Computational modeling of the effects of process parameters on the grain morphology of additively manufactured stainless steel

Identifying the suitable process parameters is one of the necessities to control the microstructure, and consequently various properties of additively manufactured (AM) parts. To obtain suitable process parameters, it is crucial to understand the effects of each process parameter on various aspects of microstructure of the printed material. In this work, we have conducted a parametric study on the effects of AM process parameters on the grain morphology of the metallic parts, fabricated via directed energy deposition (DED), through the Kinetic Monte Carlo (KMC) simulations. The characteristics of the melt pool and the heat-affected zone (HAZ) were incorporated into the models, and microstructural effects of altering the layer thickness, hatch spacing, scanning speed, and laser power were investigated. We used the Rosenthal equation, to predict the geometry of the melt pool and heat-affected zone formed by certain laser powers. The resulting grain morphology (i.e. the grain size and inclination) was analyzed for a large number of combinations of different process parameters. It was observed that by increasing the laser power, the number of fine and equiaxed grains decreases. On the other hand, increasing the scanning speed had a significant effect on formation of more fine grains in the final model.


Introduction
Additive manufacturing (AM) has been increasingly utilized to fabricate parts for automotive, aerospace, and medical applications. Compared to the conventional methods of manufacturing, AM offers many advantages like eliminating expensive tooling, dies and casting molds [1][2][3]. Among the AM methods, directed energy deposition (DED) has attracted attention for manufacturing functional metallic or metal-alloy parts. DED can also be used for remanufacturing and repairing damaged parts, which makes it an environment-friendly manufacturing [4]. The laser DED (DED-L) process utilizes a laser beam with highly concentrated energy and a stream of raw material, which can be in powder or wire form. The laser melts the material at the focal point, forming a melt pool [5], while an inert gas shields that spot. The highly concentrated energy applied by the laser beam and rapid motion of the laser beam constitute a steep temperature gradient in all the three dimensions at the neighborhood of the melt pool. This temperature gradient results in the rapid solidification of the melt pool, after passage of the laser spot [6]. The layer-by-layer nature of DED fabrication, exposes the material to thermal cycles and leads to directional cooling and phase transformation. The latter two phenomena alongside with the rapid solidification significantly affect the microstructure of the deposited material [7]. As a result, there is a noticeable variability in the microstructure of the AM parts fabricated with different process parameters and even at different regions of one AM part [8,9]. The heterogeneity of microstructure appears as a combination of equiaxed and elongated/columnar grains mostly formed periodically over the volume of the part [10]. The patterns of the grain types (i.e. equiaxed or elongated) depend on the thermal gradient and solidification front velocity [11], and can greatly affect the properties and performance of the part [12][13][14][15].
It is important to note that different microstructures significantly affect the mechanical properties of the material, such as ductility, yield stress, and toughness [16][17][18][19][20]. For example, it has been observed that fine equiaxed grains will result in enhanced ductility [21]. Moreover, considering the large number of process parameters in DED, such as laser power (P), scanning speed (v), hatch spacing (h), and layer thickness (t), obtaining desired material properties via an experimental approach is not time-and cost-effective. Therefore, simulating the formation of microstructure of the AM parts will be very advantageous for tailoring the properties of the fabricated parts. A calibrated model can be used with a systematic parametric study [22] to understand the effect of process parameters on the microstructure and properties of the fabricated parts.
A large number of experimental and computational studies have investigated the effects of process parameters on the microstructure of AM metals. Based on experimental work, Amine et al. [23] observed that in DED of 316L stainless steel (SS), increasing the laser power significantly increases the peak temperature, dimension of the melt pool, and cooling rate, which result in an increase in the size of grains, and decreases the hardness of the printed material. Wang et al. [16] studied the DED parts made of 304L SS and reported that the smaller ratio of the laser power to the scanning speed, results in finer microstructure and higher tensile strength. The effects of scanning speed on the electron beam AM of Ti-6Al-4V samples were experimentally studied by Wang et al. [24], who reported that Young's modulus and hardness increase with increasing scanning speed due to the formation of finer microstructure. The effect of high cooling rate on the microstructure of Ti-6Al-4V cylinders in a laser based DED system was studied by Marshall et al. [25]. They reported that the microstructure varies from columnar grains near the substrate to equiaxed grains around 2-3 mm away from the substrate. They attributed this transition in grain shape to smaller thermal gradient resulting from the temperature history on the previous layers.
