Ultrasonics 60 (2015) 109–116

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The influence of temperature variations on ultrasonic guided waves in anisotropic CFRP plates O. Putkis a,b,⇑, R.P. Dalton b, A.J. Croxford a a b

Ultrasonics and NDT group, University of Bristol, Bristol BS8 1TR, UK QinetiQ plc, Farnborough GU14 0LX, UK

a r t i c l e

i n f o

Article history: Received 4 November 2014 Received in revised form 8 February 2015 Accepted 2 March 2015 Available online 13 March 2015 Keywords: Ultrasonic guided waves Anisotropic materials Temperature Structural health monitoring Subtraction

a b s t r a c t Carbon Fibre Reinforced Polymer (CFRP) materials are lightweight and corrosion-resistant and therefore are increasingly used in aerospace, automotive and construction industries. In Structural Health Monitoring (SHM) applications of CFRP materials, ultrasonic guided waves potentially offer large area inspection or inspection from a remote location. This paper addresses the effect of temperature variation on guided wave propagation in highly anisotropic CFRP materials. Temperature variations cause changes in guided wave velocity that can in turn compromise the baseline subtraction procedures employed by many SHM systems for damage detection. A simple model that describes the dependence of elastic properties of the CFRP plates on temperature is presented in this paper. The model can be used to predict anisotropic velocity changes and baseline subtraction performance under varying thermal conditions. The results produced by the model for unidirectional and 0/90 CFRP plates are compared with experimental measurements. Ó 2015 Published by Elsevier B.V.

1. Introduction Ultrasonic guided waves can travel long distances in plate-like structures without significant attenuation and therefore potentially offer large area inspection, or inspection from a remote location, with a relatively small number of sensors in Structural Health Monitoring (SHM) applications [1–4]. Carbon fibre reinforced polymer (CFRP) materials are strong, lightweight and corrosion-resistant materials and therefore are increasingly used in the construction, automotive and aerospace industries [5]. There is a demand from industry to develop SHM techniques for CFRP materials and structures. The quantification of propagation characteristics in CFRP materials is crucial when designing guided-wave-based SHM systems and it remains the focus of current research [6–10]. This paper examines the effect of temperature variation on guided wave propagation and its influence on the performance of baseline subtraction techniques used in SHM. Temperature response is well understood for guided waves in isotropic materials [2,11,12], however studies for CFRP materials concentrate on quasi-isotropic cases only [13,14].

⇑ Corresponding author at: Ultrasonics and NDT group, University of Bristol, Bristol BS8 1TR, UK. http://dx.doi.org/10.1016/j.ultras.2015.03.003 0041-624X/Ó 2015 Published by Elsevier B.V.

The SHM paradigm is based on observation of the relative changes in a structure by means of permanently installed transducers. The baseline signal characterizing the structure, I0 ðtÞ, is firstly recorded, when it is known to be in a damage-free condition. The baseline waveform contains guided wave scattered signals from all the structural features. I0 ðtÞ is then compared with a measurement, I(t), made during the monitoring and any deviation infers damage in the structure. One of the widely adopted methods of comparison is the baseline subtraction technique, where the baseline signal is subtracted from the waveform acquired during the monitoring stage: [15,2–4]

uðtÞ ¼ IðtÞ  I0 ðtÞ

ð1Þ

The resulting residual signal, uðtÞ, would ideally isolate any small signals corresponding to damage that could otherwise be masked by the signals associated with structural features, or give perfect subtraction when there is no damage. However, environmental changes like temperature variation affect guided wave propagation and result in elevated residual signal levels that can be mistaken for damage. The maximum amplitude in the residual signal, expressed as a fraction of the maximum amplitude in the original recorded signal, for isotropic materials can be expressed as: [2,3]

