Analytical modelling of intragranular backstresses due to deformation induced dislocation microstructures

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