected literature in this study is presented in Figure 2. The first year of publication in this topic was in 2014, and except for 2015, there have been publications every subsequent year. Please note that the number of publications in 2021 only includes publications in January, due to the work being finalised in January of 2021.
-Table 1 gives an overview of the number of studies that investigated the different approaches. In general, adjusting process parameters are the most investigated approach. However, these are often adjusted in combination with other approaches. For instance, the effect of adding additives to the $\mathrm{Al}$ alloy in combination with changing the scan speed has been investigated by many. Of all the process parameters, layer thickness was the least investigated parameter and was investigated in only two studies.
-Seven different additives were investigated in the collected literature, which can be seen in Table 2 and Table 3 for $2 \mathrm{xxx}$ series alloys and 7xxx series alloys respectively. Additionally, Aversa, et al. [26] made a new alloy mix by mixing $50 \%$ $\mathrm{Al} 7075$ with $50 \% \mathrm{AlSi10Mg}$.
-While scan speed is a common parameter, an alternative measure was used by Ahuja, et al. [12] and Stopyra, et al. [31] who looked at the point to point distance and exposure time. The scan speed, however, is by far the most investigated parameter, which was investigated in 20 different studies, but it was usually investigated together with other parameters such as laser power or hatch spacing.
-One article mentioned that they did annealing [32], eight performed Tx treatment, while six performed other types of heat treatment that do not fulfil the requirements of any of the Tx treatments.
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_392391e00aace0077bd8g-3}
-\end{center}
-Fig. 2 Year of publications regarding high strength $\mathrm{Al}$ alloys
-\section*{4.1. $2 x x x$ series}
-Table 2 shows the different approaches investigated regarding $2 \mathrm{xxx}$ series alloys in the collected literature. Among these alloys, the scan speed is the most investigated approach, followed by laser power and hatch spacing. As can be seen in Table 2, these parameters are often investigated together, where more than one of the parameters are adjusted in the same experiment. It is observed that investigations regarding additives generally adjust fewer process parameters.
-Hatch spacing was investigated in six studies, but always in combination with other parameters. However, they were never investigated in combination with additives. Post heat treatment was performed in eight investigations, whereas five of them explicitly said they did a T6 or T4 treatment.
-The least investigated approach is layer thickness, which was investigated in two studies. In the category Other we find the study [12], that investigated exposure time and point to point distance instead of scan speed.
-\section*{4.2. $7 x x x$ series}
-Different approaches investigated for $\mathrm{Al}$ alloys in the $7 \mathrm{xxx}$ series is presented in Table 3. The most investigated parameter was scan speed with a total of nine investigations, while the second most investigated approach was additives with seven investigations. The most investigated additive for the $7 \mathrm{xxx}$ series alloys was Si. Instead of adding one or two alloying elements to the alloy powder, Zhou, et al. [21] created a mix of $50 \% 7075$ and $50 \% \mathrm{AlSi} 10 \mathrm{Mg}$, which increased the total $\mathrm{Si}$ $\mathrm{wt} \%$ of the alloy composition in the final part.
-In all but one of the studies that investigated scan speed, the laser power was also investigated. The laser power on the other hand was never adjusted without the scan speed also being adjusted. In the study by Qi, et al. [45] however, different defocusing distances was investigated. Post heat treatment was performed in seven studies, where three said explicitly that they performed a T6 treatment. For alloys in the 7xxx series, none investigated the layer thickness.
-It can also be noted that in the studies on alloys in the $7 \mathrm{xxx}$ series, all but one of the investigated alloys was Al7075 with slightly different notations depending on the standard that was
-Table 1. Number of investigations of the respective approaches
-\begin{center}
-\begin{tabular}{llll}
-\hline
-Approaches &  & References & Total \\
-\hline
-Additives &  & $[2,15,18,21,33-38]$ & 10 \\
-\hline
-\begin{tabular}{l}
-Process \\
-parameters \\
-\end{tabular} & \begin{tabular}{l}
-Layer- \\
-thickness \\
-\end{tabular} & $[39,40]$ & 2 \\
- & \begin{tabular}{l}
-Hatch \\
-spacing \\
-\end{tabular} & $[12,17,26,31,35,39,41-44]$ & 10 \\
- & Scan speed & $[2,15,17,26,29,31,33-37,39-$ & 20 \\
- &  & $47]$ & 15 \\
-\cline { 2 - 4 }
- & Laser power & $[2,12,15,17,26,29,31,35-37$, & 15 \\
-\hline
-\multirow{2}{*}{}\begin{tabular}{ll}
-Heat \\
-treatment \\
-\end{tabular} & Annealing & $[32]$ & 1 \\
-\cline { 2 - 4 }
- & Tx treatment & $[18,21,27,38-40,43,46]$ & 6 \\
-\cline { 2 - 4 }
- & Others & $[2,26,31,35,36,48]$ & 1 \\
-\hline
-Others &  & $[12]$ & 6 \\
-\hline
-\end{tabular}
-\end{center}
-Table 2. Approaches 2xxx series alloys
-\begin{center}
-\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
-\hline
- & Alloy & Additives & \begin{tabular}{l}
-Laser \\
-power \\
-\end{tabular} & \begin{tabular}{c}
-Scan \\
-speed \\
-\end{tabular} & \begin{tabular}{l}
-Hatch \\
-spacing \\
-\end{tabular} & \begin{tabular}{c}
-Layer \\
-thickness \\
-\end{tabular} & \begin{tabular}{c}
-Heat \\
-treatment \\
-\end{tabular} & Other \\
-\hline
-Nie, et al. [33] & $\mathrm{Al}-4.24 \mathrm{Cu}-1.97 \mathrm{Mg}-0.56 \mathrm{Mn}$ & $\mathrm{x}(\mathrm{Zr})$ &  & $\mathrm{x}$ &  &  &  &  \\
-\hline
-Ahuja, et al. [12] & AW-2219 and AW-2618 &  & $\mathrm{x}$ &  & $\mathrm{x}$ &  &  & $x^{*}$ \\
-\hline
-Wang, et al. [46] & $\mathrm{Al}-3.5 \mathrm{Cu}-1.5 \mathrm{Mg}-1 \mathrm{Si}$ &  & $\mathrm{x}$ & $\mathrm{x}$ &  &  & $\mathrm{x}(\mathrm{T} 6)$ &  \\
-\hline
-Casati, et al. [32] & 2618 &  &  &  &  &  & $\mathrm{x}$ (annealing) &  \\
-\hline
-Zhang, et al. [41] & $\mathrm{Al}-\mathrm{Cu}-\mathrm{Mg}$ (close to AA2024) &  &  & $\mathrm{x}$ & $\mathrm{x}$ &  &  &  \\
-\hline
-Zhang, et al. [34] & \begin{tabular}{l}
-$\mathrm{Al}-\mathrm{Cu}-\mathrm{Mg}(4.24 \mathrm{Cu}, 1.97 \mathrm{Mg}$ \\
-$0.56 \mathrm{Mn})$ \\
-\end{tabular} & $\mathrm{x}(\mathrm{Zr})$ &  & $\mathrm{x}$ &  &  &  &  \\
-\hline
-Qi, et al. [42] & 2195 &  &  & $\mathrm{x}$ & $\mathrm{x}$ &  &  &  \\
-\hline
-Rasch, et al. [39] & AW-2024 &  & $\mathrm{x}$ & $\mathrm{x}$ & $\mathrm{x}$ & $\mathrm{x}$ & $\mathrm{x}(\mathrm{T} 4)$ &  \\
-\hline
-Karg, et al. [17] & AW-2022 and 2024 &  & $\mathrm{x}$ & $\mathrm{x}$ & $\mathrm{x}$ &  &  &  \\
-\hline
-Zhang, et al. [48] & $\mathrm{Al}-\mathrm{Cu}-\mathrm{Mg}$ &  &  &  &  &  & $\mathrm{x}$ &  \\
-\hline
-Karg, et al. [27] & EN AW-2219 (AlCu6Mn) &  &  &  &  &  & $\mathrm{x}(\mathrm{T} 6)$ &  \\
-\hline
-\begin{tabular}{l}
-Raffeis, et al. \\
-$[36]$ \\
-\end{tabular} & AA2099 & \begin{tabular}{l}
-x (Ti-alumide and \\
-Al) \\
-\end{tabular} & $\mathrm{x}$ & $\mathrm{x}$ &  &  & $\mathrm{x}$ &  \\
-\hline
-Qi, et al. [40] & 2195 &  &  & $\mathrm{x}$ &  & $\mathrm{x}$ & $\mathrm{x}(\mathrm{T} 6)$ &  \\
-\hline
-Tan, et al. [38] & 2024 & $\mathrm{x}(\mathrm{Ti})$ &  &  &  &  & $\mathrm{x}(\mathrm{T} 6)$ &  \\
-\hline
-Tan, et al. [47] & 2024 &  & $\mathrm{x}$ & $\mathrm{x}$ &  &  &  &  \\
-\hline
-Pekok, et al. [44] & AA2024 &  & $\mathrm{x}$ & $\mathrm{x}$ & $\mathrm{x}$ &  &  &  \\
-\hline
-\end{tabular}
-\end{center}
-*Ahuja, et al. [12] looked at time exposure and point to point distance instead of scan speed
-followed. The only alloy different from A17075 was an AlZnMgScZr alloy, investigated by Zhou, et al. [21].
-\subsection*{5.1. Additives}
-\section*{5. Discussion}
-The collected literature indicates that there has been less research on 7xxx series alloys than 2xxx series alloys. For both the series, the scan speed is the most investigated process parameter. This may be because the scan speed is relatively easy to adjust, and a change in scan speed can greatly influence whether the alloy powder is fully melted or not. A high laser power is required to enable full melting of the Al powder, and with limitations in the machine parameters, there is a limit to how high the laser power can be adjusted. By reducing the scan speed, the volumetric energy density will increase which in turn can ensure full melting of the powder. However, by increasing the volumetric energy density, some elements with a low melting point can evaporate.
