Multilevel model of polycrystals: application to assessing the effect of texture and grains misorientation on the critical deformation of the dynamic recrystallization initiation

The current state of materials constitutive models and the computer technology development make it possible to numerically implement complex multilevel models that allow describing the material structure evolution. In this regard, it is possible to formulate optimal control problem for metal forming processes in order to create the required performance characteristics of finished products and their ingots. To solve this problem in this study, the effective multilevel modeling approach is used to describe the thermomechanical treatment of polycrystalline materials. The model is based on this approach with the introduction of internal variables, in which the carriers and physical mechanisms of the processes of hot intense plastic deformation are explicitly considered. At deformation temperatures order of 0.5 homologous and above, recrystallization process have a special effect on the formation and change of the grain and defect material structure. The paper considers the problem of determining the critical deformation of dynamic recrystallization initiation, that depending on the material texture and the mutual misorientation of neighboring grains. Numerical experiments of the multilevel model are used to simulate two stages of inelastic deformation for this purpose. At the first stage, cold inelastic deformation by simple shear and compression is considered, that leading to the formation of a corresponding texture. At the second stage, uniaxial hot tension deformation is considered. The initial distribution of crystallographic grain orientation is assumed to be uniform. Two variants of the grains mutual misorientation with the prescribed increased and decreased values of the average misorientation angles are considered. The recrystallization process is not explicitly modeled. The current model is intended to assess the recrystallization critical deformation. It is shown that the mutual misorientation of grains, rather than texture, has the most influence on the critical deformation. An increase in the angle of grains mutual misorientation contributes to an earlier start of the dynamic recrystallization process. The formation of a deformation texture leads to a decrease in the angle of mutual misorientation, and, accordingly, to a decrease in dynamic recrystallization intensity. Despite this, with an increase of deformation, the driving force of recrystallization (the average value of the difference of stored energy between neighbor grains) is increases, which leads to the implementation of dynamic recrystallization.