Numerical and Experimental Investigations of Laser Metal Deposition (LMD) Using STS 316L

: This study aimed to understand the e ﬀ ect of heat accumulation on microstructure formation on STS 316L during multilayer deposition by a laser metal deposition (LMD) process and to predict the microstructure morphology. A comprehensive experimental and numerical study was conducted to quantify the solidiﬁcation parameters (temperature gradient (G) and growth rate (R)) in the LMD multilayer deposition process. During deposition, the temperature proﬁle at a ﬁxed point in the deposit was measured to validate the numerical model, and then the solidiﬁcation parameters were quantiﬁed using the model. Simultaneously, the microstructure of the deposit was investigated to conﬁrm the microstructure morphology. Then, a relationship between the microstructure morphology and the G / R was proposed using a solidiﬁcation map. The ﬁndings of this study can guide the design of scanning paths to produce deposits with a uniform structure.


Introduction
In the multilayer deposition process of metals using additive manufacturing (AM) technology, a heat-accumulation phenomenon occurs owing to the repeated heat input from the deposition of each layer. Researchers have been concerned by the changes in the cooling rate of each layer due to this accumulated heat because these changes have a significant influence on the formation of microstructures that, in turn, affect the mechanical properties of the deposit [1][2][3][4][5][6].
Solidification parameters such as the temperature gradient (G) and growth rate (R) determine the solidification characteristics. These parameters significantly influence the formation of microstructures and the mechanical properties of the deposit. During the deposition process, the solidification parameters vary in each layer of the deposit depending on the accumulated heat from the repetitive heat input, and these variations cause differences in the mechanical properties between layers. Therefore, it is necessary to quantify the solidification parameters for a structure with uniform properties. However, it is not easy to calculate or measure quantitative information about the solidification parameters during the deposition process, and repeated experiments require considerable time and cost.
To overcome these shortcomings, various types of models can be utilized [7][8][9][10][11]. For example, a numerical model based on previous studies [7,10,11] can be used as an alternative means to obtain quantitative information on solidification parameters. Several researchers have conducted numerical studies on the calculation of the solidification parameters. Bertoli et al. [12] studied the relationship between the solidification parameters and the microstructure of multilayer deposits in a powder bed fusion (PBF) process by using a laser heat source and STS 316L powder. They verified the Figure 1 shows a schematic diagram of the experimental setup for the LMD process. A high-power fiber laser (IPG Photonics, Oxford, USA) was used as the heat source. The laser head was moved in a zig-zag pattern, and deposition was performed layer-by-layer with no interlayer time. The powder was supplied in real time onto the substrate coaxially with the laser. An STS 316L substrate (POSCO, Pohang, Republic of Korea) with dimensions of 200 × 80 × 20 mm and gas-atomized STS 316L powder with a particle diameter of 53-106 µm (Titd metal materials, Changsha, China) were used for deposition. Table 1 shows the chemical compositions of the substrate and powder, and Table 2 shows the optimized process parameters based on prior experiments. During the deposition process, the temperature was measured in real time by using a pyrometer (LumaSense Technologies GmbH, Frankfurt, Germany) that can measure temperatures between 580 and 3300 • C. The pyrometer was fixed at point 1 in Figure 1 (located at 50 mm in the +x direction and 0.8 mm in the +z direction). The emissivity of the pyrometer was suitably set for solid-state STS 316L.

Numerical model
In this study, a finite element (FE) model was developed to calculate the solidification parameters. The laser heat source has a Gaussian beam and is mathematically expressed as follows [16][17][18] where P is the power of the laser; r, the radius of the laser beam; v, the scanning velocity of the laser beam; and t, the scanning time.
The deposition process is modeled as transient heat transfer with a moving heat source; the three-dimensional heat transfer equation is expressed as follows: , where ρ is the mass density; Cp, the heat capacity; T, the unknown temperature; t, the time; k, the conductivity; and a, the laser absorptivity. The initial temperature, T0, at time t = 0 is a room temperature of 27 °C. The boundary between the deposit and the substrate surface was considered to be conductive, whereas the rest of the surface boundary was considered to be radiative and convective [6]. Boundary conditions such as heat conduction, radiation, and convection are applied as follows: where ks is the thermal conductivity at the surface of the base metal, q is the input heat flux, h is the convection heat transfer coefficient, σ is the Stefan-Boltzmann constant, and ε is the surface emissivity. The thermophysical properties of STS 316L, including the density, specific heat, and

