Replacing a slab containing random cracks or cavities with an effective solid using SH waves

Abstract

Abstract: Effective acoustic and material properties of solids containing cracks or elliptic cavities are evalu-ated with shear horizontal (SH) ultrasonic waves. Simple formulae are derived for these effective quantities. Low-frequency approximations are then given. The derivation is based on the multiple-scattering approach of Waterman and Truell. Key words: multiple scattering, coherent scattering, effective properties. A. Introduction Propagation of ultrasonic SH waves in an elastic solid containing a slab with a random and uniform distri-bution of identical line cracks or elliptical cylindrical cavities is considered. In the framework of Waterman and Truell [1], we focus on the system of coherent waves inside and outside the slab, and on the effective macro-scopic properties such as mass density and shear stiffness of two-phase materials. Observe that each cylinder of finite cross-section is replaced with an equivalent line-like scatterer. First, the amplitudes of coherent waves inside and outside the slab are given. Then, the jump relations of the displacement derivative at the boundaries of the slab are obtained. Thus, an average energy equation for harmonic scalar waves, over one period of duration 2/πω, is established. Then, we show that the slab behaves macro-scopically as a homogeneous medium and we determine the effective material properties. Numerical results are presented for line cracks and empty cylindrical cavities of elliptical cross-section for various eccentricities when the incident SH wave propa-gates parallel to the minor axis of the elliptic cylinders. Finally, closed-form formulae for effective acoustic and material properties are established in the low-frequency limit.