Orientation dependence of stress distributions in polycrystals deforming elastoplastically under biaxial loadings

The influence of biaxiality of the loading on the crystallographic orientation dependence of crystal stress distributions is examined for polycrystalline solids deformed well into the elastoplastic regime. The examination is couched in terms of two decompositions of the stress. The first is a split of the tensor into its hydrostatic and deviatoric components; the second is a spectral decomposition of the deviatoric stress from which we express the relative values of the principal components as a function of the biaxiality of the stress. Using the framework provided by these decompositions, we investigate trends observed in the lattice strains in polycrystals subjected to biaxial loadings, comparing strains measured by neutron diffraction with finite element simulations. We conclude by showing how the orientation dependence of the stress distributions is influenced by the load biaxiality and by connecting features of the distributions to the elastic and plastic properties of the crystals. Implications of the results are discussed relative to the modeling of strain hardening and defect initiation.