Structural analysis of CFRP
using eddy current methods
R. Lange and G. Mook
Institute for Material Science and Material Testing, University of Magdeburg,
Magdeburg, Germany
Non-destructive inspection of carbon fibre-reinforced plastics (CFRP) using eddy
current methods is not only based on the conductivity of the fibres. High frequencies
(up to 10 MHz) enable the exploitation of capacitive effects reflecting the properties
of the matrix. The paper presents a method using rotating eddy current probes to
measure the anisotropic electrical properties. Potential applications of the method
are structural identification of laminates and estimation of their degradation. For
example, the strength properties of constructions based on unidirectional CFRP are
very sensitive to small differences in fibre direction angle. Best detection of these
angles could be obtained above 7.5 MHz. In addition, a signal perpendicular to the
fibre orientation was found and termed the plateau effect. It is a result of capacitive
connections between the fibres and presents new opportunities for the
characterization of matrix properties.
Keywords: structural analysis, eddy current method, CFRP
The strength properties of constructions of unidirectional
CFRP (carbon fibre reinforced plastic) are very sensitive
to small differences in the fibre direction angle (Figure
1). The aim of the investigations was to detect small fibre
orientation angles in bidirectional CFRP and the ply
stacking of multidirectional reinforced CFRP using eddy
current methods.
Experimental conditions
Specimens
Details of the specimens are shown in Table 1. The
thickness of the flat specimens (110 x 110 mm2 ) is
1.4 mm and their fibre content is about 60% T-300 fibres.
Measurement equipment
The detection of different fibre orientations requires a
rotary scanner (Figure 4) which provides 2048 samples
Eddy current probes
The special demands on the design of eddy current probes
to detect fibre orientations in CFRP with a high
resolution are:
• high directivity;
• sufficient signal-to-noise ratio of the output signal;
• working frequencies of some MHz due to the low
conductivity of CFRP;
• shielded transmitter and receiver to suppress undesired
electromagnetic fields.
The coil system is shielded. For these investigations only
a transformer probe is possible. The directivity of a
parametric probe design is much lower.
0963-8695/94/05/0241 -08
© 1994 Butterworth-Heinemann Ltd
Figure 1
Strength as a function of fibre orientation[1]
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Structural analysis of CFRP: Ft. Lange and G. Mook
flat cores
fibre orientation
Figure 2
Schematic probe design and its lateral resolution with unidirectional reinforced CFRP in comparison with the probe in Reference 3
Table 1.
Specimen no.
Stacking sequence
1
2
3
4
5
6
7
8
9
[0°2 ,3°2 , 0°]s
[0°2 ,6°2 , 0°]s
[0°2 ,9°2 , 0°]s
[0°2 ,12°2, 0°] s
[0°5] s
[0°2 ,+/-45°, 0°] s
[0°2 ,+45°, 0°, -45°] s
[0°2 , 90°, 0°, 90°]s
[0°2 ,+45°, 90°, -45°]s
Experimental investigations
Test parameters
Figure 3
Stacking sequences of specimens
for every turn. The CFRP specimens located on
the rotary scanner modulate the signal in the
probe depending on fibre direction and scanning
angle.
Using the Elotest Bl eddy current device, the signal
is amplified, phase sensitive rectified and low-pass
filtered. The Y-component of the measurement
signal is A/D-converted and stored. To minimize
the influence of noise the results of 15 turns are
averaged. Because of the signal's symmetry it is
sufficient to evaluate only 180° of a whole turn.
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The lift-off can cause disturbance when measuring
the fibre direction. It was fixed at 0.1 mm.
Even at the highest test frequency of 10 MHz, the
specimen was fully penetrated. As expected, the
directivity increased with increasing transmitterreceiver distance (TRD). At the same time the
signal-to-noise ratio decreased. The best
compromise was a TRD of 12 mm. The criteria
for the choice of frequency are:
•
•
•
•
•
the penetration depth of the eddy currents;
the relation to the resonance frequency;
the signal-to-noise ratio;
the directivity;
the direction of lift-off and conductivity
effects in the impedance plane.
Structural analysis of CFRP: R. Lange and G. Mook
shaped like a plateau. Testing frequencies below 5.0 MHz
do not provide separable maxima in the +/ —45° fibre
direction for specimens 6 and 7 (Figure 5), and therefore
the frequency range was chosen between 7.5 MHz and
9.9 MHz.
Measurement of fibre direction
The specimen was firmly fixed to the rotary scanner.
Depending on the tilt between the fibres and the probe
separable signals were found for every specimen. The
newly developed probe provides a unique separation of
specimen number 1 from specimen number 5 (Figure 6).
