Ultrasonic crack characterization via a constrained inversion algorithm

The Kirchhoff approximation is used to show that the time domain impulse response of an isolated flat crack can be given a simple geometrical interpretation in terms of the derivative of a projected length function. For an elliptical crack, this derivative can be obtained explicitly to yield the two edge-diffracted waves which originate from the flashpoints of the crack. An explicit coordinate invariant expression is obtained from this elliptical crack solution which relates the time difference, t, between the arrival of these edge-diffracted waves and the crack size and orientation. Previously, we have proposed that this expression, together with t measurements in different scattering directions, could be used in a regression analysis as the basis for performing a constrained inversion of crack scattering data (i.e., where we attempt to obtain the best equivalent flat elliptical crack that fits the scattering measurements). Here we will demonstrate some results of applying the proposed algorithm using noisy synthetic data. The sensitivity of the results to both, number of measurements and transducer orientation, will be discussed.