Fully Coupled Two-Phase Composite Model for Microstructure Evolution during Non-Proportional Severe Plastic Deformation

A fully coupled micro-macro interaction model is proposed for the grain refinement caused by severe plastic deformation of cell-forming metallic materials. The model is a generalization of a previously proposed two-phase composite model suggested for the evolution of dislocation populations corresponding to the interior of the dislocation cells and dislocation cell walls. Just as within the original framework, the evolution of the material microstructure depends on the applied hydrostatic pressure, strain rate, and the loading path. Backstresses are used to define a measure of the strain path change. Thereby, the model can describe the experimentally observed dissolution of dislocation cells and the reduction of dislocation densities occurring shortly after load path changes. The large strain kinematics is accounted for in a geometrically exact manner using the nested split of the deformation gradient tensor, proposed by Lion. Within the extended model, the macroscopic strength of the material depends on the microstructural parameters. In that sense, the new model is fully coupled. It is thermodynamically consistent, objective, and w-invariant under isochoric changes of the reference configuration. A physical interpretation is provided for the nested multiplicative split in terms of the two-phase microstructure composite model.