Elastic-cracked model for penetration into unreinforced concrete targets with ogival nose projectiles

In this research an elastic-cracked model for determining the forces on an ogival nose projectile is developed to estimate the resistance to penetration into an unreinforced concrete target. The model developed is guided by the post-test observation that concrete will crack in the region surrounding the projectile. In this model the spherical cavity expansion approximation is extended by assuming a cracked region and an elastic region to simulate penetration into an unreinforced concrete target. Thus, an elastic-cracked model is developed here for predicting the resistance to penetration, where it is assumed that the interface of the cracked region and elastic region, which satisfies the Hugoniot jump conditions, is controlled by the radial compressive strength p₀. Solutions that determine the boundary for the elastic region for both incompressible and compressible cases are given. A calculation shows that the incompressible solution is of first-order for the compressive solution when Poisson's ratio equals 0.5. The resistance to penetration depends on the following factors of the concrete target : Poisson's ratio v, locked volumetric strain η*, strength of the material and velocity V. The present model predictions of depth of penetration appear to be in good agreement with existing experimental measurements that involve a steel projectile penetrating a thick, unreinforced concrete slab at normal incidence.