Two inhomogeneities of irregular shape with internal uniform stress fields interacting with a screw dislocation - 14/05/16

Doi : 10.1016/j.crme.2016.02.008

Xu Wang ^a , Peter Schiavone ^b,^{^⁎}
^a School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China
^b Department of Mechanical Engineering, University of Alberta, 10-203 Donadeo Innovation Centre for Engineering, Edmonton, Alberta T6G 1H9, Canada

^⁎Corresponding author. Tel.: +1 780 492 3638.

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Abstract

Using complex variable methods and conformal mapping techniques, we demonstrate rigorously that two inhomogeneities of irregular shape interacting with a screw dislocation can indeed maintain uniform internal stress distributions. Our analysis indicates that while the internal uniform stresses are independent of the existence of the screw dislocation, the shapes of the two inhomogeneities required to achieve this uniformity depend on the Burgers vector, the location of the screw dislocation, and the size of the inhomogeneities. In addition, we find that this uniformity of the internal stress field is achievable also when the two inhomogeneities interact with an arbitrary number of discrete screw dislocations in the matrix.

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Keywords : Internal uniform field, Two inhomogeneities of irregular shape, Screw dislocation, Anti-plane deformation, Complex variable methods, Conformal mapping