Numerical Model
In this study, a finite element (FE) model was developed to calculate the solidification parameters. The laser heat source has a Gaussian beam and is mathematically expressed as follows [16][17][18]: where P is the power of the laser; r, the radius of the laser beam; v, the scanning velocity of the laser beam; and t, the scanning time.
The deposition process is modeled as transient heat transfer with a moving heat source; the three-dimensional heat transfer equation is expressed as follows: where ρ is the mass density; C p , the heat capacity; T, the unknown temperature; t, the time; k, the conductivity; and a, the laser absorptivity. The initial temperature, T 0 , at time t = 0 is a room temperature of 27 • C.
The boundary between the deposit and the substrate surface was considered to be conductive, whereas the rest of the surface boundary was considered to be radiative and convective [6]. Boundary conditions such as heat conduction, radiation, and convection are applied as follows: where k s is the thermal conductivity at the surface of the base metal, q is the input heat flux, h is the convection heat transfer coefficient, σ is the Stefan-Boltzmann constant, and ε is the surface emissivity. The thermophysical properties of STS 316L, including the density, specific heat, and thermal conductivity, can be found elsewhere [14,19]. To minimize the computational load for designing the process parameters, such as the scanning path, the flow of the molten pool and metal transfer are not considered. Figure 2 shows the mesh of the full-scale numerical model used in this study. To reduce the simulation time, a symmetric half model of the deposit to the X-Z plane was applied. Further, a non-uniform mesh was applied to increase the simulation accuracy and reduce the simulation time [13,20]. The deposit part was composed of a fine hexahedral mesh with a size of 0.0375 mm. The mesh in the base metal zone gradually became coarser as it moved away from the deposit part. The total number of elements in the model was 800,000.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 9 thermal conductivity, can be found elsewhere [14,19]. To minimize the computational load for designing the process parameters, such as the scanning path, the flow of the molten pool and metal transfer are not considered. Figure 2 shows the mesh of the full-scale numerical model used in this study. To reduce the simulation time, a symmetric half model of the deposit to the X-Z plane was applied. Further, a nonuniform mesh was applied to increase the simulation accuracy and reduce the simulation time [13,20]. The deposit part was composed of a fine hexahedral mesh with a size of 0.0375 mm. The mesh in the base metal zone gradually became coarser as it moved away from the deposit part. The total number of elements in the model was 800,000.   Figure 3(b) shows the temperature profile measured using a pyrometer (solid line) and the temperature calculated through the simulation model (dotted line) at point ①. The difference in the peak temperatures between the two temperature profiles is 6.5% at maximum and 4.1% at minimum. In Figure 3(b), because point ① is fixed at the height of the fourth layer, there are no temperature profiles from the first to the third layers. As mentioned in Section 2, the pyrometer cannot measure temperatures below 580 °C; therefore, the measured temperature profile in Figure 3(b) is shown as a straight line at 580 °C. In addition, some errors occurred at ~580 °C because of electrical noise after the temperature decreased to this value. Figure 3(b) shows a difference of ~5% on average between the peaks of the two temperature profiles. However, except for the temperature near the peaks, which were above the melting point of STS 316L (1400 °C), the measured and the simulated temperature profiles are almost identical. This indicates that the developed numerical model fits well. During the cooling process of each layer, the slope of the temperature profile at the melting point of STS 316L indicates the cooling rate when the molten powder solidifies. Note that the solid-liquid interface was simplified and assumed to be a melting point in this study. Therefore, the solidification parameters obtained at the melting point have an important effect on the characteristics of the microstructure morphology. In other words, it is important to obtain a continuous temperature history, including the melting point, of the cooling process through the simulation model. By doing so, quantified solidification parameters can be derived through the model.  Figure 3a shows the position (point 1 ) where the pyrometer continuously measured the varying temperature for validating the numerical model. Figure 3b shows the temperature profile measured using a pyrometer (solid line) and the temperature calculated through the simulation model (dotted line) at point 1 . The difference in the peak temperatures between the two temperature profiles is 6.5% at maximum and 4.1% at minimum. In Figure 3b, because point 1 is fixed at the height of the fourth layer, there are no temperature profiles from the first to the third layers. As mentioned in Section 2, the pyrometer cannot measure temperatures below 580 • C; therefore, the measured temperature profile in Figure 3b is shown as a straight line at 580 • C. In addition, some errors occurred at~580 • C because of electrical noise after the temperature decreased to this value. Figure 3b shows a difference of~5% on average between the peaks of the two temperature profiles. However, except for the temperature near the peaks, which were above the melting point of STS 316L (1400 • C), the measured and the simulated temperature profiles are almost identical. This indicates that the developed numerical model fits well. During the cooling process of each layer, the slope of the temperature profile at the melting point of STS 316L indicates the cooling rate when the molten powder solidifies. Note that the solid-liquid interface was simplified and assumed to be a melting point in this study. Therefore, the solidification parameters obtained at the melting point have an important effect on the characteristics of the microstructure morphology. In other words, it is important to obtain a continuous temperature history, including the melting point, of the cooling process through the simulation model. By doing so, quantified solidification parameters can be derived through the model.  Figure 4 shows the solidification map. The temperature gradient (G) (shown on the y-axis in the map) indicates the temperature difference at the solid-liquid interface and the growth rate (R) (shown on the x-axis) represents the travel speed of the solid-liquid interface. In the map, the G/R value determines the morphology of the microstructure and the cooling rate, expressed as G × R, determines the size of the microstructure [22,23]. As shown in Figure 4, the morphology transforms from planar to cellular, cellular dendritic, columnar dendritic, and finally, equiaxed dendritic as the G/R value decreases. In addition, the higher the cooling rate, the finer is the microstructure that is formed and the more improved are mechanical properties such as the tensile strength and hardness [24][25][26]. In this study, G and R were calculated using a mathematical model validated through the measured temperature profiles. A deposit with the same configuration as the real deposit was built in the mathematical model. After calculating G and G × R by using the mathematical model, R was inversely derived. These parameters were all calculated at the spatial location where the temperature was passing through the last melting point in each layer.    Figure 4 shows the solidification map. The temperature gradient (G) (shown on the y-axis in the map) indicates the temperature difference at the solid-liquid interface and the growth rate (R) (shown on the x-axis) represents the travel speed of the solid-liquid interface. In the map, the G/R value determines the morphology of the microstructure and the cooling rate, expressed as G × R, determines the size of the microstructure [22,23]. As shown in Figure 4, the morphology transforms from planar to cellular, cellular dendritic, columnar dendritic, and finally, equiaxed dendritic as the G/R value decreases. In addition, the higher the cooling rate, the finer is the microstructure that is formed and the more improved are mechanical properties such as the tensile strength and hardness [24][25][26]. In this study, G and R were calculated using a mathematical model validated through the measured temperature profiles. A deposit with the same configuration as the real deposit was built in the mathematical model. After calculating G and G × R by using the mathematical model, R was inversely derived. These parameters were all calculated at the spatial location where the temperature was passing through the last melting point in each layer.

