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Continuously distributed edge dislocations in pileups near a circular inhomogeneity

Xu Wang and Peter Schiavone

Vol. 10 (2022), No. 1, 75–84
Abstract

We use the theory of continuously distributed dislocations to formulate the static equilibrium condition for an edge dislocation pileup near a circular elastic inhomogeneity in terms of a singular integral equation. The singular integral equation is solved numerically using the Gauss–Chebyshev integration formula to arrive at the dislocation distribution function and the number of edge dislocations in the pileup. In our discussion, either the leading edge or the trailing end of the pileup can be located at the circular interface.

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Keywords
edge dislocation pileup, circular inhomogeneity, equilibrium condition, continuous pileup, singular integral equation, dislocation distribution function
Mathematical Subject Classification
Primary: 45E99, 74B05, 74E30
Milestones
Received: 12 January 2022
Revised: 14 January 2022
Accepted: 14 March 2022
Published: 20 October 2022

Communicated by David J. Steigmann
Authors
Xu Wang
School of Mechanical and Power Engineering
East China University of Science and Technology
Shanghai
China
Peter Schiavone
Department of Mechanical Engineering
University of Alberta
Edmonton
Canada