## 3 Experimental Results and Analysis  
### Spatial Distribution of BAD in the Striking Area  
After an EFP penetrates the target, the fragments behind the target scatter in different directions, forming a debris cloud. The shape of the BAD cloud reflects the spatial distribution of the fragment velocity, and the striking area in multi-layered witness plates after the fragment penetrates reflects the spatial distribution of the fragment energy. Figure 4 shows the high-speed photographic images of the BAD clouds for the three EFPs. Figure 4 shows that the BAD cloud expanded continuously in the axial and radial directions and that the overall shape is ellipsoid, as shown by the red line in the figure. The major axis of the debris cloud increased significantly with increasing \(L/D\) of the EFP. This was due to the velocity of the residual EFP, while the increase in the minor axis was weak, thus indicating that an increase in the EFP \(L/D\) led to a larger increase in the axial scattering velocity of the fragments versus the radial scattering velocity, i.e., the fragment axial energy  
Figure 4: High-speed images of the behind-armor debris cloud. (**a**) \(L/D=1.66\) (**b**) \(L/D=2.4\) (c) \(L/D=3.86\). Figure 3: Experimental setup. was mainly increased due to the large \(L/D\). Because a reduction in EFP diameter leads to an increase in specific kinetic energy and an increase in input energy received by the target material per unit mass, the overall scattering velocity of BAD increases. The velocity gradient of the fragments causes the shape of the BAD cloud to be approximately ellipsoid, but there are differences between the spatial distribution of the BAD energy, the damaged area and the spatial distribution of BAD velocity. Therefore, in-depth analysis of the BAD information in the recovery plates behind the target is required. One key component of damage assessment is the striking area of the BAD in relation to multiple targets. The spatial density of BAD was large, and the fragments scattered in different directions and struck different parts of the targets. They eventually stopped in the recovery plates with varying depths due to the exhaustion of energy. Since the fragment deeply embedded in the multi-layered recovery plates must penetrate the previous layers of the recovery plate, the spatial distribution of the final positions of the BAD after penetrating the multi-layered recovery plates reflects the damaging effect behind the target to a certain extent. Thus, it is necessary to first quantitatively describe the distribution field of the BAD in the three-dimensional striking area to obtain the energy spatial distribution of the BAD. The coordinate system shown in Figure 5 was established to characterize the striking area behind the target. The \(x\) axis is the incident direction of the EFP, the \(y\) axis is the transverse direction, the \(Z\) axis is the longitudinal direction, and the exit on the back of the steel target was the origin \(O\). The positions where the fragments were embedded on each layer of the recovery plate were collected, namely, the positions where the fragments impact the recovery plate of this layer. Additionally, we calculated the coordinates of each fragment relative to the residual EFP perforation center \(O^{\prime}\) in the local coordinate system \(Y^{\prime}O^{\prime}Z^{\prime}\) of the witness plate. In turn, the spatial coordinates (\(x_{i}\), \(y_{i}\), \(z_{i}\)) of each fragment were obtained. The distance \(R_{i}\) (\(R_{i}=\sqrt{{y_{i}}^{2}+{z_{i}}^{2}}\)) between the fragment position in the recovery plate and the center perforation of residual EFP was taken as the radial scattering distance of the fragment, a factor which reflects the radial penetration ability. Figure 6 shows a schematic diagram of the method for measuring \(R\) on the recovery plate. The scattering angle \(\beta\) of the fragment is the angle between the line formed by the fragment position and the origin versus the \(x\) axis (Figure 5).