Boundary Effect and Dynamic Response Study for the Penetration of Rigid Projectiles into Thick, Finite-Radius, Metallic Targets

Abstract

This study uses the unified strength theory to analyse the elastoplastic stage and plastic stage of a linear strain-hardening target material while considering the effects of the intermediate principal stress and the free lateral boundaries of the target. In this investigation, analytical solutions of the radial stress in the cavity wall are obtained, and a unified penetration model of the target material is built. On this basis, penetration resistance formulas and penetration depth formulas for rigid projectiles with various nose shapes penetrating into thick, finite-radius, metallic targets are deduced, the solutions of which are obtained by utilizing the Simpson method. Accordingly, the proposed method offers a broader scope of application and higher accuracy than previous methods. Through this method, a series of analytical solutions based on different criteria can be obtained, and the penetration depth ranges of targets under different striking velocities can be effectively predicted. Moreover, penetration processes under different conditions are numerically simulated using the software ANSYS/LS-DYNA to study the motion law of the projectiles and the dynamic response of the targets. From the theoretical and numerical approaches, a list of influencing factors for terminal ballistic effects are analysed, including the strength criterion differences, the strength parameter b, the striking velocity $v_0$ , the projectile nose shape, and the target radius-to-projectile radius ratio rt/a. The results indicate that, as b changes from 1 to 0, the penetration depth Dmax increases by 22.45%. Additionally, Dmax increases by 40.76% when rt/a changes from 16 to 4; hence, it cannot be calculated as an unlimited-size target anymore when rt/a ≤ 16. In weapons field tests, the radius of the metallic target can be conservatively designed to be greater than 28 times the projectile radius to ignore the effect from the free lateral boundaries of the target.