A new mean field micromechanical approach to capture grain size effects

Although homogenization methods based on the Eshelby inclusion problem well capture the effects of heterogeneous local behaviours, volume fractions and morphologies of constituents on the macroscopic behaviour, inclusion size is still not considered. However, grain size effects are known to mainly participate on experimental results. 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 (i.e., with net Burgers vector equal to zero) mainly participate in the plastic flow of the material, and, the matrix phase which is a region close to grain boundaries where plastic strain gradients and associated geometrically necessary dislocations (i.e., dislocations with net Burgers vector different from zero) are present. The macroscopic material behaviour is retrieved by applying a relevant self-consistent modelling for elastic–viscoplastic materials based on the “translated fields” technique and using secant viscoplastic compliances for each phase. By accounting for plastic strain gradient effects, the present modelling is able to well capture the observed grain size effect on the overall strain hardening. The model is applied to polycrystalline ferritic steels with different grain sizes and different chemical compositions. Numerical results in terms of macroscopic behaviours, local mechanical fields, evolution of dislocation densities as well as Bauschinger effect are discussed and compared with experimental ones.