Void growth and constitutive softening in a periodically voided solid

Abstract

A three-dimensional finite element model of a periodically voided elastic-plastic solid is used to predict void growth and constitutive softening under tensile plastic deformation. The analysis considers an infinite block of material containing a three-dimensional periodic array of voids, subjected to a remote deformation or stress field. The predicted initial dilatational and extensional void growth rate, as a function of stress triaxiality and material work-hardening rate, agrees well with the analytical results of Budiansky et al. ( Mechanics of Solids, The Rodney Hill 60th Anniversary Volume, edited by H.G. H opkins and M.J. Sewell, p. 13, Pergamon Press, Oxford, 1982) for an isolated void in a viscous solid. Increased initial void volume fraction (⨍) has little effect on the dilatational growth rate, but strongly affects the extensional growth rate at high levels of triaxiality. The effect of void aspect ratio on void growth rate was seen during uniaxial tensile deformation, during which extensive void elongation caused a reduction in the final or asymptotic void growth rates. Constitutive softening is shown to be primarily a function of porosity and stress triaxiality.