In this paper the plane elasticity problem of two bonded dissimilar functionally graded strips containing an interface crack is studied. The governing equation in terms of Airy stress function is formulated and exact solutions are obtained for several special variations of material properties in Fourier transformation domain. The mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. Numerical results show that fracture toughness of materials can be greatly improved by graded variation of elastic modulus and the influence of the specific form of elastic modulus on the fracture behavior of FGM is limited.
In this paper, a finite crack with constant length （Yoffe type crack） propagating in a functionally graded coating with spatially varying elastic properties bonded to a homogeneous substrate of finite thickness under anti-plane loading was studied. A multi-layered model is employed to model arbitrary variations of material properties based on two linearly-distributed material compliance parameters. The mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. Some numerical examples are given to demonstrate the accuracy, efficiency and versatility of the model. The numerical results show that the graded parameters, the thicknesses of the interfacial layer and the two homogeneous layers, the crack size and speed have significant effects on the dynamic fracture behavior.
