Deformation induced dislocation microstructures appeared in Face-Centred Cubic metals and alloys if applying large enough tensile/cyclic strain. These microstructures were composed of a soft phase with a low dislocation density (cell interiors, channels…) and a hard phase with a high dislocation density (walls). It was well known that these dislocation microstructures induce back-stresses, which gave kinematic hardening at the macroscopic scale. A simple two-phase localization rule was applied for computing these intragranular back-stresses. This was based upon Eshelby’s inclusion problem and the Berveiller–Zaoui approach. It took into account an accommodation factor. Close-form formulae were given and permitted the straightforward computation of reasonable back-stress values even for large plastic strains. Predicted back-stress values were compared to a number of back-stress experimental measurements on single crystals. The agreement of the model with experiments was encouraging. This physical intragranular kinematic hardening model could easily be implemented in a polycrystalline homogenization code or in a crystalline finite element code. Finally, the model was discussed with respect to the possible plastic glide in walls and the use of enhanced three-phase localization models.

Analytical Modelling of Intragranular Backstresses due to Deformation Induced Dislocation Microstructures. M.Sauzay: International Journal of Plasticity, 2008, 24[5], 727-5