Crack-tip stress fields for dynamic fracture in functionally gradient materials

An asymptotic expansion of the stress field around a crack propagating at c onstant velocity in a Functionally Gradient Material (FGM) is developed. Al l the three modes of crack propagation are analyzed for FGMs having two dif ferent types of property variations in the direction of crack propagation. The assumed property variations are (1) exponential variation of shear modu lus and mass density and (2) linear variation of the shear modulus with con stant mass density. The Poisson's ratio is assumed to be constant throughou t the analysis. The analysis reveals that the crack-tip stress fields retai ns the inverse square root singularity and only the higher order terms in t he expansion are influenced by the material nonhomogeneity. Expression for stresses and strains in the form of a series, in powers of the radial dista nce from the crack tip, is obtained for the tearing mode of fracture. For t he opening and shear modes of fracture, an expression for the first stress invariant under plane stress conditions is obtained in a series form in whi ch the coefficient of the first term is proportional to the dynamic stress intensity factor. Contours of constant out of plane displacement, which is of interest in experimental techniques such as the coherent gradient sensin g, are also given for different levels of nonhomogeneity. The stress fields are developed for large scale property variation where transient effects c an be neglected. (C) 1999 Elsevier Science Ltd. All rights reserved.