Analysis of Branched Cracks

TLDR

The integral equation introduced here allows different branched crack problems to be solved in a unified manner, contrasting with other approaches in the literature. This paper presents a method for solving a class of two‑dimensional elastic branched crack problems. Using Muskhelishvili’s potential formulation and a Green’s function technique, the authors derive a singular integral equation in complex form that accommodates asymmetrically, symmetrically, and doubly symmetrically branched cracks, with the branch‑to‑main crack length ratio varied arbitrarily and its zero‑limit obtained analytically. Numerical stress‑intensity factors at branched crack tips are computed and compared to literature values, resolving previously reported disagreements.

Abstract

This paper presents a method for solving a class of two-dimensional elastic branched crack problems. In contrast to other approaches in the literature, the integral equation presented here enables different branched crack problems to be solved in a unified manner. Muskhelishvili’s potential formulation is used to derive, by means of a Green’s function technique, a singular integral equation in complex form. The problems of the asymmetrically, symmetrically, and doubly symmetrically branched cracks are considered. The ratio of the length of the branched crack to that of the main one may be varied arbitrarily and the limit in which this ratio goes to zero is obtained analytically. Stress-intensity factors at the branched crack tip are computed numerically and the results, where possible, are compared to those in the literature. Disagreements in the literature are discussed and clarified with the aid of the present results.