The time domain elastodynamic Kirchhoff approximation for cracks: The inverse problem

Ultrasonic Crack Characterization: A Constrained Inversion Algorithm

“…This solution can form the basis for obtaining the size and orientation of an unknown flat crack by performing a constrained inversion, i.e., d a n n a aS a n n a n a + sine Ssine sin(~ -~ )] 2 }~ a n n a where the dimensions a and b are normalized by an arbitrary reference length d. Equation (6) is the generalization of the results obtained in Ref. [5] to an arbitrary pitch-catch type of experimental set-up. In Ref.…”

“…In Ref. [5] we only considered the special case of a pulse-echo experiment, where the incident wave was a P-wave. By using as few as eight "exact" synthetic ~t measurements and a nonlinear least squares algorithm, it was demonstrated in Ref.…”

“…Here, we will demonstrate that a similar constrained inversion procedure can be developed using the Kirchhoff approximation [2-4) for a flat elliptical crack. Using the results of our previous paper [5), an explicit coordinate-invariant expression that relates the time difference, ~t, between the arrival of the waves diffracted from the flashpoints of the crack and the crack shape and orientation is obtained. This expression, together with ~t measurements in different scattering directions is placed into a regression analysis to obtain a set of equivalent flat elliptical crack parameters.…”

Ultrasonic flaw classification and sizing

“…This approach has been developed based on ultrasonic scattering models such as the Bom approximation for volumetric flaws [49,50] or the Kirchhoff approximation for cracks [51]. Recently, a unified algorithm that can be applied to both volumetric flaws and cracks was developed by Schmerr and et al [52].…”

“…In between the two extremes of conventional methods and detailed scanning methods, there is a model-based approach called equivalent flaw sizing [49,50,51]. In this approach, flaws are reconstructed in terms of "bestfit" equivalent ellipsoids (for volumetric flaws) or ellipses (for cracks)…”