# WFNDEC Benchmark Problem 2 - Eddy Current Inspection of Inconel Pipe

Sensors & NDT with MagNetWFNDEC's^{1} Eddy Current Benchmark Problem 2 involves the inspection of an Inconel pipe using an internal pancake coil situated with its axis perpendicular to the axis of the pipe. Small defects of various depths in the external wall of the pipe are scanned in the axial and circumferential directions. Defects are detected as a change in the impedance of the coil.

The pancake coil induces eddy currents in the pipe wall, which are disrupted in the presence of the flaw. This is detected as a change in impedance of the coil. MagNet's 3D Time-Harmonic solver is used to simulate the distribution of the eddy currents, as well as to find the voltage (both magnitude and phase) across the pancake coil. Only one simulation is necessary as the position of the coil can be easily parameterized to generate multiple solutions for each coil position.

^{1}The World Federation of Non-Destructive Evaluation Centers (WFNDEC) publishes benchmark problems for NDE/NDT applications.

### METHODS and RESULTS

## EDDY CURRENT DENSITY on the INNER SURFACE of the TUBE

MagNet's 3D Time-Harmonic Solver is used to model the eddy current distribution in the region of the flaw. The image shows the eddy current density on the inner surface of the tube, directly underneath the coil.

View larger image

## CHANGE in IMPEDANCE -- 20% defect

The change in impedance is plotted in the x-theta (axial and azimuthal scan directions) plane. Three different defects (corresponding to 20%, 40% and 60% of the tube wall thickness) are shown for comparison. The height of the plots has been normalized to show the increased response to the deeper defects. The 20% defect shows the smallest signal.

View larger image

## CHANGE in IMPEDANCE -- 40% defect

The response to the 40% defect is correspondingly larger, both in terms of the affected area and the strength of the signal.

View larger image

## CHANGE in IMPEDANCE -- 60% defect

The 60% defect has the largest response of all, showing two clear peaks near +/- 10 degrees azimuthal.

View larger image

## IMPEDANCE PLANE DIAGRAM

Shown here is an impedance plane (Lissajous) plot of the real part (resistance) against the imaginary part (reactance) for three axial scans of 20%, 40% and 60% defects.

View larger image

## MAGNITUDE CHANGE in the IMPEDANCE

For three different scan frequencies (100 kHz, 150 kHz and 200 kHz) the magnitude and phase change in the impedance were plotted as a function of axial position. The set-up of the many problems solved (990 in all) is handled easily through parameterization in MagNet. Scripting can be used to automate the process and to logically structure the results.

View larger image

## PHASE CHANGE in the IMPEDANCE

The phase change for the same three frequencies is also computed. MagNet's post-processing tools allow for the quick computation of these global quantities for each solution point.

View larger image

## MAGNITUDE CHANGE in the IMPEDANCE PLOTTED

These three curves show the resistance (magnitude) change, but this time the response is plotted to a scan in the azimuthal/circumferential direction, from zero to 50 degrees. The three curves also correspond to three different defects (20%, 40, and 60%) and all scans were performed at 150 kHz.

View larger image

## PHASE CHANGE in the IMPEDANCE PLOTTED

Phase plots for three azimuthal scans.

View larger image