Stress analysis of a crack near an elastic layer

Abstract

The plane problem of a bonded medium, comprising of an elastic strip or layer sandwiched between two elastic half-planes, is considered. The elastic properties of the strip differ from the bounding half-planes. One of the two half-planes contains a crack, which is located at an arbitrary distance from the strip. Two orientations of the crack are considered, either parallel or perpendicular to the bi-material interface. The crack problem is solved within the framework of the distributed dislocation technique. The governing integral equations are formulated using the edge dislocation solution for the given problem geometry and the equations are solved numerically using the Gauss-Chebyshev quadrature method. The dependence of the stress intensity factors on the governing non-dimensional parameters is presented and the results are validated against the well-known solution for a crack near a bimaterial interface.