A time-dependent model for long-rod penetration

Abstract

The one-dimensional, quasi-steady-state, modified Bernoulli theory of Tate [ J. Mech. Phys. Solids, 15, 287 (1967)] is often used to examine long-rod penetration into semi-infinite targets. In general., the time histories of penetration predicted by the Tate model can be in good agreement with those computed from numerical simulations. However, discrepancies exist between the model and numerical simulations at the beginning and at the end of penetration. From insights provided by numerical simulations, assumptions are made concerning the velocity and stress profiles in the projectile and the target. Using these assumptions, the time-dependent, cylindrically-symmetric, axial momentum equation is explicitly integrated along the centerline of the projectile and target to provide the equation of motion. The model requires the initial interface velocity—which can be found, for example, from the shock jump conditions-and material properties of the projectile and target to compute the time history of penetration. Agreement between the predictions of this one-dimensional, time-dependent penetration model are in good agreement with experimental results and numerical simulations.