Nonlinear interaction of plane ultrasonic waves with an interface between rough surfaces in contact

A theoretical investigation of the nonlinear interaction between an acoustic plane wave and an interface formed by two rough, nonconforming surfaces in partial contact is presented. The macroscopic elastic properties of such a nonlinear interface are derived from micromechanical models accounting for the elastic interaction that is characteristic of spherical bodies in contact. These results are used to formulate set of boundary conditions for the acoustic field, which are to be enforced at the imperfect interface. The scattering problem is solved for plane wave incidence by using a simple perturbation approach and the harmonic balance method. Sample results are presented for arbitrary wave polarization and angle of incidence. The relative magnitude of the nonlinear signals and their potential use toward the nondestructive evaluation of imperfect interfaces are assessed. In particular, attention is drawn to the enhanced nonlinear response of an interface insonified by a shear vertical wave in the neighborhood of the longitudinal critical angle. The motivation for this investigation is provided by the need to develop nondestructive methods to detect and localize small, partially closed cracks in metals with coarse microstructures.