Role of discrete intra-granular slip bands on the strain-hardening of polycrystals

This work investigates a new micromechanical modeling of polycrystal plasticity, accounting slip bands for physical plastic heterogeneities considered as periodically distributed within grains. These intra-granular plastic heterogeneities are modeled by parallel flat ellipsoidal sub-domains, each of them may have a distinct uniform plastic slip. To capture the morphology of slip bands occurring in plastically deforming polycrystals, these interacting sub-domains are considered as oblate spheroids periodically distributed and constrained by spherical grain boundaries. In this paper, we focus the study on the influences of internal length scale parameters related to grain size, spatial period and thickness of slip bands on the overall material’s behavior. In a first part, the Gibbs free energy accounting for elastic interactions between plastic heterogeneities is calculated thanks to the Green function’s method in the case of an isolated spherical grain with plastic strain occurring only in slip bands embedded in an infinite elastic matrix. In a second part, the influence of discrete periodic distributions of intra-granular slip bands on the polycrystal’s behavior is investigated considering an aggregate with random crystallographic orientations. When the spatial period of slip bands is on the same order as the grain radius, the polycrystal’s mechanical behavior is found strongly dependent on the ratio between the spatial period of slip bands and the grain size, as well as the ratio between the slip band thickness and the grain size, which cannot be captured by classic length scale independent Eshelby-based micromechanics.