Evolution of dislocation patterns and its application in prediction of flow stress

The feature of dislocation patterns generated in plastic deformation is the ordered structure of alternative appearance of high and low dislocation density zones. With regard to the system of edge and screw dislocations, a nonlinear partial differential equation (eq. (13) in the text) including high order terms is established based on the reaction-diffusion equation. The contribution of cross slip of screw dislocations to the edge dislocation density is also considered in the analysis. The established equation has the typical feature of nonlinear system. Therefore, one does not need to deal with the complex expressions of the reaction and generation terms for dislocations. By theoretical analysis, the distance between adjacent high dislocation density zones (cell size or distance between cell walls) is obtained. By using this relationship, the flow stresses of ultrafine grained (UFG) copper and aluminum are predicted. The calculated results are well consistent with the experimental.