-Of the collected literature, among the 7xxx series alloys investigated, all but one was Al7075. This indicates that this alloy is of great interest within AM. This can be due to the highly regarded properties of this specific alloy.
-The amount of an alloying element added into an alloy can change the composition of the alloy to the extent where it can no longer be categorised as the original alloy. When additional elements are added, the new composition does not necessarily meet the specific alloy requirements of the initial composition. Therefore, the new alloy blend may not qualify as an existing alloy but is rather considered a new alloy. This is closely related to the issue of alloying elements evaporating during the LPBF process. If a significant amount of an alloying element evaporates, the alloy composition in the final part might not qualify as the initial alloy. In the study by Kaufmann, et al. [29] the chemical composition of the LPBF produced parts differed from the composition of the $\mathrm{Al}$ alloy powder. This results in the amount of both $\mathrm{Zn}$ and $\mathrm{Si}$ no longer be inside the $\mathrm{min} / \mathrm{max}$ requirement for AW-7075, according to NS-EN 573-3:2019. Kaufmann, et al. [29] concludes that it must be either an evaluation of trade-off or a different alloy composition is needed to compensate for the loss of alloying elements.
-Instead of adding one or two alloying elements to the alloy powder, Zhou, et al. [21] created a mix of 50\% Al7075 and
-Table 3. Approaches 7xxx series alloys
-\begin{center}
-\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
-\hline
- & Alloy & Additives & \begin{tabular}{c}
-Laser \\
-power \\
-\end{tabular} & \begin{tabular}{c}
-Scan \\
-speed \\
-\end{tabular} & \begin{tabular}{l}
-Hatch \\
-spacing \\
-\end{tabular} & \begin{tabular}{c}
-Layer \\
-thickness \\
-\end{tabular} & \begin{tabular}{c}
-Heat \\
-treatment \\
-\end{tabular} & Other \\
-\hline
-Montero-Sistiaga, et al. [2] & $\mathrm{A} 17075$ & $\mathrm{x}(\mathrm{Si})$ & $\mathrm{x}$ & $\mathrm{x}$ &  &  & $\mathrm{x}$ &  \\
-\hline
-Martin, et al. [18] & $\mathrm{A} 17075$ & $\mathrm{x}(\mathrm{Zr})$ &  &  &  &  & $\mathrm{x}(\mathrm{T} 6)$ &  \\
-\hline
-Qi, et al. [45] & $\mathrm{A} 17075$ &  &  & $\mathrm{x}$ &  &  &  & $x^{*}$ \\
-\hline
-Aversa, et al. [26] & 7075 & $\mathrm{x}(\mathrm{AlSi} 10 \mathrm{Mg}) * *$ & $\mathrm{x}$ & $\mathrm{x}$ & $\mathrm{x}$ &  & $\mathrm{x}$ &  \\
-\hline
-Kaufmann, et al. [29] & AW 7075 &  & $\mathrm{x}$ & $\mathrm{x}$ &  &  &  &  \\
-\hline
-Zhou, et al. [21] & $\mathrm{AlZnMgScZr}$ & $\mathrm{x}(\mathrm{Sc}+\mathrm{Zr})$ &  &  &  &  & $\mathrm{x}(\mathrm{T} 6)$ &  \\
-\hline
-Otani and Sasaki [15] & 7075 & $x(\mathrm{Si})$ & $\mathrm{x}$ & $\mathrm{x}$ &  &  &  &  \\
-\hline
-Wu, et al. [37] & $\mathrm{A} 17075$ & $\mathrm{x}$ (TiN nanoparticles) & $\mathrm{x}$ & $\mathrm{x}$ &  &  &  &  \\
-\hline
-Stopyra, et al. [31] & AA 7075 &  & $\mathrm{x}$ & $\mathrm{x}^{* * *}$ & $\mathrm{x}$ &  & $\mathrm{x}$ &  \\
-\hline
-Li, et al. [35] & AL7075 & $\mathrm{x}(\mathrm{Si})$ & $\mathrm{x}$ & $\mathrm{x}$ & $\mathrm{x}$ &  & $\mathrm{x}$ &  \\
-\hline
-O E, et al. [43] & $\mathrm{Al7075}$ &  & $\mathrm{x}$ & $\mathrm{x}$ & $\mathrm{x}$ &  & $\mathrm{X}(\mathrm{T} 6)$ &  \\
-\hline
-\end{tabular}
-\end{center}
-time exposure and point to point distance\\
-$50 \% \mathrm{AlSi} 10 \mathrm{Mg}$, which will drastically change the alloy composition in the final part. It can, however, be debated whether this should be regarded as an additive or rather a new alloy or alloy blend. Only half of the alloy is now A17075 which belongs to the wrought alloy $7 \mathrm{xxx}$ series, and the other half is $\mathrm{AlSi10Mg}$ which is a cast alloy. Therefore, it can also be questioned if the new alloy blend qualifies as a high strength alloy and if so, if it would belong to the $7 \mathrm{xxx}$ series.
-\subsection*{5.2. Layer thickness}
-It seems from the collected literature that layer thickness is of least interest, only investigated in two studies, both investigating alloys in the $2 \mathrm{xxx}$ series. However, the layer thickness can influence the laser power and scan speed required to fully melt the powder. As stated by Ahuja, et al. [12] melting depth of three times the layer thickness, would be the most suitable, and therefore it can be argued that a thinner layer thickness can decrease the required laser power and/or increase the scan speed. However, how thin the powder layer can be, is limited by the particle size of the powder.
-An issue with thinner layers is that the production time might increase. However, higher scan speed can decrease the build time, and it can be assumed that with thinner powder layers, the scan speed can be increased, and still result in fully melting the powder. Also, insufficient melting of powder is an issue that can lead to defects such as pores [36], and with thinner powder layers, it may be easier to fully melt the powder.
-\subsection*{5.3. General notes}
-Figure 2 shows that there is a growing interest in LPBF of high strength alloys, despite the difficulties associated with these alloys. However, there might be more research published that has not been included in this study. Therefore, this overview can be used as an indicator of the current trend, but the numbers cannot be used as an absolute. Also, this study was finalized in January 2021, so the numbers for 2021 are only up to this point and more literature on this topic can be published within this year. However, it is interesting to note that the number of publications in January 2021 is already equal to the number published in 2018. This indicates that there may be an exponential growth in interest in this topic.
-All the reviewed studies report promising results to different extents. Some were able to produce fully dense parts with close to no defects, while others were able to increase the density and reduce the number of defects. However, different approaches can lead to different challenges.
-It is known that more literature on this topic exists in other languages, predominantly German, in which the author lacks a sufficient skillset. Therefore, these are not included in the study, which means that this study does not give a complete picture of what approaches are the most investigated. However, it is intended to give an indicator of the current trends in research of high strength $\mathrm{Al}$ alloys in the 2xxx and 7xxx series.
-This study is also limited to a subset of approaches selected for this study. This means that there can be other promising approaches that enable successful processing of high strength $\mathrm{Al}$ alloys that are not considered in this study.
-\section*{6. Conclusion}
-Relevant literature on high strength $\mathrm{Al}$ alloys in the $2 \mathrm{xxx}$ and 7xxx series in LPBF has been collected to give an overview of the current state of research on this topic. The different approaches considered in this paper was adding additives to the alloy powder, adjusting the process parameters, (i) laser power, (ii) scan speed, (iii) hatch distance and (iv) layer thickness, as well as heat treatment. Some main conclusions can be drawn from this:
-\begin{enumerate}
-  \item For Al alloys in the $2 \mathrm{xxx}$ series, scan speed was the most investigated approach. However, it was always investigated in combination with other approaches.
-  \item For Al alloys in the 7xxx series, scan speed was the most investigated approach, and laser power being the second most investigated approach.
-  \item Layer thickness was investigated in only two studies and was the least investigated approach in the collected literature.
-\end{enumerate}
-There is a significantly larger amount of research efforts towards $\mathrm{Al}$ alloys in the $2 \mathrm{xxx}$ series than in the $7 \mathrm{xxx}$ series. Also, Al7075 was the only alloy investigated in the $7 \mathrm{xxx}$ series, except for one study. Therefore, more research efforts on $7 \mathrm{xxx}$ series alloys, especially other alloys than A17575 could be valuable for this field of study.
-Insufficient melting of the $\mathrm{Al}$ alloy powder is an issue in LPBF, and layer thickness may influence this. As this was the least investigated approach, this parameter should be considered in future research efforts.
-\section*{Acknowledgements}
-The KPN VALUE project at NTNU, co-funded by industry and the Norwegian Research Council.
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-[46] Wang P, Gammer C, Brenne F, Prashanth KG, Mendes RG, Rümmeli MH, et al. Microstructure and mechanical properties of a heat-treatable Al3.5 Cu-1.5Mg-1Si alloy produced by selective laser melting. Mater. Sci. Eng. A. 2018;711:562-70.
-[47] Tan Q, Liu Y, Fan Z, Zhang J, Yin Y, Zhang M-X. Effect of processing parameters on the densification of an additively manufactured $2024 \mathrm{Al}$ alloy. J Mater Sci Technol. 2020;58:34-45.
-[48] Zhang H, Zhu H, Nie X, Qi T, Hu Z, Zeng X. Fabrication and heat treatment of high strength $\mathrm{Al}-\mathrm{Cu}-\mathrm{Mg}$ alloy processed using selective laser melting. SPIE; 2016.