Evaluation
The nature of the eddy current distribution in CFRP and
the geometric probe design do not allow direct
determination of small fibre angles. The determination
of these small differences in fibre orientation can only be
accomplished using special procedures.
Deconvolution methods
Inverse filtering
Figure 4
Inverse filtering is the reverse of convolution. To restore
the unknown fibre orientations we can use the
convolution theorem. Deconvolution is not defined in
the time domain but can only be accomplished in the
frequency domain, where the convolution is equivalent
to a multiplication of Fourier-transformed signals.
Measurement equipment
In Figure 7:
s (φ)*h(φ ) → e (φ)
(1)
Figure 5 Influence of frequency on the lateral resolution of an eddy current
probe normalized to the maximum
Figure 6 Normalized signals of uni- and bidirectional CFRP
specimens
The increase in directivity
frequency is shown in Figure 5.
with
increasing
The plateau effect
With increasing testing frequency there was a considerable maximum in the uni- and bidirectional reinforced
CFRP perpendicular to the fibre direction. This effect is
Figure 7
Convolution
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Structural analysis of CFRP: R. Lange and G. Mook
reason is the spectral division at and near the
zero-crossing points of s(φ).
Wiener filtering
To avoid this problem, Wiener filtering adds a noise term
to the denominator.
H(f) = E(f)*S*(f)/(S(f)*S*(f) + R)
(5)
S*(k) is the conjugated complex function of probe
aperture. R is an empirical noise term. Varying this noise
term we tried to detect h(φ) for bidirectional CFRP. As an
example, the results of Wiener filtering are shown for
specimen 4 and specimen 5 in Figure 8.
The Wiener filtering improved the signal but could not
be qualified to detect the angle between fibre orientation.
Depending on the noise term the algorithm for Wiener
filtering detects in a bidirectional specimen three or more
fibre orientations.
Correlation methods
Figure 8
These methods compare a synthetic bidirectional
with the real bidirectional signal. The synthetic
sy(φ) is produced using the convolution of the
aperture function s(φ) with an ideal bidirectional
Wiener filtering of specimens 4 and 5
h(φ).
signal
signal
probe
signal
Sy(φ) is now correlated with the real bidirectional signal
e(φ). Varying h(φ) a specially developed program
determines the maximum similarity of e(φ) and sy(φ). The
largest similarity indicates the correct h(φ) and the angle
between fibre orientations. This procedure includes the
opportunity to define the number of fibre
orientations. This evaluation method only presumes a
known aperture function of the probe and it is able to
detect more than two fibre orientations.
Figure 9
Figure 10 shows the resolution of the correlation method
depending on the test frequency. At high frequencies the
influence of the plateau effect increases. At a frequency
of 8.3 MHz the best correspondence was found.
Correlation procedure (schematic)
where s(φ) is the probe aperture function (characteristic
of transducer), real measurement result, h(φ) is the
weighting function (fibre orientation), unknown function,
and e(φ) is the resulting function, the real measurement
result.
The Fourier transform of Equation (1) gives:
S(f)*H(f) = E(f)
(2)
A qualitative assessment of fibre orientation in
multidirectional CFRP specimens is possible, because the
fibre directions in the investigated specimens are clearly
detectable.
The trajectories of eddy currents in a multidirectional
material are very complicated. They depend on the
orientation, the depth of layers, the plateau effect and so
on. Hitherto it has not been possible to quantify the
depth of the layer.
H(f) can be obtained by converting Equation (2).
H(f) = E(f)/S(f)
(3)
Now the unknown fibre orientation h(φ) can be found
theoretically using the inverse FFT.
FFT-1(H(f))>h(φ)
(4)
The practical use of this procedure for real signals does
not improve the investigations of fibre orientation. The
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Modelling of eddy current distribution
in CFRP
The development of eddy current methods for CFRP
testing is in its initial stages. This paper should help in
understanding measuring signals using an electrical
model.
