On the contribution of screw dislocations to internal stress fields associated with dislocation cell structures

Abstract

The internal elastic stress fields associated with dislocation cells are studied using numerical three-dimensional simulations. The paper deals exclusively with static dislocation arrangements. The dislocations are treated as line defects embedded in an otherwise linear isotropic elastic medium. The dislocation lines are decomposed into piecewise straight segments. Two types of three-dimensional dislocation ensemble are investigated. The first arrangement represents a conventional subgrain structure. It consists of pure small angle tilt and twist boundaries with alternating sense of misorientation according to the model of Kuhlmann-Wilsdorf. The second one consists of interface dislocations according to the model of Mughrabi. The stress fields of both types of cell structures are calculated both with and without screw dislocations. The simulations substantiate that in the first case (Kuhlmann-Wilsdorf) the contribution arising from screw dislocations is negligible. However, in the second case (Mughrabi) the screw dislocations lead to an increase in the maximum shearing stress in the cell interor by about 67%. The total value of the maximum shearing stress arising from screw and edge dislocations, T~~ can in the present case empirically be described by the expression T~~ = r2D’+ r2D2g - u) where rZD represents the contribution of the edge dislocations and T (1 - u) the contribution of the screw dislocations. The influence of the number of involved slip systems and of the boundary conditions on the internal stress fields are investigated. The latter results show that the stress fields of three-dimensional dislocation arrangements must be calculated for cells which are embedded in larger translational threedimensional grids, in order to provide sufficiently accurate boundary conditions.