Modeling dynamic spherical cavity expansion in elasto-viscoplastic media

Abstract

In this paper, we extend the dynamic spherical cavity expansion model for rate-independent materials developed in refs. [1, 2, 3] to viscoplastic media. For that purpose, we describe the material behavior with an isotropic Perzyna-type overstress formulation [4, 5] in which the material rate-dependence is controlled by the viscosity parameter \eta. The theoretical predictions of the cavity expansion model, which assumes that the cavity expands at constant velocity, are compared with finite element simulations performed in ABAQUS/Explicit [6]. The agreement between theory and numerical simulations is excellent for the whole range of cavitation velocities investigated, and for different values of the parameter \eta. We show that, as opposed to the steady-state self-similar solutions obtained for rate-independent materials [1, 2, 3], the material viscosity leads to time-dependent cavitation fields and stress relaxation as the cavity enlarges. In addition, we also show that the material viscosity facilitates to model the shock waves that emerge at the highest cavitation velocities investigated, controlling the amplitude and the width of the shock front.