A micropolar model of plastic deformation of polycrystals at the mesolevel

Experimental and theoretical research of the last few years have shown that it is impossible in principle to describe macroscopic properties of plasti c flow when only the dislocation theory is adopted. It is necessary to take into consideration one or more intermediate mesoscopic levels at which vol umes of finite sizes are the objects of study. The heterogeneity of a mater ial's internal structure and formation of substructures of essentially a gr eater scale than separate dislocation are to be taken into account obviousl y during plastic deformation in mesovolumes, Hence, an adequate model of th e mesovolume behaviour should consider displacement, rotations and interact ion 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 indepe ndent rotations of mesofragments of finite size without obvious calculation of couple-stress and torsion-curvature. As rotation and displacement of in dividual 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 tenser from additional physical reasons, It is supposed in the model that at the stage of perfectly elastic deformation the stress tenser is symmetric, and its asymmetrical part appears only at the stage of plast ic deformation and is proportional to the function of plastic strain accumu lated in the considered local area. Test calculations carried out have show n that the model is able to simulate the behaviour of crystals with a limit ed 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 t he parameter) of rotation of local mesovolumes of a material. (C) 2000 Else vier Science B.V, All rights reserved.