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.
Interaction Between an Edge Dislocation and a Crack With Surface Elasticity
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.
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Wang, X., and Schiavone, P. (February 1, 2015). "Interaction Between an Edge Dislocation and a Crack With Surface Elasticity." ASME. J. Appl. Mech. February 2015; 82(2): 021006. https://doi.org/10.1115/1.4029472
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