Variational self-consistent estimates for viscoplastic polycrystals with highly anisotropic grains

A recently established variational procedure is used to compute self-consistent estimates for viscoplastic polycrystals with highly anisotropic ionic and HCP grains. For large values of the grain anisotropy M, the predictions for the macroscopic flow stress are found to scale as M^γ, where γ depends on the number (less than 5) of independent slip systems that are available for plastic flow, but not on the strain-rate sensitivity. The predictions of other nonlinear extensions of the self-consistent scheme are inconsistent with this scaling law, suggesting that they may be less accurate than the variational estimates proposed here.