Plane Problems of Cracks in Dissimilar Media

TLDR

The study examines in‑plane extension of two dissimilar materials with cracks or fault lines along their common interface. The authors propose a method to solve such interface crack problems. The method integrates complex variable techniques with an eigenfunction‑expansion approach. The approach yields a single complex potential, providing closed‑form solutions, reducing effort compared to conventional methods, and enabling calculation of stress‑intensity factors for fracture initiation.

Abstract

The in-plane extension of two dissimilar materials with cracks or fault lines along their common interface is considered. A method is offered for solving such problems by the application of complex variables integrated with the eigenfunction-expansion technique presented in an earlier paper. The solution to any problem is resolved to finding a single complex potential resulting in a marked economy of effort as contrasted with the more laborious conventional methods which have not yielded satisfactory results. Boundary problems are formulated and solutions are given in closed form. The results of these evaluations also give stress-intensity factors (which determine the onset of rapid fracture in the theory of Griffith-Irwin) for plane problems.