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-\title{Review }
-\author{Alberico Talignani ${ }^{\mathrm{a}, 1}$, Raiyan Seede ${ }^{\mathrm{b}, 1}$, Austin Whitt ${ }^{\mathrm{b}}$, Shiqi Zheng ${ }^{\mathrm{a}}$, Jianchao $\mathrm{Ye}^{\mathrm{c}}$,\\
-Ibrahim Karaman $^{\text {b,*, }}$, Michael M. Kirka ${ }^{\text {d,* }}$, Yutai Katoh ${ }^{\text {e, }}$, Y. Morris Wang ${ }^{\text {a,* }}$\\
-a Department of Materials Science and Engineering, University of California, Los Angeles, CA 90049, USA\\
-${ }^{\mathrm{b}}$ Department of Materials Science and Engineering, Texas A\&M University, College Station, TX 77843, USA\\
-' Materials Science Division, Lawrence Livermore National Laboratory, Livermore, CA 94005, USA\\
-${ }^{\mathrm{d}}$ Manufacturing Science Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA\\
-${ }^{\mathrm{e}}$ Materials Science \& Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA}
-\date{}
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-\begin{document}
-\maketitle
-\section*{A review on additive manufacturing of refractory tungsten and tungsten alloys}
-\section*{A R T I C L E I N F O}
-\section*{Keywords:}
-Tungsten
-Tungsten alloys
-Additive manufacturing
-Laser powder-bed-fusion
-Laser directed-energy-deposition
-Electron beam powder-bed-fusion
-\begin{abstract}
-A B S T R A C T We review the progress of additive manufacturing effort on refractory metal tungsten and tungsten alloys. These materials are excellent candidates for a variety of high temperature applications but extremely challenging to fabricate via additive manufacturing due to a series of existing issues during the manufacturing. We outline these issues and discuss the current understanding and progress to tackle them. Laser powder-bed-fusion, laser directed-energy-deposition, and electron beam powder-bed-fusion are three common techniques that have been applied to additively manufacture pure tungsten. This overview discusses current observations and understanding on the issues associated with each of these techniques. We identify future research opportunities in additive manufacturing of refractory metals.
-\end{abstract}
-\section*{1. Introduction}
-Due to their high density, excellent thermal conductivity and high temperature capabilities, high strength and hardness, and minimal sputtering yield and hydrogen interactions, refractory metal tungsten and tungsten alloys have a broad range of potential applications, including plasma facing components for fusion reactors [1,2], fusion targets [3], armor penetrators [4], and nuclear space power and propulsion [5]. For many of these applications, additive manufacturing (AM) offers unique geometrical design freedom and rapid prototyping capability, which is unparalleled by conventional manufacturing techniques. Moreover, AM offers additional potentials to fabricate functionally graded transitions from tungsten to various dissimilar materials. Due to its extremely high melting temperature (for pure tungsten, the melting temperature $\mathrm{T}_{m}=3422^{\circ} \mathrm{C}$ ) and brittle nature, tungsten is notoriously difficult to fabricate via either laser- or electron-beam-based AM techniques. Nevertheless, encouraging progress has been made in the past few years in AM tungsten and its alloys. Given the rising importance of refractory metals in various high temperature applications for harsh environments, this article aims at providing a timely overview of recent development in AM of refractory metals, in particular, tungsten and tungsten alloys.
-To date, laser powder-bed-fusion (L-PBF) [sometimes also known as selective laser melting (SLM)], laser directed-energy-deposition (LDED), and electron beam powder-bed-fusion (EB-PBF) [or electron beam melting (EBM)] are the most common techniques to fabricate tungsten materials. The first two utilize laser energy to melt tungsten powder, and the latter electron energy. This review is arranged according to the materials made by the above three AM techniques, each of which has its own unique set of promises, challenges, and opportunities. As processing conditions determine the manufacturing defects, microstructure, and subsequent mechanical properties, Table 1 summarizes some key features and limitations of each AM technique, which help readers to better understand the microstructural origins of each type of materials and subsequent challenges involved in each approach. Notably, L-PBF offers substantially higher cooling rate and stronger temperature gradient compared to other two techniques, and thus may influence the residual stresses and cracking behavior. This review focuses on pure tungsten, as it is arguably one of the most challenging materials for AM. We contend, however, that many challenges and issues encountered in tungsten
-\footnotetext{\begin{itemize}
-  \item Corresponding authors.
-\end{itemize}
-E-mail addresses: \href{mailto:ikaraman@tamu.edu}{ikaraman@tamu.edu} (I. Karaman), \href{mailto:kirkamm@ornl.gov}{kirkamm@ornl.gov} (M.M. Kirka), \href{mailto:ymwang@ucla.edu}{ymwang@ucla.edu} (Y.M. Wang).
-1 These authors contributed equally to this work.
-}
-Table 1
-A summary of some key processing features [7] of three commonly used AM techniques for tungsten and tungsten alloys; i.e., laser powder-bed-fusion (L-PBF), laser directed-energy-deposition (L-DED), and electron beam powder-bed-fusion (EB-PBF).
-\begin{center}
-\begin{tabular}{llll}
-\hline
- & L-PBF & L-DED & EB-PBF \\
-\hline
-Source power $(\mathrm{W})$ & $10^{2}-10^{3}$ & $10^{2}-10^{4}$ & $10^{2}-10^{3}$ \\
-Beam size $(\mu \mathrm{m})$ & $30-200$ & $10^{2}-10^{3}$ & $10^{2}-10^{3}$ \\
-Scanning speed $(\mathrm{mm} / \mathrm{s})$ & $10^{1}-10^{3}$ & $10-10^{2}$ & $10^{1}-10^{3}$ \\
-Cooling rate $(\mathrm{K} / \mathrm{s})$ & $10^{5}-10^{7}$ & $10^{2}-10^{5}$ & $10^{3}-10^{4}$ \\
-Temperature gradient (K/ & $10^{6}-10^{7}$ & $10^{4}-10^{6}$ & - \\
-$\quad$ m) &  &  &  \\
-Environment & Argon, & Argon & Vacuum, trace \\
- & nitrogen &  & helium \\
-Material waste & High & Minimal & High \\
-Pre-sintering & No & No & Yes \\
-Spattering & Yes & No & No \\
-\hline
-\end{tabular}
-\end{center}
-manufacturing are likely applicable to a general class of refractory metals including high entropy alloys [6], which are prone to cracking during manufacturing. The review ends with our recommendations on the future opportunities for AM refractory metals, in the hope to spur future research in these interesting materials.
-\section*{2. Laser powder-bed-fusion}
-\subsection*{2.1. Method}
-L-PBF is a well-known additive manufacturing technique for metals and alloys and sometimes ceramics. During this process, the powder is deposited layer-by-layer ( $\sim 20-150 \mu \mathrm{m}$ thick), and a laser beam (either continuous or pulsed wave) is applied to selectively melt the desired region. Some critical parameters that influence the build quality of materials include build layer thickness, laser power, scan speed, and hatch spacing. These parameters influence the volumetric energy density of processing conditions. Laser absorptivity is another important variable that determines the percentage of laser energy coupled into the powder layer. Notably, L-PBF is typically performed in an argon environment with oxygen levels ranging from tens to hundreds of ppm. Compared to L-DED and EB-PBF, the beam size of L-PBF is appreciably smaller, leading to a higher cooling rate and stronger temperature gradient, Table 1. Powder spattering and denudation phenomenon are common features of L-PBF processes, which cause processing defects/ pores that are difficult to eliminate $[8,9]$.
-\subsection*{2.2. Cracking}
-The ability of powerful lasers to melt essentially any types of metals makes L-PBF a natural choice to fabricate tungsten. However, cracking has been the biggest challenge in L-PBF W. None of the available literature has reported crack-free samples except when a femtosecond laser source was used [10]. As such, understanding the cracking mechanisms during L-PBF processes has been a central focus of recent studies. Generally speaking, two types of cracks have been observed in L-PBF W: longitudinal (with the crack direction parallel to the laser scanning direction) and branched or transverse cracks (with the crack inclined to the laser scan direction) [11-16].
-The crack nucleation and propagation in L-PBF W are considered to be associated with the high ductile-to-brittle transition temperature (DBTT) $\left(\sim 200-400^{\circ} \mathrm{C}\right)$ of tungsten. The direct evidence supporting the above proposition is the appreciable time delay between the
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-02(4)}
-\end{center}
-(c) Frame $150, \mathrm{t}=3.00 \mathrm{~ms}$
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-02(3)}
-\end{center}
-Frame $329, \mathrm{t}=6.58 \mathrm{~ms}$
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-02(1)}
-\end{center}
-Frame $459, \mathrm{t}=9.18 \mathrm{~ms}$
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-02(2)}
-\end{center}
-Frame $638, \mathrm{t}=12.76 \mathrm{~ms}$
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-02}
-\end{center}
-Fig. 1. Scanning electron micrographs showing cracking behavior of tungsten bare plate during single-track experiments. (a) The laser power was set at $\mathrm{P}=300 \mathrm{~W}$ and speed $v=300 \mathrm{~mm} / \mathrm{s}$. Melt pool is marked with a dashed line. A branched crack is shown by the black arrow. (b) $\mathrm{P}=450 \mathrm{~W}$ and $\mathrm{v}=100 \mathrm{~mm} / \mathrm{s}$. The melt pool is well defined by the grains. Branched cracks are observed [12]. (c) Images taken from in-situ high speed camera experiments with $\mathrm{P}=300 \mathrm{~W}$ and $\mathrm{v}=100 \mathrm{~mm} / \mathrm{s}$. Cracks are highlighted inside red rectangles. The amount of time elapsed is shown in each image [15].\\
-solidification and the appearance of cracks, as recorded by an in-situ high speed camera during single track experiments, Fig. 1 [12,15]. Another important observation is that cracks tend to propagate along high angle grain boundaries (HAGBs) [11-16], examples of which are shown in Fig. 2 [11]. This behavior can be attributed to the sensitivity of grain boundaries (GBs) in tungsten to impurities. Oxygen is a known impurity in tungsten powder and has been reported ranging from 30 to $370 \mathrm{ppm}[12,17]$. Several groups attributed the formation of cracks to aggregation of tungsten oxides during solidification [11,14,18,19]. However, cracks are not fully eliminated even when the oxygen level is very low [12], suggesting that impurities might not be the only factor influencing the cracking behavior. A systematic study of oxygen or other impurities such as hydrogen effects on the brittleness of L-PBF W remains missing. Tungsten powder size, shape, and distribution have also been reported to influence the cracking behavior of L-PBF materials [20]. However, a systematic study is needed in order to fully clarify this phenomenon.
