A micromechanics-based elastic-viscoplastic model with non local effects due to geometrically necessary dislocations

Homogenization methods based on the Eshelby inclusion problem well capture the effects of local behaviour, volume fractions and morphologies of constituents on the macroscopic behavior but still suffer from a lack of representation of internal lengths in the material associated with non-local effects or gradients. In this contribution, we propose a new micromechanical approach based on the representation of the material as a two-phase composite: the inclusion phase which corresponds to the grain core region for which statistically stored dislocations mainly participate in the plastic flow of the material, and, the matrix phase which is a region close to grain boundaries where additional plastic strain gradients and associated geometrically necessary dislocations are present. The macroscopic material behavior is retrieved by applying a relevant self-consistent modeling for elastic-viscoplastic materials based on the "translated fields" technique and using secant viscoplastic compliances for each phase. The model is then applied to polycrystalline ferritic steels with different grain sizes. Numerical results in terms of macroscopic behaviors, local mechanical fields, evolution of dislocation densities are discussed and compared with experimental ones. © AES-Advanced Engineering Solutions.