A Finite Element Analysis of the Effects of Preheating Substrate Temperature and Power Input on Selective Laser Melting

Abstract

Several parameters are defined before the Selective Laser Melting printing process, which may depend on the manufacturer of the equipment, but in general, we commonly encounter hatch distance, scanning speed, layer thickness, laser power input, scanning strategy, overlap distance, and substrate preheating temperature as the parameters that mainly define the printing process. The last parameter is the focus of this study, which is applied to a finite element model to simulate temperature distributions over one layer thickness of the powder bed. The substrate temperature and power input affect the cooling rates and temperature gradients imposed on the powder bed, consequently influencing the component’s final property, surface finishing, and accuracy (dimensioning tolerances). The current FEM model showed that the preheat substrate temperature played different roles depending on which power input is used; however, there is an observed trend that is the reduction in temperature gradients in the powder bed overall when higher substrate temperatures are used.

1. Introduction

Selective Laser Melting (SLM) is a powerful Powder Bed Fusion (PBF) manufacturing process that consolidates metal powder into the desired component shape by selectively scanning a powder bed with a high-powered laser beam. Several researchers have demonstrated that process and environmental parameters play an important role in determining the final mechanical properties of the parts produced by PBF [1]. Experimental studies investigate the mechanical properties, microstructures, the effect of varying the parameters (sensitivity), and several other aspects of the material. These studies have been performed since the commercialization of this technology first began. Many valuable research findings have helped improve the process overall. However, experimental studies are incredibly costly since numerous process parameters are involved in this technology. A relatively large investment was made by the vanguard in this sector to validate the commercialized alloys that they provided along with their machines. Although several investigators have uncovered excellent mechanical properties when using optimal process parameters with particular alloys, a variety of new alloys that could be used in this technology have not yet been validated.

The materials used thus far by SLM technology include Ti6AL4V, SS-316L, AlSi10Mg, Hastelloy X, IN718, IN625, IN939, Invar36, CuSn10, 17-4PH, Maraging Steel, etc. These materials have their optimal parameters already defined by each manufacturer. The manufacturer nearly always recommends using their metal powder only, making the process prohibitively expensive and inflexible in most situations. Manufacturers also prohibit new alloys from being used on their commercial equipment, and violations can void the equipment warranty in most cases [2,3].

Without using optimal parameters, many issues can arise that affect the integrity of the built part. Residual stresses, layer delamination, cracking, warping, and undesired porosity are the main problems when printing metal using PBF. These problems are primarily due to the high-temperature gradients induced by the laser in a short time frame. As a result, the powder (loose material) melts, causing the previous layers to lose strength owing to the high temperature of the top layer. At the same time, the expansion of the top layer is restricted by the deep layers, and elastic compressive strains are introduced. The top layer is finally plastically compressed at the yield strength of the material. When cooling, the plastically compressed upper layers begin contracting, and bending occurs [4,5].

Another issue that arises when incorrect parameters are used during the sample printing is related to the porosity and poor mechanical properties of the final built part. Porosity and poor mechanical properties are generally associated with each other since high porosity will reduce the yield strength of the material [6]. Porosity is caused mainly by low-level laser energy density; however, high-level laser energy density can also bring some degree of porosity to the final part, primarily due to the presence of gas bubbles [7]. Some of the material characterization in SLM usually involve the development of laser energy density equations that associate the main parameters of the process, such as power input, scanning speed, hatch distance, and layer thickness [8]. By applying the laser energy density formulation, different trends can be observed, such as high residual stresses for high laser energy density and low porosity for low laser energy density, depending on the combination of the parameters.

In this study, we investigate the preheat substrate temperature and laser power input effects in the temperature distributions along a single-track and single layer of the powder bed. Power inputs of 100, 200, and 400 W are utilized along with preheating temperatures of 298, 373, and 648 K. The shape of the melt pool is explored to visualize the heat-affected zone, and results are acquired through selected cross-sections, thickness, and longitudinal directions.