-To further understand the role played by residual stresses in cracking of L-PBF W, electron backscatter diffraction (EBSD) studies have been performed on cross-sections of printed tungsten samples [13, 16, 17, 19, 21-25]. A correlation between the density of HAGBs and cracks was observed. Although HAGBs are more prone to cracking than low-angle GBs (LAGBs), the formed cracks help to relieve intergranular stresses [13,19,23,24]. As shown in Fig. 3 [19], most cracks are observed along HAGBs, and perhaps even more importantly, the regions right next to the cracks have lower Kernel Average Misorientation (KAM) values compared to regions in which cracks are absent - evidence that most of the plastic deformation experienced by the material is concentrated near HAGBs [19]. Similar observations were made by another group, Fig. 4 [24], where cracks tend to appear near HAGBs (instead of LAGBs).
-\subsection*{2.3. Strategies to mitigate cracks}
-\subsection*{2.3.1. Alloying}
-To suppress cracks in L-PBF W, incorporation of rare earth or other elements into pure tungsten has been explored. Researchers mixed pure tungsten powder with $1 \mathrm{wt} \%, 5 \mathrm{wt} \%$, and $10 \mathrm{wt} \%$ of Ta powder [23]. As shown in Fig. 5 [23], addition of $5 \mathrm{wt} \%$ Ta significantly decreased the grain size. However, no further grain refinement was observed with $10 \mathrm{wt} \% \mathrm{Ta}$. The refinement of grain size appears to reduce the cracks. The same approach was reported by another group [26,27], where alloying with Ta was found to reduce the average crack length per unit area by $30.7 \%$. One possible reason is that Ta has higher electron affinity to oxygen than $\mathrm{W}$ (the formation Gibbs free energy of $\mathrm{Ta}_{2} \mathrm{O}_{5}$ is $-1904 \mathrm{~kJ} / \mathrm{mol} \mathrm{vs}-761.5 \mathrm{~kJ} / \mathrm{mol}$ for $\mathrm{WO}_{3}$ ). Thus, Ta has the tendency of attracting oxygen and mitigating the impurity segregation along GBs. In a similar approach, $5 \mathrm{wt} \%$ of $\mathrm{Nb}$ was added to tungsten powder during L-PBF (the formation Gibbs free energies of $\mathrm{Nb}_{2} \mathrm{O}_{5}, \mathrm{NbO}_{2}$, and $\mathrm{NbO}$ are $-921 \mathrm{~kJ} / \mathrm{mol},-771 \mathrm{~kJ} / \mathrm{mol},-416 \mathrm{~kJ} / \mathrm{mol}$, respectively), and it was also found effective in suppressing cracks [24]. Although these alloying approaches achieved a certain degree of success, the underlying mechanisms have been poorly understood and require further investigations.
-In a different study, $0.5 \mathrm{wt} \%$ of $\mathrm{ZrC}$ was added to tungsten. Grain refinement was observed and a reduction of crack density as high as $88.7 \%$ was achieved [25]. The beneficial effect of yttrium oxides $\left(\mathrm{Y}_{2} \mathrm{O}_{3}\right)$ has also been studied. In this case, no significant change of average grain size was noticed, crack reduction was still observed and attributed to tungsten grain shape changes [19]. A comparison between micro- and nano-sized $\mathrm{Y}_{2} \mathrm{O}_{3}$ was also carried out. The addition of nano- $\mathrm{Y}_{2} \mathrm{O}_{3}$ was found to reduce cracks due to the formation of a large fraction of LAGBs, whereas a reduction in hardness was seen with the addition of micro-sized $\mathrm{Y}_{2} \mathrm{O}_{3}$ [19]. In contrast, a separate single track experiment [28] found the addition of $\mathrm{Al}_{2} \mathrm{O}_{3}, \mathrm{Y}_{2} \mathrm{O}_{3}$, and $\mathrm{ZrO}_{2}$ to have no influence on suppressing cracks. The above results suggest that there is no consensus in the scientific community in terms of the choice of alloying element and other additives.
-\subsection*{2.3.2. Remelting, scanning strategies, and substrate heating}
-Other reported strategies to suppress cracks in L-PBF W include\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_b812db9e8fc840c3b338g-03}
-Fig. 2. Electron backscatter diffraction (EBSD) images of two sides of a L-PBF W sample showing surface cracks. (a, c) As-printed W cross sections on different axes. Longitudinal, branched, and parallel build direction (BD) cracks are visible (red and blue arrows). (b, d) EBSD inverse pole figure (IPF) maps of (a, c). Scan tracks and scanning directions (SD) are visible, and 'ladder-shaped' grains and cracks along the grain boundaries are seen. The effect of rotation by 67 plus remelting between each layer is shown [11].\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_b812db9e8fc840c3b338g-04}
-Fig. 3. Scanning electron micrographs (SEM), electron backscatter diffraction (EBSD), and Kernel average misorientation (KAM) data from the surface of a L-PBF W sample. Cracks are observed along high angle grain boundaries in L-PBF W. (a) SEM image of the L-PBF W sample. (b) EBSD inverse pole figure (IPF) map. (c) Image quality map. (d) KAM map [19].
-scanning strategy adjustment, remelting, and substrate heating. These processes aim to alleviate or minimize the residual stresses formed in tungsten during printing, which are due to the high temperature gradients near the melt pool. Remelting plus rotating strategy has been studied in a series of tungsten builds [11]. It was found that rotating 67 between each layer randomized the grain orientation and shape, thus reducing the so-called "ladder-shaped" structure formed by grains without rotation (see Fig. 2). This process hindered the formation of cracks since the ladder-shaped grains provide crack-formation sites. While only one example is given, almost all works in the literature adopted the scan vector rotation strategy in between build layers most used 67 so as to minimize scan alignment in the same orientation, while others opted for either $45^{\circ}$ or $90^{\circ}[23,29]$. Remelting refers to the process of scanning a track more than once before recoating the sample with fresh powder. In conjunction with rotation strategies, remelting eliminated the columnar grains and helped to suppress longitudinal cracks [11]. As a result, the remelt sample was found to have smaller grain sizes and the average surface roughness was reduced [30]. Nonetheless, the combination of scan rotation and remelting was not sufficient to fully suppress cracks [11,30,31]. In addition, it was suggested that remelting may impact the density of the sample compared to a non-remelted reference [30]. This phenomenon is not well understood.
-Substrate heating (up to $1000{ }^{\circ} \mathrm{C}$ ) is another strategy to suppress cracks in L-PBF W [29]. The purpose of substrate heating is two-fold: to reduce the temperature gradient (and thus residual stresses during L-PBF) and to bypass the DBTT of tungsten. Given that the DBTT is above room temperature $\left(200-400^{\circ} \mathrm{C}\right)$, embrittlement is likely to occur during solidification and cooling $[12,31,32]$. Theoretically, if the substrate is preheated above the DBTT, the screw dislocations in tungsten will have enough mobility and accommodate the plastic strain induced by the temperature gradient during melting and subsequent cooling [29]. Another important aspect is that maintaining an impurity-free environment during printing is crucial, as the DBTT of tungsten can be theoretically shifted by $200{ }^{\circ} \mathrm{C}$ between $10 \mathrm{ppm}$ and $50 \mathrm{ppm}$ of oxygen content [12]. Despite tremendous effort [29], substrate heating between 80 and $1000^{\circ} \mathrm{C}$ has not been enough to fully eliminate cracking. A detailed study of how to optimize the preheating conditions (e.g., temperature and cooling rate) is needed in the future in order to fully understand their influences on cracking behavior.\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_b812db9e8fc840c3b338g-05(1)}
-Fig. 4. Electron microscopy was used to characterize surface cracks in Nb-alloyed W. (a) Scanning electron microscope (SEM) image of W-5 wt\% Nb alloy. Cracks are present and pointed by arrows. (b) Electron backscatter diffraction (EBSD) inverse pole figure (IPF) map of image (a), cracks are again indicated with arrows. (c) Inverse pole figure (IPF) grain boundary (GB) distribution map. Red lines represent high angle GBs. Cracks appear only on red lines. (d) GB distribution plot. Those images are adopted from [24].\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_b812db9e8fc840c3b338g-05}
-Fig. 5. Electron backscatter diffraction (EBSD) images of three Ta-alloyed L-PBF W samples. From left to right, normal direction inverse pole figure (IPF) maps of cross-sections from pure W, W-5 wt\%Ta, and W-10 wt\% are shown. Grains become more refined between (a) and (b), while a smaller change is noticed in (c) [23].
-\subsection*{2.4. Processing parameter windows}
-Aside from cracks, achieving a high relative density is crucial in LPBF W. As summarized in Table $2[7,9,10,12-19,22-26,27]$, the relative density of tungsten obtained in the literature ranges from $\sim 80 \%$ to $\sim 99 \%$ [14]. To obtain good processing parameters for high density samples, laser power versus scan speed graphs have been used $[21,32$, 33]. In such a graph, different processing zones are marked according to a combination of laser power and speed, such as irregular crack region, regular crack region, balling region, warped region, and dense region $[21,32,33]$. Similar graphs have also been adopted to study cracking behavior in single-track experiments [12,32,33]. However, it has been demonstrated in the literature that such graphs are only useful for a specific type of L-PBF machine and with a fixed build layer thickness. An energy input diagram or normalized enthalpy diagram would be more useful to identify processing windows for tungsten and offer better
-Table 2
-A summary of laser processing parameters for L-PBF W and resultant mechanical properties in the literature.
