Symmetry-adapted single crystal yield criterion for non-Schmid materials

Abstract

All yield criteria that determine the onset of plastic deformation in crystalline materials must be invariant under the inversion symmetry associated with a simultaneous change of sign of the slip direction and the slip plane normal. We demonstrate the consequences of this symmetry on the functional form of the effective stress, where only the lowest order terms that obey this symmetry are retained. A particular form of yield criterion is obtained for materials that do not obey the Schmid law, hereafter called non-Schmid materials. Application of this model to body-centered cubic and hexagonal close-packed metals shows under which conditions the non-Schmid stress terms become significant in predicting the onset of yielding. In the special case, where the contributions of all non-Schmid stresses vanish, this model reduces to the maximum shear stress theory of Tresca.