Complete solution for the axisymmetric problem of a penny-shaped crack near and parallel to an arbitrarily graded interface in FGMs

Abstract

Previous analytical treatments to the crack problems in functionally graded materials (FGMs) were mostly based on the assumption that only the shear modulus is variable according to special functions while the Poisson’s ratio is constant. However, the material inhomogeneity in real FGMs is more complex than that can be well approximated using the assumption. This paper examines the axisymmetric problem of a penny-shaped crack near and parallel to a graded interface with arbitrarily variable shear modulus and Poisson’ s ratio. To consider the general material inhomogeneity, a new efficient solution of general axisymmetric edge dislocation loop in multilayered elastic medium is derived first using the General Kelvin’s Solution (GKS) based method. This method allows the approximation of general material inhomogeneity using large number of homogenous sublayers without the loss of computational efficiency, accuracy and stability. The challenging issue in multilayered elasticity associated with the calculation of near-source elastic field is also tackled, which enables the high precision evaluation of crack tip field. Exact solutions are given for the full elastic field. Numerical studies are conducted to explore the fracture mechanics of FGMs. The results show that the gradation pattern can have certain effect on the fracture response if the crack is very closed to the graded interface.