Analysis of a Crack Bridged by a Single Fiber

Abstract

With the goal of assessing the accuracy of a widely used approximate method of analyzing bridged matrix cracks, an idealized problem representing a crack bridged by a single fiber is studied in detail. Our solution technique, which accounts for frictional slip at the fiber-matrix interface explicitly, involves the use of distributions of edge dislocations to represent the opening of the crack faces and the slip at the interface. Through this method, the solution is reduced to a set of three coupled singular integral equations which are solved numerically. The results are compared with those from the approximate method, and some sources of discrepancy between the two results are explored.