Studies Of Hyper-singular Integral Equation Method To Three-Dimensional Crack In Bi-materials

Cracks of composite material usually begin from or near interface, and therefore it is of theoretical and practical significance to study the stress field caused by the flaws of composite material on the interface. Compared with homogenous materials, however, composite materials have the characteristics such as different mechanical features, complex singularity index of the stress field near interface point, and different linear elastic fracture theories — thus, the study is more difficult. At present, the research mainly focuses on two-dimensional crack, and a few were reported on the three-dimensional composite material cracks. The dissertation systematically studies the problem of three-dimensional bi-material cracks with the method of hyper-singular integral equations, presents the hyper-singular integral equations for the problem and high-accuracy numerical solution, and obtains numerical results of some typical examples. The main contents are as follows.1. Relied on previous data, the general expression of displacement fundamental solution for three-dimension bi-materials under coordinate system oblique to interface is given. Based on the expression, the general solutions for displacement and surface traction are provided by using Somigliana displacement formula. This type of crack problem is further reduced to solving a set of hyper-singular integral equations with crack interface displacement discontinuities as an unknown function, and the behavior of unknown solutions on crack tips is analyzed. Among them, applying the hyper-singular integral equations to three-dimensional bi-materials inclined cracks is reported for the first time.2. Based on analytic results of unknown solutions of hyper-singular integral equations on crack tips, the numerical method of shear crack perpendicular to interface in three-dimensional bi-materials is constructed by factor method and finite-part integrals, and the exact hyper-singular integral equations and computation expression of stress intensity factor on crack tips are provided.3. According to the numerical methods above, some examples of typical cracks are computed, and the numerical results of stress intensity factors on crack tips are obtained. The change rules of stress intensity factors with variables are also investigated. The results show that the numerical method in this paper has high-accuracy and nice convergent performance.