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

TL;DR

This paper investigates how curvature-dependent surface tension affects singularities at the tips of an interface crack, showing it removes classical power and oscillating singularities, with numerical solutions demonstrating these effects.

Contribution

It introduces a semi-analytical method incorporating curvature-dependent surface tension to eliminate classical crack tip singularities.

Findings

Elimination of classical power singularity at crack tips.

Removal of oscillating singularity in linear elasticity solutions.

Numerical solutions obtained via Taylor polynomial approximation.

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.