Normal Compression and Radial Shear Waves Scattering at a Penny-Shaped Crack in an Elastic Solid

The Hankel transform is used to obtain a complete solution for the dynamic stresses and displacements around a penny-shaped surface of discontinuity or crack embedded in an elastic solid, which is excited by normal compression and radial shear waves. By referring to a set of polar coordinates r1 and θ1 measured from the crack periphery, the dependence of the local stresses on r1 and θ1 is determined in closed elementary form, while the magnitude of these stresses, governed by the dynamic stress-intensity factors, is calculated numerically from a system of coupled Fredholm integral equations. As in the static case, the stresses possess the familiar inverse square-root singularity at the crack boundary. The stress-intensity factors, however, are found to depend on the incident wavelength and Poisson's ratio of the elastic solid. For certain values of the wavelengths, they are shown to be larger than those encountered in the theory of static elasticity.