2. Thermal Modelling

2.1. Powder Properties

The powder properties are temperature and state-dependent, allowing precision in capturing thermal behavior in the printing process. Special attention is devoted to the effective powder thermal conductivity representing the main thermal properties used in the study. For this work, SS-304L is utilized, following the thermal properties produced by the Argonne National Laboratory [9], henceforth referred to as Kim’s report. The effective thermal conductivity calculation, $k_{eff}$, was based on Kim’s report; however, several formulations of powder-packed bed were utilized, including Wakao and Kagei [10], Sih and Barlow [11], and Kovalev and Gusarov [12]. The main parameters to perform the calculation are the packing density of the powder bed, the temperature-dependent thermal conductivity, the powder diameter, the elastic properties of the material (responsible for determining the contact area between powders), the power bed porosity, the emissivity of the powder bed due to conductivity, radiation, and others [13].

Three different packing structures were analyzed for the calculation of the effective thermal conductivity of the powder. The simple cubic (SC), generally known as a cubic structure, is a packing structure with a relative density of 0.523 and represents the least dense packing structure in this study. The body-centered cubic (BCC) packing structure has an intermediate relative density of 0.68. The face-centered cubic (FCC) packing structure, generally referred to as a close-packed structure, has a relative density of 0.74. Relative density is described by the atomic packing factor (AFP), as demonstrated by Gusarov and Kovalev [14].

The solid–liquid temperature-dependent density, thermal conductivity, and specific heat are shown in Figure 1, while Figure 2 shows the temperature-dependent effective thermal conductivity up to the melting point of the powder bed for different powder sizes, packing densities, and temperature conditions.

An equation derived from Dul’nev and Zarichnyak’s model is applied to define the porosity-dependent emissivity of the powder bed. Abyzov et al., Kovalev, and Gusarov later successfully applied this equation in their models to calculate effective thermal conductivity, which was also applied in this study [12,15,16,17]. Porosity, φ, is expressed as a function of the coordination number, N, as shown in Equations (1) and (2) below:

$$\varphi =\frac{3N-4}{N(N-1)}$$

(1)

$$N=\frac{1}{M}{\displaystyle \sum _{j=1}^M{k}_j}$$

(2)

where the mean coordination number of a given particle, N, is defined as the number of its neighbor’s particles that have their respective centers at a distance that corresponds exactly to the diameter of the original particle when studying monodispersed spheres. The correlation in Equation (2) is the mathematical representation of N, while M is the total number of particles in the domain and k_j is the number of contacts of a given particle j. The mean coordination numbers for the FCC, BCC, and SC packing structures are 12, 8, and 6, respectively, resulting in porosities of 0.2424, 0.3571, and 0.467, respectively. For this study, the powder bed porosity used is 0.467, corresponding to the SC packing density, yielding an emissivity of 0.44. The emissivity of the powder is used as input for the calculation of the radiation, which was modeled using the user-defined subroutine FILM in Abaqus, combined with the convection coefficient in efforts to reduce the computational cost. According to a study by Vinokurov, the loss of accuracy is approximately 5% when using this approach [18].

$$h=h_{\mathrm{c}}+\epsilon \sigma (T^2+T_0^2)(T+T_0)\cong 2.41\times {10}^{-3}{\epsilon }_{\mathrm{p}}{T}^{1.61}$$

(3)

The effective thermal conductivity is calculated for the solid-state powder condition until $T_{solid}$ of the material, as for the mushy zone ($T_{solid}<T<T_{liquid}$) and for the liquid region ($T_{liquid}\le T$), the original data from Kim’s report are utilized. The $k_{eff}$ includes three different powder diameters and three different packing densities, as seen in Figure 2. The effective thermal conductivity is used for the temperature-dependent properties of the FEA model.

2.2. FEM Thermal Modelling

The thermal model is defined in a way to handle different material phases (liquid, solid, and powder) as well as their variations at different temperatures. A three-dimensional model is established using DC3D8 hexahedron elements with $25 \mathsf{\mu }\mathrm{m}$ and an overall domain size of $1500\times 1500\times 75 \mathsf{\mu }\mathrm{m}$. A small domain, in this case, is justifiable given the small laser spot diameter, 50 μm, used in the model and the very low thermal conductivity present in the powder bed. A study on the effect of the computational domain size (cf. Appendix A) showed that the results presented in this work are independent of the domain size.

