Viscoplastic analysis of plate-impact spallation

A model to predict material damage and spall fracture under high strain-rate conditions is applied to plate impact experiments. The model uses the Perzyna viscoplastic constitutive theory, appropriately modified to include a nonlinear isotropic hardening law that allows for saturation of the hardening with increase of strain. The constitutive equation contains a scalar variable for description of the material damage, expressed as the void volume fraction of the polycrystalline solid with microvoids. Incorporation of the damage parameter into the completely phenomenological elasto-viscoplastic constitutive equations permits description of rate-dependent, compressible, inelastic deformation, and ductile fracture. The evolution equation for the parameter describes microvoid nucleation and growth. The model for microvoid growth is based upon a random distribution of microvoids, idealized as spherical holes of arbitrary size. Microvoid coalescence is considered by incorporation of void interaction functions to describe enhanced nucleation and growth rates. A local spall fracture criterion based upon the attainment of a critical microvoid volume is utilized. The constitutive equations are specialized to uniaxial deformation with multiaxial stress, which is appropriate for the planar impact experiments. A finite-difference wave propagation computer code is used to solve the equation of motion. The computed stress wave profiles demonstrate the effect of using a viscoplastic material description. Calculations predicting the rear-surface velocity-time profile and the stress-time profiles of the OFHC copper target are compared with measured profiles. The damage (void volume) distribution across the plate thickness is also calculated and compared with experimental data.