Non-Schmid effects and localized plastic flow in intermetallic alloys

Abstract

A general strain rate dependent crystallographic slip theory which incorporates both non-Schmid effects and thermal deformation is presented. The theory is applied to the description of deformation in intermetallic alloys such as Ni 3Al. For Ni 3Al, as an example, it is shown that the approach embodies descriptions of stress state dependent yielding as observed experimentally as well as described by existing models such as that of Paidar, Pope and Vitek ( Acta Metall., 32 (1984)435). Finite element calculations of crystals deforming on only one slip system demonstrate that Asaro and Rice's ( J. Mech. Phys. Solids, 25 (1977) 309) criterion for bifurcation is a necessary condition for the formation of shear bands in crystals undergoing slip on only one slip system. Geometric effects are shown, however, to play an important role in the development of such localized shear bands. Strain rate sensitivity can delay significantly the formation of the localization, and lattice rotations relative to the surrounding lattice inside the shear bands are found to be quite small. This is in contrast to the case in multiple slip where lattice rotations play an important role in the localization process. In multiple slip the criteria for localized plastic flow are found to be of the sort described by Asaro ( Acta Metall., 27 (1979) 445; Mech. Mater., 4 (1985) 343), although localization generally occurs much sooner in the deformation process as a result of deviations from Schmid's rule.