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

TL;DR

This paper develops a symmetry-based yield criterion for crystalline materials, especially non-Schmid types, accounting for inversion symmetry and providing insights into when non-Schmid stresses influence yielding.

Contribution

It introduces a new yield criterion that incorporates inversion symmetry for non-Schmid materials, extending traditional models to more accurately predict yielding behavior.

Findings

The model reduces to Tresca's maximum shear stress theory when non-Schmid stresses are negligible.

Application to BCC and HCP metals shows conditions where non-Schmid stresses are significant.

The criterion emphasizes the importance of symmetry considerations in yield modeling.

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.