ULTRASONIC WAVE-PROPAGATION THROUGH A CRACKED SOLID

The propagation of ultrasonic waves through a perfectly elastic medium containing a random distribution of equally-sized penny-shaped cracks with spring boundary conditions across the crack faces is considered. As limiting cases results for open and fluid-filled cracks are derive d also. The medium with the crack distribution is modelled as an effec tive viscoelastic medium, using the non-interacting scatterer approxim ation and Foldy's theory. For this purpose scattering by a single crac k is solved by an integral equation method, Distributions of both rand omly oriented and parallel cracks are considered. Numerical results ar e presented for the phase velocity and attenuation. For parallel crack s when the effective medium is transversely isotropic two further issu es are investigated. The first is the extension of a static result due to Kachanov, who showed the transverse isotropy to be of a very speci al kind. The second is consistency of the wave speeds obtained by usin g Foldy's theory, with the fact that the effective material is transve rsely isotropic. In particular, the vertically polarized shear wave sh ould have the same wave speeds in directions parallel and normal to th e cracks. It is found that the relations established by Kachanov and t he consistency requirements are satisfied by the phase velocity for al l frequencies considered.