-\begin{center}
-\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}
-\hline
-Ref. & Machine & \begin{tabular}{l}
-Laser \\
-Power \\
-(W) \\
-\end{tabular} & \begin{tabular}{l}
-Energy \\
-Density $^{1}$ \\
-$\left(\mathrm{~J} / \mathbf{m m}^{3}\right)$ \\
-\end{tabular} & \begin{tabular}{l}
-Beam/ \\
-Hatch \\
-$(\mu m)$ \\
-\end{tabular} & \begin{tabular}{l}
-Layer \\
-Thick. \\
-$(\mu m)$ \\
-\end{tabular} & \begin{tabular}{l}
-Max Density \\
-$(\%)$ \\
-\end{tabular} & \begin{tabular}{l}
-Hardness $^{4}$ \\
-$(\mathrm{GPa})$ \\
-\end{tabular} & \begin{tabular}{l}
-Preheating \\
-$\left({ }^{\circ} \mathrm{C}\right)$ \\
-\end{tabular} & \begin{tabular}{l}
-Powder \\
-Size $(\mu m)$ \\
-\end{tabular} & Alloying & Cracking \\
-\hline
-[31] & \begin{tabular}{l}
-Renishaw \\
-AM250 \\
-\end{tabular} & \begin{tabular}{l}
-200 \\
-(pulsed) \\
-\end{tabular} & - & $75 / 90$ & - & 82.90 & - & No & 19.4 & No & Yes \\
-\hline
-[23] & \begin{tabular}{l}
-Custom \\
-Built, DMP \\
-320 \\
-\end{tabular} & 300 & $150-900$ & 90 & - & $\sim 81-98.7$ & - & $0-400$ & - & \begin{tabular}{l}
-No and \\
-Yes (Ta) \\
-\end{tabular} & \begin{tabular}{l}
-Yes. Cracks are less \\
-evident with alloying. \\
-Both transverse and \\
-longitudinal cracks are \\
-observed. \\
-\end{tabular} \\
-\hline
-$[21]$ & \begin{tabular}{l}
-Renishaw \\
-AM400 \\
-\end{tabular} & \begin{tabular}{l}
-$150-400$ \\
-(pulsed) \\
-\end{tabular} & $88-1185$ & \begin{tabular}{l}
-$75 /$ \\
-$75-150$ \\
-\end{tabular} & 30 & $\sim 80-96$ & $\sim 2-3.79$ & No & 28 & No & Yes \\
-\hline
-$[11]$ & \begin{tabular}{l}
-Renishaw \\
-AM400 \\
-\end{tabular} & \begin{tabular}{l}
-400 \\
-(pulsed) \\
-\end{tabular} & 474 & $75 / 100$ & 30 & $92.5-96.5$ & - & No & 28 & No & \begin{tabular}{l}
-Yes, cracks are longer \\
-than $1 \mathrm{~mm}$ (along \\
-HAGBs). \\
-Transverse and \\
-longitudinal cracks are \\
-observed. \\
-\end{tabular} \\
-\hline
-[13] & \begin{tabular}{l}
-Renishaw \\
-125 \\
-\end{tabular} & \begin{tabular}{l}
-200 \\
-(pulsed) \\
-\end{tabular} & $641-930$ & \begin{tabular}{l}
-$43 /$ \\
-$115-155$ \\
-\end{tabular} & 50 & $94-98$ & - & No & $\sim 47$ & No & Yes \\
-\hline
-[19] & \begin{tabular}{l}
-Renishaw \\
-AM400 \\
-\end{tabular} & \begin{tabular}{l}
-250 \\
-(pulsed) \\
-\end{tabular} & 544-1587 & \begin{tabular}{l}
-$70 /$ \\
-$50-100$ \\
-\end{tabular} & $20-35$ & $94.5-98.30$ & $\sim 3.63-4.21$ & 180 & \begin{tabular}{l}
-$15-45 \mathrm{~W}$ \\
-$15-53$ \\
-$\mathrm{Y}_{2} \mathrm{O}_{3}$ \\
-\end{tabular} & \begin{tabular}{l}
-No and \\
-Yes \\
-$\left(\mathrm{Y}_{2} \mathrm{O}_{3}\right)$ \\
-\end{tabular} & \begin{tabular}{l}
-Yes, hundreds of \\
-microns and in all \\
-directions. \\
-Oxides reduce \\
-cracking. \\
-\end{tabular} \\
-\hline
-$[30]$ & EOS M290 & $150-350$ & $\sim 94-875$ & 100 & 20 & 98.40 & $\sim 4.02-4.47$ & 180 & 15.8 & No & \begin{tabular}{l}
-Yes, fewer cracks in \\
-the bulk. \\
-Remelting improves \\
-cracking. \\
-\end{tabular} \\
-\hline
-[17] & EOS M290 & $200-370$ & $250-1850$ & 50 & 20 & $97.72-98.50$ & $\sim 4.36-4.58$ & 50 & 16.24 & No & Yes \\
-\hline
-$[22]$ & \begin{tabular}{l}
-SLM® \\
-Solution \\
-$125 \mathrm{HL}$ \\
-\end{tabular} & $200-400$ & 198-905 & 70/105 & 30 & 98.51 & - & 200 & $5-25$ & No & Yes \\
-\hline
-[14] & \begin{tabular}{l}
-EOSM100 \\
-DMLS \\
-\end{tabular} & $100-170$ & 125-1062 & \begin{tabular}{l}
-$40 /$ \\
-$40-70$ \\
-\end{tabular} & 20 & 99.61 & $\sim 4.12$ & 80 & $10-25$ & No & \begin{tabular}{l}
-Yes. Longitudinal: \\
-straight, $30-100 \mu \mathrm{m}$. \\
-Transverse: shorter \\
-and S shaped along \\
-GBs. \\
-\end{tabular} \\
-\hline
-[18] & \begin{tabular}{l}
-Custom \\
-Built \\
-\end{tabular} & $200-350$ & $500-1167$ & 50 & 20 & $87.8-89.4$ & $\sim 4.65$ & 200 & 14.41 & No & Yes \\
-\hline
-$[24]$ & EOS M280 & $250-370$ & - & $70-110$ & 30 & $93.3-98.0$ & $6.69-10.31$ & 200 & \begin{tabular}{l}
-$5-25 \mathrm{~W}$ \\
-$1-10 \mathrm{Nb}$ \\
-\end{tabular} & Yes, Nb & \begin{tabular}{l}
-Yes, along HAGBs. Nb \\
-alloying partially \\
-suppresses \\
-cracks. \\
-\end{tabular} \\
-\hline
-[29] & \begin{tabular}{l}
-Aconity 3D \\
-GmbH \\
-\end{tabular} & $375-400$ & $196-446$ & $100 / 80$ & 40 & $\sim 94.7-98.5$ & - & $600-1000$ & $15-45$ & No & \begin{tabular}{l}
-Yes (reduced at \\
-$1000^{\circ} \mathrm{C}$ ). \\
-\end{tabular} \\
-\hline
-$[26]$ & SLM 280 & 400 & - & 100 & - & - & - & - & \begin{tabular}{l}
-$32 \mathrm{~W}$, \\
-$18 \mathrm{Ta}$ \\
-\end{tabular} & Yes, Ta & \begin{tabular}{l}
-Crack density reduced \\
-by alloying. \\
-\end{tabular} \\
-\hline
-$[27]$ & \begin{tabular}{l}
-Renishaw \\
-AM400 \\
-\end{tabular} & \begin{tabular}{l}
-400 \\
-(pulsed) \\
-\end{tabular} & - & 100 & - & - & - & - & - & Yes, Ta & \begin{tabular}{l}
-Yes, less with Ta \\
-(along GBs). \\
-\end{tabular} \\
-\hline
-$[16]$ & SLM 125HL & 400 & 238-1667 & \begin{tabular}{l}
-$80 /$ \\
-$100-120$ \\
-\end{tabular} & 30 & $\sim 90-97$ & - & $\mathrm{HIP}^{3}$ & 32 & No & Yes, reduced with HIP. \\
-\hline
-\end{tabular}
-\end{center}
-${ }^{1}$ Energy Density $=\frac{P}{l \times v \times D_{\text {beam }}}$, where $\mathrm{P}$ is power, 1 is layer thickness, $\mathrm{D}$ is beam diameter and $\mathrm{v}$ is laser speed. Speed is calculated using point distance and exposure time for pseudo-pulsed laser machines.
-2 These values are not calculated according to the equation in note 1 but are reported as found in the respective papers.
-${ }^{3}$ HIP: Hot Isotactic Pressing. Note that HIP is not preheating. ${ }^{4}$ A compressive strength in the range of $900-1523$ MPa has been reported for L-PBF W [17,18,22,30,32].
-machine-to-machine variation comparison [34-38]. Regretfully, such laser processing maps for pure tungsten do not exist yet.
-\subsection*{2.5. Mechanical properties}
-Due to the poor sample quality, few studies have been conducted on documenting the mechanical properties of L-PBF W. The available data are limited to hardness and compressive mechanical properties, Table 2. Depending on the processing parameters, a hardness value of 3.63-4.47 GPa [14, 17-19, 30, 32] was reported for L-PBF W, which was superior to samples made by conventional powder metallurgy and spark plasma sintering (the hardness values range between 3.14-3.92 GPa; i.e., $320-400 \mathrm{HV}$ [17]). Alloying with $5 \mathrm{wt} \% \mathrm{Nb}$ was found to elevate the hardness from $6.69 \mathrm{GPa}$ to $8.01 \mathrm{GPa}$ [24]. Similarly, the addition of nano-yttrium oxides increased the hardness to $\sim 4.51 \mathrm{GPa}(\sim 460 \mathrm{HV})$. The effect was attributed to dispersion strengthening. In the same study, it was also shown that introducing micro-yttrium oxides (instead of nano-sized oxides) resulted in lower hardness than that of conventionally manufactured tungsten. The reduction in hardness was rationalized by the agglomeration of micro-sized yttrium oxides, which weakened the material [19]. In terms of compressive properties, a wide range of compressive strength (900-1523 MPa) was reported [17,18,30,32,33], whereas no strength/ductility data were found in tension. With the ubiquitous existence of cracks, it is not surprising to see rather poor mechanical property data on L-PBF W.
