## 3 Experimental Validation and Discussion  
In this research, an analytical modeling strategy was developed for the molten pool geometries prediction in LPBF. The process conditions-dependent laser absorptivity was calculated by an empirical model. The molten pool shapes were determined by comparing melting temperature with the temperature field predicted by a closed-form point moving heat source model. Ti6 Al4V was employed as the material to validate the prediction accuracy of the presented analytical method. The experimental measurements of the molten pool size of Ti6 Al4V in single-track experiments were used for validation, and were reported in [22]. The process conditions and experimental data of molten pool size are shown in Table 1. It should be noted that the molten pool dimensions were measured through image analysis of the optical micrographs of the molten pool cross-sections. To calculate the absorptivity under different process conditions, the material properties of Ti6 Al4V are needed as inputs, which are shown in Table 2. These material properties are assumed to be temperature-independent, which are chosen as the values at melting temperature (\(T_{m}\)) of Ti6 Al4V. The minimal absorptivity (\(A_{m}\)) of Ti6 Al4V in the transition regime from conduction mode to keyhole mode was measured as 0.45 [43]. The laser beam radius is 50 \(\mu m\)[22]. The calculated absorptivity under various process conditions is also shown in Table 1. It should be noted that the initial temperature for the LPBF process in \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Case** \\ **Number** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Power** \\ **(W)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Scanning** \\ **Speed** \\ **(mm/s)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Normalized** \\ **Enthalpy** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Calculated** \\ **Absorptivity** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Depth** \\ **(\(\mu\)m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Width** \\ **(\(\mu\)m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Depth** \\ **(\(\mu\)m)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Width** \\ **(\(\mu\)m)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Length** \\ **(\(\mu\)m)** \\ \end{tabular} } \\ \hline
1 & 100 & 500 & 4.6 & 0.57 & 43.6 & 117.9 & 54.5 & 105.5 & 180.9 \\
2 & 100 & 750 & 3.7 & 0.48 & 31.9 & 98.0 & 42.4 & 85.4 & 145.7 \\
3 & 150 & 500 & 6.9 & 0.65 & 100.9 & 145.0 & 72.7 & 145.7 & 291.5 \\
4 & 150 & 750 & 5.6 & 0.57 & 72.0 & 134.4 & 58.6 & 115.6 & 251.3 \\
5 & 150 & 1000 & 4.9 & 0.51 & 52.7 & 115.3 & 46.5 & 95.5 & 216.1 \\
6 & 150 & 1200 & 4.4 & 0.46 & 49.2 & 108.1 & 42.4 & 85.4 & 201.0 \\
7 & 195 & 500 & 8.9 & 0.68 & 174.9 & 192.8 & 86.9 & 175.9 & 386.9 \\
8 & 195 & 750 & 7.3 & 0.62 & 110.5 & 160.6 & 68.7 & 135.7 & 351.8 \\
9 & 195 & 1000 & 6.3 & 0.57 & 81.1 & 129.7 & 58.6 & 115.6 & 316.6 \\
10 & 195 & 1200 & 5.8 & 0.53 & 63.9 & 122.5 & 50.5 & 95.5 & 286.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison between experimental [22] and predicted molten pool size of Ti6 Al4V. this study is room temperature. The proposed model can consider the preheating effect by changing the initial temperature to the preheating temperature of the LPBF process. With the information on thermal properties, process conditions, and absorptivity, the point moving heat source model was employed to compute the temperature distribution and obtain the estimation of molten pool dimensions. Figure 1 shows the temperature profiles and molten pools of the central cross-section in the \(x\), \(z\) plane (\(x\) axis is parallel to the scanning direction). The predicted molten pool width and depth with different absorptivity are shown in Table 1. The molten pool dimensions increase with the laser power and decrease with the scanning speed.