Torsional impact response of a cylindrical interface crack between a functionally graded interlayer and a homogeneous cylinder

The torsional impact problem of a cylindrical interface crack between a functionally graded material (FGM) interlayer and its external homogeneous cylinder is investigated in this paper. The shear modulus and mass density of the FGM interlayer are assumed to vary continuously between those of the two coaxial dissimilar homogeneous elastic cylinders. The mixed boundary value problem is first reduced to a singular integral equation with a Cauchy type kernel in the Laplace domain by applying Laplace and Fourier integral transforms and introducing dislocation density function. The singular integral equation is then solved numerically and the dynamic stress intensity factor (DSIF) in the physical domain is also obtained by a numerical Laplace inversion technique. It is found that the DSIF rises rapidly to a peak and then oscillates with a decreasing magnification and tends to the corresponding static value, and that both crack geometry configuration and material gradient of the FGM interlayer have all important influences on the DSIF.