The material is modeled as temperature and state-dependent, allowing for a reasonably accurate representation of temperature distributions. Some considerations were made to preserve a low computational time/cost. The principal assumptions are:

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Thermo-fluid effects are not included, thus the Marangoni effect and fluid flow in the melt pool are not considered in this study.

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Vaporization of the material is not implemented, but the phenomenon only occurs when utilizing a considerably high laser power input (P = 400 W).

-

A single track of laser is simulated, and the influence of the hatch distance is neglected in order to only focus on the effect of the packing structure and particle diameter in the temperature distributions.

-

Only the average diameter of powder particles is considered when calculating the effective thermal conductivity of the powder state.

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The contact between powder and substrate was omitted. Instead, the preheat temperature of the substrate is accounted for as a boundary condition in order to isolate the variable and study the effect of the temperature alone within the analysis.

The maximum temperature obtained in this analysis may differ from the actual temperature in the process since the considerations (assumptions) above were made and not all the physical phenomena could be reproduced in our model. That being said, this manuscript focuses on the comparative analysis between the three different power inputs and substrate temperatures and their respective temperature gradients/distributions.

Abaqus/CAE 2020 (Johnston, RI, USA) is the software used to perform the analysis since its subroutines allow to model the moving heat source and keep track of the material’s state. The subroutines DFLUX and FILM were implemented in this study for the Gaussian double ellipsoidal profile for the heat flux and convection/radiation definitions, respectively. The solution given is the temperature distribution of the process, described as $T\left(x,y,z,t\right)$. The three-dimensional heat conduction equation describes the problem with the respective manufacturing and chamber environmental boundary conditions [13,19].

The contact powder and substrate were omitted, and the preheating temperature from the substrate was entered as a boundary condition. Previously produced layers were not modeled in this study; nevertheless, excluding them did not affect the effective thermal conductivity value of the powder itself. The only perceivable impact occurred on the temperature at the bottom of the new layer, which could achieve higher temperatures than the initial substrate temperature [20]. We have found that different powder diameters at the same packing density have no impact on the final temperature distributions of the model. However, the temperature differs between the three packing densities [13].

For the three-dimensional model using transient thermal analysis, the distributor of Abaqus recommends that the following equation be used to determine the minimum time increments required:

$$\Delta \mathrm{t}>\frac{\rho C_p}{6k}\Delta l^2$$

(4)

where $C_p, \rho , k,$ and $\Delta l$ are, respectively, the specific heat, density, thermal conductivity, and element size of the meshing. This calculation prevents false oscillations that may appear in the boundary vicinities as well as inaccurate solutions for very small-time increments [21]. To execute and debug subroutines that are written in Fortran, the software is linked with Intel Parallel Compiler 17.0 and Visual Studio 2012 [22].

Following the FEM software recommendation and for convenience, a time increment of $1.5\times {10}^{-6} \mathrm{s}$ was used with 1000 increments, yielding a total time of $1.5 \mathrm{ms}$. The total time was calculated based on the speed of the laser, which was defined as $1 \mathrm{m}/\mathrm{s}$. Other model parameters used in the study are listed in Table 1 [13].

The temperature was measured at nodal mesh points with acquisition points for the time-dependent temperature measurements (total time = $1.5 \mathrm{ms}$), shown in yellow in Figure 3, taken through the thickness of the layer. Acquisition points for the cross-section measurements, shown in black in Figure 3, were collected for half of the cross-section; since the Gaussian model uses a symmetric formulation, temperatures on both sides are mirrored.

2.3. Model Verification

We utilized the work of Parry et al., which used Ti6Al4V in the analysis, to verify our model parameters [19,23]. This comparison is critical for matching the comet-shaped melt pool and hence determining the parameters for the double ellipsoidal profile. Despite this being a thermal study, accounting for an appropriate profile helps predict precise values of temperature distribution through the bed, even though there are no fluidic considerations prior included. Figure 4 shows the comparison between both molten pool profiles.

