Ductile failure simulations using a multi-surface coupled damage-plasticity model

Ductile failure of isotropic porous materials is studied using a coupled damage-plasticity model, accounting for void growth by diffuse plastic flow as well as void coalescence by plastic flow localization in the inter-void ligaments. The model is based on a multi-surface yield criterion, consisting of the Gurson yield criterion for a porous representative volume element (RVE) undergoing diffuse yielding, and additional yield criteria corresponding to localized yielding of the RVE within discrete coalescence bands whose orientations depend on the applied state of stress. Approximate closed form solutions for the orientations of the potential coalescence bands as a function of the applied stress are obtained; and a closed form expression for the coalescence criterion, expressed in terms of the principal stresses, is proposed. The predicted shapes of the multi-surface yield loci at large values of the porosity have a marked resemblance to the Mohr-Coulomb yield locus for granular materials on octahedral section planes, and reduce approximately to the Gurson yield locus for small values of the porosity. The plasticity model is integrated numerically under proportional loading conditions, and predictions for the strains to failure are obtained as a function of the loading path parameters, the stress triaxiality and the Lode parameter. The predicted trends for the loading path dependence of ductility are shown to be in good qualitative agreement with the results of recent micromechanical voided cell simulations under combined tension and shear. Finally, predictions for the strains to failure in smooth and notched bar tension experiments are obtained from finite element simulations using the multi-surface and the widely used Gurson-TvergaardNeedleman (GTN) models. It is shown that the multi-surface model, in the absence of heuristic adjustable parameters, quantitatively predicts similar values of the overall strains to failure as the GTN model; using typical values of the parameters in the latter model.