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In the map, the G/R value determines the morphology of the microstructure and the cooling rate, expressed as G × R, determines the size of the microstructure [22,23]. As shown in Figure 4, the morphology transforms from planar to cellular, cellular dendritic, columnar dendritic, and finally, equiaxed dendritic as the G/R value decreases. In addition, the higher the cooling rate, the finer is the microstructure that is formed and the more improved are mechanical properties such as the tensile strength and hardness [24][25][26].
In this study, G and R were calculated using a mathematical model validated through the measured temperature profiles. A deposit with the same configuration as the real deposit was built in the mathematical model. After calculating G and G × R by using the mathematical model, R was inversely derived. These parameters were all calculated at the spatial location where the temperature was passing through the last melting point in each layer. Figure 5 shows the cooling rate, temperature gradient, and growth rate depending on the height of the deposits. Figure 5a shows the locations where G and R were calculated. The sample size is 1.8 mm (W) × 2.5 mm (H). The bottom is at 0.13 mm in the -Z direction from the base metal surface. The middle is at 0.88 mm in the +Z direction from the base metal surface. The top is at 1.63 mm in the +Z direction from the base metal surface. Figure 5b shows the changes in G × R, G, and R at each layer. G × R, G, and R tend to decrease as the location moves from bottom to top. Further, the decrease in slope between the middle and the top was smaller than that between the bottom and the middle. This means that during deposition, a significant portion of the heat input supplied by the laser heat source is rapidly transferred to the base material, and the difference between the decreasing slopes of each solidification parameter reflects the effect of heat accumulation for each layer of the deposit due to repeated heat input. As shown in Figure 5b, G × R was in the range of 1 × 10 3 to 2.5 × 10 3 • C/s, which agrees with the results of other studies [15,27,28].
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 9 Figure 5 shows the cooling rate, temperature gradient, and growth rate depending on the height of the deposits. Figure 5(a) shows the locations where G and R were calculated. The sample size is 1.8 mm (W) × 2.5 mm (H). The bottom is at 0.13 mm in the -Z direction from the base metal surface. The middle is at 0.88 mm in the +Z direction from the base metal surface. The top is at 1.63 mm in the +Z direction from the base metal surface. Figure 5(b) shows the changes in G × R, G, and R at each layer. G × R, G, and R tend to decrease as the location moves from bottom to top. Further, the decrease in slope between the middle and the top was smaller than that between the bottom and the middle. This means that during deposition, a significant portion of the heat input supplied by the laser heat source is rapidly transferred to the base material, and the difference between the decreasing slopes of each solidification parameter reflects the effect of heat accumulation for each layer of the deposit due to repeated heat input. As shown in Figure 5(b), G × R was in the range of 1 × 10 3 to 2.5 × 10 3 °C/s, which agrees with the results of other studies [15,27,28]. As shown in Figure 6, cross sections of the deposit were analyzed using an optical microscope to investigate the relationship between the calculated solidification parameters and the formed microstructure. Figure 6(a)-(c) shows the microstructures at the bottom, middle, and top regions of the deposit for 0-s interlayer time. A cellular structure was observed in the three figures; however, a small amount of cellular dendrite was additionally observed in the top region in Figure 6(c). This is because G/R decreases from the bottom to the top area, as shown in Figure 5. This phenomenon was also observed in different locations of the deposit, as shown in Figure 6(d)-(f). These results suggest the possibility of quantifying the conditions for morphology change between cellular and cellular dendrite. In addition, Figure 6 clearly shows that the size of the cell gradually increases from the bottom (a,d) to the top (c,f) owing to the effect of the cooling rate described in Figure 5.

