Elastic wave propagation and scattering in solids with uniaxially aligned cracks

In this article, elastic wave propagation and scattering in a solid medium permeated by uniaxially aligned penny-shaped microcracks are studied. The crack alignment refers to the case in which the unit normals of all cracks are randomly oriented within a plane of isotropy. The analysis is restricted to the limit of the noninteraction approximation among individual cracks. Explicit expressions for attenuations and wave speeds of the shear horizontal, quasilongitudinal, and quasishear vertical waves are obtained using stochastic wave theory in a generalized dyadic approach. The ensemble average elastic wave response is governed by the Dyson equation, which is solved in terms of the anisotropic elastic Green's dyadic. The analysis of expressions is limited to frequencies below the geometric optics limit. The resulting attenuations are investigated in terms of the directional, frequency, and damage dependence. In particular, the attenuations are simplified considerably within the low frequency Rayleigh regime. Finally, numerical results are presented and discussed in terms of the relevant dependent parameters.