Micromechanical modeling and simulation of the loading path dependence of ductile failure by void growth to coalescence

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The loading path dependence of ductile failure by void growth to coalescence is studied using a unit cell model of a porous material, containing a periodic distribution of voids in an elasto-plastic power law hardening matrix. The unit cell is subjected to triaxial proportional loading paths, and predictions for the strains to failure, defined as the onset of void coalescence by plastic strain localization in the inter-void ligaments, are obtained as a function of the loading path parameters, the stress triaxiality and the Lode parameter. Analogous simulations of a macroscopic material element subjected to proportional loading are performed using a multi-surface plasticity model, which accounts for void growth by diffuse plastic flow and void coalescence by the localization of plastic strains inside a micro-scale representative volume element. A phenomenological hardening law that approximately accounts for the physics of strain hardening during both pre- and post-coalescence deformation is proposed. The strains to failure in the continuum simulations are determined as the equivalent strains to the onset of void coalescence at the micro-scale of the voids. It is shown that the multi-surface plasticity model quantitatively predicts the loading path dependence of the strains to failure obtained from the cell model simulations over a wide range of values of the Lode parameter, from axisymmetric to shear dominated states, and moderate to large values of the stress triaxiality. Quantitative agreement with cell model simulations is obtained for two representative values of the strain hardening exponent, and in the absence of heuristic adjustable parameters in the model.