Accurate estimates for the creep behavior of hexagonal polycrystals

Abstract

A recently proposed “variational” self-consistent model is used to estimate the macroscopic response of various types of HCP viscoplastic polycrystals, including titanium, ice, and zirconium. Unlike the “incremental” and “tangent” models, which lead to predictions that tend to the Taylor upper and Reuss lower bounds, respectively, in the strongly nonlinear, rate-insensitive limit, the new model leads to estimates that tend to neither bound and which are somewhat intermediate between the two. The new estimates are quite possibly the most accurate to date, especially for polycrystals with highly anisotropic grains. In addition, the new self-consistent model is capable of handling the commonly occurring situation of different rate-sensitivity exponents for different slip families. Sample calculations for zirconium show a clear transition—from the high to the low rate-sensitivity exponent—in the response curve for the polycrystal, but only if at least four independent systems are available for each slip family.