The light-grey color in Figure 4 represents the liquid material, and it will be adopted for the further representation of liquid material in this study, i.e., regions that reach 1733 K (liquidus temperature) or higher.

3. Sensitivity Analysis of Substrate Temperature and Power Input

The substrate temperature, $T_0$, is set at three temperatures: 298, 373, and 643 K (25, 100, and 370 °C) to evaluate the temperature distribution variance within the ranges [3,24]. A study performed by Li et al. [25] demonstrated how substrate temperature influences the built part since it plays an important role in defining the interface bonding between the substrate and the part as well as the microstructures of the final part. The authors concluded that a higher substrate temperature increased the quality of the bond and can be attributed to the high cooling rate and larger melt pool volume. A lower substrate temperature has a higher cooling rate at the beginning of the laser scanning; however, the small melt pool induced by the laser is responsible for producing a strong boundary and gap between the printed part and the substrate, thus preventing an effective conductive heat transfer and reducing the actual cooling rate [26]. The substrate temperature was entered as a boundary condition for all data sets in the model. The mechanical contact between the interfaces was ignored since the focus here is on the thermal behavior.

Table 1. Common parameters used for the SLM simulation [13].

Parameters	Values
Latent heat of fusion, Lf [J/Kg]	273,790.0 [9]
Solidus temperature, Ts [K]	1703 [9]
Liquidus temperature, TL [K]	1733 [9]
Porosity of the bed, φ [%]	0.467 [13]
Solid emissivity, ε	0.44 [27]
Powder emissivity, εp [ ]	0.6 [13]
Preheat Temperature, T0 [K]	298, 373, and 648 [3]
Absorption coefficient, ηabs [ ]	0.40 [26]
Laser spot diameter, [µm]	50 [3]
Layer thickness, [µm]	75 [3]
Laser Power input, P [W]	100, 200, 400 [3]
Scanning speed, v [m/s]	1.0 [3]
Average powder diameter, xR [µm]	20 [28]
Convection coefficient, h [W/(m^2K)]	10 [29]
Gas thermal conduct, kg [W/mK]	0.016 [30]
Time step, t [ms]	1.5 [13]

Table 1. Common parameters used for the SLM simulation [13].

Parameters	Values
Latent heat of fusion, Lf [J/Kg]	273,790.0 [9]
Solidus temperature, Ts [K]	1703 [9]
Liquidus temperature, TL [K]	1733 [9]
Porosity of the bed, φ [%]	0.467 [13]
Solid emissivity, ε	0.44 [27]
Powder emissivity, εp [ ]	0.6 [13]
Preheat Temperature, T0 [K]	298, 373, and 648 [3]
Absorption coefficient, ηabs [ ]	0.40 [26]
Laser spot diameter, [µm]	50 [3]
Layer thickness, [µm]	75 [3]
Laser Power input, P [W]	100, 200, 400 [3]
Scanning speed, v [m/s]	1.0 [3]
Average powder diameter, xR [µm]	20 [28]
Convection coefficient, h [W/(m^2K)]	10 [29]
Gas thermal conduct, kg [W/mK]	0.016 [30]
Time step, t [ms]	1.5 [13]

Figure 5 presents the results for $T_0=298 \mathrm{K}$ for all power inputs, packing densities, and powder diameters. Figure 6 and Figure 7 show the results for $T_0=373 \mathrm{K}$ and $643 \mathrm{K},$ respectively. The plots were placed side by side to show the longitudinal temperature distribution and its cross-sectional counterpart.

It is clear that by increasing the substrate temperature, the maximum temperature achieved increases as well. However, the temperature gradients measured through the thickness of the layer decrease, as shown in

Table 2. Temperature gradients ($\nabla T$) and maximum temperature ($T_{\max }$ in Kelvin) for all simulated substrate and power conditions.

