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arXiv · 1207.1321

The effect of a curvature-dependent surface tension on the singularities at the tips of a straight interface crack

A. Y. Zemlyanova
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Abstract

A problem of an interface crack between two semi-planes made out of different materials under an action of an in-plane loading of general tensile-shear type is treated in a semi-analytical manner with the help of Dirichlet-to-Neumann mappings. The boundaries of the crack and the interface between semi-planes are subjected to a curvature-dependent surface tension. The resulting system of six singular integro-differential equations is reduced to the system of three Fredholm equations. It is shown that the introduction of the curvature-dependent surface tension eliminates both classical integrable power singularity of the order 1/2 and an oscillating singularity present in a classical linear elasticity solutions. The numerical results are obtained by solving the original system of singular integro-differential equations by approximating unknown functions with Taylor polynomials.

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A. Y. Zemlyanova. 2012-07-06. The effect of a curvature-dependent surface tension on the singularities at the tips of a straight interface crack. https://arxiv.org/abs/1207.1321

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