Application of strain gradient plasticity modelling to high pressure torsion

An analytical model describing the deformation behaviour of copper during the high-pressure torsion (HPT) processing is presented. The model was developed on the microstructural basis where the material is partitioned in two 'phases', the dislocation densities in cell walls and the dislocation densities cell interior, entering the model as scalar internal variables. The resulting 'phase mixture' model is combined with strain gradient theory to account for strain non-uniformity inherent in SPD. It was demonstrated that gradient plasticity model is capable of describing the experimentally observed trends and accounting for a homogenisation of the accumulated shear strain across the HPT sample. The predictions of the model with respect to the ultrafine grain size produced by HPT and evolution of dislocation densities are in good agreement with experimental results reported by other research groups.