## Advances in Eddy-Current Modeling

Kenji Krzywocz

EPRI NDE Center, 1300 Harris Blvd., Charlotte, NC 28262

and

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.

### Background

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.