# Analytical Prediction of Balling, Lack-of-Fusion and Keyholing Thresholds in Powder Bed Fusion
## 3 Experimental Validation and Discussion  
This study proposes analytical methods to predict the defect generation in laser powder bed fusion additive manufacturing. The occurrence of lack-of-fusion, balling and keyholing defects were predicted under various combinations of process conditions and validated by experimental study of different materials. All the experimental data used in this study are adopted from the literature. The prediction accuracy of the proposed analytical thermal model has been validated in previous papers of our group. The presented model has shown acceptable accuracy in the prediction of molten pool dimensions in powder bed fusion. Furthermore, it has been validated that the consideration of boundary heat loss can improve the prediction accuracy for the molten pool dimensions [18]. Table 1, Table 2 and Table 5 show the predicted molten pool dimensions for three different materials under various process conditions. The energy density in the table is defined as  
For the prediction of the formation of lack-of-fusion defect, Ti6 Al4V and Inconel 718 were employed as the materials. Tables 1 and 2 show the process conditions for Ti6 Al4V and Inconel 718, respectively. Table 3 shows the thermal properties of Ti6 Al4V and Inconel 718. The powder size distributions of the two materials are shown in Figure 3. With the advancing front approach, the powder packing pattern was obtained, as shown in Figure 4. By image analysis of the packing pattern using Image J, the porosity of the powder bed was calculated, as shown in Table 4. To investigate the influence of the powder numbers on the calculation of powder bed porosity, the porosity was calculated at least triple under different levels of powder number. From the results, it shows that the influence of powder number is negligible during the calculation of powder bed porosity. The average porosities were used in this study, which is 12.88% for Ti6 Al4V and 13.47% for Inconel 718. With the results of molten pool geometries, the lack-of-fusion thresholds were computed. The calculated results are shown in Tables 1 and 2, which is 110 J/mm\({}^{3}\) for Ti6 Al4V and 160 J/mm\({}^{3}\) for Inconel 718. To validate the prediction accuracy of the proposed analytical methods, the predicted thresholds were compared with experimental measurements, as shown in Figure 5. The predicted results have good agreements with experimental data for the two materials. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Power (W)**} & \multirow{2}{*}{ \begin{tabular}{c} **Scanning** \\ **Speed (mm/s)** \\ \end{tabular}  } & \begin{tabular}{c} **Computed** \\ **Molten Pool** \\ **Depth (\(\mu\)m)** \\ \end{tabular}  & \begin{tabular}{c} **Computed** \\ **Molten Pool** \\ **Width (\(\mu\)m)** \\ \end{tabular}  & \ \begin{tabular}{c} **Energy** \\ **Density** \\ **Density** \\ **(J/mm\({}^{3}\))** \\ \end{tabular}  & \begin{tabular}{c} **Measured** \\ **Porosity (\%)** \\ \end{tabular}  & \(\frac{\text{H}^{2}}{\text{W}^{2}}+\frac{\text{L}^{2}}{\text{D}^{2}}\) \\ \hline
40 & 1200 & 20.2 & 38.1 & 11.1 & 22.6 & 9.1 \\
40 & 1080 & 22.2 & 42.1 & 12.3 & 19.5 & 7.5 \\
40 & 960 & 24.2 & 46.1 & 1 \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Powder Number**} & \multicolumn{2}{c}{**Powder Bed Porosity (\%)**} \\ \cline{2-3}  & **Inconel 718** & **Ti6 Al4V** \\ \hline
100 & 13.66 & 12.87 \\
200 & 14.01 & 13.21 \\
300 & 13.96 & 12.62 \\
400 & 13.29 & 12.76 \\
500 & 12.41 & 12.95 \\ Average & 13.47 & 12.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Powder bed porosity. Figure 3: Powder size information. (**a**) Powder size distribution of Ti6 Al4V [27]. (**b**) Powder size distribution of Inconel 718 [28].