Analysis of the velocity relationship and deceleration of long-rod penetration

Abstract

The relationship between the average penetration velocity, $$ \bar{U} $$ , and the initial impact velocity, $$ V_{ 0} $$ , in long-rod penetration has been studied recently. Experimental and simulation results all show a linear relationship between $$ \bar{U} $$ and $$ V_{ 0} $$ over a wide range of $$ V_{ 0} $$ for different combinations of rod and target materials. However, the physical essence has not been fully revealed. In this paper, the $$ \bar{U} - V_{ 0} $$ relationship is comprehensively analyzed using the hydrodynamic model and the Alekseevskii–Tate model. In particular, the explicit $$ \bar{U} - V_{ 0} $$ relationships are derived from approximate solutions of the Alekseevskii–Tate model. In addition, the deceleration in long-rod penetration is discussed. The deceleration degree is quantified by a deceleration index, $$ \alpha = {{2\bar{\mu }} \mathord{\left/ {\vphantom {{2\bar{\mu }} {(K\varPhi_{Jp} )}}} \right. \kern-0pt} {(K\varPhi_{Jp} )}} \approx Y_{p} \rho_{p}^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-0pt} 2}}} \left( {\rho_{p}^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-0pt} 2}}} + \rho_{t}^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-0pt} 2}}} } \right)V_{0}^{ - 2} , $$ which is mainly related to the impact velocity, rod strength, and rod/target densities. Thus, the state of the penetration process can be identified and designed in experiments.