Influence of AlSi10Mg Thermophysical Properties on the Melt Pool Morphology During High-Fidelity Simulation of Laser Powder Bed Fusion

Abstract

Laser powder bed fusion (LPBF) is an advanced additive manufacturing method, but its productivity is relatively low, which limits its application. Performance can be increased without hardware modifications by enlarging the powder-layer thickness. However, this approach requires deeper investigation because the probability of defects (keyhole porosity, lack of fusion) rises substantially, and experiments become costly since each thickness value requires a separate LPBF run. High-fidelity simulation under such conditions can reduce the experimental workload. Reliable predictions, however, require numerous thermophysical parameters; reported values are often inconsistent or unavailable, and few studies have quantified their influence on simulation outcomes. A Lattice Boltzmann-based model is adopted to simulate the keyhole melting mode of AlSi10Mg. The effects of laser spot diameter, laser absorptivity, and the temperature dependence of thermal diffusivity and surface tension on the results are investigated. Predicted melt-pool morphologies are compared with cross-sections of experimental single tracks.

1. Introduction

Laser powder bed fusion (LPBF) is currently one of the most advanced and widely used technologies for additive manufacturing of metal products. The technology involves the synthesis of volumetric metallic parts from powder layer by layer using laser irradiation as a heat source. This principle allows synthesizing products of almost any shape from a wide range of materials and has a high resolution [1]. The resolution of standard LPBF machine is about 150 μm (lower limit), while maximum size of a part is limited by chamber dimensions.

Initial material for LPBF is metallic powder with spherical particles and narrow particle size distribution providing high flowability and tap density of the powder, which is important for smooth powder layer formation during synthesis. Such spherical powders are usually produced via gas atomization and subsequent sieving. Among the wide range of materials adopted for LPBF, the most widely used are aluminum (AlSi10Mg), titanium (Ti-6Al-4V) alloys, and stainless steel (316L) [2,3,4]. AlSi10Mg alloy possesses excellent combination of high mechanical properties, corrosion resistance, low density, and relatively low price, which made it very popular in practice for the production of various parts for aerospace, automotive and other areas [5].

One of the limiting factors of LPBF technology is the long duration of the synthesis, which causes low productivity and limits the widespread application of the technology in industry. Reducing the synthesis time and increasing the productivity of LPBF is possible due to printing with an increased scanning speed and/or with an increased powder layer thickness. In this case, varying the layer thickness is more significant for overall productivity [6]. The greater the powder layer thickness, the smaller the total number of layers during product synthesis, which can significantly affect the overall time consumption. The practical implementation of this approach was shown in [7] using a higher-power laser and an increased diameter of the laser beam spot on the powder layer in order to increase dimensions of melt pool. A number of experimental works are known [8,9,10,11], in which studies were conducted on the effect of increased layer thickness on the structure and properties of various materials without modifying the equipment. However, an increased layer thickness can lead to negative effects, such as an increase in the number of defects (pores, unmelted areas), deterioration in surface quality, and a decrease in the resolution of the technology. Thus, when implementing high-speed printing using the LPBF method, it is necessary to select a balanced layer thickness value, which, on the one hand, will ensure an increase in productivity, and on the other hand, will not lead to a significant increase in material defects and, as a consequence, a decrease in functional properties. To select such a balanced synthesis mode, it is necessary to construct dependencies of the material properties on the synthesis parameters, which is associated with a large volume of experimental work on printing and certification of samples. The creation of a model that allows predicting the structure and properties of the material after printing depending on the synthesis mode allows minimizing the amount of experimental work and reducing the costs of its implementation.

Numerical simulation is recognized as an alternative solution to the experimental approach to process-parameter optimization, which allows us to predict the final state of the manufactured material and to reduce costs. Many studies are focused on the simulation of the LPBF process, and various methods and techniques have been developed, such as the Lattice Boltzmann method, the finite element method, the finite volume method, smooth particle hydrodynamics, etc. [12]. The whole range of scales (from melt pool to part) has been considered depending on specific objective. Part-scale modeling comes down to heat transfer and equilibrium equations supplemented in some cases by metallurgical transformation equations [13]. Such modeling is similar to welding simulations; appropriate approaches and techniques have been developed, and the finite element method is usually used for this purpose, allowing to study and predict heat transfer and residual stress effects [14,15]. However, the limitations and simplifications of the part-scale simulation lead to its low accuracy. Mesoscale modeling deals with melt pool simulation that allows consideration of fluid dynamics and surface tension and, in turn, predict single-track morphology and temperature fields [16]. Powder is usually considered as a continuum layer. Further accuracy can be achieved at the powder scale, i.e., by resolving every particle and taking into account interaction between powder and liquid metal and laser. It makes it possible to conduct deep investigations of melt pool stability, heat and mass transfer, defect formation, and other subtle effects depending on LPBF process parameters, but requires high computational resources [17,18,19].

