A dislocation density-based model for the work hardening and softening behaviors upon stress reversal

The mechanical behaviours of microalloyed and low-carbon steels under strain reversal were modelled based on the average dislocation density taking into account its allocation between the cell walls and cell interiors. The proposed model reflects the effects of the dislocations displacement, generation of new dislocations and their annihilation during the metal-forming processes. The back stress is assumed as one of the internal variables. The value of the initial dislocation density was calculated using two different computational methods, i.e. the first one based on the dislocation density tensor and the second one based on the strain gradient model. The proposed methods of calculating the dislocation density were subjected to a comparative analysis. For the microstructural analysis, the high-resolution electron backscatter diffraction (EBSD) microscopy was utilized. The calculation results were compared with the results of forward/reverse torsion tests. As a result, good effectiveness of the applied computational methodology was demonstrated. Finally, the analysis of dislocation distributions as an effect of the strain path change was performed.