###### Abstract  
To understand the influence of the length-diameter ratio (\(L/D\)) of explosively formed projectiles (EFPs) on the energy spatial distribution of behind-armor debris (BAD), three EFPs with different \(L/D\)s were designed in this study. The scattering characteristics of the BAD formed by the EFP penetrating a steel target were investigated. High-speed photography was used to observe the shape of the BAD cloud. Fiber and foam plates were sequentially stacked to recover the fragments. The three-dimensional damaged area by the BAD was obtained based on the spatial position information of a large amount of BAD. Finally, the energy spatial distribution characteristics of the EFP and target material fragments were analyzed. The results showed that a large EFP \(L/D\) increased the total energy of the BAD, and the proportion of the energy of projectile fragments increased. The difference in the energy spatial distribution between EFPs with varying \(L/D\)s was mainly in the scattering angle range of 3-17\({}^{\circ}\). The total energy of fragments within 17\({}^{\circ}\) of scattering angle accounted for 85% of the total energy of all fragments. The BAD energy of the EFP with a large \(L/D\) (\(L/D\) = 3.86) was concentrated in a small scattering angle range in which the residual projectile was located. The average projectile fragment energy of the EFP with a moderate \(L/D\) (\(L/D\) = 2.4) was evenly distributed in the scattering angle range of 5-20\({}^{\circ}\). As a result, the energy distribution of the BAD from EFP (\(L/D\) = 2.4) shifted towards the large scattering angle, thus leading to a uniform radial distribution of the striking area within the range of 500-1100 mm behind the target. However, with the increase in the distance behind the target, the radial direction of the striking area of the other two EFPs was gradually reduced. The reason was explained according to the force analysis of the fragments resulting from the bulge fracture of target. The spatial energy distribution of BAD is closely related to the damage ability of EFP in relation to the armored target. Thus, it is necessary to design EFPs with appropriate \(L/D\)s in order to maximize the damaging effect behind the armor. Behind-armor debris (BAD); explosively formed projectile (EFP); length-diameter ratio (\(L/D\)); radial scattering distance; energy spatial distribution +
Footnote †: journal: Applied Sciences  
depth, incident perforation diameter, and emergent perforation diameter; the damaging effect of the secondary behind-armor debris (BAD) should also be evaluated [8; 9]. EFP is required to have penetration and perforation ability as well as sufficient behind-armor damage power. Existing studies on this topic mainly have focused on the influence of EFP impact velocity and target thickness [10; 11] on the number and mass distribution of BAD fragments. EFPs with a large \(L/D\) can increase the penetration depth, but it is unclear whether they can enhance the damaging effect behind the target. Thus, it is necessary to study the effect of the \(L/D\) of EFPs on the distribution of BAD. Researchers previously used EFPs with a specific shape or simulated EFPs to study the influence of shape and \(L/D\) of an EFP. For instance, [PERSON] et al. [12] studied the radial expansion velocity of the BAD cloud of simulated EFPs with different solidities and \(L/D\)s. [PERSON] [13] found that the shape of the semi-hollow EFP leads to the existence of jets, formed inside the BAD cloud in the reverse flight direction of the EFP. However, the EFP formation is affected by numerous factors such as the liner and the charge structure, and thus it is challenging to quantitatively control a single forming parameter. Therefore, BAD characteristics for real EFP \(L/D\) are more complex relative to simulated projectiles. In terms of the hypervelocity impact of space debris and penetration of kinetic energy projectile, promising achievements have been made in BAD cloud modeling [14].