		$\mathit{T}\mathbf{0}\mathbf{=}298 \mathbf{K}$	$\mathit{T}\mathbf{0}\mathbf{=}373 \mathbf{K}$	$\mathit{T}\mathbf{0}\mathbf{=}643 K$
$P=100 \mathrm{W}$	$T_{\mathrm{m}ax}$	$560$	$1300$	$1550$
	$\nabla T_{0 \mathsf{\mu }\mathrm{m}\to -25 \mathsf{\mu }\mathrm{m}}$	$70$	$50$	$80$
	$\nabla T_{-25 \mathsf{\mu }\mathrm{m}\to -50 \mathsf{\mu }\mathrm{m}}$	$180$	$220$	$170$
	$\nabla T_{-50\mathsf{\mu }\mathrm{m}\to -75 \mathsf{\mu }\mathrm{m}}$	$225$	$200$	$210$
	$\nabla T_{0 \mathsf{\mu }\mathrm{m}\to -75 \mathsf{\mu }\mathrm{m}}$	$475$	$470$	$460$
$P=200 \mathrm{W}$	$T_{\mathrm{m}ax}$	$1733$	$1760$	$1900$
	$\nabla T_{0 \mathsf{\mu }\mathrm{m}\to -25 \mathsf{\mu }\mathrm{m}}$	$3$	$40$	$70$
	$\nabla T_{-25 \mathsf{\mu }\mathrm{m}\to -50 \mathsf{\mu }\mathrm{m}}$	$110$	$30$	$100$
	$\nabla T_{-50 \mathsf{\mu }\mathrm{m}\to -75 \mathsf{\mu }\mathrm{m}}$	$420$	$400$	$210$
	$\nabla T_{0 \mathsf{\mu }\mathrm{m} \to -75 \mathsf{\mu }\mathrm{m}}$	$533$	$470$	$380$
$P=400 \mathrm{W}$	$T_{\mathrm{m}ax}$	$2950$	$3000$	$3200$
	$\nabla T_{0 \mathsf{\mu }\mathrm{m}\to -25 \mathsf{\mu }\mathrm{m}}$	$150$	$170$	$200$
	$\nabla T_{-25 \mathsf{\mu }\mathrm{m}\to -50 \mathsf{\mu }\mathrm{m}}$	$450$	$430$	$450$
	$\nabla T_{-50 \mathsf{\mu }\mathrm{m}\to -75 \mathsf{\mu }\mathrm{m}}$	$560$	$550$	$450$
	$\nabla T_{0 \mathsf{\mu }\mathrm{m}\to -75 \mathsf{\mu }\mathrm{m}}$	$1160$	$1150$	$1100$

. The main implication of the results is that an increase in the substrate temperature causes the powder bed to use less energy from the heat flux, consequently decreasing the temperature gradient through the layer thickness. Nevertheless, this increase is not linear, meaning that a rise of $100 \mathrm{K}$ in the temperature does not bring about a $100 \mathrm{K}$ change in the temperature distribution obtained. The packing density does not significantly affect the temperature distributions, especially for high laser power inputs such as $200$ and $400 \mathrm{W}$. The only observable impact through the thickness is seen in the case of $P=100 \mathrm{W}$, with SC and FCC differing in $30 \mathrm{K}$ between each other, as seen in Figure 7a. The powder diameter, on the other hand, did not affect the temperature distributions in any of the conditions justified by the high rate of temperature change over a small timeframe as well as the small difference of $k_{eff}$ among the powder diameters of the same packing density, as observed in Figure 2. It is important to emphasize, however, that the packing density and powder diameter only affect the temperature distributions that are below the melting point ($T_{solidus}$).

The best scenario among all conditions is $P=200 \mathrm{W}$ and $T_0=643 \mathrm{K}$, with a lower gradient of $380 \mathrm{K}$ between the bottom and top surfaces. Although the case of $P=100 \mathrm{W}$ has a lower heat flux, it produced a higher temperature gradient when compared with the case of $P=200 \mathrm{W}$, mainly because the former condition did not cause the substrate to reach the melting point. The latter resulted in one or more points through the layer thickness being above the melting point or in the mushy zone. When the material is in the mushy zone, it requires a great deal of energy to change the state (solid to liquid), and thus the gradient was reduced in the case of $P=200 \mathrm{W}$.

