## 3 Experimental Results and Analysis
### Total Energy Distribution of BAD  
The effective large-area damage to the internal instruments and crew of the armored target is mainly inflicted by the BAD group. The focus of the damaging effect assessment is on the energy of the damaged element (i.e., the kinetic energy of the fragments). Thus, the spatial energy distribution of the BAD is key to damage assessment. The layer number of the witness plates penetrated by the BAD reflects the total penetration depth of the fragment to some extent [35]. [PERSON] et al. [36] assumed that all the kinetic energy of fragments was spent in moving against the resistance force in the recovery material. They then established the energy conservation formula based on the penetration depth of the fragments in the recovery plate. Thus, the penetration depth is closely related to the energy of the fragments. This is the case for all fragments recovered in the experiment penetrated the first layer of aluminum plate, but the number of layers of fiber plate penetrated is different. Therefore, the length of penetration path in the fiber plate was used as a measure of the fragment energy for simplification. The energy of each fragment is calculated as follows:  
\[E=ne/\cos\beta \tag{2}\]  
where \(\beta\) is the scattering angle of the fragments, \(n\) is the number of fiber layers penetrated by the fragments, and \(e\) is the energy consumed by penetrating one layer of fiber plate vertically. It should be noted that \(E\) is the fragment energy after penetrating the first aluminum layer. To facilitate the subsequent analysis of fragment energy distribution, the following assumptions were made:  
(1) The energy consumed by a fragment vertically penetrating one layer of fiber plate is constant and is denoted as \(e\). (2) If a fragment is embedded in the fiber plate, then the energy consumed when impacting the plate is 0.5\(e\). (3) The fragments embedded in the foam plate are considered to have no ability to penetrate the next layer of fiber plate. Because the density of foam plate is far less than that of fiber plate [30,33], the energy consumed by the fragments moving in the foam plate is ignored. Based on the above assumptions, Equation (2) can calculate the energy of all fragments. Since the lethality of fragments with a mass below 0.1 g is minimal, the energy of these fragments is not calculated. By averaging the total energy of fragments in the two tests of each EFP, the total energy of BAD and that of the fragments of the two materials are obtained, as shown in Figure 10. Some fragments in the recovery plate were not retrievable. For those fragments, only the position information of the fragments was obtained, and it was impossible to determine the fragment material. Therefore, the total energy was greater than the sum of the energy of the steel (target) and copper (EFP) fragments. The energy of the copper-steel bonded fragments was calculated separately. Figure 10 shows that when the \(L/D\) increased from 1.66 to 3.86, the total energy of the all fragments and EFP fragments increased by 54.8% and 167.7%, respectively, whereas the total energy of the target fragments decreased slightly. When the steel target remained the same, the total energy of the target fragments gradually approached a certain level, and the total energy of the EFP fragments increased significantly with increasing \(L/D\). Hence, the proportion of the energy of the EFP fragments increased from 35.6% to 61.6%. According to the experimental results, the total mass of the BAD (>0.1 g) of the three types of EFPs was 388.37 g, 304.93 g, and 202.93 g, respectively, of which the total mass of the target fragments was 239.84 g, 135.14 g, and 88.10 g, respectively. The relationship between fragment total mass and EFP cross-sectional area is shown in Figure 11.  
It can be seen that there was a certain linear relationship between the total mass of all fragments, target fragments and the cross-sectional area of EFP.