Mixed Multi-Layered Model for Fracture Analysis of Functionally Graded Interfacial Zone under Anti-Plane Loading

In this paper, a new mixed multi-layered model is put forward to study the crack problem of the functionally graded interfacial zone between tow homogeneous half-spaces. In the model, the interfacial zone is divided into some sub-layers with the properties of each layer varying in linear and exponential manners alternately. By applying Fourier transform and using the transfer matrix method, the mixed boundary problem of anti-plane fracture can be reduced to a Cauchy singular integral equation, which is solved numerically. Stress intensity factors of some examples are derived. The results show that the present model is effective and accurate and compared with the liner multi-layered model, the present one can save more CPU time in computation.