Boundary Effects in Penetration or Perforation

For the analysis of stress distributions around a projectile tip in penetration or perforation, a point force P associated with an expansion source E^z, which depends on the geometry of the projectile, is employed to simulate the projectile. Using the method of half-space analysis by Mindlin (1936), the boundary effects on the projectile are analyzed. The analytical solutions of an expansion source associated with a concentrated force are derived for the prediction of the damage zones in a target, as the projectile either approaches or leaves the boundary. As a projectile perforates a target, it forms a cratering area at the impact surface and leaves a cone-like spalling area at the exit surface. The presence of these two areas and the fact that the spalling area is larger than the cratering area in perforation, can be explained by the stress analysis of boundary effects. Solution of the cavity expansion source in a half-space is derived. This solution provides a theoretical evidence for the conclusion obtained from the empirical analysis by Forrestal et al. (1994). Their conclusion states that when the projectile is at about twice its shank diameters, it can be approximately treated as though it were in the infinite medium.