In addition to experimental studies, computational modeling was employed by researchers to evaluate the effect of process parameters on microstructure of AM parts. Liu et al. [26] used a multiscale phase field model, and demonstrated that columnar-to-equiaxed transition of microstructure is mostly controlled by undercooling in the melt pool, which causes more heterogeneous formation of solidification nuclei (that contributes to equiaxed grain growth) compared to epitaxial or columnar grain formation during rapid solidification. Liu et al. [27] used a multiscale finite volume model to simulate the grain evolution in the DED process of a single track of IN718 superalloy. They reported that high scanning speed as well as high laser power increase the fraction of equiaxed grains, which form at the location of the melt pool. Akram et al. [28] adopted cellular automata method to simulate the microstructure of AM Ti-6Al-4V alloy fabricated via different methods such as SLM, DED, and EBM. They observed that by reducing the cooling rate and thermal gradient, zigzag grain morphology changes to unidirectional grains even when using bi-directional scanning pattern. Sunny et al. [29] performed finite element simulation of the thermal history in a thin-walled structure made of IN625 using SLM. They found that due to reduced intralayer heat accumulation near the ends of the part, finer grains form in those areas compared to central regions.
Although many studies have tried to understand the effect of a various process parameter on the grain size and morphology, there has not been extensive research quantifying the effect of many process parameters on the grains size and shape. This information is necessary in developing procedures for designing AM processes to obtain desired mechanical properties (by incorporating into formulations such as Hall-Patch equation). As a step toward this objective, this work tries to explore the correlation between various process parameters of AM and the final grain morphology via the Kinetic Monte Carlo method. Although this method is not physics-based, once calibrated it provides a useful tool for such a sensitivity analysis study considering the much faster analysis and the extensive amount of simulations needed. In this work, we simulated the grain morphology of DED-fabricated 304L SS cuboids. We performed a parametric study to investigate the effect of different process parameters, such as laser power, scanning speed, hatch spacing, and layer thickness on the grain morphology of the final part. To better understand the effect of various parameters, the results were interpreted both qualitatively and quantitatively.

The Kinetic Monte Carlo Potts model
The Kinetic Monte Carlo (KMC) Potts model was employed to simulate the evolution of grain growth in mesoscale. To start the simulation using the KMC Potts model, a continuum microstructure is discretized into lattice sites where each site is allotted an index. Neighboring sites with the same indices belong to the same grain and the interfaces between sites with different indices represent the grain boundaries [30]. In the KMC Potts model, the grain growth is curvature-driven and is obtained by minimizing the grain boundary energy [11]. Therefore, the grain boundary energy (E) is considered the sum of bonds between contiguous sites with different indices: The International Journal of Advanced Manufacturing Technology (2023) 125: [3513][3514][3515][3516][3517][3518][3519][3520][3521][3522][3523][3524][3525][3526] where N is the total number of lattice sites, L is the number of each site's neighbors, q i is the index of each lattice site, q j is the index of each neighboring site, and is the Kronecker delta function, which is 1 when q i = q j and 0 otherwise. Grain evolution begins by randomly reassigning a lattice site's index to a neighboring site with a dissimilar index leading to a change in the total energy of the system. The probability of acceptance of index reassignment will be according to Metropolis algorithm, based on the energy change in the system: where ΔE is the system's energy change before and after index reassignment, i.e. ΔE = E 2 − E 1 ( E 1 is the energy before index reassignment and E 2 is the energy after index reassignment), k B is the Boltzmann's constant and T s is the simulation background temperature. If the system's energy change is negative (ΔE < 0), the index reassignment is accepted, while the index reassignment that leads to an increase in the energy may be accepted or rejected following the Boltzmann distribution [31]. The procedure for the latter case is continued by generating a random number R such that 0 < R < 1. If , the change is accepted, if not then the original index is restored. Grain growth occurs if reassignment of the indices is accepted, otherwise, grain growth will not happen.
