Similarities in the penetration depth of concrete impacted by rigid projectiles

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.,ρkinetic,I∗ln and N′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 byρkinetic,which is consisted by non-dimensional effective length Leff and non-dimensional quantity Dpn=ρpv20AY 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 Dpn,enhanced by projectile effective length Leff under a multiplication relation,and optimized by projectile nose geometry in the formation of I∗ln.