A Simple Analytical Model for Evaluation of Penetration Depth and Resistant Strength of Concrete Targets

This paper presents a simple analytical model for evaluation of penetration depth and resistant strength of concrete target. The model is based on the assumption that the deformation and failure of the projectile are negligible. Normal impact is assumed in the model. It is also assumed that the penetration is steady state within the time step, the momentum balance equation can be integrated, resulting in an explicit expression for the pressure at the target interface. The expressions for spherically symmetric cavity expansion for a material with locked hydrostatic stress and constant shear strength have been developed. The constants for failure criterion are derived based on Mohr–Coulomb and Tresca-limit yield line theories. Final depth of penetration has been derived using the results of spherically symmetric cavity expansion analysis, relating the radial stress at the cavity surface to cavity expansion velocity and Newton’s second law of motion. Target resistant strength parameter is expressed as a function of penetration depth, projectile velocity, nose performance coefficient, target density, mass of projectile, and radius of the projectile. The expressions for velocity, acceleration and displacement at any instant of time have been deduced based on total depth of penetration and target resistant strength. To validate the methodologies, numerical studies have been conducted and observed that the penetration depth and target resistant strength obtained in the present study are in good agreement with the corresponding experimental values reported in the literature. It is also observed that the time history of penetration depth and projectile velocity are in good agreement with the corresponding literature values.