To simulate the process of grain growth in AM, three new parameters, namely melt pool and heat-affected zone (HAZ) characteristics and a temperature-dependent grain boundary mobility, M(T) , were introduced to the Potts model [11]. Melt pool is defined as a region with a temperature higher than the material's melting point and HAZ is the high temperature region surrounding the melt pool and having a steep thermal gradient. Grain evolution occurs by the kinetics provided by the melt pool and HAZ which govern the local grain boundary mobility [32,33]. The grain boundary mobility, M(T) , is calculated as: where M 0 is the Arrhenius pre-factor, Q is the activation energy for grain boundary motion, R is the gas constant (8.31 J·mol −1 ·K −1 ), and T is the temperature. Incorporating the mobility in Eq. (3) into Eq. (2) results in: The simulation of the grain growth occurs in the fusion zone (i.e. melt pool and HAZ) in which the grain boundary mobility is the highest. As the fusion zone moves forward, the mobility decreases suddenly in regions beyond it.

Modeling procedure
A rectangular cuboid with 8 mm × 8 mm × 2.5 mm dimensions was modeled using the open-source SPPARKS Monte Carlo suite [34]. The model parameters were first calibrated based on experimental results and were used to conduct the parametric study throughout this paper. The AM process that is modeled  in this work is a DED-L process with a bi-directional scanning path. Figure 1 shows the details of the models indicating the geometry, dimensions as well as the laser scanning pattern.

Model calibration
To obtain valid simulation process parameters, the melt pool and HAZ dimensions, scanning speed, layer thickness, and hatch spacing, were calibrated to match the experimental results by Nishida et al. [35] for which the process parameters were reported in [11]. They fabricated a rectangular solid part made of 304L SS using DED with a high-power laser beam and bi-directional scanning pattern. The values of the experimental and calibrated simulation process parameters are presented in Table 1. It should be noted that to simulate the DED-L process using the KMC Potts model by SPPARKS, modeling parameters should be converted into lattice site unit.
To quantitatively study the grain morphology, various features of the grains such as aspect ratio, grain inclination angle, 1 and grain size distribution were considered. The grain morphology was visualized, and each grain was estimated by a best-fit ellipse. The size of each grain was then determined as the size of the major axis of the best-fit ellipse to that grain. The reported aspect ratio of a grain in this work indicates the ratio of the minor to major axes of the ellipse that was fitted to the grain. As such, aspect ratio of a grain holds a value between 0 and 1; an aspect ratio close to 1 indicates an equiaxed grain and as the aspect ratio reduces, the grain will look more elongated and will seem needle-like for aspect ratios close to 0. Moreover, the angle between the major axis of the ellipse and the y-axis of the model (see Fig. 1) is considered the grain inclination angle. Due to the large volume of results in this work, especially for the parametric study, only the top view (XY plane) of the simulated models were analyzed and are reported. Figure 2 presents the Electron BackScatter Diffraction (EBSD) results of the experimental study, their corresponding simulation results, and grain aspect ratio histograms for both cases. As can be seen in Fig. 2a and b, for both experimental and simulation results, the microstructure shows a banded distribution of grains such that fine equiaxed grains are formed at the centerline of the melt pool along the scanning path. Around equiaxed grains, elongated grains can be observed with an inclination toward the direction of the laser travel. This is the outcome of bi-directional scanning pattern and overlapping melt pools in each pass. The histogram of the grain size distribution (the area of grains with a given aspect ratio normalized by the total area of the XY plane) with respect to the aspect ratio of grains for both models are presented in Fig. 2c and d for the XY plane. In both histograms, the peak fraction of the grains is for an aspect ratio between 0.2 and 0.4. Moreover, the total area fraction of the elongated grains with aspect ratio smaller than 0.5 (calculated as the sum of the Fig. 2 a Grain morphology of the experimental study [11], b grain morphology of the simulated model, c distribution of grains aspect ratio in the experiment [11], d distribution of grains aspect ratio in the simulation

Melt pool centerline
SimulaƟon Experiment fraction of corresponding aspect ratios) is more than 60%, which is due to the larger size of individual elongated grains. It is also observable in the histograms that there are less equiaxed grains as the value of the grain fraction decreases when the aspect ratio increases to 1 (equiaxed grain), which is mainly due to the small size of the individual equiaxed grains.

