Size effects on the plastic shock formation in steady-state cavity expansion in porous ductile materials

Abstract

In this paper, we have studied the hypervelocity expansion of a spherical cavity in an infinite medium modeled with the extension of the porous plasticity criterion of Gurson (1977) developed by Chen and Yuan (2002) to account for plastic strain gradient induced size effects. Following the self-similar, steady-state solution derived by Cohen and Durban (2013) for size-independent porous materials, we have computed the critical cavity expansion velocity which leads to the emergence of plastic shock waves for a wide range of initial void volume fractions and different values of the length scale parameter that controls the effect of size. We have shown that size effects hinder the emergence of plastic shock waves, so that as the length scale parameter increases, the expansion velocity required for the plastic shock to be formed increases. In addition, while porosity favors the formation of plastic shocks, as shown by Cohen and Durban (2013), our results indicate that the effect of initial void volume fraction on plastic shock wave formation decreases for size-dependent materials.