-\section*{3. Laser directed-energy-deposition}
-\subsection*{3.1. Method}
-L-DED is an AM technique in which metal powder is fed into a melt pool created by a laser. After the first layer is deposited the powder feeder moves upward and deposition of the second layer begins. L-DED is usually conducted under an argon atmosphere that utilizes an argon blower. L-DED is suitable for the manufacture of large parts relatively quickly and offers excellent design freedom due to the additional parameters involved in the process. Some unique features of L-DED are powder feed rate and the option to change input powder composition using multiple hoppers to manufacture composite materials or grade composition throughout AM parts. L-DED can also be used to repair parts due to its ability to accurately deposit material anywhere in the build chamber. These features allow L-DED to process functionally graded structures, which can mitigate the challenges associated with joining dissimilar materials such as $\mathrm{W}$ and ferritic-martensitic steels. Fig. 6 displays a schematic of the L-DED process [39] showing the laser power source, powder feeder, and build platform.
-In this section, we will assess the current state-of-the-art in L-DED W and tungsten alloys and the effects of L-DED processing on their structure and properties. To understand these processes and how to successfully implement them, it is critical to recognize the processing challenges and defects associated with L-DED of tungsten and its alloys, and possible mitigation strategies.
-\subsection*{3.2. L-DED tungsten and tungsten alloys}
-\subsection*{3.2.1. Deposition of pure tungsten}
-Several studies have demonstrated that tungsten can be printed with moderate success utilizing L-DED. However, these studies also reported difficulties in fully melting tungsten powder during deposition. Polygonal tungsten powder was printed on a reduced activation ferritic/ martensitic (RAFM) steel substrate in [40]. Single tracks were printed using the processing parameter combinations in the range of $\mathrm{P}=2000-$ $4000 \mathrm{~W}$ and $\mathrm{v}=200-600 \mathrm{~mm} / \mathrm{min}$ at a constant powder feed rate $(\dot{\mathrm{m}}=$ $29.3 \mathrm{~g} / \mathrm{min}$ ). Significant compositional mixing was observed between the steel substrate and powder, with tungsten content ranging from 12 to $55 \mathrm{wt} \%$ at various locations within the melt pools. Fig. 7 [40] displays single track melt pool cross sections at various parameter sets. Unmelted tungsten particles can be observed throughout the melt pools at each of the parameter sets displayed in Fig. 7. These unmelted tungsten particles were also observed in single laser clads of tungsten and tungsten-nickel alloys printed on a mild steel substrate studied in [41]. Mixing between substrate material and the deposited tungsten reportedly increased with laser power, which corresponded to a decrease in overall tungsten content and hardness of the single tracks [40]. This is due to increased laser penetration into the steel substrate, increasing the relative amounts of $\mathrm{Fe}$ and $\mathrm{Cr}$ in the melt pool.
-Microstructural evaluation of multi-layer tungsten prints was also conducted [40]. Intermetallic precipitates were observed in the scanning electron micrograph (SEM) in Fig. 8a and were identified to be $\mathrm{Fe}_{7} \mathrm{~W}_{6}$ from transmission electron microscopy (TEM) analysis (Fig. 8b and c). Energy dispersive spectroscopy (EDS) analysis of the precipitates was consistent with the TEM observations of $\mathrm{Fe}_{7} \mathrm{~W}_{6}$. X-ray diffraction peaks of single- and double-layer prints on the RAFM steel substrate (Fig. 8e) identified the existence of W, $\mathrm{Fe}, \mathrm{Fe}_{7} \mathrm{~W}_{6}$, and $\mathrm{Fe}-\mathrm{Cr}$ phases. In a 9-layer print conducted at $3000 \mathrm{~W}$ and $3000 \mathrm{~mm} / \mathrm{min}$, the authors observed a significant compositional gradient from $25.23 \mathrm{wt} \% \mathrm{Fe}$, $2.73 \mathrm{wt} \% \mathrm{Cr}$, and $72.04 \mathrm{wt} \% \mathrm{~W}$ near the substrate to $3.91 \mathrm{wt} \% \mathrm{Fe}$, $0.28 \mathrm{wt} \% \mathrm{Cr}$, and $95.82 \mathrm{wt} \% \mathrm{~W}$ at the top of the build, as can be seen in Fig. 9 [40]. These observations show that although tungsten content increases with each additional layer, $\mathrm{Fe}$ and $\mathrm{Cr}$ from the substrate continue to diffuse into the upper layers of the matrix after 9 deposited layers of tungsten. SEM analysis of this multi-layer build indicates the existence of unmelted W-rich particles, dendrite structures, and microcracking within the tungsten particles. Overall, this study highlighted the need for designing a compositionally graded transition from steels to tungsten to avoid producing the undesirable intermetallic phases.
-Cracking and porosity were observed within tungsten single tracks, single layers, and multi-layer deposits as can be seen in Fig. 9j \& k [40]. Cracks were speculated to be due to liquation cracking and residual stresses from the rapid heating and cooling cycles. Single layer cracking occurred at the top of the deposit and propagated toward the substrate causing $\mathrm{W}$ particles along the crack path to internally fracture and others to de-bond with the matrix. Spherical porosity also occurred within single layers of deposited tungsten, likely due to gas trapped within the melt pool during solidification. Pores are a typical defect observed in materials manufactured via L-DED and can be mitigated by manipulating process parameters [42]. Multi-layer tungsten deposits contained tungsten particles with a large number of microcracks near the top of the deposits, as can be seen in Fig. 9d \& g [40]. These microcracks did not appear as frequently in the lower layers of the build. This may be due to the higher degree of remelting experienced at the bottom of the sample, relative to the top.
-Many commercially available L-DED machines are not capable of achieving the large laser powers utilized in reference [40]. A study [43] attempted to print $12 \mathrm{~mm}$ high thin-walled vertical tungsten tubes using L-DED using polyhedral $99.7 \%$ purity tungsten powder at lower values of laser power. They printed 35 samples with parameters ranging between $\mathrm{P}=600-1000 \mathrm{~W}, \mathrm{v}=50-350 \mathrm{~mm} / \mathrm{min}, \dot{\mathrm{m}}=5-25 \mathrm{~g} / \mathrm{min}$, and a laser diameter $=750 \mu \mathrm{m}$ to determine optimal parameters for printing the material. With a fixed layer thickness of $100 \mu \mathrm{m}$ and a constant but undisclosed hatch spacing, they reported 7 of the 35 parameter sets reached the targeted build height with the rest of the specimens either
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-07}
-\end{center}
-Fig. 6. A schematic of the directed-energy-deposition process showing the laser source, powder feeder or sprayer, and the build platform [39].
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-08}
-\end{center}
-Fig. 7. Single tracks fabricated at various parameter sets (a-f), displaying different melt pool dimensions as well as varying levels of unmelted W particles [40].
-exceeding or falling short of the target range, as can be seen in Fig. 10 [43]. However, no analysis of microstructural homogeneity or degree of melting the tungsten particles was conducted in the study.
-\subsection*{3.2.2. Deposition of tungsten alloys}
-3.2.2.1. Tungsten-nickel deposition. Due to the various applications of tungsten alloys, many studies attempted to print tungsten alloys. One group successfully printed a $60 \mathrm{~W}-40 \mathrm{Ni}$ collimation component (Fig. 11a) using L-DED with the following parameters [41]: $2000 \mathrm{~W}$ laser power, $300 \mathrm{~mm} / \mathrm{min}$ scan speed, and $8 \mathrm{~g} / \mathrm{min}$ feed rate. Single laser clads of $60 \mathrm{~W}-40 \mathrm{Ni}$ printed on a mild steel substrate were observed to contain unmelted tungsten particles and dendritic structures that were speculated to be $\mathrm{Ni}_{4} \mathrm{~W}$ and $\mathrm{NiW}_{2}$ intermetallic phases.
-Another group similarly observed unmelted tungsten particles in a LDED W-15Ni alloy along with a $\gamma$-Ni phase containing $15 \mathrm{wt} \% \mathrm{~W}$ [44]. They reported a layered microstructure with unmelted tungsten particles dominating regions of the deposit that were only subjected to initial melting, and $\mathrm{W}$ dendrite structures in regions that were subjected to remelting by the subsequent layer (Fig. 11d and e). These W-15Ni specimens had tensile strengths of $\sim 500 \mathrm{MPa}$ and were prone to brittle fracture ( $\sim 3 \%$ strain to fracture) at room temperature.
