Backscattering of Bulk Waves from A Surface-Breaking Crack under A Compressive Stress

Abstract

A recent investigation into the scattering of a Rayleigh wave from a one-dimensional surface-breaking crack under a compressive stress field has shown the occurrence of a surprising phenomenon. When the crack depth is of the order of a wavelength or larger, and the compressive stress is lower than a characteristic value, a significant increase of the reflected signal is predicted theoretically and observed experimentally. The purpose of this work is to extend the previous investigation to the case when the incident field is either a longitudinal or a shear wave.

The effect of the compressive stress on the scattering event is modeled by using the quasi-static approximation for two rough surfaces in contact. The spring elastic constants K _N and K _T , which simulate the macroscopic elastic behavior of the contacting crack faces, may vary along the crack faces. This additional degree of freedom allows the model to consider situations where the crack is either uniformly partially closed along its whole extent, or partially closed at its tip, or at its mouth only. The scattered field is evaluated in its far-field zone. The dependence of the backscattered signal on i) the intensity and spatial dependence of the compressive stress, ii) the direction of incidence of the inspecting ultrasonic wave, and iii) the normalized crack depth is investigated, and possible implications for the detection and characterization of the partial closure of a surface-breaking crack is discussed.