umax ¼

xr

vp



a

kp

vp

 dT

ð2Þ

O. Putkis et al. / Ultrasonics 60 (2015) 109–116

where x is the angular centre frequency of the signal, r is the propagation distance, v p is the phase velocity, a is the coefficient of thermal expansion, dT is a temperature change and kp ¼ dv p =dT is a coefficient of velocity change with respect to temperature change. In anisotropic materials v p is directionally dependent and so are the coefficients kp and a, implying that the maximum residual is also a function of propagation direction. For CFRP plates a is smaller, by at least an order of magnitude, than kp =v p , determined later in the paper ignoring a, and hence it is excluded from calculations in this paper [16]. A model that predicts guided wave velocity response to temperature variations in CFRP plates, which in turn can determine the baseline subtraction performance using Eq. 2, is presented in Section 4. It is a relatively simple model with only two linear equations involved to describe the influence of temperature on the elastic moduli of CFRP plates. Firstly, a brief overview of guided wave propagation phenomenon in highly anisotropic plates is given in the next section. Following this, an experimental procedure used to investigate guided wave propagation under thermally varying conditions is described in Section 3. The experimental data was used to evaluate the subtraction performance predicted by the model discussed in Section 4. The overall anisotropic subtraction performance is also discussed for unidirectional and cross-ply plates and conclusions drawn in the last section.

2. Overview of anisotropic propagation CFRP materials are anisotropic materials with directionally dependent physical properties leading to directionally dependent propagation of guided waves such as dispersion as shown in the example case of fundamental guided wave modes in unidirectional CFRP plate in Fig. 1. Not only dispersion becomes directionally dependent, phase and energy velocity vectors generally do not point in the same direction in anisotropic materials [8,10,9,6,7]. Direction of energy velocity vector is perpendicular to the tangent of the phase slowness (inverse of phase velocity) corresponding to a particular phase velocity direction (see Fig. 2). This phenomenon is known as steering [6,7] and the angle difference between the velocity directions of phase, hp , and energy, he , is called the steering or skew angle, w. Since velocity vectors point in different directions, only a projection is observed of the phase velocity vector in the energy velocity direction and vice versa. Experimental

0.5 0.45

Phase Slowness, s/km

110

0.4 vp

0.35 ve

0.3 0.25

ψ

0.2 0.15 0.1

0

10

20

30

40

50

60

70

80

90

Phase Velocity Direction, deg Fig. 2. A typical phase slowness curve for unidirectional (0°) CFRP plate for S0 mode at low frequencies. Phase and energy velocity vectors point in the same direction only in principal directions, i.e. hp ¼ 0 and hp ¼ 90.

measurements are typically made in the he direction and hence it is more convenient to consider v p ðhe Þ rather than v p ðhp Þ, as shown in Fig. 3. Steering also leads to energy focussing [17,18], which results in increased or decreased amplitude excitability in particular directions as shown in Fig. 4(a). It can be seen that there is a relatively large energy focussing for the A0 and S0 modes towards fibre direction, which makes excitation in non-fibre directions more difficult. In addition, steering can give rise to multiple energy velocity values in certain energy velocity directions, as in the example case for SH0 mode shown in Fig. 4(a), which can result in guided wave mode signal travelling as multiple wavepackets in certain directions. Moreover, the distinction of different guided wave modes through their mode shapes is no longer obvious in anisotropic materials and, for example, the mode shapes of S0 and SH0 modes are very similar in certain directions. In this paper, Lamb’s notation for the modes of an isotropic plate are employed for simplicity. The Semi-analytical Finite Element (SAFE), also called spectral element, method [19,8,20,10] was used in this paper to calculate dispersion curves for anisotropic CFRP plates. In SAFE model the plate is discretized along the thickness of the plate with each element representing a single ply in the plate. The displacement along the propagation direction is assumed to be harmonic. Then, finite

9000

Phase velocity, m/s

8000 o

7000

A0(0 )

6000

SH0(0o)

5000

S (0o)

ve ψ

0

vp

ve

o

A0(45 )

4000

ψ

o

SH0(45 )

3000

S0(45 )

2000

vp

θe

o o

A (90 ) 0

1000 0

S0(90o) 0

1

2

3

4

Frequency, Hz

5

6 5

x 10

Fig. 1. Examples of dispersion curves of fundamental modes in unidirectional CFRP plate in different phase velocity directions. Curve corresponding to SH0 mode in 90° is the same as in 0° and therefore is not shown. Plate is 2 mm thick, its elastic are constants given in Table 1.

Omnidirectional Excitation transducer Fig. 3. A diagram indicating the meaning used for v p ðhe Þ in this paper: magnitude of phase velocity vector corresponding to energy velocity vector pointing in he direction.

