MULTILEVEL MODELS OF POLYCRYSTALLINE METALS: COMPARISON OF RELATIONS DESCRIBING THE CRYSTALLITE LATTICE ROTATIONS

摘要

Multilevel models of materials give an explicit description of the physical mechanisms, evolution of material structure, and physical and mechanical properties in inelastic deformation. This allows one to apply such models to improve the existing technologies of mechanical treatment (including the ones for submicrocrystalline and nanocrystalline materials) and develop some new ones. A key point in multilevel modeling of poly crystalline metals and alloys is the formulation of kinematic and constitutive relations at the mesolevel (the level of individual crystallites), which would apply to large displacement gradients peculiar to most processes of thermomechani-cal treatment of metals and alloys. Various formulations of the constitutive mesolevel models used in multilevel models of polycrystalline metals and alloys are considered. These are the relations in the unloaded configuration in the finite form, which are based on the motion decomposition with an explicit separation of the motion of the moving coordinate system, and the relations written in the rate form in the current configuration. The relationships used in these formulations to describe the rotations of the crystallite lattices are analyzed and compared. The analysis reveals the equivalence or closeness (in the sense of the response to be estimated) of the spins under consideration (with the exception of the logarithmic spin). The results of numerical calculations carried out for a polycrystal under arbitrarily chosen kinematic impacts lend support to the analytical conclusions.