Plastic deformation development in polycrystals based on the cellular automata and relaxation element method

Based on the Relaxation Element Method, the propagation of zones of localized plastic deformation in a polycrystal under loading has been simulated within the framework of continuum mechanics. The model can be referred to the class of geometrical models, known as cellular automata. Plastic deformation is considered to occur under the action of differently scaled stress concentrators. A plastically deformed grain acts as a stress concentrator at the mesoscale level. The involvement of a cell into plastic deformation was determined by the value of the critical shear stress in the cell center along the slip system. This approach allows to analyze the number and interaction of slip systems and accounts for work-hardening on the patterns of the propagation of the bands of localized plastic deformation in aluminum polycrystals.