A simplified and modified model for long rod penetration based on ovoids of Rankine

Abstract

This paper proposes an alternative to the Alekseevskii-Tate model, denoted by AT, for erosion of a long rod penetrator. Specifically, the model uses simplified equations of the model for long rod penetration based on ovoids of Rankine developed in (Roisman et al., 2001). The resulting modified ovoid of Rankine model, denoted by MOR, proposes differential equations for the velocity of the projectile’s tail, the penetration velocity into the target, the erosion of the projectile’s mass and the penetration depth, as well as an algebraic equation to determine the point of separation of the target material from the projectile’s surface. The MOR model uses shock conditions to determine the initial value of the penetration velocity and it predicts the initial transient decrease of this velocity to its value for quasi-steady-state projectile erosion. This model also includes an expression for the crater diameter which predicts values close to experimental data. Relative to the AT model, the MOR model introduces a single empirical parameter in a modified evolution for mass erosion which significantly influences the penetration depth without affecting the crater diameter. This parameter models the interface between the deforming projectile’s nose and its rigid tail where the projectile’s tail is rapidly decelerating due to mushrooming and mass erosion. Its value is determined by comparing model predictions of the penetration depth with experimental data. Future research is needed to replace this empirical parameter with an analytical model and to better model the termination process of penetration.