General solution to the problem of microcracks near the tip of a main crack

Abstract

A general solution is obtained to the two-dimensional problem of the interaction between a main crack and multiple microcracks. Analysis is based on the method of pseudo-tractions, which is a general method for interaction problems. The stress intensity factors at the tips of both the main crack and microcracks are obtained in asymptotic forms and approximate closed-form solutions are also derived. Typical examples are presented for one collinear microcrack, one arbitrarily located microcrack and two arbitrarily located microcracks near the tip of the main crack. For one collinear microcrack the present solution is shown to coincide with the Taylor expansion of the exact solution, and inconsistencies in several previous solutions are compared. For arbitrarily located microcracks, the effects of the main crack—microcrack interaction and the microcrack—microcrack interaction are investigated. Application of the present model to the fracture process zone problem is discussed.