An analysis of inclusion morphology effects on void nucleation

Deformations of a planar doubly periodic array of square elastic inclusions in an isotropically hardening elastic-viscoplastic matrix are analysed. The arrays considered have multiple inclusions per unit cell, but in each array all inclusions have the same size. Overall plane strain tension with a superposed tensile biaxial stress is imposed. A finite deformation formulation is used with a cohesive surface constitutive relation describing the bonding between the inclusion and the matrix. A characteristic length is introduced from dimensional considerations since the cohesive properties include the work of separation and the cohesive strength. The system analysed is used to study inclusion distribution effects on void nucleation, with the aim of providing background for incorporating the effect of clustering on void nucleation into phenomenological constitutive relations for progressively cavitating plastic solids. For low values of the triaxiality of the imposed stress state, void nucleation occurs after extensive overall plastic straining and regular distributions have a higher value of the void nucleation strain than random distributions. For larger values of stress triaxiality, where void nucleation occurs at relatively small overall plastic strains, the effect of inclusion size dominates the effect of inclusion distribution and smaller inclusions give rise to higher void nucleation strains. The ability of various scalar measures of clustering to characterize the computed dependence of void nucleation on inclusion distribution is explored. Within the context of a phenomenological description of void nucleation, it is found that the effective void nucleation stress is approximately a linear function of the overall hydrostatic tension with a coefficient 0.40-0.44 for regular distributions and 0.25-0.35 for random distributions. The results also suggest a possible dependence of the effective void nucleation stress on a simple scalar measure of clustering.