4. Melt Pool Analysis

Identifying the melt pool region in SLM processes is important for determining each scanned track’s heat-affected zone (HAZ). Usually, the melt pool exceeds the diameter of the laser beam depending on parameters such as scanning speed and power input. The following results are for a substrate temperature of $643 \mathrm{K}$, SC packing density, and a $20 \mu \mathrm{m}$ powder diameter. The remaining packing density and powder diameter data sets have not been compiled here since the previous sensitivity analysis showed a minimal impact on temperature distributions [30].

When using $P=100 \mathrm{W}$, the powder does not effectively melt. Temperature distributions are kept below the melting point through the entire thickness of the layer. Figure 8 shows the temperature output; notice that the maximum temperature is 1544 K. For $P=200 \mathrm{W}$ (Figure 9a), the maximum temperature value was fixed at $1733 \mathrm{K}$, and the minimum temperature value was fixed at $1703 \mathrm{K}$ in the output countour; thus, the light grey region in the temperature field corresponds to the melt pool region ($1733 \mathrm{K}<T<1703 \mathrm{K})$. The comet shape formed in the melt pool region is an expected feature since the Goldak heat flux input used in the current model resembles this shape [30]. Note that all temperatures are expressed in degrees Kelvin ($\mathrm{K})$.

The molten material at $P=400 \mathrm{W}$ (Figure 9b) occurs along the entire distance of the bed scanned by the laser and through all the powder bed thicknesses. At the beginning of the track, it is apparent that the melt pool area increases in width over time. This change indicates that the melt pool has high energy and is exchanging heat with the nearby powder, melting it and increasing the HAZ.

Regarding the melt pool dimensions for $P=200 \mathrm{W}$ and $400 \mathrm{W}$, the feasibility of using a power input of $200 \mathrm{W}$ is evident, given the small HAZ present. Figure 10 and Figure 11 show the melt pool size for $P=200 \mathrm{W}$ and $400 \mathrm{W}$ along different cross-sections.

The material becomes fully molten at $P=200 \mathrm{W}$ up to $-50 \mu \mathrm{m}$; the light grey in Figure 10 and Figure 11 represents the region where temperatures exceed $1733 \mathrm{K}$ ($T_{liquidus}$). The remaining colours are $1703–1733 \mathrm{K}$, representing the mushy zone, a mixture of solid and liquid material. Finally, the dark grey represents temperatures below $1703 \mathrm{K}$ ($T_{solidus}$). The dimension of the melt pool at $P=200 \mathrm{W}$ is $75\times 425 \mu \mathrm{m}$, a width that is 1.5× larger than the laser beam diameter used in the model.

On the other hand, at $P=400 \mathrm{W}$, the thickness of the layer is above the melting point, with $100 \mu \mathrm{m}$ of the width at the bottom surface and $150 \mu \mathrm{m}$ of the width at the top of the powder bed; three times larger than the laser beam diameter. The entire track is also molten ($750 \mu \mathrm{m}$ in length), and at the end of the laser scanning period, at $1.5 \mathrm{m}s$, the melt pool width at the beginning scan point is $~180 \mu \mathrm{m}$.

5. Discussion

Power input and substrate temperature played a significant role in the analysis, with all the scenarios having specific implications:

