Overall softening and anisotropy related with the formation and evolution of dislocation cell structures

In this work, a model, based on a representation of the dislocation cell microstructures by a non-local two-phase material with evolving microstructures, is proposed for the elastic–plastic behavior of metals under monotonic and sequential loading. The first phase represents the cell interior and the second one, the cell walls. The evolution of the microstructure is taken into account considering the cell-wall interfaces as free boundaries. Finally, the accumulation within walls of dislocations crossing the cells defines a non-local hardening process. Assuming a piecewise uniform plastic strain field and assuming ellipsoidal cells, the free energy of the system is calculated. The driving and critical forces associated with the plastic flow of the two-phases and the morphology of the cells are established. In a third part, numerical results are presented for monotonic and sequential loading. The results show an overall softening related to the destabilization of the dislocation microstructures which occurs in sequential as well as monotonic paths.