Ray Analysis of Surface-Wave Interaction with an Edge Crack

Abstruct-A ray-theory approach is presented to analyze scattering of Rayleigh surface waves by a surface-breaking crack. The two-dimensional problem of normal incidence on an edge crack of depth d in an elastic half-space is discussed in detail. The basic diffraction mechanisms in the high-frequency range at the mouth and the edge of the crack are investigated one by one on the basis of elastodynamic ray theory. The results are then superimposed to yield simple expressions for the backscattered and forward-scattered Rayleigh surface waves and for the elastodynamic stress-intensity factors, in terms of reflection, transmission, and diffraction coefficients. These approximate results are compared with exact numerical results. Good agreement is observed for d/A > l, where A is the wavelength of the incident surface wave. A simple formula for the inverse problem is presented, which relates the periodicity of the amplitude modulation in the high-frequency range directly to the depth d of the crack. PROMISING method for the detection of a surfacebreaking crack, and for the subsequent determination of its size, shape, and orientation, is based on the scattering of Rayleigh surface waves. For a two-dimensional configuration of a line crack normal to the free surface of a half-space, an exact solution to the direct scattering problem has only recently been obtained by Mendelsohn et al. [l] . This exact solution does, however, involve a substantial computational effort, since it is based on the numerical solution of two singular integral equations with kernels that are themselves complicated integrals. Because of this numerical aspect, little guidance to the inverse problem is obtained from the exact solution to the direct problem. The results of [l] are, however, very useful for the testing of approximate methods of analysis. In this paper we present a simple approximate approach to scattering of Rayleigh surface waves by surface-breaking cracks, which is valid in the high-frequency range. Solutions are shown to agree well with the results of [l] for wd/cR > 6, where W is the circular frequency, d is the depth of the crack, and cR is the velocity of Rayleigh surface waves. The method of analysis which is based on elastodynamic ray theory can potentially be A