Ultrasonic wave scattering from rough, imperfect interfaces. Part II. Incoherent and coherent scattered fields

Abstract

A theoretical model for ultrasonic wave scattering for geometrically irregular and imperfectly bonded interfaces is presented. Part I presents the stochastic interface characterization and a model for its mechanical response based on a micromechanics model of asperity contact. Part II uses this interface representation to write the well used “quasi-static” boundary conditions for scattering from a.flat imperfect interface¹ directly on the irregular interface profile. The boundary conditions are then expanded in an asymptotic series in the roughness parameter (standard deviation of the surface height) which is small compared to wavelength. The slope of the profile must also be everywhere small. These equations are solved exactly for the zero-th and second order terms, which are the flat coherent solution and its' first coherent correction, and the first order term, which is the first term in the expansion for the incoherently scattered solution. Results for obliquely incident longitudinal and shear waves show a strong dependence on the roughness in both the coherent and incoherent reflected fields, but little if any dependence on the roughness in the transmitted fields. In particular, the reflected coherent fields show markedly increasing attenuation compared to the flat compliant interface with increasing roughness and increasing ultrasonic frequency, the latter result being in qualitative agreement with results for scattering from an inhomogeneous array of individual scatterers.² There is evidence in the incoherent reflected fields for the existence of an incoherent leaky interface disturbance which manifests itself as a bulk incoherent shear wave at a scattering angle equal to the critical longitudinal angle. A coherent true interface wave is also supported by the rough interface which is shown to further attenuate the coherent reflected fields compared to the flat compliant interface solution.