MATHEMATICAL MODELING OF INTENSIVE INELASTIC DEFORMATIONS OF SUBMICROCRYSTALLINE AND NANOCRYSTALLINE MATERIALS

Abstract

This article is devoted to issues related to the description of the processes of inelastic deformations of polycrystalline materials, for which the influence of the grain size on the process of evolution of the internal structure and the accompanying change in physical and mechanical properties are essential. As a basic model, we accepted a two-level mathematical model of polycrystalline elastoviscoplastic deformation, which is supplemented by the description of the hardening processes, including due to the grain boundaries, and rotations of crystal lattices. To account for hardening mechanisms we suggested an additional term in the hardening law, describing an increase in the critical shear stress of dislocations due to the interaction of the latter ones with orientation mismatch dislocations and explicitly taking into account the mutual lattice misorientation of neighboring grains. To describe the rotation mechanism, fragmentation and grain crushing we introduced an intermediate structural level and suggested a sub-model, where the incompatibility of inelastic deformations in neighboring grains is considered to be the main cause of rotations, and the fragment-grain structure analysis is carried out by determining the type of grain boundaries. Numerical experiments on the deformation of a polycrystal representative volume were carried out; the results are consistent with the Hall-Petch law. In addition, new results were obtained that help to assess the nature and dynamics of the crystal lattice rotations, resulting in grain fragmentation and crushing.