Crack-tip stress fields for dynamic fracture in functionally gradient materials
An asymptotic expansion of the stress field around a crack propagating at constant velocity in a Functionally Gradient Material (FGM) is developed. All the three modes of crack propagation are analyzed for FGMs having two different types of property variations in the direction of crack propagation. The assumed property variations are (1) exponential variation of shear modulus and mass density and (2) linear variation of the shear modulus with constant mass density. The Poisson's ratio is assumed to be constant throughout the analysis. The analysis reveals that the crack-tip stress fields retains the inverse square root singularity and only the higher order terms in the expansion are influenced by the material nonhomogeneity. Expression for stresses and strains in the form of a series, in powers of the radial distance from the crack tip, is obtained for the tearing mode of fracture. For the opening and shear modes of fracture, an expression for the first stress invariant under plane stress conditions is obtained in a series form in which 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 sensing, are also given for different levels of nonhomogeneity. The stress fields are developed for large scale property variation where transient effects can be neglected.