Bounds for the plastic strength of polycrystalline voided solids

Abstract eng:
The elastoplastic response of polycrystalline voided solids is idealized here as rigid-perfectly plastic. Bounds on the macroscopic plastic strength for prescribed microstructural statistics and single-crystal strength are computed be means of a linear-comparison homogenization technique. Hashin-Shtrikman and Self-Consistent results in the form of yield surfaces are reported for cubic and hexagonal polycrystals with isotropic texture and varying degrees of crystal anisotropy. Improvements over earlier linear-comparison bounds of up to forty per cent are found at high stress triaxialities. In the case of deficient crystals, the Self-Consistent results assert that voided aggregates of crystals with four independent systems can accommodate arbitrary deformations, those with three independent systems can dilate but not distort, and those with less than three independent systems cannot deform at all. We report the sharpest bounds available to date for all classes of material systems considered.

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