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Research Papers

Interaction Between an Edge Dislocation and a Crack With Surface Elasticity

[+] Author and Article Information
Xu Wang

School of Mechanical and Power Engineering,
East China University of Science and Technology,
130 Meilong Road,
Shanghai 200237, China
e-mail: xuwang@ecust.edu.cn

Peter Schiavone

Department of Mechanical Engineering,
University of Alberta,
4-9 Mechanical Engineering Building,
Edmonton, AB T6G 2G8, Canada
e-mail: p.schiavone@ualberta.ca

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 16, 2014; final manuscript received December 22, 2014; accepted manuscript posted December 31, 2014; published online January 7, 2015. Assoc. Editor: Pradeep Sharma.

J. Appl. Mech 82(2), 021006 (Feb 01, 2015) (8 pages) Paper No: JAM-14-1582; doi: 10.1115/1.4029472 History: Received December 16, 2014; Revised December 22, 2014; Accepted December 31, 2014; Online January 07, 2015

We undertake an analytical study of the interaction of an edge dislocation with a finite crack whose faces are assumed to have separate surface elasticity. The surface elasticity on the faces of the crack is described by a version of the continuum-based surface/interface theory of Gurtin and Murdoch. By using the Green's function method, we obtain a complete exact solution by reducing the problem to three Cauchy singular integrodifferential equations of the first-order, which are solved by means of Chebyshev polynomials and a collocation method. The correctness of the solution is rigorously verified by comparison with existing analytical solutions. Our analysis shows that the stresses and the image force acting on the edge dislocation are size-dependent and that the stresses exhibit both the logarithmic and square root singularities at the crack tips when the surface tension is neglected.

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Figures

Grahic Jump Location
Fig. 1

The distribution of b1(x) for different values of Se with ψ = 0 and z∧0 = i/2

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Fig. 2

The distribution of Δu1 for different values of Se with ψ = 0 and z∧0 = i/2

Grahic Jump Location
Fig. 3

The distribution of f1(x) for different values of Se with ψ = 0 and z∧0 = i/2

Grahic Jump Location
Fig. 4

The distribution of b1(x) for different values of Se with ψ = π/2 and z∧0 = i/2

Grahic Jump Location
Fig. 5

The distribution of Δu1 for different values of Se with ψ = π/2 and z∧0 = i/2

Grahic Jump Location
Fig. 6

The distribution of f1(x) for different values of Se with ψ = π/2 and z∧0 = i/2

Grahic Jump Location
Fig. 7

The variation of Δu1 for different values of z∧0 with ψ = 0 and Se = 1

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Fig. 8

The image force on a glide edge dislocation located on the positive real axis for different values of Se

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