The effect of geometric scale on impact induced fragmentation, and its application to the design of dual plate armor

An analysis is presented which predicts that, for a fixed impact velocity, impact induced fragmentation becomes more severe as geometric scale increases. Test data is presented which supports this prediction, and which allows calculation of material dependent coefficients. The analysis was based on a minimization with respect to radius, for an expanding body, of a total energy density term (expansion kinetic energy per unit volume plus surface energy per unit volume). The test configuration was a steel sphere impacting an aluminum plate, with fragmentation recorded by a stack of spaced witness panels. The tests were run at full and half scale. Correlation between testing and analysis was achieved for the number of fragments perforating the front witness panel when a term analogous to a threshold energy was introduced. While the fragment count showed a dependence on geometric scale, the relative depth of penetration (number of witness panels perforated) did not. This suggested that the targets were fragmented, but that the projectile remained in one piece. A reduction in penetration depth with increasing impact velocity was seen, and was attributed to increased projectile deformation. For cases where the projectile would fragment (for example, if a harder target material were used), the effect of geometric scale on the performance of dual plate armor is predicted by analysis. The prediction is that, for impact velocities where projectile breakup at the outer plate of dual plate armor is a factor, the armor required to stop a large scale projectile can be lighter, on a relative basis, than the armor required to stop a small scale projectile.