A model of ultrasonic nondestructive testing for internal and subsurface cracks

TLDR: In this article, a surface integral equation with the half-space Green tensor is employed to discretize the crack opening displacement in terms of Chebyshew functions having the correct square root behavior along the crack edges.

Abstract: The scattering of elastic waves in a half-space containing a striplike crack is investigated. As a special case it seems that the crack may be surface breaking. A surface integral equation with the half-space Green tensor is employed. The key point of the method is the expansion of the Green tensor in Fourier representations with the free part of the Green tensor expanded in the crack coordinate system and the half-space part in the half-space coordinate system. The integral equation is discretized by expanding the crack opening displacement in terms of Chebyshew functions having the correct square root behavior along the crack edges. The incident field is emitted from an ultrasonic probe and a recent model for this is employed. The signal response in another (or the same) probe is modeled by a reciprocity argument and the stationary phase approximation is employed to simplify the final answer, which is thus only valid in the far field of the probes (yielding essentially a spherical wave). Numerical results are given and are compared with both other methods and with available experiments.