A new model for fracture analysis of a functionally graded interfacial zone under harmonic anti-plane loading

A new model for fracture analysis of functionally graded materials with properties of arbitrary variation has been developed. Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the functionally graded material with material properties varying continuously in an arbitrary manner is modeled as a multi-layered medium with the elastic modulus and mass density varying linearly in each sub-layer and continuous at the interfaces between sub-layers. With this model, the problem of a crack in a graded interfacial zone bonded to two homogeneous half-spaces subjected to the harmonic anti-plane shear load is investigated. By using transfer matrix method and Fourier integral transform technique, the problem is reduced to the solution of a Cauchy singular integral equation. Stress intensity factors are calculated. The new model is compared to other models and its advantages are discussed.