The development of technological methods for processing and manufacturing of functional (with a priori targeted properties) polycrystalline materials and products made of these materials still remains an acute problem. A multilevel modeling approach offers researchers the opportunity to describe inelastic deformation by applying internal variables that give an effective characterization of the material structure at different structural scale levels. High temperature plastic deformation is accompanied by these processes, which leads to a significant rearrangement of the meso- and microstructure of the material. The most substantial contribution to changing the properties of polycrystals is made by the evolution of grain and defect structures at the expense of dynamic recrystallization, which significantly depends on dynamic recovery. In this paper, we consider the problem of the coalescence of subgrains undergoing rotation during inelastic hot deformation. This process is called subgrain coalescence, and it is one of the dynamic recovery mechanisms responsible for changes in the fine subgrain structure. Under applied thermomechanical loads, the coalescence process promotes the formation of recrystallization nuclei and their subsequent growth, which can greatly change the grain structure of a polycrystal. The problem was solved in terms of the advanced statistical model of inelastic deformation, modified to describe the subgrain coalescence process. The model takes into account the local interactions between contacting structural elements (subgrains). These have to be considered so that the grain coalescence caused by a decrease in subboundary energies during their progressive merging can be adequately analyzed. For this purpose, a subgrain structure quite similar to the real structure was modeled using Laguerre polyhedra. Subgrain rotations were investigated using the developed model, which relies on the consideration of the excess density edge component of the same sign dislocations on incidental subgrain boundaries. The results of modeling of a copper polycrystal are presented, and the effects of temperature and strain rate on the subgrain coalescence process is demonstrated.

Physical multilevel models of inelastic deformation that take into account the material structure evolution hold promise for the development of functional materials. In this paper, we propose an advanced (modified via analyzing the mutual arrangement of crystallites) statistical multilevel model for studying thermomechanical processing of polycrystals that includes a description of the dynamic recrystallization process. The model is based on the consideration of homogeneous elements (grains, subgrains) aggregated into a representative volume (macropoint) under the Voigt hypothesis. In the framework of this statistical approach, there is no mandatory requirement for continuous filling of the computational domain with crystallites; however, the material grain structure cannot be created arbitrarily. Using the Laguerre polyhedra, we develop a method of grain structure simulation coupled with subsequent processing and transferring of the necessary data on the grain structure to the modified statistical model. Our research is of much current interest due to the fact that the mutual arrangement of crystallites, as well as the interfaces between them, has a significant impact on the properties of polycrystals, which are particularly important for physical mechanisms that provide and accompany the processes of inelastic deformation (recrystallization, grain boundary hardening, grain boundary sliding, etc.). The results of the simulations of the high-temperature deformation of a copper polycrystal, including the description of the recrystallization process, are presented.

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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.

Thermomechanical processing of metals and alloys is accompanied by deep changes of the material structure (including grain structure), which determines physical and mechanical properties and the working characteristics of products made from them. Its change is possible due to mechanical (fragmentation process) and/or temperature (recrystallization process) influences. Because of this, an urgent task is to create mathematical models that allow describing changes in the material structure and the stress-strain state under thermomechanical treatment. For this purpose, the multilevel physically oriented model was developed for researching inelastic deformation of polycrystals. The problem of modeling two stages deformation of a polycrystalline copper sample was formulated. At the first stage, preliminary cold intense plastic deformation under complex loading was investigated. Two variants of preliminary deformation were considered. They were homogeneous deformation corresponding to equal-channel angular compression (ECUP), and deformation with closed deformation trajectory. At the second stage, uniaxial high-temperature deformation was considered prior to the beginning of an intensive dynamic recrystallization. The paper describes the method for estimating the recrystallized material volume fraction within the framework of the multilevel model. The influence of the deformation temperature, the preliminary deformation, the deformation texture, and the average angle of mutual misorientation of neighboring grains on recrystallization was investigated. These parameters determine the development of dynamic recrystallization, since its main physical cause is the difference in stored energy between neighboring grains. It was shown that the developed mathematical model is suitable for describing the thermal activation of dynamic recrystallization at temperatures in the range of 0,4–0,7 homologous temperature. The deformation trajectory complexity determines the type of deformation texture, its “sharpness” or “dispersion”, the angles of neighboring grains mutual misorientation. The results of computational experiments are presented. According to the proposed method, the deformation at the high-temperature stage is determined, at which the intensive migration of new grains begins during recrystallization.