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.     

The backstress effect of evolving deformation boundaries in FCC polycrystals

Shape change of metal systems generates deformed microstructures of dislocation arrays that are comprised of walls of high density separating low density cells. The flow stresses of these composite structures are equilibrated by an evolving internal stress due to the blockage of dislocation passage resulting in kinematic hardening in the meso-scale. The method of intra-granular backstress of Eshelby using Kröner based approach in closed form formulae can easily be incorporated into a crystal-plasticity-based model to predict the kinematic hardening. We have previously developed finite element analyses based on the rate dependent crystal plasticity theory, which can incorporate electron backscatter diffraction (EBSD) maps. We will use this model with inclusion of the calculated backstress to investigate the effect of changes in strain paths.