Several features of a viscoplastic study of plate-impact spallation with multidimensional strain

Abstract

A viscoplastic constitutive theory that contains a scalar variable description of damage is applied to a two-dimensional axisymmetric analysis of plate-impact spallation. The model uses the Perzyna viscoplastic constitutive formulation with inclusion of a nonlinear isotropic hardening law that saturates with increasing strain. For ductile metals the damage variable is taken to be the void volume fraction of the polycrystalline solid. The evolution equation for damage is based on the nucleation, growth, and eventual coalesence of the microvoids. A spallation criterion based on critical void volume fraction is utilized. The theory is applied to normal impact of circular plates where the diameter of the flyer is smaller than the diameter of the target. Multidimensional axisymmetric strains are developed where, because of the edge effect of the smaller flyer plate, nonplanar as well as planar waves are generated. The equations for balance of mass and momentum are solved using a Lagrangian finite-element computer program with explicit time integration. Four-noded uniform strain quadrilateral elements are used for the spatial discretization. Numerical simulations of impact are performed over a wide range of initial velocities. Contours of the void volume fraction illustrate the damage threshold and the effect of increasing impact stress on damage evolution. Material damage and spall fracture are also illustrated by plots of the deformed geometry, in which the material softening associated with increase in the void volume fraction results in extensive local deformations that, in effect, simulate the openings that are observed in spalled plates. Additional simulations are performed to study the effect of varying parameters that appear in the microvoid evolution equations.