A yield criterion based on mean shear stress

This work investigates the relation between shear stress and plastic yield considering that a crystal can only deform in a limited set of directions. The shear stress in arbitrary directions is mapped for some cases showing relevant differences. Yield loci based on mean shear stress are con- structed. The Tresca yield criterion can be improved by averaging the shear stress over directions near the direction of maximum shear stress. Yield criteria based on averaging over crystallographic direction show a clear influence of the actual orientation of this direction, notably in case of few crystallographic directions. The general finding is that the higher the isotropy of a crystal, the lower the plane strain factor. The shape of the yield loci is comparable to those derived by the Hershey criterion with exponents lower than 3.