Rigid Penetrators
This chapter describes the penetration process of rigid penetrators into semi-infinite targets. This is the basic science behind the so-called penetration mechanics field. We start with the basic question regarding the deceleration of rigid projectile and
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Rigid Penetrators
Abstract This chapter describes the penetration process of rigid penetrators into semi-infinite targets. This is the basic science behind the so-called penetration mechanics field. We start with the basic question regarding the deceleration of rigid projectile and use both empirical data and numerical simulations to show that this deceleration is constant for projectiles impacting at ordnance velocities. At a certain threshold velocity the deceleration becomes velocity dependent and we follow this process numerically. The effect of the entrance phase on the penetration process is also treated numerically and the model developed here is shown to account for existing data for various projectile/target combinations.
3.1
The Mechanics of Deep Penetration
The penetration of a very thick (semi-infinite) target by a rigid projectile has been the subject of intense research for over two centuries. A large number of empirical relations and engineering models have been proposed over these years, as reviewed Backman and Goldsmith (1978). These relations account for the penetration depth of a given projectile in terms of its impact velocity, and they differ from each other by the basic assumptions concerning the retarding forces (stresses) on the projectile. With the recent advancements in the quality and reliability of numerical simulations, these analytical models can be further validated, as will be demonstrated in this chapter. We start the discussion with a short review of the more popular models which have been proposed over the years. This is followed by a careful examination of a certain set of experimental data, which will lead to the proper choice of an analytical model for the deep penetration by rigid penetrators. Numerical simulations are then used in order to enhance the validity of this model and to explore the role of its physical parameters. The penetration process of a rigid penetrator is determined by the retarding force which the target exerts on it during penetration. Since, by definition, the mass (M) of the rigid penetrator does not change during penetration, the process is governed by its deceleration (a). Thus, the following discussion concentrates on the deceleration of a rigid penetrator. Replacing the time variable (dt) with the penetration increment (dx), the deceleration is given by: © Springer Science+Business Media Singapore 2016 Z. Rosenberg and E. Dekel, Terminal Ballistics, DOI 10.1007/978-981-10-0395-0_3
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3 Rigid Penetrators
a¼
dV dV ¼V dt dx
ð3:1aÞ
from which we get the penetration increment: dx ¼
V dV aðVÞ
ð3:1bÞ
The penetration depth (P) of the rigid penetrator is obtained by integrating this equation between the boundaries: V = V0 at x = 0 and V = 0 at x = P. Thus, one can write for the final penetration depth: Z0 P¼
V dV aðVÞ
ð3:1cÞ
V0
The only unknown quantity in this equation is the actual dependence of the deceleration on penetration velocity, a = a(V). Various functional forms for a(V) have been suggested over the years for different projectile/t
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