Multilevel Models in Physical Mesomechanics of Metals and Alloys: Results and Prospects

The development of new structural materials (primarily metals and alloys) and their processing technologies for the manufacture of high-performance products is and will be the focus of many research areas and industries. In recent decades, the complex problems of material design and processing have been solved using various mathematical models, many of which are based on macrophenomenological continuum theories of elastoplasticity. However, it is known that the physical and mechanical properties of metals as well as the performance characteristics of metal products are almost fully determined by their meso- and microstructures, whose evolution cannot be described by the above theories. This gap has been successfully filled in the last 15–20 years by multilevel models that explicitly describe the physical mechanisms of inelastic deformation and their carriers causing structural changes in the material at various structural scale levels. Multilevel models can be considered an effective tool for the implementation of the main principles, approaches and methods of physical mesomechanics, developed in the works of Victor Panin et al. This paper discusses the structure and constitutive equations, hypotheses, classification, applications and limitations of multilevel models used to describe the thermomechanical processing of metals and alloys. Since a large number of technological processes for the manufacture of high-performance parts and components involve severe plastic deformation, special attention is paid to taking into account geometric nonlinearity in the relationships included in the model. Application examples of our original models are given, in particular, for describing superplastic deformation, recrystallization processes, the effect of external and internal crystallite boundaries on the deformation of polycrystalline samples, and for complex loading analysis. The further development of multilevel models with the involvement of deeper structural scale levels into the models is discussed.