Analysis of crack-tip fields in functionally graded materials

Functionally Graded materials (FGMs) have been developed as super-resistant materials for propulsion systems and airframe of space shuttles in order to decrease thermal stresses and to increase the effect of protection from heat. It has been experimentally observed that crack in FGMs is the most common failure mode of a metal-ceramic FGM when it is subjected to some dangerous loads such as a thermal shock or mechanical shock. Therefore, it is very important to consider the thermally and mechanical induced fracture behaviors of FGMs. In this paper, a new multi-layered model for fracture analysis of functionally graded materials with arbitrarily varying elastic moduli under plane deformation has been developed. In this model, the FGM is divided into several sub-layers and in each sub-layer the reciprocal of the shear modulus is assumed to be a linear function of the depth while the poisson's ratio is assumed to be a constant. With this new model, a FGM strip containing a Griffith crack under in-plane mechanical loads is investigated. Employment of transfer matrix method and Fourier integral transform technique reduces the problem to a system of Cauchy singular integral equations which are solved numerically. Stress intensity factors of a Griffith crack of a FGM strip are then obtained.