Abstract
Dispersion and attenuation of surface waves propagating over the free surface of a half-space containing distributed surface-breaking cracks are investigated. The 3-D problem of scattering of surface waves by a single surface-breaking crack is first formulated and the characteristic amplitude factor of the scattered surface wave is expressed in terms of the crack opening displacements. A relation between this amplitude factor and the scattered power flow is then derived. The scattering cross section is introduced as a measure of energy removal from the incident surface wave. By using energy considerations, the coefficient of attenuation is subsequently expressed in terms of the scattering cross section. Use of the Kramers–Krönig relation then yields an expression for the phase velocity. Numerical results are given for both the coefficient of attenuation and the phase velocity, as functions of the crack density, a characteristic length dimension of the crack and the frequency. The theoretical framework provided in this paper may lead to a novel application of surface waves for the detection and characterization of fatigue damage of metals under cyclic loading.
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