• $P=100 \mathrm{W}$ was the lowest power input at which temperatures did not reach the melting point. According to Gibson, the powder can sinter at half the melting point temperatures, and in the current investigation, the achieved $T_{\mathrm{m}ax}$ was around $1500 \mathrm{K}$ for $T_0=643 \mathrm{K}$. The $T_{solidus}$ of the material was $1703 \mathrm{K}$, more than enough for necking to occur among the particles. However, we cannot draw further conclusions on the degree to which the material would effectively consolidate since the temperature mentioned is only at the surface of the powder bed. On the bottom surface, the temperature was $1100 \mathrm{K}$, sufficient to start the sintering between the particles at a smaller scale. $T_0=643 \mathrm{K}$ is strongly recommended to be used with $P=100 \mathrm{W}$, given the aforementioned statements. When using $T_0=298 \mathrm{K}$ and $T_0=373 \mathrm{K}$, the achieved $T_{\max }$ was around $1250$ and $1300 \mathrm{K}$, respectively, and the $T_{\min }$ was around $775$ and $850 \mathrm{K}$, on the threshold of the sintering condition mentioned by Gibson and thus not enough to fully consolidate the material.
• $P=200 \mathrm{W}$ is the ideal situation among all the power inputs analyzed, given the melt pool behavior and the temperature gradients. For $T_0=643 \mathrm{K}$, we achieved the optimal temperature gradient of $380 \mathrm{K}$, the lowest of all the conditions simulated, and thus this temperature is strongly recommended with this power input. The main reason is that the temperature distribution was just enough to reach the $T_{solidus}$ for $h=0 \mu \mathrm{m}$, $–25 \mu \mathrm{m}$, and $–50 \mu \mathrm{m}$, with a $T_{\mathrm{m}ax}=1900 \mathrm{K}$. In this case, when the temperatures are between the $T_{solidus}$ and $T_{liquidus}$, the latent heat of fusion plays an important role, consuming most of the heat to change the phase from the solid state to liquid and vice versa. For this reason, the temperature gradient is relatively small compared to other power inputs, even for the other substrate temperatures.
• $P=400 \mathrm{W}$ is not recommended as a power input to be used for SS-304L, the reason being that temperatures reached $3200 \mathrm{K}$ when using $T_0=643 \mathrm{K}$, with a temperature gradient of $1100 \mathrm{K}$ between the top and bottom of the powder bed. Another observation is the high cooling rate in Figure 7e from $3200 \mathrm{K}$ at the top surface to $2100 \mathrm{K}$, where all layers’ temperatures are equalized. This can be explained by the fact that the model accounted for convection and radiation, which is an exponential function of the temperature as seen in Equation (3). Therefore, when in a liquid state, the cooling rate is much higher, especially in Figure 7e, but also for Figure 5e and Figure 6e. In addition, the entire thickness of the powder bed exceeded the melting point, as the melt pool analysis showed; consequently, the HAZ is very large, indicating that re-melting from previously layers or substrate could occur.

Overall, the observed temperature distributions closely followed the behavior of SS-304L in other experimental studies found in the literature. Abd-Elghany and Bourel printed SS-304L to investigate its mechanical properties using different setups. The authors produced manufactured specimens using a machine with a power input of $100 \mathrm{W}$ and $30$, $50$, and $70 \mathsf{\mu }\mathrm{m}$ layer thicknesses, concluding that a higher layer thickness produced specimens with low density and poor mechanical properties [7]. This can be used as a reference to our setup of $P=100 \mathrm{W}$ and layer thickness of $75 \mathsf{\mu }\mathrm{m}$, in which case the laser input was not enough to bring the temperature to the melting point, and thus consolidation between powder particles was poor.

6. Conclusions

The parametric low-cost FEM thermal model proposed in this study can measure temperature distributions through a powder bed and, consequently, the temperature gradient of a single layer and a single track of laser scanning using the SLM process. Parameters such as the power input, powder diameter, powder packing density, and substrate temperature were analyzed. Packing density and powder diameter influenced the effective thermal conductivity of the power, as seen in previous works. These parameters were implemented in the simulation to analyze substrate temperature effects and melt pool size.

The substrate temperature is a variable that cannot be neglected when manufacturing/printing parts using SLM technologies. The proper preheating of the chamber depends upon it and the quality of the printed parts. We have found that, depending on the alloy used and its thermal properties, the substrate temperature can help to improve the quality of the produced part ($P=200 \mathrm{W}$) by decreasing the temperature gradients within the layer thickness, thus helping to reduce residual stresses. However, in some cases where the power input is too low or too high ($P=100 \mathrm{W}$ and $400 \mathrm{W}$), the effects are insignificant, as previously observed. The melt pool analysis showed that $P=400 \mathrm{W}$ brought a large HAZ into the powder bed, the undesirable factor that can induce a very large adjacent track and underneath layer material melting. A proper balance between parameters, thermal properties, and environmental conditions is necessary to manufacture components with acceptable mechanical properties.