PEC FINITE ELEMENT MODELING OF PULSED EDDY CURRENT SIGNALS FROM ALUMINUM PLATES HAVING DEFECTS

FINITE ELEMENT MODELING OF PULSED EDDY CURRENT
SIGNALS FROM ALUMINUM PLATES HAVING DEFECTS
V. K. Babbar, D. Harlley, and T. W. Krause
Department of Physics, Royal Military College of Canada, Kingston, ON, K7P 2W2
ABSTRACT. The pulsed eddy current technique is being developed for detection of flaws located at
depth within conducting structures. The present work investigates the pulsed eddy current response
from flat-plate conductors having defects by using finite element modeling. Modeling revealed the
optimum probe position with respect to a multilayer defect geometry. Models were also produced to
investigate the effect of changing some probe parameters on pickup signal and penetration depth.
Keywords: Pulsed Eddy Current, Electromagnetic Modeling, Transient Electromagnetic Fields
PACS: 81.70.Ex, 85.70.Ay
INTRODUCTION
Nondestructive pulsed eddy current (PEC) technique is being developing for
investigation of multilayer aircraft wing structures where fatigue induced crack growth
may occur within the inner layers [1-5]. The defects located within the inner layers are
difficult to inspect by conventional techniques, such as eddy current or ultrasonics. PEC
employs a square wave excitation of the coil to induce a transient response from
electromagnetic field interactions deep within the conducting aluminum structures. A
number of publications on this subject are aimed at a theoretical understanding of the
phenomenon, development of appropriate probes, improvements in experimental test
systems, and finite element (FE) modeling of the input and output signals [6-8]. The
authors recently demonstrated the success of FE modeling, using COMSOL commercial
software [9], by modeling coaxial reflection-type probes to simulate input and output
signals that matched closely with those obtained from the experimental set-up having
identical parameters [10]. The present work investigates improvements to the signal
response of the flat reflection-type PEC probe by examining probe position relative to
defect location and modifying some probe parameters, such as number of turns of the
driver and length and permeability of the ferrite core.
EXPERIMENTAL DETAILS
The circuit diagram of the reflection-type probe used for the present work was
described in an earlier publication [10]. The parameters of three different probes used for
experimental work as well as FE modeling are given in Table 1. The measurements were
made on a multilayer specimen consisting of a stack of Al2024T3 aluminum plates each of
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dimensions 200 mm × 200 mm × 0.40 mm with the lower-most plate having a hole of
diameter 5 mm. To eliminate the air gaps between the plates, the stack was placed inside a
vacuum bag attached to a vacuum pump that maintained a constant pressure on the outer
surface of the plates. The total lift-off of the probe from the sample surface was 0.23 mm.
FINITE ELEMENT MODELING
We used COMSOL Multiphysics 3.4 commercial software for all the modeling
work. Both two-dimensional (2D) and three-dimensional (3D) models were used
depending on the geometry of the measurement set-up. For example, a 2D model was used
to model a ‘no defect’ sample geometry used to study the effect of probe lift-off. For
sample geometries involving localized defects, such as circular holes, 3D half-models were
employed. A 2D quarter-model of a reflection-type probe placed over a stack of three
conducting plates is shown in Fig. 1. The plates had no defect, so it was convenient to use
cylindrical symmetry. Models were produced for a number of plates varying from 0 (air
case) to 10, each of thickness 0.4 mm. The modeled plates had no air gap between them, so
the plate region was essentially a continuum.
RESULTS FOR ‘NO DEFECT’ CASE (2D MODEL)
Surface Current Density
The screen snapshot of a solved 2D model depicting the azimuthal component of
surface current density distribution for the ‘no defect’ case of 3 plates is shown in Fig. 2. It
gives a visual indication of currents that penetrate inside the conducting plates. This
distribution was recorded at a time that corresponds to the peak amplitude of the pickup
signal. As expected, the maximum current density is obtained in a region of plates between
the driver and the pickup coil.
TABLE 1. Probe specifications used for the experimental work as well as FE modeling.
