# Study on Bulge State of PCnNi3 MoV Target Plates Penetrated by Square Fragments
## 4 Validation  
In order to validate the predictions of the bulge height of a gun steel target plate impacted by square tungsten alloy fragments, 6-mm square tungsten alloy fragments were used to carry out armor-piercing tests on gun steel target plates of different thicknesses, and a high-speed camera was used to measure the fragment velocities. The bulge height of  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & \(\mathbf{a}\) & \(\mathbf{b}\) & \(\mathbf{x}\) & \(\mathbf{y}\) \\ \hline Calibration value & \(-0.4911\) & \(-2.5281\) & \(0.6924\) & \(-0.8090\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Parameter calibration values.  
Figure 6: Variation of the bulge height with the fragment energy. (**a**) Condition 1 (fragment length: 6 mm, target plate thickness: 6 mm) (**b**) Condition 2 (fragment length: 6 mm, target plate thickness: 9 mm).  
the target plate was calculated using Equation (14). The results are shown in Table 7. The calculation error is  
\[\delta=\left|\frac{\text{Experimental values}_{h_{g}}-\text{Calculated value}_{h_{g}}}{\text{Experimental values}_{h_{g}}}\right|\times 100\% \tag{15}\]  
Since Equation (14) was obtained by fitting the test results after dimensional analysis, it is suitable for the calculation of the bulge height of a gun steel target plate. The applicable parameter ranges are \(v<1400\) m/s, \(0.42<l/h<1\). Some of the data in Table 7 were compared with the values calculated using the following equation [18]:  
\[h_{g}=Avm^{U} \tag{16}\]  
where \(A\) and \(U\) are the fitting coefficients, \(A=1.4\times 10^{-3}\), and \(U=0.79\). \(m\) is the mass of the fragment (kg), and \(v\) is the striking velocity of the fragment (m/s).  
As shown in Table 7, the average relative error between the bulge height calculated using Equation (14) and the test value was 7.07%, and the maximum error was 15.91%. In comparison, the relative error between the calculated value using Equation (16) and the test value was more than 90%. Therefore, the model established by the dimensional analysis in this study had a higher accuracy. Figure 7 shows that about 95% of the calculation points of the equation in this study were concentrated within 15%, and about 60% were within 10%. According to the above analysis, the model established in this study meets the requirements of engineering applications.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Fragment Length (mm)** & **Target Plate Thickness (mm)** & **Striking Velocity (m/s)** & **Striking Kinetic Energy (J)** & \multicolumn{2}{c}{**Bulge Height (mm)**} & \multicolumn{1}{c}{**Relative Error**} \\ \cline{3-8}  & **Fragment Length (mm)** & **Target Plate Thickness (mm)** & **Striking Velocity (m/s)** & **Striking Kinetic Energy (J)** & \multicolumn{2}{c}{**Test Value**} & **Calculated Value** & **Error** \\ \hline
2-1 & 6 & 14 & 742 & 1104.06 & 0.49 & 0.529 & 7.95 \\
2-2 & 6 & 14 & 759 & 1153.52 & 0.56 & 0.582 & 3.92 \\
2-3 & 6 & 14 & 883 & 1559  
Figure 8 shows that, as the thickness of the target plate changed, the bulge height increased linearly with the increase in the kinetic energy of the fragment. Under the same kinetic energy of the fragment, an increase in the thickness of the target plate led to a decrease in the bulge height. This was because when the fragment impacted the target plate, the target plate was compressed, and the energy absorbed by the homogeneous material was proportional to its volume. The greater the thickness of the target plate, the smaller the plastic deformation.