-3.2.2.2. Tungsten-nickel-iron deposition. Unmelted W-rich particles embedded in an FCC Ni-Fe matrix were observed in L-DED manufactured $90 \mathrm{~W}-7 \mathrm{Ni}-3 \mathrm{Fe}[45,46]$, similar to what was observed in $\mathrm{W}$ and W-Ni deposits. An alternating microstructure with layers dense in unmelted tungsten and partially melted tungsten particles was also observed [45,46], similar to those observations in W-15Ni, Fig. 11 [41, 44]. Tensile testing of $90 \mathrm{~W}-7 \mathrm{Ni}-3 \mathrm{Fe}$ samples resulted in high strength (1037 MPa) and low ductility (3.5\% elongation). These as-printed materials displayed significantly higher ultimate tensile strength (UTS) and lower ductility than those of traditionally manufactured $90 \mathrm{~W}-7 \mathrm{Ni}-3 \mathrm{Fe}$ via liquid phase sintering (LPS), Fig. 12a [45]. Additionally, large periodic variations in microhardness ( $\sim 76 \mathrm{HV}$ ) were observed, Fig. 12b. These variations are attributed to a periodic sublayer change where $\mathrm{W}$-particle dense regions are observed above and below the regions with lower relative amounts of W particles. L-DED materials have an average hardness of $\sim 415 \mathrm{HV}$, higher than specimens made by LPS. This is due to higher amounts of hard W-particles embedded in the matrix in L-DED specimens. Fig. 13 displays fracture surfaces of $90 \mathrm{~W}-7 \mathrm{Ni}-3 \mathrm{Fe}$ where large pores were observed, indicating that the porosity acts as fracture initiation sites [45]. Lower ductility during tensile testing in the as-deposited specimens compared to traditional LPS is attributed to the residual porosity observed at these fracture surfaces. Tungsten particle cleavage and tearing of the ductile Ni-Fe matrix were also observed at the fracture surfaces.
-\subsection*{3.3. Challenges in L-DED tungsten}
-Common challenges associated with L-DED $\mathrm{W}$ on ReducedActivation-Ferritic-Martensitic (RAFM) steels are illustrated in Fig. 14. There are many critical parameters that affect melt pool morphology during L-DED, including laser power (P), scan speed (v), hatch spacing (h), laser focus (f), substrate temperature, powder size distribution and morphology, and powder feed rate ( $\dot{m}$ ). These variables are critical in
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-09(1)}
-\end{center}
-(e)
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-09}
-\end{center}
-Fig. 8. Phase analysis of pure W printed on a RAFM steel substrate using (a) scanning electron microscopy (SEM), (b, c) transmission electron microscopy (TEM), (d) energy dispersive spectroscopy (EDS), and (e) x-ray diffraction (XRD) [40].
-achieving successful prints in L-DED. Only a limited number of these variables have been explored in L-DED W and tungsten alloys. Challenges such as attaining targeted build heights and mitigating porosity can be resolved by optimizing parameters such as $\mathrm{P}, \mathrm{v}, \mathrm{h}$, and $\dot{\mathrm{m}}$ as well as improving feedstock quality [42, 47-49]. Additionally, residual stress-induced cracking has been shown to be mitigated by substrate preheating [50-53] which, to our knowledge, has not been attempted on L-DED W. Substrate preheating may also result in increased melting of tungsten particles that would remain unmelted if printed on a room temperature substrate. Mitigation of intermetallic particle formation may be achieved by introducing filler alloys between the steel base plate and tungsten, circumventing regions in the alloys' phase diagrams in which detrimental phases are stable. These strategies may improve the feasibility of additively manufacturing tungsten via directed energy deposition.
-\section*{4. Electron beam melting}
-\subsection*{4.1. Method}
-The EBM or EB-PBF process belongs to the powder bed family of additive manufacturing technologies. Similar to L-PBF, the heat source is selectively moved across the powder bed to melt the regions of interest in a layer-by-layer process. Electron beams, compared to lasers, are high in energy density exceeding several kilowatts focused into spot sizes of several hundred microns in diameter when melting. EB-PBF occurs under controlled vacuum conditions to both maintain the quality of the electron beam spot size and offset fluctuation in pressure associated with
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-10}
-\end{center}
-Fig. 9. Scanning electron microscope (SEM) and energy dispersive spectroscopy (EDS) analysis of a 9-layer W sample printed at $3000 \mathrm{~W}$ and $3000 \mathrm{~mm} / \mathrm{min}$. (a, b) Low magnification cross-sectional SEM images of the specimen, indicating where EDS analysis was conducted. (c) The results of EDS analysis conducted on the areas displayed in (b). (d-f) Higher magnification images of the top, middle, and bottom of the specimen, respectively. (g-i) High magnification images displaying W particles, dendrite structures, and microcracks [40]. (j, k) Low and high magnification images displaying cracks and porosity in W deposited on RAFM steel [40].
-vaporization of the metal in the liquid state as the beam is melting. Additionally, in EB-PBF the powder bed is heated to elevated temperatures through defocusing the electron beam and rapidly rastering it across the powder bed surface to allow for the powder particles to loosely sinter to one another and conduct the negative charge of the electron beam away. If the negative electrical charge of the imparted electrons is not conducted away, the powder bed will build-up a negative charge which results in the repulsion of the powder particles from one another, i.e., a "smoking" event. In the instance of tungsten, the powder bed is heated to between 1000 and $1400{ }^{\circ} \mathrm{C}$ [54]. As a result of heating the powder bed, materials processed through EB-PBF often have lower levels of residual stress than corresponding materials processed through L-PBF [54]. One of the advantages of the EB-PBF process over that of L-PBF is the ability to rapidly manipulate the electron beam heat source over the entirety of the build area to locally control thermal conditions of the material. This has been shown as beneficial for controlling the microstructure [55] as well as stress states of the material to suppress defects such as cracks in non-weldable materials [56].\\
-(a)
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-11(2)}
-\end{center}
-$10 \mathrm{~mm}$
-(b)
-\section*{Proper build domain}
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-11(1)}
-\end{center}
-$10 \mathrm{~mm}$\\
-Over build domain
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-11}
-\end{center}
-$10 \mathrm{~mm}$
-(c)\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_b812db9e8fc840c3b338g-11(3)}
-Fig. 10. Tungsten specimen fabricated at various parameter sets displaying heights that are either below, matching, or exceeding the targeted build height [43]. (a) Images of specimens that are under built, over built, or matching the targeted height. (b) The measured height increment for each layer in samples printed at different speeds plotted against laser power. (c) Cubes printed at various parameters in the under build, over build, or target printing regimes.
-\subsection*{4.2. Porosity}
-Various levels of success in the processing of tungsten through EBM (EBM W) have been reported. Key to the processing of tungsten is the ability to obtain materials that approach the theoretical density of pure tungsten at $19.3 \mathrm{~g} / \mathrm{cc}$. In literature, four states for EBM $W$ based on density and porosity of the material have been identified, as depicted in Fig. 15 [57].
-In the figure, volumetric energy densities ranging from 208 to $3840 \mathrm{~J} / \mathrm{mm}^{3}$ with a substrate temperature of approximately $850{ }^{\circ} \mathrm{C}$ were used. These states are (a) limited fusion, (b) insufficient fusion, (c) proper fusion, and (d) excessive fusion. Limited fusion is characterized by resultant relative densities of $<70 \%$ with excessive balling of the tungsten observed within the melt layers. Insufficient fusion exhibits relative densities between $70 \%$ and $90 \%$, however, significant interconnected porosity exists within the material including chimney porosity [58]. Proper fusion is the optimal processing state where densities greater than $90 \%$ are achievable and interconnected porosity is mitigated through full melting and wetting of the tungsten. The last state, excessive fusion, can be defined as fully dense material that exhibits swelling due to too much energy being imparted into the material. Similar trends were also identified in work that varied the linear energy used to melt tungsten from 333 to $5000 \mathrm{~J} / \mathrm{m}$ with a powder bed temperature of $1000{ }^{\circ} \mathrm{C}$ [59].
-Various levels of porosity have been reported in the literature, with many studies achieving success for high density tungsten. Densities as high as $\mathbf{9 9 . 5 \%}$ have been measured; nevertheless, microcracking was found $[57,59]$. SLM and EBM W have also been compared and it was found that comparable densities could be obtained using either technique, although the build temperature greatly influenced the porosity level and defect levels [60]. Lastly, nondestructive techniques such as in-situ near-infrared (IR) defect detection have been used to report defect-free, highly dense samples (>99\%) [61,62].
-\subsection*{4.3. Cracking}
-The occurrence of cracking in EBM $\mathrm{W}$ is a problem akin to that observed in SLM processed tungsten with the debate ongoing for the specific mechanism(s) by which tungsten cracks during processing. It has been suggested that cracks occur in the solid state as a result of significant inelastic deformation along grains neighboring GBs [61]. This was supported through electron backscatter diffraction (EBSD) analysis of the areas surrounding cracks that revealed localized orientation gradients near the edges of cracks. Representative EBSD micrographs showing the cracking in tungsten are shown in Fig. 16 [61]. This is consistent with other studies that observed the cracking phenomena through high-speed in-situ videos of the SLM process with a heated powder bed temperature range above and below the DBTT range of tungsten. This was attributed to the development of significant von Mises stresses when the tungsten cycled below DBTT [12]. It was theorized that thermal stress generated from thermal gradients during SLM processing of tungsten can only be compensated by crack formation along low-strength GBs, particularly those with impurities [19,63].
-From the reported studies, the influence of the build substrate temperature and the overall build temperature has a clear influence on the cracking in AM W. A report [29] utilized a SLM system with substrate preheating and showed that increasing build temperature from $200{ }^{\circ} \mathrm{C}$ to $1000^{\circ} \mathrm{C}$ significantly reduced cracking in AM tungsten, though it did\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_b812db9e8fc840c3b338g-12(2)}
-Fig. 11. Laser directed-energy-deposition (LDED) of W-Ni alloys. (a) W60-Ni40 collimation component printed at $2000 \mathrm{~W}$ laser power, $300 \mathrm{~mm} / \mathrm{min}$ scan speed, and $8 \mathrm{~g} / \mathrm{min}$ feed rate [41]. (b, c) Low and high magnification SEM micrographs showing the microstructure of a single laser clad of W60-Ni40 printed on a mild steel substrate [41]. (d) Scanning electron micrographs of a W-15Ni L-DED part showing a layered microstructure containing unmelted $\mathrm{W}$ particles in regions subjected to initial laser melting [44], and (e) dendritic W structures in remelted regions of the deposit [44]. (a)
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-12}
-\end{center}
-(b)
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-12(1)}
-\end{center}
-Fig. 12. Mechanical properties of additively manufactured W-Ni-Fe alloys. (a) Engineering stress-strain curves for $90 \mathrm{~W}-7 \mathrm{Ni}-3 \mathrm{Fe}$ specimens manufactured by laser metal deposition (LMD, alternatively directed-energy-deposition) and liquid phase sintering (LPS). (b) Hardness values along the build direction for 90W-7Ni-3Fe specimens manufactured by LMD and LPS [45].
