A micropolar model of plastic deformation of polycrystals at the mesolevel

Abstract

Experimental and theoretical research of the last few years have shown that it is impossible in principle to describe macroscopic properties of plastic flow when only the dislocation theory is adopted. It is necessary to take into consideration one or more intermediate mesoscopic levels at which volumes of finite sizes are the objects of study. The heterogeneity of a material's internal structure and formation of substructures of essentially a greater scale than separate dislocation are to be taken into account obviously during plastic deformation in mesovolumes. Hence, an adequate model of the mesovolume behaviour should consider displacement, rotations and interaction of structural elements, which are available in the mesovolume. A medium like this requires to take account of internal non-compensated moments and only for a representative mesovolume the total (averaged) moment is equal to zero. A simple model is offered here which allows one to consider independent rotations of mesofragments of finite size without obvious calculation of couple-stress and torsion-curvature. As rotation and displacement of individual mesofragment, and its strain as well, are completely determined by its velocity field, it is necessary to define an asymmetrical part of the force-stress tensor from additional physical reasons. It is supposed in the model that at the stage of perfectly elastic deformation the stress tensor is symmetric, and its asymmetrical part appears only at the stage of plastic deformation and is proportional to the function of plastic strain accumulated in the considered local area. Test calculations carried out have shown that the model is able to simulate the behaviour of crystals with a limited number of active slip systems well. In the case of two-dimensional flow, a spin parameter determines both magnitude and direction (by the sign of the parameter) of rotation of local mesovolumes of a material.