Thus, the application of deep modeling to investigate the effect of high-speed printing on the manufactured material is rational and promising. This work is the first necessary step towards solving the problem. The aim of the work is to investigate the influence of the main thermophysical properties on the melt pool morphology with the help of a high-fidelity model describing the LPBF process with the possibility of varying the synthesis mode and allowing determination of the parameters of the melt pool. The creation of such a model together with its verification by experimental results is the first stage of the practical implementation of the theoretical prediction of the structure and properties of the material after LPBF, including high-speed printing with increased scanning speeds and powder layer thickness.

2. Mesoscopic Molten Pool Dynamics Model

For modeling single tracks, the KiSSAM (Kintech Simulation Software for Additive Manufacturing, www.kissam.cloud) software package was used. The software is based on the hydrodynamic modeling of the melt pool using the Lattice Boltzmann method (LBM) [20,21]. LBM is one of the most efficient CFD methods and provides a high degree of parallelism and computational performance and at the same time ensures the necessary accuracy and convergence at the mesoscopic level where the characteristic size of the melt pool is about 100 μm. The fluid dynamics simulation kernel is also extended with additional models that are relevant for LPBF, such as surface tension, wetting, phase transitions, evaporation and fluid-gas interaction models at the fluid interface, a thermal solver, and laser beam tracing.

Strictly speaking, LBM does not have a well-defined stability condition. In real world, the standard BGK collision term usually provides stability at Reynolds numbers Re < 1000 and Mach numbers Ma ≲ 0.3 [22]. Here, the Mach number is not a physical quantity but is defined as $Ma={\displaystyle \frac{u}{c_s}}={\displaystyle \frac{u\surd 3∆t}{∆x}}$, where u is a characteristic speed of liquid melt, c_s is a lattice sound speed, and Δx and Δt are the spatial and time steps, respectively.

LBM also has the second order of convergence in the Ma number, so it should be as low as possible. So, finally, there are two constraints on the choice of spatial and time steps (∆x and ∆t):

$$1000>Re={\displaystyle \frac{uL}{\nu }}\stackrel{\mathrm{in\; dimensionless\; units\; LBM}}{\approx }\frac{c_{s}Ma·10∆x}{(\tau -1/2)c_s^2}=\frac{Ma·10∆t\surd 3}{\tau -1/2}\lesssim \frac{10}{\tau -\frac{1}{2}}<1000;$$

(1)

$$Ma={\displaystyle \frac{u∆t}{∆x}}\ll 1$$

(2)

The condition (1) requires that the relaxation parameter τ should be greater than 0.51, that is, $3\widehat{\nu }+0.5={\displaystyle \frac{3\nu ∆t}{{∆x}^2}}+0.5>0.51$, where $\widehat{\nu }$ is the kinematic viscosity in LBM units, and ν is the kinematic viscosity in physical units (SI). As a result, the following simple condition was obtained:

$$∆t\gtrsim 0.003{\displaystyle \frac{∆x^2}{\nu }}$$

(3)

From the second condition Ma ≪ 1 from Equation (2) and assuming that typical velocities in the melt pool are of the order of 1 m/s, the following condition was obtained:

$$∆t\ll {\displaystyle \frac{∆x}{1m/s}}$$

(4)

And also, the third relation must be satisfied—the Courant condition for the thermal solver:

$$∆t<{\displaystyle \frac{1}{6}}{\displaystyle \frac{∆x^2}{\kappa }}$$

(5)

where κ is the thermal diffusivity of the material in the solid phase and in the liquid phase at low temperature.

In combination with this, the time step ∆t should be chosen after the spatial step ∆x as follows:

$$∆t=min({\displaystyle \frac{0.003∆x^2}{\nu }},{\displaystyle \frac{∆x^2}{6k_{max}}})$$

(6)

where κ_max is the maximum value of thermal diffusivity for the temperature range T < 1.1 T_l (T_l is the liquidus temperature).

Note that the peculiarity of aluminum alloys is that they have a relatively high thermal conductivity. This imposes stronger restrictions on the time step. Considering that, for the AlSi10M alloy, the kinematic viscosity ν = 10⁻⁶ m²/sec and κ_max = 6.5 × 10⁻⁵ m²/sec (at a temperature of 300 K) [23], the recommended parameters for the steps in space and time are presented in

Table 1. Recommended parameters for the steps in space and time.

