Anisotropic yield and plastic flow of polycrystalline solids

Deformation induced anisotropy in polycrystalline solids results mainly from crystallographic slip due to dislocation motion at the grain level and texture development due to grain rotation at the aggregate level. To describe these characteristics, the so-called scale invariance approach is adopted which allows information and constitutive relations pertaining to single slip to be cast in a form of macroscopic constitutive equations. An orientation distribution function (ODF) and a texture tensor are introduced into the earlier version (based on the hypotheses of single slip at the grain level and isotropic distribution of the crystallites at the aggregate level) of the scale invariance framework to describe texture effects in plastically deformed polycrystals. The texture tensor is calculated either directly through the solution of ODF, or indirectly through an appropriate set of evolution equations for the orientation tensors and the use of a closure approximation. Theoretical predictions for anisotropic yield and plastic flow behavior compare well with available experimental data.