Modeling void growth in polycrystalline materials

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Most structural materials are polycrystalline aggregates whose constituent crystals are irregular in shape, have anisotropic mechanical properties and contain a variety of defects, resulting in very complicated damage evolution. Failure models of these materials remain empirically calibrated due to the lack of a thorough understanding of the controlling processes at the scale of the materials’ heterogeneity, i.e. the mesoscale. This paper describes a novel formulation for a quantitative, microstructure-sensitive three-dimensional mesoscale prediction of ductile damage of polycrystalline materials, in the important void growth phase of the process. Specifically, we have extended a formulation based on fast Fourier transforms to compute growth of intergranular voids in porous polycrystalline materials. In this way, two widely used micromechanical formulations, i.e. polycrystal plasticity and dilatational plasticity, have been efficiently combined, with crystals and voids represented explicitly, to predict porosity evolution. The proposed void growth algorithm is first validated by comparison with corresponding finite-element unit cell results. Next, in order to isolate the influence of microstructure on void growth, the extended formulation is applied to a face-centered cubic polycrystal with uniform texture and intergranular cavities, and to a porous material with homogenous isotropic matrix and identical initial porosity distribution. These simulations allow us to assess the effect of the matrix’s polycrystallinity on porosity evolution. Microstructural effects, such as the influence of the Taylor factor of the crystalline ligaments linking interacting voids, were predicted and qualitatively confirmed by post-shocked microstrostructural characterization of polycrystalline copper.