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

Abstract

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.

Level set methods for inverse scattering

“…These two parts are separated by a flat interfaceΓ. Embedded in Ω 2 is a volumetric shape D. We assume that we know the Green functions G (11) k , G (12) k , G (21) k , and G (22) k for the medium without the embedded shape D, where the superindices indicate whether starting point (second superindex) and end point (first superindex) of the Green function are located in medium Ω 1 or Ω 2 . The three regions Ω 1 , Ω 2 \D and D have constant electromagnetic parameters which we denote by the subindices o (referring to Ω 1 ), e (referring to Ω 2 \D), and i (referring to D).…”

Transient response of a driver-pickup coil probe in transient eddy current testing

“…To this end, considerable efforts have been made to develop mathematical models that enable the interpretation of inspection data. The common approach is to formulate time-harmonic solutions, which describe the electromagnetic fields in a system, in order to calculate the change in a coil's impedance as it interacts with a conducting structure [4][5][6][7][8]. In a less developed approach, transient eddy current models consider the voltage induced in a pickup circuit [9][10][11][12][13][14] given a prescribed current that has been applied to a driver coil.…”

Instrumentation: Nondestructive Examination for Verification of Canister and Cladding Integrity. FY2014 Status Update

“…Numerical (finite element, finite difference, boundary element, etc.) techniques enable modeling of more complex flaw geometries and arbitrary skin depth to flaw dimension ratios and many of the initial efforts focused on "ideal crack" approximations, which assume the flaw region is defined as having zero width (2-dimensional) and zero conductivity (see Figure 2.1) (Bowler 1994;Bowler et al 1994;Bowler 2002). (Bowler et al 1994).…”