## 3 Experimental Results and Analysis
### Spatial Distribution of Relative Cumulative Energy of BAD
When the steel target was the same, the energy distribution of the fragments within the large scattering angle range (>25\({}^{\circ}\)) caused by the spallation of the target was close. Thus, the difference in the energy distribution of the BAD in the scattering angle range of 0-20\({}^{\circ}\) was large due to the effects of the \(L/D\) and the shape of the EFP head. Because the three EFPs could penetrate the target, the difference in the radial distribution of fragments was mainly related to the diameter of the EFP rather than the length. The BAD was mainly formed by the rupture of the bulge on the back of the target [21]. During the penetration process, the head of the EFP was thickened to form a mushroom-shaped head, which resulted in a bulge on the back of the target. The bulge gradually expanded, cracks were generated under the action of tensile stress, and the cracks connected each other and finally penetrated the bulge wall. Then, the bulge broken, and the residual EFP together with a large number of projectile erosion fragments and target spall fragments are ejected from the rear of the target, forming a BAD. Assuming that the shape of EFP mushroom head and bulge is spherical, then the bulge is completely broken, EFP erosion is complete, and the material in mushroom is no longer in a fluid state. At this time, the residual EFP velocity is usually greater than the target fragment velocity. Because of the velocity difference between the two, friction is generated along the contact surface. At the time of complete rupture, the force of a fragment generated by a fracture on the bulge, as is shown in Figure 17. The forces are expressed as:  
\[F_{p}=m_{f}a_{p} \tag{4}\]  
\[F_{N}=F_{p}\cos\theta \tag{5}\]  
Figure 14:0  
where \(F_{p}\) is the force acting on the contact surface between the projectile and the fragment, \(a_{p}\) is the corresponding acceleration, and \(m_{f}\) is the fragment mass. \(F_{N}\) is the normal force, \(F_{f}\) is the friction force, \(\mu_{s}\) is the friction coefficient, and \(\theta\) is the included angle between the projectile axis and the line which connects the fragment with the center of the mushroom. The friction force is decomposed in axial and radial directions:  
Figure 14:1  
Figure 14:2  
where \(F_{fx}\) and \(F_{fr}\) are the force components in the axial and radial directions, respectively. In addition, the corresponding acceleration components are expressed as follows:  
Figure 14:3Figure 14:4  
where \(a_{fr}\) and \(a_{fp}\) are the acceleration components in the axial and radial directions, respectively. The fragment velocity component under the residual EFP motion is:  
Figure 14:5  
Figure 14:6  
In the equation, \(v_{r}\) is the residual EFP velocity, \(t_{p}\) represents the time interval between the complete rupture of the bulge and the formation of the initial BAD cloud, after which the BAD cloud maintains a stable shape and expands proportionally. The fragment scattering angle \(\beta\) is calculated using the following:  
Figure 14:7  
In the process of EFP penetrating the target, according to the axial stress balance equation of the projectile-target interface in the A-T model [38], the axial stress of the bulge element squeezed by EFP is:  
Figure 14:8  
where \(Y_{p}\) and \(\rho_{p}\) is EFP strength and density. When the bulge is completely broken, the residual EFP can freely rush out of the target bulge, and the erosion of the mushroom deformation zone stops because it depends on the target material which is completely separated from the main body of the target [39]. At this time, the velocity \(v_{c}\) of the undeformed part of the EFP is equal to the penetration velocity \(u_{c}\)[40], and the force of the fragment generated by the bulge fracture is:  
Figure 14:9  
where, \(A_{f}\) refers to the contact area between the fragment and projectile.