Infinite-contrast periodic composites with strongly nonlinear behavior: Effective-medium theory versus full-field simulations

This paper presents a combined numerical-theoretical study of the macroscopic behavior and local field distributions in a special class of two-dimensional periodic composites with viscoplastic phases. The emphasis is on strongly nonlinear materials containing pores or rigid inclusions. Full-field numerical simulations are carried out using a Fast-Fourier Transform algorithm [H. Moulinec, P. Suquet, C. R. Acad. Sci. Paris II 318, 1417 (1994)] Moulinec, P. Suquet, C. R. Acad. Sci. Paris II 318, 1417 (1994), while the theoretical results are obtained by means of the `second-order' nonlinear homogenization method [P. Ponte Castaneda, J. Mech. Phys. Solids 50, 737 (2002)]. The effect of nonlinearity and inclusion concentration is investigated in the context of power-law (with strain-rate sensitivity m) behavior for the matrix phase under in-plane shear loadings. Overall, the `second-order' estimates are found to be in good agreement with the numerical simulations, with the best agreement for the rigidly reinforced materials. For the porous systems, as the nonlinearity increases (m decreases), the strain field is found to localize along shear bands passing through the voids (the strain fluctuations becoming unbounded) and the effective stress exhibits a singular behavior in the dilute limit. More specifically, for small porosities and fixed nonlinearity m>0, the effective stress decreases linearly with increasing porosity. However, for ideally plastic behavior (m = 0), the dependence on porosity becomes non-analytic. On the other hand, for rigidly-reinforced composites, the strain field adopts a tile pattern with bounded strain fluctuations, and no singular behavior is observed (to leading order) in the dilute limit.Comment: 28 pages, 28 B&W figures, 2 tables of color maps, to be published in International Journal of Solids and Structures (in press

Viscoplasticity of voided cubic crystals under hydrostatic loading

International audienceA micromechanical study of the viscoplasticity of voided cubic crystals is presented. The microscopic void distribution is isotropic and the macroscopic loading is hydrostatic. Three different approaches are considered. The first approach consists in idealizing the voided crystal as a hollow sphere assemblage and bounding from above the corresponding dissipation potential à la Gurson. The second approach consists in idealizing the voided crystal as a sequential laminate of infinite rank and computing the corresponding dissipation potential exactly. Finally, the third approach consists in idealizing the voided crystal as a periodic medium with a complex unit cell and computing the mechanical fields numerically via a Fast Fourier Transform (FFT) algorithm. Predictions are reported for a wide range of crystals deforming by power-law creep and rate-independent plasticity. When the plastic anisotropy is weak, a fairly good agreement between all three approaches is observed. When the plastic anisotropy is strong, by contrast, discrepancies arise. In the extreme case of plastically deficient crystals, the various predictions can exhibit different asymptotics. While estimates based on hollow-sphere assemblages predict that any deficient voided crystal is rigid under hydrostatic loading, FFT simulations and sequential laminates suggest that some deficient voided crystals with more than two linearly independent systems may dilate. Overall, estimates based on sequential laminates are found to be superior to Gurson-type estimates based on hollow sphere assemblages and to predict the hydrostatic response of cubic voided crystals with reasonable accuracy, even for relatively strong plastic anisotropies. © 2018 Elsevier Lt

Dilatational viscoplasticity of polycrystalline solids with intergranular cavities

We propose constitutive models for polycrystalline aggregates with intergranular cavities and test them against full-field numerical simulations. Such conditions are prevalent in many engineering applications and failure of metallic components (e.g. HIPing and other forming processes, spallation under dynamic loading conditions, etc.), where the dilatational effects associated with the presence of cavities must be accounted for, and standard polycrystalline models for incompressible plasticity are not appropriate. On the other hand, it is not clear that the use of porous plasticity models with isotropic matrix behavior is relevant, particularly, when large deformations can lead to significant texture evolution and therefore to strong matrix anisotropy. Of course, finite strains can also lead to significant changes in the porosity and pore shape, resulting in additional anisotropy development. In this work, we make use of 'variational linear-comparison' homogenization methods to develop constitutive models simultaneously accounting for texture of the matrix, porosity and average pore shape and orientation. The predictions of the models are compared with full-field numerical simulations based on fast Fourier transforms to study the influence of different microstructural features (e.g. overall porosity, texture of the matrix phase, single-crystal anisotropy, etc.) and type of loading (triaxiality) on the dilatational viscoplastic behavior of voided polycrystals. The results are also compared with the predictions of isotropic-matrix porous plasticity models to assess the effect of the possible matrix anisotropy in textured samples. © 2011 Taylor & Francis