## 3 Results and Discussions
### SLM Inconel 718  
We now apply the proposed heat source for the SLM Inconel 718, and the experimental results are taken from [PERSON] et al. [32]. The initial parameter \(\eta_{t=0}\) is equal to 40 \(\upmu\)m, and \(z_{0}\) is \(0.4*\eta_{t}\). The reported absorptivity of Inconel 718 varies from 0.3-0.87 [27,44]; therefore, 0.7 is used in this study. The processing parameters (scanning speed and laser power) used are shown in Table 2, and other parameters can be found in the work of [PERSON] et al. [27].  
Figure 18 presents the melting pool at different moments during the simulation. Compared to the temperature distribution in Figure 13, the heat diffuses very slowly in Inconel 718 because of its low diffusivity.  
Figure 19 shows the final simulated molten pool shape (speed: 200 mm/s, power: 100 Watt). The molten pool depth increases in the transient stage and keeps constant in the steady-state stage. Boundary effects become negligible due to low diffusivity. Thus, the melt pool depth in the steady-state stage does not increase as we observed in SLM ALSi10 Mg.  
Similarly, the effect of the time step is studied in SLM Inconel 718. Figure 20 presents the molten profiles after the SLM process and the variation of melt pool depth in the scanning direction. In the steady-state stage, a maximum difference of 2.9% is observed, and we can conclude that the precision is satisfactory.  
Finally, a comparison of the molten pool dimensions given by experiments and numerical simulations is presented in Figure 21. The simulated melt pool depth gives good precision compared to experiments, while the width is slightly under-estimated. Thus, a maximal relative error of 9.6% is found.  
\begin{table}
\begin{tabular}{c c c c c} \hline Scanning speed (mm/s) & 200 & 200 & 200 & 200 \\ \hline Laser power (Watt) & 100 & 150 & 200 & 300 \\ \hline Beam radius (\(\upmu\)m) & & & 37.5 & \\ \hline Layer thickness (\(\upmu\)m) & & 40 & \\ \hline Absorptivity & & 0.7 & \\ \hline Initial temperature (\({}^{\circ}\)C) & & 20 & \\ \hline \end{tabular}
\end{table}
Table 2: Scanning speed and laser power in SLM Inconel 718 [32].  
Figure 17: Comparison of molten pool dimensions given by experiments [33] and numerical simulations: fixed laser power of 200 Watt (**a**) and fixed scanning speed of 600 mm/s (**b**).  
Figure 19: Final simulated molten pool shape in SLM Inconel 718 (V200-P100) (**a**) and the evolution of melt pool depth in scanning direction (**b**).  
Figure 20: Investigation of effect of time step (0.050 ms, 0.075 ms, 0.100 ms, 0.125 ms) in SLM Inconel 718 (V200-P100): melt pool depth in the symmetrical plane (**a**) and comparison of the evolution of melt pool depth simulated for different time steps (**b**).  
The proposed heat source is therefore validated through the comparisons of its results (melt pool morphology for two materials: AlSi10 Mg and Inconel 718) with those of the existing numerical method (anisotropic thermal conductivity technique) and experimental tests. Compared to the anisotropic thermal conductivity technique, the procedure of parameter calibration in the proposed heat source (only the parameter \(z_{0}\) must be calibrated) is easier. Moreover, numerical investigation shows that the proposed heat source is slightly sensitive to the choice of the time step. In contrast, a sharp increase of thermal conductivity induced by the anisotropic thermal conductivity technique leads to the difficulty of converging, which results in only very small time steps being applied. The difficulty of converging could be further increased if the metallurgical transformation is considered. Therefore, the proposed heat source is more efficient in terms of computation cost than the anisotropic thermal conductivity technique. Note that the proposed heat source can be subsequently used for other materials and processes (for example, laser welding by the keyhole technique).