Research of fracture problem of composite plate with curved crack by conformal mapping

Abstract

In this paper, the fracture problem of an anisotropic composite plate with a curved crack is solved by conformal mapping method. Using the conformal mapping method, the problem with boundary conditions is transformed into boundary value problem of partial differential equations, which can be solved analytically by complex function method. Based on the quoted conformal mapping function, the crack curve is mapped into a unit circle. The fracture analysis near the curve crack tip for both Mode I and Mode II of anisotropic composite materials in a state of plane stress is made. The stress functions are determined under the stress boundary conditions. Then the analytical expressions of stress intensity factors, stress fields and displacement fields near the curved crack tip for Mode I and Mode II in anisotropic composite materials are obtained.