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Nondestructive evaluation (NDE) is to materials and structures as CAT-scanning is to the human body--an attempt to look inside without opening it. As in CAT-scanning, modern NDE requires sophisticated mathematical software to perform the mathematical "inversion" operations that allow one to infer the internal state of a structure from external measurments. In this note we will show how VIC-3D® fulfills this need. In reading this example, keep in mind that the data could be taken with a conventional impedance analyzer, such as the HP4194A. For higher frequencies, up to 180MHz,or so, the HP4915A series can be used. There is nothing exotic about the instrumentation; the exotic stuff is in VIC-3D®.
The semi-elliptical slot, shown here, is often used to model fatigue cracks, stress-corrosion cracking, and other anomalies. For this reason, it is one of the canonical shapes that VIC-3D® includes in its library of flaws.

In "Benchmark Problems for Defect Size and Shape Determination in Eddy-Current Nondestructive Evaluation," J. Nondestructive Evaluation, Vol. 15, 1996, D. J. Harrison, L. D. Jones, and S. K. Burke have performed careful experiments to provide eddy-current impedance data and experimental parameters for use in a series of benchmark problems for verification of theoretical inversion techniques. Data for four slots were taken under computer control by scanning a probe coil along the line of the axis of the slots in steps of 1.0 mm for each of sixteen frequencies, spaced at equal logarithmic intervals between 0.25 kHz and 50 kHz. One of the slots is semi-elliptical, with length 22.10 mm, depth 8.61 mm, and width 0.33 mm.

We have taken the impedance data of Harrison et al at 250 Hz, and inverted it using VIC-3D® as the driver of an inversion algorithm. The variables to be determined by inversion are the two semi-axes of the ellipse. For each trial value of the pair of variables, VIC-3D® computes a solution of the forward problem with the semi-elliptical flaw, whose semi-axes take the trial value. Because the semi-elliptical flaw is already in the VIC-3D® flaw library, this calculation is done quickly.

In this manner we computed the length to be 22.99 mm and the depth 8.21 mm. (We fixed the width to be 0.33 mm.) We consider this result to be within experimental error, because Harrison et al admit an uncertainty of ±0.5 mm in locating the center of the slot. This information is important in modeling the data-scan.