Three-dimensional cellular automata for simulation of microstructure evolution during recrystallization

A cellular automation method is one of calculation methods, which allows for modeling of complex joint phenomena that take place in material during and after the deformation in the meso- and micro-scale. The phenomena, which can be taken into consideration with high precision, are processes connected with microstructure evolution. For modeling by cellular automata (CA) are mainly used two-dimensional ones, because of more expensive calculations by three-dimensional CA. But three-dimensional phenomena cannot be generally reduced to two-dimensional solution. In the paper a description of a modified three-dimensional CA is presented. The model of microstructure contains three parts: deformation of grains, recrystallization and grains growth after recrystallization. Recrystallization is considered as a process without division on the different kinds (dynamic, metadynamic or static). It consists of two stages: nucleation and new grains growth. Nucleation rate and grain growth rate are dependent on parameters of deformation. In the model such parameters as temperature, strain, strain rate, dislocation density, crystallographic orientation and some others are taken into account. Along with calculation of microstructure evolution, model allows for prediction of mechanical properties, for example flow stress. A flow stress calculations reckon processes of hardening and softening using model of the dislocation density development in consideration with an effect of the recrystallization. Some results of simulations based on 3D cellular automaton are presented in the paper.