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You jum As shown in Figure 6, cross sections of the deposit were analyzed using an optical microscope to investigate the relationship between the calculated solidification parameters and the formed microstructure. Figure 6a-c shows the microstructures at the bottom, middle, and top regions of the deposit for 0-s interlayer time. A cellular structure was observed in the three figures; however, a small amount of cellular dendrite was additionally observed in the top region in Figure 6c. This is because G/R decreases from the bottom to the top area, as shown in Figure 5. This phenomenon was also observed in different locations of the deposit, as shown in Figure 6d-f. These results suggest the possibility of quantifying the conditions for morphology change between cellular and cellular dendrite. In addition, Figure 6 clearly shows that the size of the cell gradually increases from the bottom (a, d) to the top (c, f) owing to the effect of the cooling rate described in Figure 5.  Figure 7 shows the calculated G/R values for the deposit. The G/R value gradually decreases from the bottom to the top of the deposit. This trend was consistent with the trends of G, R, and G × R as shown in Figure 4(b). G/R has the same order of magnitude of 10 2 °C·s/mm 2 for the bottom, middle, and top positions. However, other researchers reported that the G/R values of STS 316L deposits with cellular appearance in the deposit were of the order of 10 2 °C·s/mm 2 [12] or 10 2 -10 3 °C·s/mm 2 [15]. In addition, the G/R value for planar and equiaxed appearance in STS 316L deposits is ~5 × 10 4 °C·s/mm 2 [12] or higher and ~10 °C·s/mm 2 [29] or lower, respectively. In summary, planar and equiaxed formations were not expected to appear in the bottom, middle, or top of the deposits investigated in this study. Therefore, it can be concluded that the microstructure observed in Figure  6 was formed with the G/R values shown in Figure 7. Finally, by combining Figures 5-7, the relationship between G/R and the microstructure characteristics can be derived as follows:

