Evolution of the grain structure of metals and alloys under intense plastic deformation: multilevel models

It is well known that the performance properties of products made of metals and alloys are determined mainly by the meso- and microstructure of the latter. The structure of materials is formed and undergoes significant changes in the processes of manufacturing parts and structures using thermomechanical processing methods. A very important parameter that determines the physical and mechanical characteristics of materials is the grain structure (size, shape, relative positions of grains and inclusions of various phases). In recent decades, in this regard, special attention has been paid to the processes of severe plastic deformation (SPD), which make it possible to obtain a submicro- and nanocrystalline grain structure, which provides a significant increase in the performance properties of products made of metals and alloys. The development of SPD technologies in modern conditions is unthinkable without mathematical modeling of the processes under consideration; the most important component in the development of such a "toolkit" are constitutive relations (or, more broadly, constitutive models). In connection with the foregoing, the latter should be able to describe the evolutionary structure at various scale levels. Until now, the practice of developers of materials processing technologies has been dominated by the use of macrophenomenological models based on classical continuum theories of plasticity, viscoplasticity, and creep. From the second half of the 20th century to the present, various improvements to the constitutive models of the above class have been proposed, in which additional parameters and kinetic equations are introduced for them, describing certain characteristics of the structure of materials. As a rule, such models make it possible to obtain an adequate picture of the changing structure, however, for specific materials and methods of thermomechanical treatment. At the same time, such models, unfortunately, do not have the necessary universality; when changing the material or processing method, they have to be significantly “customized” to specific conditions, up to a complete change in the relationships included in the model. A brief review of works devoted to the creation and application of models of this class is given in the previous article by the authors. The most promising and possessing a significant degree of universality, according to the authors, are currently multilevel constitutive models based on the introduction of internal variables and physical theories of plasticity (elastoviscoplasticity). A review of works that consider various aspects of the formulation, modification, numerical implementation and application of such models is proposed in this article. The main attention is paid to models focused on the description of changes in the structure of materials due to dislocation-disclination mechanisms; a brief note is given on models that take into account thermally activated diffusion mechanisms, due to which the processes of recovery and recrystallization are realized.