∆x = 2 µm	∆t = 10 ns
∆x = 3 µm	∆t = 22 ns
∆x = 4 µm	∆t = 40 ns
∆x = 5 µm	∆t = 60 ns
∆x = 6 µm	∆t = 90 ns
∆x = 7 µm	∆t = 120 ns

.

3. Simulation of AlSi10Mg Synthesis with Increased Layer Thickness

Preliminary experiments have shown that, for the synthesis of AlSi10Mg with low defect content using common LPBF systems with a nominal laser power of no more than 400 W, the scanning speed can be increased within the 300–1700 mm/s range. This limitation is due to the low absorptivity of aluminum alloys. As a result, no significant change in productivity will be achieved in this range. Therefore, the study was aimed at increasing the powder layer thickness, which in turn affects productivity to a greater extent than other process parameters. In this work, the limiting values of the layer thickness were determined using the computational model described in the previous section.

To validate the model, calculations were performed for individual tracks on a substrate without a powder layer. The cross-section of each track was studied using experimental methods. The software was used to study the cross-sections of the simulated remelted areas. The simulation results were compared with the corresponding experimental results for the following parameters:

• the depth of melting along the centerline in the direction of laser movement (hereinafter referred to as “depth”) (see Figure 1), its average value and standard deviation;
• the width of the remelted area at the level of the upper edge of the substrate (hereinafter referred to as “width”) (see Figure 1), its average value and standard deviation;
• the shape of the cross-section of the remelted area of the track.

Since one of the goals of the study is to select the critical powder layer thickness at which sufficient weld penetration occurs to ensure low porosity, the calculation of the depth is of decisive importance in the context of applying the results to real-world problems.

During the calculations of the melting process, melt hydrodynamics, and crystallization of each track, it is necessary to take into account the thermophysical and hydrodynamic parameters of the material. During the validation process, the literature data were used, and the sensitivity of the depth and width values to changes in individual material parameters was also studied.

4. Sensitivity to Laser Beam Diameter

Since it is rather difficult to determine the true diameter of the laser beam experimentally, the dependence of the morphology of the tracks on the beam diameter (D4s) was investigated by simulation. The results of the simulation and comparison with the experiment are shown in Figure 2 and Figure 3. The scanning speed was 600 mm/s, and the power was 300 W. Here and below, the unmelted part of the substrate is shown in shades of blue and the melted area is shown in shades of purple.

An analysis of the transition modes between deep and shallow penetration, as well as the values of the track width and depth at different laser beam speeds (see Figure 4) established that the nominal value of the width D4s = 80 µm is consistent with reality (defocusing is insignificant), and this value was used in further studies.

Generally, one can see that the melt pool depth strongly depends on the laser beam diameter. However, the melt pool width is not sensitive to the beam diameter in the keyhole regime.

5. Sensitivity to Absorption in the Liquid Phase

The absorption of the liquid phase (the melt) depends on the temperature. This parameter is rarely studied in the literature, and the specific absorption value may depend on the alloy composition. The effect of the absorption coefficient on the depth and width of the melted region was studied. The results are shown in Figure 5 and Figure 6.

The depth of penetration and the morphology of the entire remelted region vary with the absorption coefficient. However, for all the studied absorption values, the track depth exceeds the experimental value, except for one point, where the melting mode changes from the “keyhole” mode to the conductivity mode (A_T=100K = 0.08). The agreement of the width of the remelted region is satisfactory for all cases. The absorption coefficient as a function of temperature for each case is shown in Figure 6a [24].

6. Sensitivity to Thermal Diffusivity

The thermal diffusivity of the AlSi10Mg alloy was measured experimentally in [25] for parts printed by LPBF, as well as for a reference sample that was thermally annealed at 300 °C for 2 h after printing. The data include measurements of the first and second passes, as well as data for the reference sample and are in good agreement with the data for alloys with similar compositions from the handbook [26] (see Figure 7).

The sensitivity of the simulation results for a single track on a substrate to the thermal diffusivity value was investigated using the data from [25] as the base value. The obtained track depth and width values are shown in Figure 8. The thermal diffusivity d in Figure 8 is indicated in m²/s in the captions along the x-axis in the format [T, d] and has a linear dependence on temperature. The sensitivity over this range of thermal diffusivity change is low. The depth and width of the tracks change insignificantly.