Driver Coil
Pickup Coil
D400
D800
D1600
Length, mm
20.0
20.0
20.0
Inner diameter, mm
18.9
18.9
18.9
5.9
Outer diameter, mm
20.9
22.8
23.9
8.2
Number of turns
405
809
1635
300
AWG
34
34
34
44
Resistance, Ω
26.0
56.2
121.6
63.2
Length of ferrite core, mm
20, 30, and 40
Diameter of ferrite core, mm
4.0
Permeability of ferrite
1500, 2300, and 3100
Conductivity of ferrite, S/m
0.5
Conductivity of aluminum, S/m
2.46 × 107
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1.0
Ferrite rod
Insulation
Driver coil
Air Box
Pickup coil
Conducting plates
FIGURE 1. Quarter-section of a two-dimensional finite element model of reflection-type probe placed over
a stack of three conducting plates. The inset shows the experimental probe of identical geometry.
FIGURE 2. Surface current density near the peak amplitude of the pickup signal shown in Fig. 3.
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0
Pickup Voltage (V)
-0.1
-0.2
0 mm
0.4 mm
-0.3
1.0 mm
2.0 mm
-0.4
Air Signal
-0.5
0
0.0002
0.0004
0.0006
0.0008
0.0010
Time (s)
FIGURE 3. Variations of driver signal and pickup signal with lift-off for 10 plates case.
0
Pickup Voltage (V)
-0.1
-0.2
-0.3
-0.4
-0.5
405 turns
809 turns
1635 turns
0
0.0002
0.0004
0.0006
0.0008
0.0010
Time (s)
FIGURE 4. Variation of pickup signal with number of turns of the driver.
Effect of Lift-Off
The effect of lift-off was studied by increasing the distance between the probe and
the plate from the default 0.23 mm up to 2.0 mm. The results are shown in Fig. 3 for 10
plates. All the pickup voltages, except the one for air, pass through a common point, called
the lift-off intersection (LOI) point. The point has been observed experimentally by some
researchers [2, 3]. The models thus provide experimental verification of the LOI point.
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Variation of Pickup Signal with Number of Turns of the Driver
The strength and shape of the pickup signal are significantly affected by the change
in the number of turns of the driver. The pickup voltage obtained from the probes D400,
D800, and D1600, where the driver has 405, 809 and 1635 turns respectively, is shown in
Fig. 4. The driver D400, with the least number of turns, produces the greatest signal
amplitude that decays at the fastest rate. This is attributed to the combined effect of
resistance and inductance of the driving circuit with inductance playing a dominant role
[8]. Higher inductance results in a greater relaxation time, which acts to slow down both
growth and decay of the driver voltage, thus causing a corresponding variation in the
pickup voltage. While a greater driver voltage is an advantage as it produces larger flux
density, a larger relaxation time is vital to detection of deep-lying defects where diffusing
currents interact with defects later in time. For the driver D1600, the signal amplitude
becomes too low. So the driver D800 seems to be a better trade-off between greater
relaxation time and larger peak amplitude.
Effect of Core Length and Permeability
The pickup signals for a driver of fixed length of 20 mm using three different core
lengths of 20, 30 and 40 mm were compared. The signal increased by about 8% for a
change in length from 20 to 30 mm and about 5% from 30 to 40 mm. Longer cores
generate flux that can penetrate deeper into the sample and produce greater current density
throughout the sample parallel to the surface. However, they make the probe bulky.
Models were also solved using core permeability of 1500, 2300 and 3000, but no
significant effect on the pickup signal was observed. A ferrite core of length 30 mm and
permeability 2300 was used for the present work.
RESULTS FOR ‘DEFECT’ CASE (3D MODEL)
Background-Subtracted Signal and Effect of Probe Position
Information about the nature, location and severity of a defect is obtained by
subtracting the ‘no defect’, reference, or background signal from ‘defect’ signal. Figure 5
shows a reference-subtracted signal for a hole in a stack of five plates along with the
corresponding experimental signal. The reference-subtracted signal shows two peaks of
different magnitudes and opposite polarity with the smaller one occurring later in time.
The amplitudes of these peaks are affected by the change in position of the probe with
respect to the defect centre. FE modeling has revealed that, for the probe dimensions used
in the present work, the maximum signal amplitude would be obtained when the outer
surface of the pickup coil coincided with the center of the hole. This corresponded to the
center-to-center distance of 4 mm between the hole and the probe, as shown in Fig. 6. The
signal strength decreased when the probe was shifted on either side of the hole center.
