Displacement and Plastic Distortion Fields Produced by Dislocations in Anisotropic Media

Abstract

The fundamental relations among dislocation density tensors, plastic distortion tensors, and dislocation flux tensors are introduced by the Fourier integral method. The proposed method is analytical rather than geometrical and powerful for further analysis of elastic fields. This method is applied to find displacement and plastic distortion fields for a given distribution of dislocations in anisotropic media. Since these quantities are not state quantities, the unique solution is obtained by designating a history of creation of the dislocations. In this paper the history is given in terms of the direction of motion in which the dislocations are introduced in the material from infinity with infinitely small uniform velocity.