Parametric study
The main objective of this study was to investigate the effect of each process parameter on grain morphology of the final part in a DED AM process of 304L SS. Considering the capabilities and limitations of the KMC Potts model that is used in SPPARKS, scanning speed, hatch spacing, and layer thickness can be altered explicitly. However, the laser power cannot be studied directly. Therefore, as is explained in Section 3.2.1, the effect of laser power was studied by considering the resulting melt pool and HAZ dimensions formed by certain laser powers.
For the parametric study, the calibrated simulation parameters of Table 1 were used as benchmark values. In studying the effect of each parameter, the corresponding parameter was varied in steps within a realistic range of values around the benchmark value, while keeping the other parameters constant, equal to the benchmark values. Table 2 summarizes the studied parameters, the number of models and corresponding values of that parameter in each model of the parametric study. Due to the large volume of data, histograms of grains aspect ratio and angle are presented only for the laser power study.

Effect of the laser power
To study the effect of laser power (P), the resulting melt pool size and HAZ are incorporated into the KMC Potts model. As part of simulation of AM process in SPPARKS, the melt pool and HAZ are modeled as two ellipsoids that are coinciding with each other and share the same axes. It should be noted that in the simulations, the melt pool and HAZ dimensions and shape remain constant during the laser pass. In other words, our simulations only account for the stable melt pool size, which is a valid assumption for relatively long laser travels. Figure 3 illustrates the geometry of the melt pool and HAZ and indicates the notation for various dimensions of these parameters.
Since the laser power is not explicitly used in the code, the dimensions of the melt pool and HAZ corresponding to a laser power were considered instead. The dimensions of the melt pool and HAZ for a certain laser power were calculated based on the temperature field around the laser spot, which itself was computed by using the Rosenthal equation [36]. According to the Rosenthal equation, the heat distribution around the center of a point heat-source can be expressed as: where T is the temperature, T 0 is the preheating temperature, P is the laser power, v is the scanning speed, R is the radial position of the point of interest from the heat source, and is the position of the point of interest along the melt pool path. λ, k, and α are the absorptivity, thermal conductivity, and thermal diffusivity of the material, respectively.
Laser power and scanning speed can affect all the dimensions of the melt pool significantly [11]. By using the Rosenthal equation, we can incorporate the effects of these two process parameters on the melt pool geometry simultaneously. However, the original Rosenthal equation defines a semi-circular cross section for the melt pool, which is not completely realistic. Therefore, we have used a modified version of this equation introduced by Pauza et al. [37], which determines a wider and deeper melt pool compared to the original equation. The modified Rosenthal equation can be presented as [37]: where y and z are coefficients that account for widening or deepening of the cross section of the melt pool. These coefficients take values between 0 and 2 [37]. We can obtain the width and depth of the melt pool for different laser powers and scanning speeds using these equations.
