Improving the self-consistent predictions of texture development of polycrystals incorporating intragranular field fluctuations

In this contribution we present how to implement the calculation of average field fluctuations inside the gains of a thermoelastic aggregate in terms of the derivatives of the stress potential given by the: standard linear self-consistent (SC) model, and how this statistical information can be used to generate second-order estimates for the mechanical behavior of non-linear viscoplastic polycrystals, by means of a rigorous non-linear homogenization procedure. To illustrate the differences between this second-order (SO) self-consistent approach and the classical first-order SC approximations, we compare them in terms of their predictions of the effective behavior of random fcc polycrystals as a function of their rate-sensitivity, and of the texture evolution in hcp ice polycrystals under uniaxial compression. In the latter case, the SO approximation is the only one able to predict a substantial accommodation of deformation by basal slip, even when the basal poles become strongly aligned with the compression direction and the basal slip systems became unfavorably oriented.