Structural analysis of CFRP using EC methods 3 · Structural analysis of CFRP ... structural analysis, eddy current method, ... are completely covered with the polymer matrix. The

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. Figure 1 Strength as a function of fibre orientation[1]

0963-8695/94/05/0241 -08 © 1994 Butterworth-Heinemann Ltd NDT&E International 1994 Volume 27, Number 5 241

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

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.

Table 1.

Specimen no. Stacking sequence

1 [0°2 ,3°2 , 0°]s 2 [0°2 ,6°2 , 0°]s 3 [0°2 ,9°2 , 0°]s 4 [0°2 ,12°2, 0°]s 5 [0°5]s 6 [0°2 ,+/-45°, 0°]s 7 [0°2 ,+45°, 0°, -45°]s 8 [0°2 , 90°, 0°, 90°]s 9 [0°2 ,+45°, 90°, -45°]s

Experimental investigations

Test parameters

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 transmitter-receiver 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.

242 NDT&E International 1994 Volume 27, Number 5

Figure 4 Measurement equipment

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

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.

In Figure 7:

s(φ)*h(φ ) → e(φ) (1)

Figure 6 Normalized signals of uni- and bidirectional CFRP specimens

The increase in directivity with increasing frequency is shown in Figure 5.

The plateau effect

With increasing testing frequency there was a consider-able maximum in the uni- and bidirectional reinforced CFRP perpendicular to the fibre direction. This effect is Figure 7 Convolution

NDT&E International 1994 Volume 27, Number 5 243

Figure 5 Influence of frequency on the lateral resolution of an eddy current probe normalized to the maximum


Figure 9 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)

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

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)

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

These methods compare a synthetic bidirectional signal with the real bidirectional signal. The synthetic signal sy(φ) is produced using the convolution of the probe aperture function s(φ) with an ideal bidirectional signal h(φ).

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 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.

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.

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.


Figure 8 Wiener filtering of specimens 4 and 5

(5)


Calculated angle for following frequencies an deviations [°] ideal 8.3 MHz 9.3 MHz 9.9 MHz

case [°] angle [°] dev [°] 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

Figure 10 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



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 possi-bility 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

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



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 16 (a) Schematic representation of a unidirectional prepreg; (b) output signal; (c) electrical model of contacting carbon fibres


Figure 15 Comparison between 'Cu-tape' and CFRP tape


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.

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

to solve the problem of the plateau effect and to establish parameters to describe the amplitude decrease at higher depths of laminate.

References

1 Weber, A. Neue Werkstoffe VDI-Verlag, Dusseldorf (1989) 2 Lange, R. 'Strukturanalyse von CFK mit Hilfe des Wirbelstrom-

verfahrens' 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

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Structural analysis of CFRP using EC methods 3 · Structural analysis of CFRP ... structural analysis, eddy current method, ... are completely covered with the polymer matrix. The