Internal Length Scale Effects on the Local and Overall Behavior of Polycrystals

Abstract

A breakthrough in the general hypothesis of spatially homogeneous intragranular fields accepted in mean field approaches based on the classic Eshelby’s inclusion problem (self-consistent schemes, etc.) is proposed. Instead of considering uniform intra-granular plastic strains as usually prescribed in mean field approaches, intragranular slip patterns are modeled in single slip configurations both by distributions of coaxial circular glide loops and by distributions of flat ellipsoids (also called oblate spheroids). Both types of modeling assume slip configurations constrained by spherical grain boundaries, and, mechanical interactions between slip bands are taken into account (for mechanical fields and free energy). It is then found that intra-granular mechanical fields strongly depend on the grain size and the slip band spacing. In addition, in the case of glide loops, the modeling is able to capture different behaviors between near grain boundary regions and grain interiors. In particular, a grain boundary layer with strong gradients of internal stresses (and lattice rotations) is found. These results are confirmed quantitatively by EBSD measurements carried out with orientation imaging mapping (OIM) on deformed Ni polycrystals and on specific grains undergoing quasi single slip. Furthermore, as a result of the computation of the elastic energy, an average back-stress over the grain (in the case of loops) or over slip bands (in the case of oblate spheroids) can be derived so that it is possible to define new interaction laws for polycrystal’s behavior which are naturally dependent on grain size and slip band spacing.