Variation of Signal with Thickness of Multilayered Structure
The variation of the reference-subtracted signal with increased number of plates (or
thickness of the multilayer structure) is shown in Fig. 7. The hole exists in the lowermost
plate. The amplitude of both the peaks decreased and the peaks shifted to later times with
increase in thickness; the shift was more prominent in the second peak, which is associated
with secondary induced currents within the conducting structure. The signal response is
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believed to be associated with a diffusion wave, which penetrates through the thickness of
the conductor with a velocity at the peaks that is given by the slope of the position-time
plot, as shown in Fig. 8. The plot corresponding to each peak is almost a straight line. The
results are in good agreement with experimental data. The velocity corresponding to the
first and second peaks is about 22 and 8 m/s respectively.
INTERPRETATION OF RESULTS
The electrodynamic response of a plate conductor to the application of a transient
magnetic field can be described in terms of induced electric and magnetic fields within the
conductor. For the timescales used in this work (~10−4 s), this is a two stage process [11].
First, the expulsion of the dynamic electric and magnetic fields occurs and, second, the
surface currents and wave fields are damped. The initial expulsion of electromagnetic
fields from within the conducting material arises by induced eddy currents as expressed by
Lenz’s law, with their depth of penetration limited by the transient skin depth [5]. Inside
the conductor, these induced currents decay (are damped), and the associated changing
magnetic field results in opposing eddy currents deeper within the sample. This may also
be described in a process similar to that of an over-damped wave. With the presence of a
discontinuity, the increase of resistance causes this damping to occur more rapidly.
Reference-Subtracted Pickup Signal (V)
0.0020
0.0015
Modelled
0.0010
Experimental
0.0005
0
-0.0005
-0.0010
0
0.0002
0.0004
0.0006
0.0008
0.0010
Time (s)
FIGURE 5. Reference-subtracted signal from five plates with a hole present in the lowermost plate.
Pickup Coil
Hole
2.85
1.15 2.50 mm
FIGURE 6. Position of the pickup coil relative to the hole that produced the maximum signal amplitude.
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Reference-Subtracted Pickup Signal (V)
0.03
0.02
1 plate
2 plates
0.01
3 plates
4 plates
9 plates
0
-0.01
0
0.0002
0.0004
0.0006
0.0008
0.0010
Time (s)
FIGURE 7. Variation of reference-subtracted pickup signal with number of plates.
600
Time-to-Peak (μs)
Second Peak
400
First Peak
200
First Peak (model)
First Peak (experiment)
Second Peak (model)
Second Peak (experiment)
0
0
1
2
3
4
Thickness (mm)
FIGURE 8. Time-to-peak versus total thickness of the conducting layers. Curves are linear best fit to Exp.
data.
In the context described above the initial positive peak shown in Fig. 5 is
associated with the initially induced eddy currents produced due to Lenz’s law. The
secondary negative peak, which is broader and appears later in time, is associated with the
reversed and more diffuse secondary induced currents. For deeper defects, the interaction
of induced currents becomes weaker and occurs later in time, but with the rate of decay of
the secondary peak occurring more slowly than the first as is evident from Fig. 7. The
progression of induced wave fronts into the stack of plates, as shown by the time position
of both the first and second peaks in Fig. 8, varies linearly with plate thickness, but with
the secondary peak occurring at a proportionately later time (3×), equivalent to a lower
frequency that the first. These observations are consistent with recent measurements that
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have demonstrated enhanced signal-to-noise of the hole when analysis techniques are
applied in the region of the second peak [8].
CONCLUSION
The FE modeling was successful in simulating the PEC response in multilayered
aluminum structures containing circular defects. It verified some known experimental
results, such as the existence of the lift-off intersection point, and contributed to the
investigation of different probe configurations and determination of optimum probe
parameters. The existence of two peaks and the shifts of the peaks were indicative of
diffusion wave phenomena, where the second peak was associated with the secondary
induced currents that have greater depth-of-penetration.
ACKNOWLEDGEMENT
The authors thank Mr. Kevin Wannamaker for technical assistance. This work is
supported by the Natural Sciences and Engineering Research Council of Canada, and the
Academic Research Program and the Aerospace Research Advisory Committee at the
Royal Military College of Canada.
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