A general solution to the antiplane problem of an arbitrarily located elliptical hole near the tip of a main crack

Abstract

A general solution is obtained to the problem of the interaction between a main crack and an arbitrarily located and oriented elliptical hole near its tip under mode III loading conditions. The analysis is based on the complex potentials for the antiplane problem and the superposition principle. The stress intensity factor at the main crack is obtained in a general series form and approximate closed-form solutions are also derived using a perturbation procedure. The present solution is shown to coincide with Taylor expansion of exact solutions for collinear elliptical holes with specific aspect ratios. Numerical examples are provided to show the effect of the geometry, location and orientation of the microdefect on the stress intensity factor of the main crack. The present work should provide a valuable insight into main crack microdefect interaction phenomena in brittle materials.