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Abstract
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 constructed. 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 these direction, notably in case of few crystallographic directions. The general finding is that the higher the isotropy of a material, 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.
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