To calculate the temperature field of the fusion zone, we can substitute the laser power into the modified Rosenthal equation of Eq. (7). The width and depth of the melt pool then can be calculated corresponding to each power level, based on the regions having temperatures above the melting temperature of the 304L SS (i.e., 1400 °C) [38]. Figure 4 shows the temperature variation with respect to the distance from the center of laser, based on the modified Rosenthal equation along the melt pool width and depth. Based on these graphs, the temperature distribution near the laser spot varies exponentially when we consider different horizontal or vertical positions for the same laser power. In addition, for a certain position, by changing the laser power, the temperature changes significantly. For instance, at 1 mm horizontal distance from the center of laser, by applying 3400 W laser power, the temperature is 1485 °C, while by setting the laser power to 5000 W, the temperature reaches 2185 °C. Dashed horizonal lines at 1400 °C on both graphs indicate material's melting temperature and the corresponding distances from the center of the heat source (i.e., laser). Accordingly, at the distances smaller than the shown values on the horizontal axes of the graphs, the material is molten. It is worth mentioning that the melt pool width is twice the distance indicated on the horizontal axes. Moreover, the length of the melt pool was estimated based on the calculated value of the melt pool width using the Rosenthal equation and the length-to-width ratio that was obtained for the calibrated melt pool in Section 3.1. In addition, the HAZ dimensions were calculated by the obtained dimensions of the melt pool from the Rosenthal equation and the ratio of the HAZ to melt pool dimensions in the calibration model (Section 3.1). It should be noted that we considered upper and lower bounds for the laser power dictated by the bounds of the melt pool width and depth since the latter values are also affected by hatch spacing and layer thickness, respectively. A laser power that is too low results in a melt pool width smaller than the hatch spacing, leaving some regions unaffected due to no overlap between two adjacent laser passes in a bi-directional scanning pattern. In addition, laser powers causing melt pool depths smaller than the layer thickness were not considered in the analyses, as they do not result in bonding between the successive layers. Five different models were simulated using different laser powers as presented in Table 2. The smallest laser power causing the lowest allowable melt pool-consistent with hatch spacing and layer thickness-was 3400 W which is almost 10% less than the benchmark value of 3800 W, and the highest laser power was 5000 W that is almost 30% higher than the benchmark value. Figure 5 exhibits the final microstructure of the model at the end of each simulation and the average and maximum grain sizes can be seen for all cases. As can be seen in Fig. 5, by an increase in the laser power the number of finer grains decreases, and the elongated grains grow thicker. This behavior is in good agreement with experimental results for 304L SS by Wang et al. [16], as they observed that by increasing the laser power, grains grow in length and the number of fine grains decreases significantly. As it can be inferred from graphs in Fig. 4, higher laser powers result in larger melt pools. Large melt pool in bi-directional scanning causes larger overlap between consecutive passes, imposing more heat to grains that are in the overlap area. In addition, it has been reported that a larger melt pool leads to a slower cooling rate [39] that allows grains to grow larger. On the other hand, based on Fig. 4, the temperature at the middle part of the melt pool is significantly higher for higher laser powers, which leads to formation of larger grains at the centerline of the melt pool at higher laser powers.
Considering the average and maximum grain sizes in Fig. 5, it can be seen that increasing the laser power, increases both the average and the maximum grain sizes. For example, by a 47% increase in the laser power (from 3400 to 5000 W) the average grain size increased from 0.43 to 0.54 mm, which shows a 25% change. Moreover, the maximum grain size increased from 1.91 to 2.60 mm, which is equivalent to 36% increase. In Fig. 6, the distribution of the aspect ratio and inclination angle of the grains are presented for models with different laser powers. As can be seen from the aspect ratio distribution plots (left column), by increasing the laser power, the peak fraction of grains, which mostly occurs around the aspect ratio of 0.3 for all laser powers, increases significantly. This fraction was 0.178 for the lowest laser power as compared to 0.354 for the highest laser power. Moreover, the distribution of the grains with aspect ratios larger than that of the peak fraction, decreases smoothly for lower laser powers, but it drops suddenly in higher powers, indicating less fraction of equiaxed grains. Considering grain inclination angle in the right column of Fig. 6, it can be seen that a large number of grains are aligned in angles less than 30° and higher than 160°, with respect to the direction perpendicular to the laser motion. This is the outcome of the bi-directional scanning pattern and the fact that elongated grains align toward scanning direction as a consequence of horizontal heat flux, resulted from moving heat source [8].

