New robust self-consistent homogenization schemes of elasto-viscoplastic polycrystals

Abstract

Three novel and robust homogenization schemes for polycrystals deforming in the elasto-viscoplastic regime are proposed, two of them of the self-consistent type and the other combining self-consistent and Mori-Tanaka methods. In addition, a non-incremental interaction equation for an elasto-viscoplastic inhomogeneity problem is also derived. Second moments of stress and strain field distributions within the grains are estimated using the algorithms developed for linear heterogeneous materials. A thorough description of the approximations, methodology and algorithms involved is given, and, using the case of a copper polycrystal, it is shown that the proposed methods obey the elastic and viscoplastic limits. The new homogenization schemes are then applied to the case of tension of stainless steel, including the prediction of intragranular averages and standard deviations of lattice strains. These predictions are compared to published experimental measurements and corresponding full-field polycrystal plasticity results. Acceptable agreement of the predicted grain-averaged lattice strains with both experiments and full-field results was observed, while the calculated standard deviations of lattice strains matched well only with the full-field predictions.