Processes of intensive plastic deformation used to improve mechanical properties of material cause a significant decrease in the size of grains which leads to the corresponding change in the yield stress. And the dependence of the yield stress on the grain size does not obey the conventional Hall-Petch relation for the size of grains obtainable in processes of intensive plastic deformation. Therefore, there is an urgent need to develop adequate constitutive equations for processes of intensive plastic deformation. In the present work, evolution equations for the size of grains taking into account some general features of processes of intensive plastic deformation and the most important characteristic trends of such processes as compared to conventional metal forming processes are proposed. In particular, the evolution equations include the dependence of the rate of change of the grain size on the rate of rotation of the principal directions of the stress tensor relative to the material. A number of widely used processes of intensive plastic deformation are analyzed to develop an experimental program for determining parameters involved in the evolution equations. Using experimental data available in the literature the magnitude of some parameters is evaluated. A relation between the size of grains and the yield stress is found by means of known experimental results for several materials. Combining this relation as well as the evolution equations and the classical equations of plastic flow a material model for describing processes of intensive plastic deformation has been obtained. Using this model a few benchmark boundary value problems have been solved. The results of these solutions are compared to solutions based on conventional models of plasticity.
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