Interaction of a Screw Dislocation With an Arbitrary Shaped Elastic Inhomogeneity

[+] Author and Article Information
Xu Wang, L. J. Sudak

Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, Alberta, Canada T2N-1N4

J. Appl. Mech 73(2), 206-211 (May 17, 2005) (6 pages) doi:10.1115/1.2073307 History: Received January 27, 2005; Revised May 17, 2005

In this paper, the interaction between a screw dislocation and an arbitrary shaped elastic inhomogeneity with different material properties than the surrounding matrix is investigated. The exact solution to this problem is derived by means of complex variable methods and Faber series expansion. Specifically, the conformal mapping function maps the matrix region surrounding the inhomogeneity onto the outside of a unit circle in the image plane, while the analytic function defined in the elastic inhomogeneity is expressed in terms of a Faber series expansion. Once the series form solution is obtained, the stress fields due to the screw dislocation can be obtained. Also the image force on the screw dislocation due to its interaction with the elastic inhomogeneity is derived. Three examples of a screw dislocation interacting with (1) an equilateral triangular inhomogeneity, (2) a square inhomogeneity, and (3) a five-pointed star-shaped inhomogeneity are presented to illustrate how the stiffness of the triangular, square or five-pointed star-shaped inhomogeneity can influence the mobility of the screw dislocation.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

A screw dislocation interaction with an arbitrarily shaped inhomogeneity

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Figure 2

The equilateral triangle described by Eq. 18

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Figure 3

The normalized image force on a screw dislocation located on the positive x axis interacting with the equilateral triangular inhomogeneity

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Figure 4

The square described by Eq. 20

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Figure 5

The normalized image force on a screw dislocation located on the positive x axis interacting with the square inhomogeneity

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Figure 6

The five-pointed star described by Eq. 22

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Figure 7

The normalized image force on a screw dislocation located on the negativex axis interacting with the five-pointed star-shaped inhomogeneity




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