Effect of the layer thickness
The effect of layer thickness was studied by simulating the process with six different layer thicknesses. The values of the layer thicknesses considered in the parametric study are reported in Table 2. Figure 7 presents the results of grain morphology for models with different layer thicknesses. As can be seen in this figure, by increasing the layer thickness from t = 1 mm, the bands of fine grains start to decrease in size and almost disappear when the layer thickness is equal to 1.15 mm. When the layer thickness is too small compared to the depth of the melt pool, after deposition of the first layer, the second pass of the laser remelts the first layer leading to a microstructure change. This means that the grains at centerline of the laser are subjected to high temperature (which leads to high solidification rate) multiple times. In general, high rate of solidification results in finer grains [40]. However, in this case, the solidification of fine grains becomes interrupted by remelting due to successive laser passes. Therefore, the evolution of fine grains occurs prematurely and without coarsening. On the other hand, when the layer thickness is larger than 1.15 mm, finer grains start to grow more. With larger layer thickness, the grains of one deposited layer at the centerline of the laser mostly fall within the heat-affected zone, when the laser passes the successive layer. Since it has been reported that grain coarsening mostly occurs in the HAZ [41], fine grains of the previous layer coarsen at the middle of the laser path as is shown in Fig. 7. More fine grains resulted from a smaller layer thickness has been observed in experimental study on DED of Inconel 718 by Yeoh et al. [42], who obtained large elongated grains by doubling the layer thickness. Figure 8 presents the average and maximum grain sizes in the models with different layer thicknesses. As can be observed, the average and maximum grain sizes increase by increasing the layer thickness up to a specific layer thickness (1.15 mm) and decrease in beyond that layer thicknesses. This threshold value correlates with the material properties as well as laser characteristics, as these factors can affect the depth of HAZ, which controls the grain growth. Based on the results of Fig. 8, by 15% increase in the layer thickness, the average grain size increases for 56%, i.e. from 0.34 to 0.53 mm, and the maximum grain size increases for 3%, from 2.13 to 2.19 mm. Further increase in the layer thickness by 9% (beyond the threshold value) results in a decrease in the average and maximum grain sizes by 18% and 9%, respectively.

Effect of hatch spacing
Five different hatch spacing values were considered in this work to study the effect of this process parameter on the final grain morphology. Since for this parametric study, all the other parameters, including the laser power, were kept constant, the hatch spacing could not hold a value smaller than the melt pool width. Otherwise, there would be unmelted powder between the two adjacent passes of the laser. Figure 9 exhibits the final grains for models with different hatch spacings. It can be observed that for smaller hatch spacings, the elongated grains become smaller in size and the opposite occurs for larger hatch spacings. In addition, no significant change is qualitatively discernible in the amount of equiaxed fine grains. However, by computing the average and maximum grain size in Fig. 9, it was found that by a 25% increase in the hatch spacing, the average and maximum grain sizes increase for 15% and 9%, respectively. In the experimental studies, it has been reported that more fine grains were present in the fabricated part, when the hatch spacing was increased [43]. This behavior is mostly attributed to the faster cooling rate in the material in the solidification process for larger hatch spacings. As a result of the faster cooling rate, fine grains will have limited time to grow and thus the final microstructure includes more fine grains in larger hatch spacing. However, due to the inherent limitations of the simulations in this study, the elongated grains cannot grow beyond half of a hatch spacing, resulting in smaller elongated grains for small hatch spacings.

