The effects of crack closure on ultrasonic scattering measurements

This chapter proposes a mathematical model to describe the effects of contacts on the ultrasonic signals scattered from a crack. The model assumes that there are many contacts per wavelength. The presented equations are equivalent to those which would be derived for the case in which the faces of an ideal crack were coupled by a massless, distributed spring. The transmission of an ultrasonic beam past the crack, and its diffraction at the crack tip, are treated by combining quasistatic boundary conditions, a Gaussian model for the ultrasonic beam profile, and a Kirchhoff approximation for the scattering. The derived model describes the increase in apparent fatigue crack length at higher frequencies as deduced from transmission measurements, and the decrease of the fatigue crack tip diffracted response with respect to an EDM notch