INTERACTION OF ANTIPLANE CRACKS WITH ELASTIC-WAVES IN TRANSVERSELY ISOTROPIC MATERIALS

The interaction of plane time-harmonic SH-waves with micro-cracks in transversely isotropic materials is investigated. Elastic wave scattering by a single micro-crack is first analyzed. The scattered displacement is expressed as a Fourier integral containing the crack opening displacement. By using this representation formula and by invoking the traction-free boundary condition on the faces of the crack, a boundary integral equation for the unknown crack opening displacement is obtained. Expanding the crack opening displacement into a series of Chebyshev polynomials and adopting a Galerkin method, the boundary integral equation is converted into an infinite system of linear algebraic equations for the expansion coefficients which is solved numerically. Numerical results are presented for the elastodynamic stress intensity factors, the scattered far-field, and the scattering cross section of a single crack. Then, propagation of plane time-harmonic SH-waves in a transversely isotropic material permeated by a random and dilute distribution of micro-cracks is investigated. The effects of the micro-crack density on the attenuation coefficient and the phase velocity are analyzed by appealing to a simple energy consideration and by using Kramers-Kronig relations.