Effect of scanning speed
The scanning speed has been reported to be a very important process parameter that affects the final microstructure of the AM parts [44,45]. To study the effect of the scanning speed, simulations were conducted on models having scanning speeds in the range of 7 to 14 mm/s, as was mentioned in Table 2. Figure 10 depicts the final grain structure of the models with different scanning speeds. Based on this figure, increasing the scanning speed results in an increase in the number of fine grains significantly and, on the other hand, the size of elongated grains become smaller, while their number grows. Moreover, based on the average and maximum grain sizes presented in Fig. 11, by doubling the scanning speed, the average and maximum grain sizes decrease by 67% and 41%, respectively. The laser energy density at higher scanning speed becomes smaller during the  deposition, resulting in a solidification with fast cooling rate [46]. Consequently, a greater number of grains is nucleated, and due to rapid solidification, they have less chance to evolve coarser. In addition, in a realistic experiment, high scanning speed may result in unmelted particles, which may be melted by passage of the laser in successive layers. However, the nucleation of those grains does not lead to a complete evolution, and at the same time, the growth of elongated grains becomes suppressed. This behavior was also reported by Zhang et al. [47] for 316 SS and by Wu et al. [46 for Ti-6Al-4V, where they observed finer grains by using higher scanning speed, and also obtained increased yield and tensile strengths.
As mentioned before, the simulation tool that was employed in this study is SPPARKS code that provides a very useful tool for modeling AM processes using the KMC Potts model. One of the advantages of this code is the relatively quick simulation time which is helpful for parametric studies. After calibration of the model, the KMC is a powerful tool for modeling grain evolution in AM, although it is not a physics-based method. However, this code cannot model additional microstructural features such as crystallographic texture of the grains. Moreover, although the geometry of the melt pool was kept constant during the simulation-which is not realistic near the edges and corners-these simulations can be a representative of the Besides, since all the grain growth occurs in the fusion zone, which consists of melt pool and HAZ, phenomena like heat sink from the substrate cannot be accounted for in these models. Furthermore, the modified Rosenthal equation that was employed in this work to compute the melt pool dimensions at different laser powers, is not capable of estimating a dynamic melt pool since the scanning speed and power input are constant. Therefore, the temperature distribution calculations happen in a quasi-stationary condition. Moreover, the heat source, which is modeled as a point source, while very easy to implement, may not lead to the most accurate computations. In addition, calculations of the melt pool and HAZ length cannot be performed using the modified Rosenthal equation. For future works, adding effect of non-stable melt pool size during the laser travel as well as the fully adjusted melt pool to consider the effect of scanning speed will deepen our understanding of the effect of process parameters on grain morphology. In addition, simulations can be performed to study the effect of scanning pattern, as a major process parameter, on the grain morphology.

Conclusions
In this study, using the Kinetic Monte Carlo Potts model, DED-L AM method was simulated to study the effect of different process parameters on the grain morphology of the final part. To do this, a parametric study was conducted on 304L SS by changing layer thickness, hatch spacing, scanning speed, and laser power. In addition, qualitative and quantitative comparisons were performed on the results. In all the models, it was observed that formation of fine equiaxed grains occurs at the centerline of the scanning path, while elongated grains are formed around fine grains. There was a significant inclination in elongated grains toward the scanning direction. Based on the results of these simulations, the following conclusions were drawn: • By increasing the laser power, the number of fine and equiaxed grains decreased and elongated grains grew larger and wider. In addition, the average grain size increased by increasing the laser power. Both these observations are related to the increased size of the melt pool and HAZ under a higher laser power, which leads to slower cooling rate and exposes the material to high temperature for longer time. • When the layer thickness was too small compared to the melt pool depth, more fine grains were formed in the part with premature evolution. This happened as a result of remelting the previously deposited layer by passing the laser in successive layers. However, beyond a certain layer thickness, the grains at the centerline of the laser in the previously deposited layer were subjected to HAZ when the laser was passing the successive layers. This led to evolution of fine grains to relatively larger equiaxed grains. • By decreasing the hatch spacing, the elongated grains became smaller and the average and maximum grain sizes decreased. • Changing the scanning speed noticeably affected the resultant microstructure. By increasing the scanning speed, the number of fine grains increased significantly. Therefore, the average and maximum grain sizes decreased. The scanning speed had the most noticeable effect on the grain morphology, resulting in more fine grains under higher scanning speeds. This behavior is attributed to nucleation of more grains at higher scanning speed, which, combined with rapid solidification, led to more fine grains.