(cellular dendrite) ≤ G/R ≤ 598 (cellular)
(4) Figure 7. Behavior of G/R at each position in deposit.  Figure 7 shows the calculated G/R values for the deposit. The G/R value gradually decreases from the bottom to the top of the deposit. This trend was consistent with the trends of G, R, and G × R as shown in Figure 4b. G/R has the same order of magnitude of 10 2 • C·s/mm 2 for the bottom, middle, and top positions. However, other researchers reported that the G/R values of STS 316L deposits with cellular appearance in the deposit were of the order of 10 2 • C·s/mm 2 [12] or 10 2 -10 3 • C·s/mm 2 [15]. In addition, the G/R value for planar and equiaxed appearance in STS 316L deposits is~5 × 10 4 • C·s/mm 2 [12] or higher and~10 • C·s/mm 2 [29] or lower, respectively. In summary, planar and equiaxed formations were not expected to appear in the bottom, middle, or top of the deposits investigated in this study. Therefore, it can be concluded that the microstructure observed in Figure 6 was formed with the G/R values shown in Figure 7. Finally, by combining Figures 5-7, the relationship between G/R and the microstructure characteristics can be derived as follows:

Conclusions
Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 9  Figure 7 shows the calculated G/R values for the deposit. The G/R value gradually decreases from the bottom to the top of the deposit. This trend was consistent with the trends of G, R, and G × R as shown in Figure 4(b). G/R has the same order of magnitude of 10 2 °C·s/mm 2 for the bottom, middle, and top positions. However, other researchers reported that the G/R values of STS 316L deposits with cellular appearance in the deposit were of the order of 10 2 °C·s/mm 2 [12] or 10 2 -10 3 °C·s/mm 2 [15]. In addition, the G/R value for planar and equiaxed appearance in STS 316L deposits is ~5 × 10 4 °C·s/mm 2 [12] or higher and ~10 °C·s/mm 2 [29] or lower, respectively. In summary, planar and equiaxed formations were not expected to appear in the bottom, middle, or top of the deposits investigated in this study. Therefore, it can be concluded that the microstructure observed in Figure  6 was formed with the G/R values shown in Figure 7. Finally, by combining Figures 5-7, the relationship between G/R and the microstructure characteristics can be derived as follows:

Conclusions
In this study, to investigate the quantitative relationship between the solidification parameters and the microstructures formed by heat accumulation owing to repetitive heat input in the multilayer Comm You ju

Conclusions
In this study, to investigate the quantitative relationship between the solidification parameters and the microstructures formed by heat accumulation owing to repetitive heat input in the multilayer deposition of STS 316L, a numerical model was developed and validation experiments were performed. This study makes the following contributions: (1) A numerical model has been developed to understand the heat transfer of the deposit in the LMD multilayer deposition process. To improve the accuracy of the numerical model, the temperature profile was obtained at a fixed point in the deposit during the experiment and the results were validated by using the numerical model. There was an average difference of~5% between the peaks of the two temperature profiles. However, except for the temperature near peaks that were above the melting point of STS 316L (i.e., 1400 • C), the profiles between the measured and the simulated temperature were almost identical. Therefore, the developed numerical model simulates the multilayer deposition process well and can be directly applied to the thermal history analysis of various types of deposits.
(2) The relationship between the microstructure morphologies and the solidification parameters was investigated. In particular, the relationship between the microstructure morphologies was quantitatively analyzed by deriving G and R affected by the heat accumulation during multilayer deposition. In this process, the relationship between cellular and cellular dendrite formation according to G/R was proposed using a solidification map. Accordingly, the resulting microstructure can be predicted through a simulation model without the need to perform real depositions, and the predicted results are useful for process variable design.