Thin-skin eddy-current inversion for the determination of crack shapes

An important aim of nondestructive evaluation is to quantify flaws in components using sensor measurements. In pursuit of this aim, a method has been developed for finding the size and shape of planar cracks in electrical conductors from single-frequency eddy-current probe impedance measurements. In the direct problem, the change in the impedance of an eddycurrent probe due to a crack in a conductor is determined in the regime where the skin depth is much smaller than the dimensions of the crack face. The thin-skin field at the crack face is represented by a potential satisfying the two-dimensional Laplace equation. In the corresponding inverse problem, the crack shape is sought from probe impedance measurements. Here the crack boundary is located using an iterative inversion scheme in which a cost function quantifying the overall difference between predictions and measurements is minimized using a gradient method. The gradient is found from the derivative of the cost function with respect to a variation of the flaw. Shape estimates found by the inversion of impedance data have been compared with the measured profiles of simulated cracks in aluminium plates. The comparisons show that the inversion scheme gives good agreement with direct physical measurements.