Dynamic fracture and spallation in ductile solids

Abstract

A mathematical model of ductile hole growth under the application of a mean tensile stress is developed and applied to the problem of spallation in solids. The object is to describe dynamic ductile fracture under a wide range of tensile loading conditions. The mathematical model presented here describes both plate-impact spallation (as observed by postshot examination and time-resolved pressure measurements) and explosively produced spallation (as observed by dynamic x-radiographic techniques) in copper. It is found to be inapplicable to ductile fracture of expanding rings, even in the absence of possible adiabatic shear banding and classical necking instabilities, because of the fact that the mean tensile stress (void growth) and the deviatoric stress (homogeneous plastic shear strain) are not independent. A phenomenological model of void growth under uniaxial stress conditions is developed independently and applied to the numerical finite-difference solution of fracture in an expanding ring. The initial porosity in a material element is a random variable following Poisson statistics and the assumption that all the void radii are equal. The necessary theoretical generalizations and supporting experimental measurements to improve our understanding of fracture and fragmentation in expanding rings are discussed.