Effective wave velocity and attenuation in a material with distributed penny-shaped cracks

Abstract

Wave propagation in a material containing distributed penny-shaped cracks was investigated. An improved approach was developed for calculating the phase velocity and the attenuation of ultrasonic waves. In this approach, the effects of neighboring cracks on a reference crack are approximated by the effects of triads of double forces of strengths proportional to the crack opening volumes, and located at the geometrical centers of the cracks. The averaged crack opening displacements and crack opening volumes of the reference crack are split into two terms. The first term corresponds to the quantities induced by the interaction of the single reference crack with an incident wave, while the second term represents the interaction between this reference crack and neighboring cracks. The averaged crack opening displacements are used in calculating the forward scattering amplitude, from which the phase velocity and the coefficient of attenuation are subsequently computed. The present analysis was limited to parallel cracks and to low frequencies, but the principle can be used for more general cases. Since crack interactions have been taken into account, the analysis provides a better approximation than the standard approach proposed by Foldy (1945, Phys. Rev.67, 107–119), especially for intermediate and large crack densities.