# Analytical Prediction of Balling, Lack-of-Fusion and Keyholing Thresholds in Powder Bed Fusion
## 3 Experimental Validation and Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Power (W)**} & **Scanning Speed (mm/s)** & **Computed Dotlen Pool (\(\mu\)m)** & **Computed Dotlen Pool (\(\mu\)m)** & **Energy Density Width (\(\mu\)m)** & **Measured Porosity (\%)** & \(\frac{H^{2}}{W^{2}}+\frac{L^{2}}{D^{2}}\) & \(\frac{\Delta H}{h_{s}}\) \\ \hline
90 & 1600 & 14.1 & 26.1 & 28.1 & 13.4 & 12.6 & 1.7 \\
90 & 1200 & 18.2 & 34.1 & 37.5 & 3.8 & 7.4 & 2.0 \\
90 & 800 & 24.2 & 46.1 & 56.3 & 0.3 & 4.1 & 2.4 \\
90 & 600 & 28.3 & 54.1 & 75.0 & 0.4 & 3.0 & 2.8 \\
90 & 400 & 38.4 & 74.1 & 112.5 & 0.4 & 1.6 & 3.4 \\
90 & 300 & 46.5 & 90.2 & 150.0 & 0.5 & 1.1 & 4.0 \\
90 & 200 & 60.6 & 118.2 & 225.0 & 0.9 & 0.6 & 4.9 \\
90 & 100 & 88.9 & 174.3 & 450.0 & 5.9 & 0.3 & 6.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of lack-of-fusion and keyholing for Inconel 718 [28]. The thresholds for the balling defect were calculated with the information of the predicted molten pool width and length. The 316L stainless steel was used to validate the proposed analytical method for balling prediction. The boundary heat loss and effects of powder bed porosity were not considered in this calculation, because the information of part size and powder size distribution were not given in the reference paper. Table 3 shows the thermal properties of 316L. Table 5 shows the process conditions and predicted results. The experimental observation of balling behavior is shown in Figure 6. The balling defect becomes obvious when the scanning speed is over 350 mm/s, which is very close to the predicted result. The prediction for the occurrence of keyholing defect was carried out with the information of material properties and process conditions. The calculated results are shown in Tables 2 and 6. The predicted thresholds are 5.4 for Ti6 Al4V and 6.2 for Inconel 718. The comparison of experimental results and analytical predictions are shown in Figure 7. Acceptable agreement can be observed between experimental results and analytical predictions. Figure 4: Powder packing pattern with 300 powders. (**a**) Ti6 Al4V, (**b**) Inconel 718. Figure 5: Predicted thresholds for lack-of-fusion defect. (**a**) Ti6 Al4V, (**b**) Inconel 718 [27,28]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Power (W)**} & \multicolumn{2}{c}{**Scanning Speed**} & \multicolumn{2}{c}{**Energy Density**} & \multicolumn{2}{c}{**Measured**} & \multicolumn{1}{c}{\(\frac{\Delta H}{h_{*}}\)} \\  & **(mm/s)** & **(J/mm\({}^{3}\))** & **Porosity (\%)** & \(\frac{\Delta H}{h_{*}}\) \\ \hline
50 & 500 & 33 & 22.1 & 1.5 \\
50 & 750 & 22 & 44.4 & 1.2 \\
50 & 1000 & 16 & 55.1 & 1.0 \\
50 & 1200 & 13 & 64.6 & 0.9 \\
100 & 500 & 66 & 0 & 2.9 \\
100 & 750 & 44 & 5.6 & 2.4 \\
100 & 1000 & 33 & 19.6 & 2.1 \\
100 & 1200 & 27 & 25.2 & 1.9 \\
150 & 500 & 100 & 7.8 & 4.4 \\
150 & 750 & 66 & 0 & 3.6 \\
150 & 1000 & 50 & 0 & 3.1 \\
150 & 1200 & 41 & 5.1 & 2.8 \\
195 & 500 & 130 & 9.2 & 5.7 \\
195 & 750 & 86 & 2.3 & 4.7 \\
195 & 1000 & 65 & 0 & 4.1 \\
195 & 1200 & 54 & 0 & 3.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of keyholing for Ti6 Al4V [10]. Figure 6: Experimental observation of single tracks for 316L [32]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Power (W)**} & \multicolumn{2}{c}{**Scanning Speed**} & \multicolumn{2}{c}{**Computed Molten**} & \multicolumn{1}{c}{**Computed Molten**} & \multicolumn{1}{c}{\(\frac{\pi w}{l}\)} \\  & **(mm/s)** & **Pool Width (\(\mu\)m)** & **Pool Length (\(\mu\)m)** & \(\frac{\pi w}{l}\) \\ \hline
190 & 20 & 427.1 & 481.0 & 2.8 \\
190 & 50 & 306.5 & 424.8 & 2.3 \\
190 & 150 & 185.9 & 372.7 & 1.6 \\
190 & 200 & 155.8 & 362.7 & 1.3 \\
190 & 250 & 135.7 & 354.7 & 1.2 \\
190 & 300 & 125.6 & 350.7 & 1.1 \\
190 & 350 & 105.5 & 346.7 & 1.0 \\
190 & 400 & 105.5 & 342.7 & 1.0 \\
190 & 450 & 95.5 & 340.7 & 0.9 \\
190 & 500 & 85.4 & 338.7 & 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of balling for 316L.