The Conformal Mapping Method Is Applied Research In The Composite Fracture Theory

With the development of human society, composite materials become essential materials in numerous industries. The theoretical study on fracture problems in composite materials is gaining high attention of people. The main methods of researching fracture problems in composite materials are the complex function method, the conformal mapping method and integral transformation method and so on. The analytical solutions of the stress and displacement fields near the complex crack tip are obtained using the conformal mapping method which is one of the effective methods.By using conformal mapping method, the composite fracture problems are researched mainly through the physical plane with complex geometric crack shapes is mapped into the infinite domain with a unit circle by the appropriate conformal mapping function. Based on the stress boundary conditions, the problems of fracture in composite materials are transformed into the solving boundary value problems of equations and the expression of stress function is determined in the infinite domain. The analytical solutions of stress intensity factors and the stress and displacement fields near crack tip are deduced by solving in the original physical plane with complex crack shapes as well. Some results are obtained in the studies of fracture problems in isotropic materials. But the theory system of fracture problems in anisotropic materials with this method is not integrated and it is waiting further studying.In this paper, the fracture problems of anisotropic composite materials are transformed into the solving boundary value problems of equations by using the conformal mapping method. Based on the quoted conformal mapping function, the crack curve is mapped into a unit circle. Under the stress boundary conditions, the stress function is determined and the expressions of the stress intensity factor and the stress and displacement fields near the central crack tip for mode I and mode II in composite materials are obtained, which are as same as the existing theoretical results. With the help of this method, the analytical solutions of the stress intensity factor, stress field and displacement field near the parabolic crack tip for Mode I and Mode II in composite materials are given as well. According to the principle of superposition, the analytical solutions of the stress intensity factor and the stress and displacement fields near the crack tip for mixed Mode I+II in composite materials are deduced. The theoretical results have important significance in fracture theory research and engineering application.