Symmetry-Adapted Yield Criterion for Non-Schmid Materials

Abstract

The current form of the effective yield criterion that is used to describe non-Schmid behavior of dislocations in crystalline materials is not invariant under the simultaneous change of the slip direction and the slip plane normal as dictated by crystallography. Here, we explore the consequences of this symmetry on the derivation of the effective stress. This is defined by a linear combination of six stress functions that are represented by their Maclaurin series. Only the lowest order terms that obey this symmetry are retained, which results in a homogeneous effective stress of order two. It is shown that the quadratic terms can be further eliminated by resolving the respective stresses into another coordinate system in the zone of the slip direction. The application of the ensuing linear yield criterion 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.