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

J. E. RAMOS NERVI; M. I. IDIART

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

ROYAL SOC

Lugar: Londres; Año: 2015 vol. 471 p. 1 - 13

1364-5021

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 and Ponte Casta~neda (Idiart & Ponte Casta~neda 2007 extit{Proc. R. Soc. A} extbf{463}, 907--924). 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. In all cases, the surfaces are smooth, closed and convex. Improvements over earlier linear-comparison bounds of up to forty per cent are found at high stress triaxialities. New Hashin-Shtrikman results can even be sharper than earlier Self-Consistent results for some material systems. 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.