Description of hardening slip systems due to the boundaries of the crystallines in a polycrystalline aggregate

The paper considers the problem of describing hardening slip systems due to the boundaries of the crystallines in the multilevel models of crystal plasticity, based on the explicit introduction of internal variables. The boundary is a two-dimensional specific area that separates the different homogeneous parts of the crystal (grain phase, twins). Grain boundaries is an effective barrier to moving dislocations. Barrier effect of the border due to a sharp change in orientation of slip systems during the transition through it. If the dislocation of the crystalline has moved to a neighboring crystalline with its Burgers vector, this vector would be randomly oriented with respect to the lattice of neighboring crystalline and the movement of such disposition would significantly complicated. As a consequence, we assume the following mechanism of dislocation motion through the boundary: lattice dislocation becomes energetically more favorable slip system of the neighboring crystalline and mismatch dislocation appears in the boundary. Next lattice dislocation moving on the same slip system of the crystalline feels pushes away from the elastic stress fields previously formed mismatch dislocation. To describe the hardening it is necessary - to determine the slip systems in neighboring crystals, which will continue to slip. It have to propose a criterion according to which this system will be determined and to evaluate the stress exerted by the mismatch dislocation at the boundary. The rate of increase of these stresses, and will characterize the rate of change of the critical shear stress. The aim is to construct and analyze the law hardening due to the boundaries of the crystallites (grain phase, twins) with the use of internal variables of the model. The proposed ratio should be acceptable for the multi-phase materials, and in his final form must enter the parameters of meso- and macroscale, which have clear physical and/or geometrical meaning, which will simplify the identification procedure.