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Advances in Eddy-Current Modeling

Kenji Krzywocz
EPRI NDE Center, 1300 Harris Blvd., Charlotte, NC 28262
Lai Wan Woo, R. Kim Murphy, Harold A. Sabbagh, Jeff C. Treece
Sabbagh Associates, Inc., 4635 Morningside Dr., Bloomington, IN 47408

(presented at the ASNT Spring 1995 Conference)

A wide diversity of component configurations and the high cost of component mock-ups make NDE procedure development and demonstration sometimes difficult to implement for each plant-specific applications. Computer modeling of eddy current NDE examinations can provide a cost effective tool for controlling the cost of inservice examinations. The computer modeling also helps increase the reliability of inservice examinations by optimizing the probe-coil configurations for given damage mechanisms. Over the years, various techniques, such as boundary integrals, volume integrals, finite element method, etc, have been developed to model the eddy current responses due to the presence of material flaws. In this paper, applications of the volume-integral method for probe-flaw interactions in half-spaces developed by Sabbagh Associates, Inc, will be presented and compared with the empirical test results. This includes comparison of experimental eddy curent measurements from Type 304 stainless steel plate samples containing compressed electro-discharge machined notches with the computed probe-flaw responses based on a transmit/receive coil configuration.


A typical problem being modeled includes a current-carrying coil placed near a workpiece that is to be evaluated. Through electromagnetic induction, eddy currents are induced in the workpiece by a transmitter coil. The receiver coil placed some distances away from the transmitter coil senses the magnetic field of these eddy-currents, which induces a complex voltage in the receiver coil. Flaws within the material perturb the eddy currents, thus changing the voltage in the receiver coil. The electromagnetic field at each scan point is determined by summing the effects of the sources at all points (including the field point itself). In summing these effects, the sources must be weighted by a function which depends on the distance between the source and the field point; this function is called the Green's function. When the effects are summed over a given volume of space, this becomes a volume integral equation.

The numerical technique involves establishing a regular grid over the flawed region of the workpiece. Each cuboid, or cell, of the grid is assigned a "volume fraction'' that specifies how much of the cuboid is filled with "flaw material''. A linearly-varying current is assumed to flow through each cuboid of the grid. The electric field in any one cell is computed by summing the effects of the currents in all the cells, weighed by the Green's function to compensate for different distances between source and field cells. The voltage in the probe is normalized to the current in the probe coil. Thus, a change in the probe impedance indicates the presence of an anomaly in the workpiece.

Transmit-Receive Coil Configuration

Latest eddy current examination methods indicate that more information can be obtained by using a bistatic (or multistatic) configuration, in which a single transmitter excites the workpiece, and one (or more) independent receiver coil detects the signal. Figure 1 shows the classical bistatic arrangement and the typical probe scanning modes being evaluated with the VIC-3D® software. This arrangement emulates the typical driver-pickup, or transmit-receive (T/R), coil configuration in either normal or parallel scan mode for the analysis results shown below, both the transmit- and receive-coils were identical 5mm diameter air-core coils with a 10 mm separation between the coils.

Bistatic arrangement
Figure 1: A bistatic arrangement of a typical transmit/receive coil configuration is shown along with the typical scan orientations.

Analysis Results

Figure 2a shows the difference in the magnitude of the coil impedance as the probe is scanned in the x-direction over the rectangular slot, whose major axis lies in the y-direction. A larger signal output was obtained by translating the T/R probe in a parallel-scan mode over the rectangulat notch. In Figure 2b the corresponding impedance plots are displayed as Lissajous patterns with signal excursions in the opposite directions, i.e., upward excursion from the parallel scan versus downward excursion from the normal scan.

Signal differences due to orientation changes
Figure 2 (a) (b): Comparison of signal outputs shows different results due to normal and parallel scan orientations. The difference in the magnitude of the coil impedance is shown in Figure 2a, while Figure 2b shows different impedance plane trajectories.
It should be noted that the 3mm long notch was centered over the X-Y coordinates of (0,0). Figure 3 shows the actual outputs based on laboratory test results, but for a crack that is much larger than the one modeled in Figure 2. The amplitude of the parallel-scan output was indeed greater than the amplitude of the normal-scan output, and the impedance trajectories extended in the opposite direction as was predicted.
Impedance plane plot
Figure 3: Impedance plane trajectories of two different scan orientations are shown based on the laboratory test results at 100 kHz.
Figure 4 shows the comparison of predicted versus actual outputs from three notches having same axial extents and widths but with different notch depths. The impedance plane trajectories at 100 kHz were produced based on the parallel scans using a T/R probe. The model correctly predicted the clock-wise orientaion of the impedance plane trajectories with increasing crack depths.
Comparison of results
Figure 4: Comparative results of predicted versus actual outputs are shown for three notches of varying notch depths. The outputs of T/R probe were obtained at 100 kHz using parallel scans.


This paper showed that analytical modeling can provide an effective and powerful tool for optimizing the probe and scan parameters for given flaw conditions.