On the accuracy of the self-consistent approximation for polycrystals: comparison with full-field numerical simulations

Abstract This paper presents comparisons between full-field numerical results and self-consistent (SC) estimates for the effective behavior and statistical fluctuations of the stress and strain-rate fields in viscoplastic polycrystals. The full-field simulations make use of a recently introduced technique, based on the fast Fourier transform (FFT) algorithm. Applications are given for linear and power-law polycrystals with randomly distributed FCC and HCP grains. For linear systems, the FFT results demonstrate the accuracy of the standard SC approximation, even for relatively large values of the grain anisotropy parameter when the field fluctuations become significant. On the other hand, of the various extensions of the self-consistent method that have been proposed for nonlinear systems, the recent ‘second-order’ method appears to give the best overall predictions for both the effective behavior and the statistical fluctuations of the stress and strain-rate fields in power-law polycrystals.