Non-associated plastic flow in single crystals

Abstract

P lastic flow by shears on well-defined crystallographic planes is associated, most often, with the Schmid yield criterion which is expressed in terms of the resolved shear stress on those planes in the direction of the shears. In this case, for time-independent (low-temperature) flow, the yield function for each slip system is also the potential for the shear and. therefore, flow is said to be associated with that function (i.e. normality). Qin and Bassani (1992. J. Mech. Phys. Solids40, 813) propose a yield criterion to accommodate various non-Schmid behaviors. In this paper it is shown that this criterion leads to a nonassociated flow rule (i.e. non-normality). Time-independent constitutive relations are derived for single crystals undergoing non-associative plastic flow. The tension-compression asymmetry predicted for initial yield persists in strain hardening as well. Strain localization in the form of shear bands is investigated for both a single-slip and a symmetric double slip model. It is shown that non-Schmid effects increase the tendency for localization.