Bounding the plastic strength of polycrystalline voided solids by linear-comparison homogenization techniques

Abstract

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 developed by Idiart & Ponte Castañeda (2007 Proc. R. Soc. A 463 , 907–924. ( doi:10.1098/rspa.2006.1797 )). Hashin–Shtrikman (HS) and Self-Consistent (SC) results in the form of yield surfaces are reported for cubic and hexagonal polycrystals with isotropic texture and varying degrees of crystal anisotropy. In all cases, the surfaces are smooth, closed and convex. Improvements over earlier linear-comparison bounds of up to 40% are found at high-stress triaxialities. New HS results can even be sharper than earlier SC results for some material systems. In the case of deficient crystals, the SC 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 fewer than three independent systems cannot deform at all. We report the sharpest bounds available to date for all classes of material systems considered.