## 3 Results and Discussion
### Perforation Diameter Analysis
#### 3.2.3 Quantitative Analysis Method for Perforation Diameter
\[d_{1}=d_{p}\times\left(10.6052\Bigg{(}\frac{Q_{s}}{d_{p}^{3}Y_{t}} \Bigg{)}^{0.7148}-0.1040\left(\frac{V}{\rho_{t}^{-\frac{1}{2}}Y_{t}^{\frac{1}{2} }}\right)^{0.7951}-0.7334\Bigg{(}\frac{E_{K}}{d_{p}^{3}Y_{t}}\Bigg{)}^{-0.1631}\right) \tag{21}\] \[d_{2}=d_{p}\times\left(19.1378\Bigg{(}\frac{Q_{s}}{d_{p}^{3}Y_{t} }\Bigg{)}^{3.4247}+0.9822\left(\frac{V}{\rho_{t}^{-\frac{1}{2}}Y_{t}^{\frac{1}{ 2}}}\right)^{-0.4941}+0.1122\left(\frac{E_{K}}{d_{p}^{3}Y_{t}}\right)^{-0.5479 }\right)\] (22) \[d_{3}=d_{p}\times\left(6.3527\Bigg{(}\frac{Q_{s}}{d_{p}^{3}Y_{t} }\Bigg{)}^{0.8689}-0.0003\left(\frac{V}{\rho_{t}^{-\frac{1}{2}}Y_{t}^{\frac{1} {2}}}\right)^{2.3834}+0.9713\left(\frac{E_{K}}{d_{p}^{3}Y_{t}}\right)^{0.5260}\right)\] (23) \[d_{4}=d_{p}\times\left(9.5401\Bigg{(}\frac{Q_{s}}{d_{p}^{3}Y_{t} }\Bigg{)}^{1.4532}-0.2560\left(\frac{V}{\rho_{t}^{-\frac{1}{2}}Y_{t}^{\frac{1} {2}}}\right)^{0.5421}+3.4162\left(\frac{E_{K}}{d_{p}^{3}Y_{t}}\right)^{2.0337}\right) \tag{24}\]  
where the fit formulas for the perforation diameter of the cylindrical reactive fragment impacting the Q345S plate, the cylindrical reactive fragment impacting the 3045S plate, the spherical reactive fragment impacting the Q345S plate, and the spherical reactive fragment impacting the 3045S plate are \(d_{1}\), \(d_{2}\), \(d_{3}\), and \(d_{4}\). However, the aforementioned technique can be utilized to estimate the perforation diameter with reasonable accuracy and can be used as a semi-empirical formula to fit the perforation diameter for various operating situations. This will have profound significance in the estimation of the experimental perforation diameter and experimental design. The following is a MATLAB plot of the equation mentioned above. As shown in Figure 11, the steel plate's perforation diameter changed when the reactive fragment impacted it, first increasing and then decreasing as the impact velocity rose. The perforation diameter was approximately 1.5-3 times the diameter of the reactive fragment. The steel plate's perforation diameter was enhanced by the combined action of tensile and shear waves during the impact process. As a result of the compressive shock wave's reflection as a tensile sparse wave on the surface of the steel plate, steel plates close to the impact surface shattered, resulting in a debris cloud. The direction of impact resulted in the creation of tensile stress. The shear stress produced by the movement of shear waves caused the steel plate surrounding the perforated zone to deform or undergo internal microscopic modifications. When the impact velocity was low in this range, the perforation diameter of the steel plate increased as the impact velocity increased because the reactive fragments still exhibited some structural strength. When the impact velocity was higher and the shock wave pressure was significantly greater than the material strength, the material exhibited a near-fluid \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Shape of Reactive** & \multicolumn{2}{c}{**Material of**} & \multirow{2}{*}{\(A\)} & \multirow{2}{*}{\(B\)} & \multirow{2}{*}{\(C\)} & \multirow{2}{*}{\(D\)} & \multirow{2}{*}{\(E\)} & \multirow{2}{*}{\(F\)} \\
**Fragments** & & & & & & & \\ \hline Cylindrical & Q345 & 10.6052 & 0.7148 & \(-\)0.1040 & 0.7951 & \(-\)0.7334 & \(-\)0.1631 \\ \hline Cylindrical & 304 SS & 19.1378 & 3.4247 & 0.9822 & \(-\)0.4941 & 0.1122 & \(-\)0.5479 \\ \hline Spherical & Q345 & 6.3527 & 0.8689 & \(-\)0.0003 & 2.3834 & 0.9713 & 0.5260 \\ \hline Spherical & 304 SS & 9.5401 & 1.4532 & \(-\)0.2560 & 0.5421 & 3.4162 & 2.0337 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Coefficients of fitting parameters. state, and its shear modulus eventually went to zero, causing the perforation diameter to decrease.