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9000 SH0 mode, 140kHz

A0 mode, 60kHz

0.9

8000

S0 mode, 140kHz

0.8

Energy velocity, m/s

Normalized Focussing Factor

1

0.7 0.6 0.5 0.4 0.3 0.2

S0 mode, 140kHz A0 mode, 60kHz

7000 6000 5000 4000 3000 2000

0.1 0 0

10

20

30

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70

80

90

1000 0

10

20

30

40

50

θe,deg

θ , deg

(a)

(b)

60

70

80

90

e

Fig. 4. Examples of predicted (a) energy focusing factor and (b) energy velocity in unidirectional CFRP plate. Plate is 2 mm thick, its elastic constants are given in Table 1. 0° direction coincide with fibre direction.

element assembling techniques together with equation of motion are used to obtain the response of the whole laminate.

UD

cross−ply

z 3. Experimental details An environmental chamber was used to investigate guided wave propagation for temperatures ranging from 10 °C to 30 °C. The accuracy of environmental chamber is 0.1 °C and the readings were taken directly from its temperature sensor. The rate of temperature change was slow enough to ensure a uniform temperature distribution within the chamber. Two CFRP plates were studied: a unidirectional and a 0/90 cross-ply. Both have been made from the same pre-preg material with five independent elastic moduli of a single ply determined experimentally from guided wave velocity measurements and given in Table 1. The coordinate system used throughout the paper is shown in Fig. 5. These elastic moduli are considered to correspond to room temperature, i.e. T ¼ 20 °C. The dimensions of the plates are 1 m  1 m  2 mm and density is 1580 kg/m3. The two fundamental modes, A0 and S0 , were investigated. For the excitation of the A0 mode, 3 mm-diameter PZT transducers (‘‘Noliac’’) with a thickness of 3 mm were used and a Hanning-windowed toneburst of 3 cycles and 60 kHz centre frequency was applied. For excitation of the S0 mode, 20 mm diameter PZT transducers (‘‘Noliac’’) with a thickness of 1 mm were used and a Hanning-windowed toneburst of 3 cycles and 140 kHz centre frequency was applied. Transducers were coupled to the plates using cyanoacrylate adhesive at the positions shown in Fig. 6. The S0 mode transducers were attached to the plates only after the experiment with A0 mode transducers ended. These particular excitation frequencies were chosen to give the highest guided wave amplitude response for the particular transducers and mode under investigation. The transducers were operated in pitch-catch

Table 1 5 independent moduli of the constitutive ply of the unidirectional and cross-ply laminates under investigation. E3 E2 G23

m23 m12

111.7 GPa 8.80 GPa 4.70 GPa 0.35 0.43

y x Reception transducer

θe r Excitation transducer

Fig. 5. Schematic diagram representing the notation employed in the paper. he was measured with respect to z axis, which coincided with fibre direction or one of the fibre directions for 0/90 plate.

configuration and different transducer-pair combinations resulted in different propagation directions, he , as represented by a single transducer-pair in Fig. 5. Multiplexing between different transmitter–receiver pairs was achieved using multiplexers based on microwave multiplexer relays that were developed at ‘‘University of Bristol’’. ‘‘Handyscope HS3’’ was used for signal excitation and recording. Example waveforms of the A0 mode in unidirectional plate at 20 °C acquired by different transducer pairs are shown in Fig. 7. The amplitude response is different for different propagation directions due to variation in energy focussing, attenuation, propagation distances and transducer coupling to the plate. This leads to varying signal-to-noise ratios for different sensor pairs and hence the varying reliability of the measurements in different directions.

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0.35

0.3

A0 mode transducers

A0 mode transducers

0.3

S0 mode transducers

0.25

S mode transducers 0

0.25

0.2

z, m

z, m

0.2 0.15 0.1

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0.02

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0.08

y, m

y, m

(a)

(b)

0.1

0.12

0.14

0.16

Fig. 6. Relative positions of transducers on (a) unidirectional and (b) 0/90 plates.

0o

0.04

15o

0.035

Amplitude, arb. units

(E3 ; E2 ; G23 ; m23 ) were determined in the temperature range 25– 140 °C. The authors discovered that only matrix dominant moduli, E2 and G23 , are significantly affected by temperature changes and the relationship with temperature was found to be linear for both moduli in the given temperature range. The study did not cover the remaining fifth, out-of-plane modulus: m12 ; therefore, in order to test its significance, it was perturbed by 30% and the velocity response observed. In this perturbation range, only a small impact on v p ðhe Þ (

The influence of temperature variations on ultrasonic guided waves in anisotropic CFRP plates.

Carbon Fibre Reinforced Polymer (CFRP) materials are lightweight and corrosion-resistant and therefore are increasingly used in aerospace, automotive ...
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