Elastic anisotropy and yield surface estimates of polycrystals

Homogenization estimates based on the self-consistent scheme are customarily used to describe the plastic yielding of polycrystals. Such estimates of the initial micro yield surface of a polycrystal depend on the morphologic and crystallographic textures, the slip system geometry, the corresponding critical resolved shear stresses and the single crystal elastic anisotropy. The usual approach relies on a rather crude description of the stress field induced by the local elastic anisotropy. This deficiency is addressed and a new concept, i.e. a “probability” yield surface is proposed. Based on a statistical description of the local fields, the latter makes use of the average and the standard deviation of the resolved shear stress on the different slip systems within a given crystalline orientation. By comparing the homogenization estimates with full-field results, it is shown that the self-consistent scheme does not present intrinsic shortcomings regarding the prediction of the micro yield stress of polycrystals with anisotropic elastic constitutive behaviour. On the contrary, it delivers realistic estimates if the local field fluctuations are taken into account in the yield criterion. The quantitative results obtained for cubic elasticity show a strong influence of the intragranular stress heterogeneity on the estimate of the micro yield stress.