Multilevel models of materials are the instrument allowing one to take into consideration micro- and nanomechanics in the description of technological processes at a macroscale level. The advantage of such models is an explicit description of physical mechanisms, evolution of material structure, and physical and mechanical properties in inelastic deformation. This allows one to apply models to improve the existing technologies of mechanical treatment (including the ones for submicrocrystalline and nanocrystalline materials) and develop some new ones. Corresponding boundary-value problems should be considered for the general case of large displacement gradients, the main problem is the formulation of the kinematic and constitutive relations. A widely recognized approach, based on the use of objective stress corotational rate, is briefly analyzed in the paper. A multiplicative representation of the deformation gradient with explicitly separated motion of the moving coordinate system at the mesolevel is proposed. The linear elastic law is satisfied in the moving coordinate system (just as within formulations with corotational derivatives). The moving coordinate system is associated with the elements of crystallite symmetry (crystallographic direction and plane). The constitutive elastoviscoplastic relations in the finite and rate forms, equivalent to each other are formulated in terms of the unloaded configuration. There is no hysteresis of stresses and no energy dissipation along closed elastic cycles. The approximate relations in the current configuration are represented in the rate form. They can be used in the description of the technological treatment of metals.

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.

In this paper, kinematic relations and constitutive laws in crystal plasticity are analyzed in the context of geometric nonlinearity description and fulfillment of thermodynamic requirements in the case of elastic deformation. We consider the most popular relations: in finite form, written in terms of the unloaded configuration, and in rate form, written in terms of the current configuration. The presence of a corotational derivative in the relations formulated in terms of the current configuration testifies to the fact that the model is based on the decomposition of motion into the deformation motion and the rigid motion of a moving coordinate system, and precisely the stress rate with respect to this coordinate system is associated with the strain rate. We also examine the relations of the mesolevel model with an explicit separation of a moving coordinate system and the elastic distortion of crystallites relative to it in the deformation gradient. These relations are compared with the above formulations, which makes it possible to determine how close they are. The results of the performed analytical calculations show the equivalence or similarity (in the sense of the response determined under the same influences) of the formulation and are supported by the results of numerical calculation. It is shown that the formulation based on the decomposition of motion with an explicit separation of the moving coordinate system motion provides a theoretical framework for the transition to a similar formulation in rate form written in terms of the current configuration. The formulation of this kind is preferable for the numerical solution of boundary value problems (in a case when the current configuration and, consequently, contact boundaries, are not known a priori) used to model the technological treatment processes.

Many of the existing constructions and parts from metals and alloys, used in various fields of technology and industry, undergo thermomechanical processing. This allows forming a grained and defect (internal) structure of the material in order to obtain the desired physical and mechanical properties. As a consequence, simulation of evolution of the internal structure of metals during plastic treatment at different temperatures is a relevant problem. For this purpose, the most advanced is the approach based on multilevel simulation and physical theories of plasticity, which explicitly describe the mechanisms of inelastic deformation and their carriers, as well as the processes that accompany plastic deformation. This approach includes two classes of models, namely, direct and statistical models. Statistical models consider the representative macrovolume of material (macropoint) as an aggregate of individual crystallites, combined in a polycrystal by the hypothesis of equality of strains (Voigt) or stresses (Reuss). Direct models are divided into two types. The first type of models considers explicitly the grain structure of the material and is applied only to the calculation of a small number of grains of the representative volume, given the existing computational restrictions. The second type of models is "hybrid" and uses numerical methods (for instance FEM). In this case, each point of integration is assigned a finite set of crystallites and polycrystalline aggregate response is determined using a statistical model. The purpose of the work is to create a two-level statistical model to describe the inelastic deformation of the representative volume of the polycrystal in a wide range of temperatures. The developed model can be integrated into a direct model of the second type. Elevated temperatures of deformation lead to the activation of the elastic stress relaxation processes, i.e., dynamic recovery and dynamic recrystallization. The first process occurs due to reconstruction of dislocation substructures; the description of the second process requires consideration of changes in the morphology and structure of the grains and their boundaries. In the present paper we consider the approach to the description of discontinuous dynamic recrystallization, which is based on the mechanism of the movement of the initially existing polycrystal boundaries. To solve this problem the Bailey-Hirsch criterion is used. This criterion is based on comparing the difference between the energy stored in the neighboring grains and the surface energy of the boundary between them. The method for determining the grain boundary energy is the basis of the Schober-Balbuffi ratio and the modified model of coincidence site lattice. The results are compared with experimental data and allow judging about the applicability of this approach to the problem.

This paper considers the influence of subgrain coalescence at initial high-angle boundaries on the initiation and growth of recrystallization nuclei (subgrains) under thermomechanical treatment. With certain processing regimes, adjacent subgrains in polycrystalline materials can be assembled into clusters during coalescence. Subgrain clusters at high-angle boundaries are the preferred potential nuclei of recrystallization. Coalescence is one of the dynamic recovery mechanisms, a competing process to recrystallization. When intensive coalescence develops on both sides of the grain boundary, recrystallization slows down or even stops. The problem formulated is solved using a multilevel modeling apparatus with internal variables. Application of the statistical multilevel model modified to take into account the local interaction between crystallites makes it possible to explicitly describe dynamic recrystallization and recovery. The results of modeling the behavior of a copper sample are presented and the effects of temperature, deformation velocity and subgrain structure on the formation and growth of recrystallization nuclei at arbitrary and special grain boundaries during coalescence are analyzed.

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.