An analysis of inclusion morphology effects on void nucleation

Abstract

Deformations of a planar doubly periodic array of square elasticinclusions in an isotropically hardening elastic-viscoplastic matrixare analysed. The arrays considered have multiple inclusions per unitcell, but in each array all inclusions have the same size. Overallplane strain tension with a superposed tensile biaxial stress isimposed. A finite deformation formulation is used with a cohesivesurface constitutive relation describing the bonding between theinclusion and the matrix. A characteristic length is introduced fromdimensional considerations since the cohesive properties include thework of separation and the cohesive strength. The system analysed isused to study inclusion distribution effects on void nucleation, withthe aim of providing background for incorporating the effect ofclustering on void nucleation into phenomenological constitutiverelations for progressively cavitating plastic solids. For low valuesof the triaxiality of the imposed stress state, void nucleation occursafter extensive overall plastic straining and regular distributionshave a higher value of the void nucleation strain than randomdistributions. For larger values of stress triaxiality, where void nucleation occurs at relatively small overall plastic strains, theeffect of inclusion size dominates the effect of inclusiondistribution and smaller inclusions give rise to higher void nucleation strains. The ability of various scalar measures ofclustering to characterize the computed dependence of void nucleationon inclusion distribution is explored. Within the context of aphenomenological description of void nucleation, it is found that theeffective void nucleation stress is approximately a linear function ofthe overall hydrostatic tension with a coefficient 0.40-0.44 forregular distributions and 0.25-0.35 for random distributions.The results also suggest a possible dependence of the effective voidnucleation stress on a simple scalar measure of clustering.