7. Sensitivity to Surface Tension

The surface tension of the liquid phase of aluminum–silicon alloys (Al-Si) has been measured in several studies [27,28]. These studies have shown that the surface tension exhibits a linear dependence on temperature, with the slope of the σ (T) function (which determines the dynamics of Marangoni convection in the liquid) depending on the Si concentration in the alloy. In our case, the silicon content in the AlSi10Mg alloy is 10%. Therefore, the effect of surface tension on the shape of the track was studied, and the result was compared with the experimental cross-section (see Figure 9). In all the studied cases, the depth of the melted region exceeds the experimental one. The track width is practically independent on the surface tension. The coefficient c, which corresponds to the silicon concentration in the alloy under study, was chosen as the base value.

The corresponding values for surface tension are shown in Figure 10 and are marked by the letters a, b, and c.

The final list of the material parameters used in the numerical model is presented in

Table 2. List of the material parameters used in the model.

Thermophysical Properties of AlSi10Mg	Value
Density at temperature Tliq, kg/m3	2500
Viscosity, m2/s	10−6
Liquidus temperature Tliq, K	867
Solidus temperature Tsol, K	831
Surface tension, N/m	1.00 − 1.52 × 10−4 T
Wetting angle of the substrate surface, °	0
Wetting angle of the powder particle surface, °	120
Thermal diffusivity in the solid phase, m2/s	7.40 × 10−5 − 3.00 × 10−8 T
Thermal diffusivity in the liquid phase, m2/s	1.88 × 10−5 + 6.43 × 10−9 T
Isobaric volumetric heat capacity, J/(m3K)	2.3 × 106, at 0 < T ≤ 600 K
	2.5 × 106, at 600 K < T ≤ 800 K
	2.8 × 106, at 800 K < T ≤ 867 K
	2.6 × 106, at T > 867 K
Absorption coefficient in solid phase	0.1
Liquid phase absorption coefficient	8.86 × 10−2 + 2.38 × 10−5 T
Latent heat of melting, J/m3	1.06 × 109
Evaporation coefficients in the formula Psat(T)[Pa] = 10A−B/(C+T[K])
A	10.917
B	16,211
C	0

.

8. Investigation of the Constructive Convergence of the Solution

It is also important to analyze the numerical convergence with respect to the spatial and temporal steps. Because the exact solution is unknown, only a constructive convergence study is possible to investigate.

The numerical convergence of the solution (track depth) for two cases was also investigated: uniform and intense melting of a single track on the substrate. For this purpose, a series of calculations with different steps in spatial and time were performed. Figure 11 shows the dependence of the track depth on the steps for the case of intense melting. In Figure 11, Figure 12 and Figure 13, the calculations performed are shown in green dots, the abscissa axis shows the step in space ∆x, and the ordinate axis shows the ratio ∆t/∆x². The condition ∆t/∆x² < 2.5 (the upper limit of the figures) is limited by the Courant condition.

Figure 12 shows the depth variation (standard deviation) for intense melting.

For the case of uniform melting, a series of calculations were also performed to study the convergence. Figure 13 shows dependence of the track depth on the steps.

The results show that adequate solution accuracy and constructive convergence can be discussed only for spatial steps of ∆x ≤ 6 μm. If we assume that the most accurate solution is achieved for ∆x, ∆t → 0, then we can state that for the case of intense melting, with a decrease in the time step, the depth generally decreases, and with a decrease in the spatial step (while maintaining the ratio ∆t/∆x² = const), the depth increases. Nevertheless, in general, the error in the track depth is no greater than the depth variation. It follows that the use of the values ∆x = 6 μm and ∆t = 90 ns is optimal in terms of ensuring high computational throughput while maintaining adequate solution accuracy. For non-intense melting, it is also clear that the values ∆x = 6 μm and ∆t = 90 ns also provide acceptable accuracy.

9. Conclusions

This study investigated the sensitivity of numerical simulations of the LPBF process to various parameters, including mesh resolution, time step, thermal diffusivity, surface tension, and laser absorption coefficient. It was determined that for the AlSi10Mg alloy, the optimal simulation parameters are a grid size of 6 µm and a time step of 90 ns, ensuring a balance between computational accuracy and efficiency for wide range of parameters.

The simulation results were also validated against experimental data. It was found that the melt pool depth is highly sensitive to both the laser beam diameter and the laser absorption coefficient in the liquid phase, with even small variations in these parameters leading to significant deviations in penetration depth. This highlights the importance of accurately defining beam characteristics for reliable model predictions. Surface tension primarily affects the cross-sectional shape of the melt track, while thermal diffusivity has a weak influence on both melt pool depth and width. Additionally, melt pool width is generally insensitive to most parameters, unless the process is operating near the transition between keyholing and conduction melting regimes.

The developed approach can be further applied to study the influence of LPBF process parameters on material structure and quality.