-not eliminate cracking entirely. Multiple studies explored the role of substrate heating: samples have been built with a powder bed temperature of approximately $850{ }^{\circ} \mathrm{C}$, and observed minor levels of cracking [57]. In a comparison between SLM and EBM, significant cracking was found in SLM, with no cracking in EBM. The lack of cracking in EBM W was attributed to a combination of build plate temperature of $1000{ }^{\circ} \mathrm{C}$ and addition of a support structure to raise the tungsten samples off the build plate $[19,60]$. Theoretically, if the substrate is heated above the\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_b812db9e8fc840c3b338g-13(1)}
-Fig. 13. Tensile fracture surfaces of $90 \mathrm{~W}-7 \mathrm{Ni}-3 \mathrm{Fe}$ fabricated via laser directed-energy-deposition (L-DED). Features such as (a) porosity, (b-d) W particle cleavage, and (d) matrix failure are indicated with white arrows [45].
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-13}
-\end{center}
-Fig. 14. Graphical representation of challenges typically encountered during directed energy deposition of tungsten on RAFM steel. These challenges include achieving targeted build heights, cracking and porosity, difficulty of melting W particles, formation of intermetallics and dendrites, and layered melted/remelted structures within the build.
-DBTT of tungsten, dislocations should be significantly more mobile, thus reducing the chance of cracking. Higher substrate temperatures allow for lower temperature gradients during cooling, reducing the stresses generated on the tungsten components. Similarly, by raising the printed components of the build plate by using a support structure, heat is not allowed to dissipate quickly, which in turn reduces the stresses on the components. The use of different metals, such as steel and titanium, as build substrates was also investigated [61]. Titanium build plates have been used due to the high degree of solubility the elements have in one another in an effort to create a metallurgical bond at the interface of part and build plate. Cracking in tungsten was observed to be sensitive to the build preheat temperature. Crack density was drastically lower when build surface temperatures of $1500{ }^{\circ} \mathrm{C}$ were used, compared to $1100{ }^{\circ} \mathrm{C}$.\\
-Additional studies leveraged an ever-higher surface preheat temperature of $1800^{\circ} \mathrm{C}$ to demonstrate the ability to successfully suppress crack formation in EBM W [62]. Mitigation techniques for suppressing cracking in tungsten aside from the processing science include alloying tungsten with elements such as tantalum. However, for nuclear fusion application tungsten-tantalum alloys are generally considered to be problematic due to tantalum's degradation into the undesirable isotopes during nuclear exposure [64].
-\subsection*{4.4. Microstructure}
-Rather distinct to the pure refractory material systems processed through AM such as tungsten, as well as some common BCC or HCP type\\
-(a) Limited fusion
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-14(2)}
-\end{center}
-(b) Insufficient fusion
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-14(1)}
-\end{center}
-(c) Proper fusion
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-14}
-\end{center}
-(d) Excessive fusion
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-14(3)}
-\end{center}
-\includegraphics[max width=\textwidth, center]{2024_04_13_b812db9e8fc840c3b338g-14(4)}\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_b812db9e8fc840c3b338g-14(5)}
-Fig. 15. Observed states of pure tungsten fabricated through EBM using different parameters. (a) Limited fusion, (b) insufficient fusion, (c) proper fusion, and (d) excessive fusion.
-The images are adopted from [57].
-\begin{center}
-\includegraphics[max width=\textwidth]{2024_04_13_b812db9e8fc840c3b338g-15(1)}
-\end{center}
-Fig. 16. Scanning electron microscope (SEM) and electron backscatter diffraction (EBSD) data of boundary cracking in EBM pure tungsten. (a) EBSD showing surrounding texture, and (b) an optical image [61].
-alloys such as Ti-6V-4Al, are the anomalous textures that form as a result of the AM process [65,66]. Shown in Fig. 17 [62] are representative EBSD micrographs depicting this anomalous texture. While many in the literature for EBM of tungsten and other refractory metals have observed the phenomena, its significance in relation to the processing science of the materials has only been briefly mentioned.
-Columnar grain structures aligned parallel to the build direction resulting from epitaxial growth of EBM W are reported in literature. Controlling the $\{001\}$ and $\{111\}$ fibrous texture of pure tungsten via $67^{\circ}$ interlayer rotation is also explored. Similar observations regarding the effect of texture on yield strength anisotropy have also been reported for tantalum $[57,60,61,67]$. The ability to obtain a mixed $\{001\}$ and $\{111\}$ fiber texture with the possibility of material having either strong $\{001\}$ or $\{111\}$ build direction fiber textures was also identified. In a similar study of EBM of molybdenum, the role played by area energy density to melt the material on the texture was also discussed [61,63]. This phenomenon was hypothesized to be associated with sensitivities of the melt pool shape to the electron beam energy density coupled with\\
-\includegraphics[max width=\textwidth, center]{2024_04_13_b812db9e8fc840c3b338g-15}
-Fig. 17. Electron backscatter diffraction (EBSD) images showing mixed $\{001\}$ and $\{111\}$ fibers in pure EBM tungsten. (a) Cross-sectional inverse pole figure (IPF) map, and (b) build direction IPF map [62]. The build direction is vertical for both images.\\
-formation of networks of LAGBs driven by thermal stresses from solidification.
-\subsection*{4.5. Performance of EBM Tungsten}
-Analysis of the performance of EBM $\mathrm{W}$ for thermomechanical behavior is currently limited. The bend strength of an EBM W during three-point bending test was measured to be $340 \mathrm{MPa}$, which is significantly lower than reference wrought tungsten [60]. This has been partially attributed to the porosity of the EBM W samples. The strength of EBM W parallel to the build direction was also evaluated, with fracture being observed to occur along the fibrous GBs via a combination of decohesion and transgranular failure [57,60]. Lastly, the hardness of EBM W as well as its surface deterrence to ITER-like plasma heat load exposures at steady state $\left(10 \mathrm{MW} / \mathrm{m}^{2}\right.$ ) and transient (105 pulses with $0.14 \mathrm{GW} / \mathrm{m} 2$ ) was also investigated [59]. Ultimately, it was found that the EBM W performed similarly to baseline wrought recrystallized tungsten product as surface deterrence to plasma heat load exposures.
-\section*{5. Summary, outlook, and recommendations}
-Although tungsten and tungsten alloys are notoriously difficult to print due to their high melting temperatures, high thermal conductivities, and brittleness, encouraging progress has been made in the last decade to additively manufacture this unique class of materials. Cracking has been and remains to be one of the dominantly challenging issues in the field. Nevertheless, advance has been made to overcome this issue. For example, EBM has shown promises to manufacture crack free samples. Another important issue, which has not been investigated to a large extent, is the pore formation and control mechanisms under keyhole mode processing conditions. In addition to cracks, porosities inevitably influence the mechanical properties of additively manufactured tungsten and tungsten alloys. Up to date, limited mechanical property data are available (especially those related to elevated temperature properties) that are of critical relevance to practical applications. With the rapid progress of additive manufacturing techniques and processing conditions, we expect to witness a rising amount of data in this direction. In addition, meticulous microstructure control and new alloy design strategies are expected in near future for this class of high temperature alloys. We further contend that many issues encountered during refractory metals additive manufacturing are likely applicable to numerous fracture-prone metals such as multi-principal alloys. Strategies are needed to enable us to "print these unprintable" alloys.
-\subsection*{5.1. Recommendations}
-Substrate heating has been proved to be an effective strategy to overcome cracking in the EBM process. Similar approaches have not been demonstrated successfully for L-PBF or L-DED. This could be partially due to the higher oxygen contents in the laser processes. Further studies are needed in this direction to make the laser AM processes feasible to manufacture crack-free W components. Microstructure control such as grain shape manipulation has been reported to be effective in reducing the residual stresses and thus cracks in brittle materials. This approach has not been well studied for tungsten and tungsten alloys yet, or any other refractory alloys. Inoculation via the addition of nanoparticles could be another rewarding strategy to overcome the cracking issue for tungsten. In addition to experimental endeavors, computer modeling of thermal history, microstructure, and resultant residual stresses is likely to further advance this field. The above recommended research directions are likely applicable to all three AM techniques reviewed in this work.
-Revision note: while this paper was under review, a parallel overview paper was published [68].
-\section*{CRediT authorship contribution statement}
-Talignani Alberico: Writing - original draft, Investigation, Conceptualization. Seede Raiyan: Writing - original draft, Investigation, Conceptualization. Whitt Austin: Writing - original draft, Investigation. Zheng Shiqi: Investigation, Conceptualization. Katoh Yutai: Writing - review \& editing, Supervision, Project administration, Investigation, Funding acquisition, Conceptualization. Wang Y. Morris: Writing - review \& editing, Writing - original draft, Supervision, Project administration, Investigation, Funding acquisition, Conceptualization. Kirka Michael M: Writing - review \& editing, Writing - original draft, Supervision, Investigation, Conceptualization. Ye Jianchao: Supervision, Investigation. Karaman Ibrahim: Writing - review \& editing, Supervision, Investigation, Funding acquisition, Conceptualization.
-\section*{Declaration of Competing Interest}
-The 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.
-\section*{Data availability}
-No data was used for the research described in the article.
-\section*{Acknowledgments}
-This research was sponsored by the US Department of Energy, Office of Fusion Energy Sciences and Advanced Research Projects AgencyEnergy (ARPA-E) under contract DE-AC05-00OR22725 with UTBattelle LLC. The work at LLNL was performed under the auspices of the US Department of Energy under contract no. DE-AC52-07NA27344.
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