Two-Level Elastoviscoplastic Model: An Application to the Analysis of Grain Structure Evolution under Static Recrystallization

Multilevel modeling of structural evolution in polycrystals, which determines the macroscopic material properties, is currently one of the central research problems. The defect and grain/subgrain structure of polycrystalline materials changes greatly during thermomechanical processing. The grain structure is significantly affected by recrystallization, which leads to the formation of slightly defective recrystallization nuclei and their subsequent growth due to the absorption of more defective neighboring grains. This paper is aimed to develop a mathematical model for describing the behavior of polycrystalline materials during plastic deformation and subsequent heating to recrystallization temperatures. The main task is to describe grain structure evolution in polycrystals during this process. The considered recrystallization mechanism is based on the displacement of original grain boundary segments. As a result of preliminary cold plastic deformation, energy accumulates at defects (primarily dislocations) in neighboring grains. The energy difference between neighboring grains is the main driving force of grain boundary migration. When the recrystallized grain grows, the extent of the new high-angle boundary increases; the amount of energy expended for the boundary formation must be smaller than the decrease in the stored energy due to defect elimination. The subgrains adjacent to the grain boundary are the recrystallization nuclei in the considered deformation mechanism. They start to grow into the more defective grain when the Bailey-Hirsch criterion is satisfied. This study deals with polycrystalline materials with low stacking fault energy for which the effect of heating on the subgrain structure is insignificant. The energy stored in grains and subgrains is calculated using a two-level statistical model that considers individual grains and subgrains. Plastic deformation is assumed to occur through edge dislocation glide. A method is proposed for isolating flat boundary regions (facets) of new (recrystallized) grains, based on minimizing the grain boundary energy in the vicinity of the new boundary. This approach describes some experimentally observed recrystallization effects, such as the elongation of recrystallized grains in the initial recrystallization direction and the appearance of grain boundary facets that allow for boundary mobility.