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Research Papers

The Effects of Surface Elasticity on an Elastic Solid With Mode-III Crack: Complete Solution

[+] Author and Article Information
C. I. Kim, C.-Q. Ru

Department of Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 2G8, Canada

P. Schiavone1

Department of Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 2G8, Canadap.schiavone@ualberta.ca

1

Corresponding author.

J. Appl. Mech 77(2), 021011 (Dec 11, 2009) (7 pages) doi:10.1115/1.3177000 History: Received January 09, 2009; Revised May 31, 2009; Published December 11, 2009; Online December 11, 2009

We examined the effects of surface elasticity in a classical mode-III crack problem arising in the antiplane shear deformations of a linearly elastic solid. The surface mechanics are incorporated using the continuum based surface/interface model of Gurtin and Murdoch. Complex variable methods are used to obtain an exact solution valid everywhere in the domain of interest (including at the crack tip) by reducing the problem to a Cauchy singular integro-differential equation of the first order. Finally, we adapt classical collocation methods to obtain numerical solutions, which demonstrate several interesting phenomena in the case when the solid incorporates a traction-free crack face and is subjected to uniform remote loading. In particular, we note that, in contrast to the classical result from linear elastic fracture mechanics, the stresses at the (sharp) crack tip remain finite.

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Figures

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Figure 1

Schematic of the problem

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Figure 2

Stress differences between the upper and bottom faces where σyz∞/μ=0.1

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Figure 3

Stress convergence versus the number of iterations (N)

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Figure 4

Stress distribution with respect to surface parameter (Se) when σyz∞/μ=0.1

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Figure 5

Stress (at the crack tip) versus surface effect when σyz∞/μ=0.1

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