Theoretical analysis of screw dislocations and image forces in anisotropic multilayered media

The elastic field induced by a screw dislocation embedded in an anisotropic elastic multilayered medium is presented in this study. A linear coordinate transformation is introduced in this study to simplify the problem. The explicit complete solutions of shear stresses and displacement for this problem consist only of the simplest solutions for a screw dislocation in an infinite homogeneous medium. The physical meaning of the solution is the image method and the magnitudes and locations of image screw dislocations are determined automatically from the mathematical method presented in this study. With the aid of the Peach-Koehler equation, the explicit forms of image forces exerted on screw dislocations are easily derived from the full-field solutions of stresses. Numerical results for full-field stress distributions in multilayered media subjected to a screw dislocation are presented. The image forces and equilibrium positions of a screw dislocation, two screw dislocations, and an array of screw dislocations are presented by numerical calculations and are discussed in detail.

©2006 The American Physical Society