Ultrasonic wave propagation through a cracked solid
Journal article, 1995
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 are considered. As limiting cases results for open and fluid-filled cracks are derived also. The medium with the crack distribution is modelled as an effective viscoelastic medium, using the non-interecting scatterer approximation and Foldy's thery. For this purpose the scattering by a single crack is solved by an integral equation method. Distributions of both randomly oriented and parallel cracks are considered. Numerical results are presented for the phase velocity and attenuation. For parallel cracks when the effective medium becomes transversely isotropic two further issues are investigated.The first is the extension of a static result due to Kachanov, who showed the transverse isotropy to be of a very special kind. The second is consistency of the wave speeds obtained by using Foldy's theory, with the fact that the effective material is transversely isotropic. In particular, the vertically polarized shear wave should have the same wave speeds in directions parallel and normal to the cracks. It is found that the relations established by Kachanov and the consistency requirements are satisfied by the phase velocity for all frequencies considered.