More on the penetration of rigid projectiles in metallic targets

Highlights

• The deceleration of a rigid projectile penetrating a metallic target is explored by numerical simulations in order to highlight the role of the target's inertia during penetration.

• We propose a simplified model for the penetration depths of rigid projectiles impacting metallic target- entrance phase.

• We derive a new relation for the resisting stresses (Rt) exerted by metallic targets on rigid projectiles.

Abstract

The deceleration of a rigid projectile penetrating a metallic target is explored through numerical simulations with very different targets, in order to highlight the role of the target's inertia during penetration. These simulations also highlight the cavitation phenomenon through which, above a certain threshold velocity, the target's inertia is playing an important role in the penetration process. In addition, we propose a simplified model for the entrance phase effect on the penetration depths of rigid projectiles impacting metallic targets. We also explore the role of Poisson's ratio in determining the resistance to penetration of a metallic target, and derive a new relation for the resisting stresses exerted by these targets on ogive-nosed rigid projectiles.

Introduction

The deep penetration of rigid projectiles in semi-infinite metallic targets is the basic process in the field of terminal ballistics. This relatively simple process has been extensively researched through empirical data, analytic models and numerical simulations, as reviewed in Rosenberg and Dekel [8]. The main question regarding this process concerns the nature of the resisting stress which the target exerts on a rigid projectile, namely, the nature of its deceleration during the penetration process. The various approaches to this issue start with different assumptions about the dependence of the resisting stress on the instantaneous velocity of the projectile (V) and on the target's density (ρ_t). For example, Goodier [2] concluded that the resisting stress depends on both the target's strength and its inertia (ρ_tV²), by analyzing several sets of data for metallic spheres impacting metallic targets. Forrestal et al. [4] followed this conjecture in their analysis of the data for rigid steel rods penetrating thick (semi-infinite) aluminum targets. In contrast, Rosenberg and Dekel [7] concluded that the deceleration of a rigid projectile, beyond a short entrance phase, is constant throughout the penetration process. Thus, the corresponding resisting stress on the projectile is constant during the so-called tunneling process, which follows the initial entrance phase. They also found, through numerical simulations, that the constant deceleration (resistance) depends on the target's dynamic strength, its Young's modulus and the nose shape of the rigid projectile, and that it does not depend on the target's density. These conjectures hold for all impact velocities below a certain threshold, namely, the cavitation velocity (V_cav), while for higher impact velocities; the target's inertia has to be included in the expression for its resisting stress. These controversies were further highlighted in Warren [13] and in Rosenberg and Dekel [9], and it seems that the dust has not settled down on this debate, as is clearly evident by the recent article of Yankelevsky and Feldgun [15].

The purpose of the present paper is to shed more light on these issues by presenting new results from a numerical study which is focused on the role of the target's density and on the projectile's velocity. The results of these simulations enhance the claim that the target's inertia (ρ_tV²) affects its resisting stress only when the projectile's velocity is higher than the threshold velocity (V_cav). In addition, we present a new procedure which accounts for the contribution of the entrance phase in metallic targets to the penetration depths of rigid projectiles. This approximate procedure is much simpler than the elaborate, numerically-based scheme in Rosenberg and Dekel [8], and we compare its predictions with several sets of data. During the course of these investigations we found that the Poisson ratio of the target material plays an important role, besides its Young's modulus, in determining its resistance to penetration. Thus, we derive a new numerically-based relation for R_t, which is more rigorous than the relation derived in Rosenberg and Dekel [7].