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.

This paper presents a combined approach to the solution of boundary value problems. The approach implies the joint application of a macro-phenomenological model and multilevel physical constitutive models for describing the behavior of a polycrystalline material. Within the framework of the proposed approach, the boundary value problem is solved for a certain product (structure) using a macro-phenomenological model of the material and the response in the chosen area is clarified using multilevel modeling techniques. The capabilities of the approach were demonstrated in a series of numerical experiments covering metal forming processes. In order to test and verify the proposed technique, in the first numerical experiment, the process of an upsetting of the sample was considered using only a multilevel physical model of the material and using the formulated combined approach. The response in the chosen domain was compared to the results obtained by different modeling approaches. The comparison showed good agreement in terms of the variables of the stress–strain state at the macro level, as well as in terms of the variables characterizing the internal structure of the material. At the same time, using the combined approach, the required computation time was reduced by more than 12 times. In the second and third numerical experiments, the process of sheet rolling and sample pressing was successfully simulated using a combined approach. The formulated approach is computationally efficient and applicable for solving the relevant boundary value problems of design and the optimization of technological processes.

The paper aims at rationalizing the distribution of grain structure parameters across a gas turbine engine (GTE) disk in order to minimize the disk’s mass while ensuring its safe operational conditions. For this purpose, advanced methods of digital design were improved and applied, including state-of-the-art approaches based on multilevel modeling of material structure and properties. The problem was solved using a combined approach. Macro-phenomenological models were employed to determine, during the flight cycle, the evolving fields of stress-strain state and temperature of the entire part. These results were then transferred into a multilevel model to analyze specific regions for the study of strength characteristics, namely, high-temperature strength (resistance to creep and long-term strength), fracture toughness, low-cycle fatigue strength, and thermal stability (resistance to recrystallization and grain boundary migration). Multilevel modeling was based on a comprehensive analysis of the literature data on the structure of the nickel alloy VV751P, as well as on the mechanisms of its deformation and failure. The results of digital design were obtained and analyzed, and recommendations were proposed for rationalizing the material’s grain structure to reduce the disk’s mass while maintaining strength characteristics. The developed approach proved to be effective in digital multilevel design for functionally critical components.

This paper presents a novel modification of the multilevel statistical model for describing the subgrain boundary migration that can explicitly account for the topology of subgrain structures in the form of Laguerre polyhedra. The evolution of a representative volume of subgrains during annealing in the temperature range after plastic deformation taking into account competing recovery processes like coalescence and subgrain boundary migration is modeled. The material used in this study is the nickel-based superalloy Inconel 718 with complex hierarchical structure and specific phase composition. The results of modeling the changes in a polyhedral subgrain structure under recovery are presented. The contribution of subgrain coalescence and migration processes to recovery is evaluated. The abnormal growth of subgrains is described by the model, the conditions of its occurrence and implementation are defined. The calculated data demonstrate good agreement with experimental results.

This study proposes and applies a mathematical model to describe the process of recrystallization nucleation on large d-phase particles in the Inconel 718 nickel alloy during annealing (the particle stimulated nucleation (PSN) mechanism). The investigation employs a multilevel approach based on an extended statistical model, in which the subgrain structure is explicitly described by an aggregate of Laguerre polyhedra. The model for the formation of new recrystallized grain nuclei is based on the physical mechanisms of recovery: subgrain coalescence and low-angle boundary migration. Additionally, the model accounts for lattice rotations of subgrains near the non-deformable particle resulting from the incompatibility of prior plastic deformation, as well as the retarding effect of dispersed γ′ and γ″ particles during subgrain boundary migration. Numerical experiments were conducted on a representative volume of subgrains at annealing temperatures range 450–950 °C. It is shown that at 450 - 850°C subgrain growth near the d-phase particle is retarded due to increased misorientation, which hinders coalescence. At temperatures above 950 °C, the dissolution of the strengthening phases γ′ and γ″ leads to a decrease in the Zener pinning force and intense boundary migration near the d-phase particle results in the active formation of recrystallization nuclei. It is established that a needle-shaped d-particle promotes more intense nucleation compared to a spherical one due to its larger interfacial area. The simulation results are in qualitative agreement with known experimental data.