Similarities in the penetration depth of concrete impacted by rigid projectiles

Abstract

Similarity can reflect common laws in the mechanism of rigid-body penetration. In this paper, the similarities in rigid-body penetration depth are demonstrated by three non-dimensional but physically meaningful quantities, i.e., $\rho_{\text{kinetic}}$, $I_{ \ln }^{*}$ and $N^{\prime}_{1}$. These three quantities represent the non-dimensional areal density of projectile kinetic energy, the effect of nose geometry, and the friction at the interactive cross section between projectile and target respectively. It is shown that experimental data of rigid projectile penetration, from shallow to deep penetration, can be uniquely unified by these three similarity quantities and their relationships. Furthermore, for ogival nose projectiles, their penetration capacities are dominated by $\rho_{\text{kinetic}}$, which is consisted by non-dimensional effective length $L_{\text{eff}}$ and non-dimensional quantity $D_{\text{n}}^{\text{p}} = \frac{{\rho_{\text{p}} v_{0}^{2} }}{AY}$ which has the same form as Johnson’s damage number. On the sacrifice of minor theoretical accuracy, the non-dimensional penetration depth $P/d$ can be understood as directly controlled by $D_{\text{n}}^{\text{p}}$, enhanced by projectile effective length $L_{\text{eff}}$ under a multiplication relation, and optimized by projectile nose geometry in the formation of $I_{ \ln }^{*}$.

Graphic abstract