Structural analysis of CFRP: R. Lange and G. Mook
Calculated angle for following frequencies an deviations [°]
ideal
case [°]
Figure 10
8.3 MHz
angle [°]
dev [°]
9.3 MHz
9.9 MHz
angle[°] dev [°]
angle [°] dev [°]
0
0
0
0
0
0
0
3
5.62
2.62
4.75
1.75
8.09
5.09
6
10.55
4.55
9.49
3.49
9.31
3.31
9
10.90
1.9
10.90
1.90
10.90
1.90
12
10.90
1.1
10.90
1.10
10.90
1.1
Calculation of fibre orientation for bidirectional CFRP
Figure 11 Amplitude values of output signal versus test frequency
for specimens 1-5
Eddy current distribution in CFRP layers
The first assumption is that the eddy currents in CFRP
are connected to carbon fibres. Carbon fibres are strictly
orientated. In an ideal material they do not touch and
are completely covered with the polymer matrix. The
Figure 12 Amplitude values of output signal versus test frequency
for specimens 6-9
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Structural analysis of CFRP: R. Lange and G. Mook
Figure 13
Output signal of specimens 6 and 7
Figure 14
Interdependence between probe design and output signal shape
eddy current field is deformed in the axis of the fibres. This
circumstance provides a sharply focused signal in the
receiver. A bidirectional material offers another possibility for eddy current flow. The boundary layer between
various fibre orientations forms a rhombic mesh. The
junctions between the fibres open current paths. The
result is an elliptically deformed eddy current field whose
shape depends on fibre orientation, fibre content and
stacking sequence. With increasing angle between fibre
orientations the flow conditions for eddy currents are
improved. Due to the resonance frequency of 11 MHz
the measurement signal increases (Figure 11) with
increasing frequency.
Specimen 6 and specimen 7 contain the same number of
layers and orientations but the tapes with +/-45°
orientation are located at different depths. The lower
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maximum of specimen 6 in the 0°-orientation is caused
by the deeper 0°-layer. Specimen 9 shows at lower
frequencies the lowest output signal, but at high
frequencies the largest value. This effect can be explained
assuming a lower resonance frequency in comparison to
the other specimens (Figure 12).
Specimen 6 provides a sharper signal for its +/-45° plies
than does specimen 7 (Figure 13).
The plateau effect
In real components fibres may contact due to the
displacement of resin. Even if no contact results, the
capacity between two fibres dramatically increases with
decreasing fibre distance. These current paths and
capacitors are responsible for the increasing eddy current
Structural analysis of CFRP: R. Lange and G. Mook
density. They are the cause of the mentioned plateau
effect. This halting is derived from the constant output
signal during a denned scanning angle. The local
minimum between the maxima corresponding with the
fibre direction and the plateau effect depends on probe
design and test frequency (Figure 14).
Using a 'tape simulation' from thin copper wires it could
be shown that the plateau effect is only caused by lateral
fibre contact and is not influenced by probe design
(Figure 15).
The results of the investigations of unidirectional
specimen 5 allow us to conclude that eddy current
distribution in the specimen is influenced by ohmic
resistances and capacitive reactances. The capacitive
component provides a phase shift. Figure 16 shows an
electrical model of parallel contacting carbon fibres.
The surface of carbon fibres is oxidized to increase the
adhesive power with the matrix. This thin oxide film is
characterized by a very high electrical resistance, and
acts like a dielectric between the carbon fibres.
According to the equation:
Zc = 1/ jωC
(7)
where Zc is capacitive reactance, C is capacity, j is the
imaginary unit and ω is angular frequency, the capacitive
reactance decreases with increasing frequency and results
in increasing electrical conductivity. This produces a
higher eddy current density and the plateau effect
increases.
The plateau effect could provide information about the
degree of epoxy cover. This effect opens the opportunity
of evaluating the fibre content as an important factor for
the mechanical properties.
Summary
The eddy current method has been shown to detect fibre
orientations and small angles between fibre orientations.
The newly developed eddy current probes with high
Figure 15
Comparison between 'Cu-tape' and CFRP tape
Figure 16
(a) Schematic representation of a unidirectional prepreg; (b) output signal; (c) electrical model of contacting carbon fibres
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directivity distinguished an angle of fibre orientation of
3° from a unidirectional specimen. A new eddy current
effect was found in CFRP which opens new opportunities
to characterize this group of materials. With increasing
frequency the conductivity of unidirectional CFRP
perpendicular to the fibre axis increases.
to solve the problem of the plateau effect and to establish
parameters to describe the amplitude decrease at higher
depths of laminate.
The best results for detection of fibre orientation were
obtained using a correlation method. This method only
presumes a known probe aperture function. The
determination of unknown fibre orientations is possible.
Moreover this procedure should be able to detect more
than two fibre orientations. Future investigations have
References
1 Weber, A. Neue Werkstoffe VDI-Verlag, Dusseldorf (1989)
2 Lange, R. 'Strukturanalyse von CFK mit Hilfe des Wirbelstromverfahrens' Diplomarbeit, TU Magdeburg (1992)
3 Vernon, S. N. and Liu, J. M. 'Eddy current probe design for
anisotropic composites' Mater Eval (January 1992) p 36