Theoretical considerations on cavity diameters and penetration depths of concrete materials generated by shaped charge jets using the targets response modes described by a modified HJC model

Abstract

The traditional dynamic cavity expansion theory generally deals with the problem of penetrator penetration into targets at lower velocity, which is considered that the materials near the penetrator/target interface are in the plastic state. For shaped charge jets penetration, the concrete materials in a certain distance away from the jet/target interface are in the fluid state. Thus, the radial stress at the cavity surface derived from the dynamic cavity expansion theory cannot be directly applied as the target resistance. The current paper aims to establish a theoretical model for shaped charge jets penetration into concrete targets based on the cavity expansion idea, assuming that the cavity expansion stress is the stress at the flow/fully dense interface. Firstly, the hydrostatic pressure-volume strain relationship described by the HJC concrete constitutive model was analyzed; result indicated that four response regions were produced when concrete subjected to load: the elastic region, the cracked region, the plastic-like (the “plastic” behavior of concrete is named as “plastic-like” since the behavior has nothing to do with the dislocation movement of metals that reflects the plastic behavior) transitional region and the fully dense region. The HJC yield surface equation was then modified by discussing the elastic-cracked-transitional-fully dense response in front of the flow/fully dense interface. With the changing particle velocity at the flow/fully dense interface, it showed that another three response modes were produced in front of the flow/fully dense interface, i.e., the elastic-transitional-fully dense response, the elastic-fully dense response, and the fully dense response. The applications of the equations of state in different response modes were analyzed. Secondly, the calculation model of the radial stress at the flow/fully dense interface was proposed based on the modified HJC model. Thirdly, the shaped charge jets penetration theories were analyzed. In the end, the depth of penetration (DOP) experiments for three different shaped charges into C200 reactive powder concrete (RPC) targets were carried out to verify the theoretical model. Results showed that the cavity diameters and penetration depths predicted by the elastic-cracked-transitional-fully dense response, the elastic-transitional-fully dense response and the elastic-fully dense response exhibited good agreement with the experimental data, whereas that by the fully dense response existed relatively large errors comparing with the other three response modes.