Essential physics of target inertia in penetration problems missed by cavity expansion models

The problem of a rigid projectile with the shape of an ovoid of Rankine penetrating an incompressible elastic-perfectly-plastic target is used as an example to study the dependence of the drag force F on the penetration velocity V. The phenomenological functional form of the contact pressure P proposed by Hill (1980) during World War II, the analytical solution in Yarin et al. (1995), the numerical simulations in Rosenberg and Dekel (2009), as well as new numerical simulations in this work all consistently reveal the importance of a physical flow field in the target material. Below a critical value Vs of V, the drag force F is constant. The critical value Vs determines the onset of separation of the target material from the projectile's surface. Axial inertia being converted into radial inertia in the target near the projectile's tip controls the physics of the separation process and the strong dependence of F on V for V > Vs. Cavity expansion models based on cylindrical or spherical flow fields miss the essential physics of this separation phenomenon and are incorrect when target inertia is important. Also, the numerical simulations indicate that the constant value of the drag force for V < Vs depends on the tip shape, which cannot be accurately predicted by cavity expansion models. Since cavity expansion models cannot accurately predict results of the simplest problem of a rigid projectile penetrating an incompressible elastic-perfectly-plastic target, it should not be assumed that these models are accurate for general target materials (which include compressibility, hardening and porosity), even though the models are simple to use.