Investigation of the Zero-crossing Technique in Measurement of Phase Velocities of the Guided Wave...

8/11/2019 Investigation of the Zero-crossing Technique in Measurement of Phase Velocities of the Guided Wave in Thin CFRP

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ISSN 1392-2114 ULTRAGARSAS (ULTRASOUND), Vol. 65, No.4, 2010.

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Investigation of the zero-crossing technique in measurement of phase velocities ofthe guided wave in thin CFRP composite plate

L. Draudvilien, L. Maeika, E. ukauskas

Ultrasound Institute, Kaunas University of Technology,Studentu Str. 50, Kaunas, LITHUANIA. Phone: +370 37 351162. Fax: +370 37 451489.

E-mail: [email protected]

AbstractOne of the main areas for application of the guided waves is inspection of composite materials. These materials usually possess

anisotropy of elastic properties. In order to investigate the possibilities of the developed phase velocity measurement technique based onaccurate measurements of the zero crossing points of ultrasonic signals the numerical modelling of a thin CFRP plate was carried out.The finite element model of the CFRP plate with thickness 0.2 mm, length 100 mm and width 40 mm was created and used in order toobtain the signals for analysis. The A0mode was excited by attaching tangential force and the S0mode by attaching normal force to theone edge of the plate. The width of the excitation zone was 10 mm and it was situated in the center of the plate. The waveform of theexcitation signal was 3 period, 400 kHz burst with the Gaussian envelope. In general, the investigations demonstrated the sameregularities as were obtained on non-homogeneous material and enable to identify different modes in the signals and to reconstruct the

segment of the phase velocity dispersion curve.Keywords:Lamb wave, mode, dispersion curves, phase velocity, zero-crossing technique, non-homogeneous material.

Introduction

In previous our articles [1-4] the phase velocitymethod based on the analysis of zero-crossing point in thesignals of the guided waves was presented. It was shownthat such technique enables to identify at least fundamentalLamb wave modes and to reconstruct the segment of thedispersion curve. As the phase velocity is related to theelastic properties of the materials it can be used for

investigation of different composite structures. Theprevious investigations [1-4] were carried out on thealuminium plate which is homogenous material. Howeverthe composite materials are more complicated and usually

possess the anisotropic acoustic properties. So, theobjective of the work presented was to investigate the

proposed method for analysis of the properties of theguided waves propagating in the composite materials withstrong anisotropic properties.

Object of the investigation

As the object for investigation a thin CFRP (carbon

fibres and epoxy) plate with one directional orientation offibbers was selected. Such plates are used to manufacturevarious components for aerospace or ground transportapplications by gluing them together at different angles. Itis known that the ultrasound velocity of the guided wavesalong and across the fibbers differs more then twice [5]. Inorder to obtain signals for analysis the propagation of theA0 and the S0 modes the 3D finite element model of theCFRP plate was created. The length of the plate was 100mm, width 40 mm and the thickness 0.2 mm. Thedispersion curves of the guided waves propagating alongfibbers direction in plate were calculated using the SAFEmethod [6-8] and are presented in Fig.1.

As can be see the asymmetric A0mode has dispersionin all frequency ranges under analysis. The symmetric S0mode in the same frequency bandwidth possesses very

small dispersion which starts slightly to increaseapproximately from 300 kHz. The an other difference

between A0and S0modes is that the phase and the groupvelocities of the S0 mode are almost the same. At thefrequency 400 kHz the phase velocity is 9510 m/s and thegroup velocity is 9511 m/s. The group velocity of A0modeis bigger then the phase velocity. At the frequency 400 kHzthe phase velocity of the A0 mode is 1040 m/s and thegroup velocity is 1687 m/s. Both of them increase with a

frequency. In Fig.1 the non-dispersive shear horizontal SHmode can be observed also.

Fig.1. The dispersion curves A0,S0and SHmodes propagating in thethin 0,2 mm thickness and 100 mm length CFRP plate

The model of the CFRP plate and obtained signals

The geometry of the 3D model of the CREP plate, thedimensions and the position of the excitation zone are

presented in Fig.2 and 3. The carbon fibbers were oriented

along axisx. The parameters of the CFRP plate used in themodelling are: the density =1570 kg/m3and the elastic

coefficients have been defined by the stiffness matrix

0 100 200 300 400 500 600 700

2000

4000

6000

8000

10000

Central frequency ofthe excitation force

c, m/sThe phase and the groupvelocities of the S0mode

SHmode

The group velocityof theA0mode

f, kHz

The phase velocityof theA0mode


2/5


8

GPaCFRP

=

48.300000

02.70000

002.7000

0009.14446.546.5

00046.559.1363.6

00046.563.659.13

C

(1)

Fig.2. The finite element model for investigation of the A0 mode ofguided waves propagating in thin CFRP plate

Fig.3. The finite element model for investigation of the S 0 mode ofguided waves propagating in thin CFRP plate

The sampling step in the spatial domain wasdx=0.1mm and dt=0.1 s in the time domain. The A0modewas excited by attaching the tangential force (Fig.2) andthe S0mode by attaching the normal force (Fig.3) to the

edge of the plate. The length of the excitation zone was 10mm and it was situated in the centre of the one of the plateedge (Fig.2-3). The waveform of the excitation signal was3 period, 400 kHz burst with the Gaussian envelope. Thewaveform of this signal is presented in Fig.4.

Fig.4. The waveform of the excitation signal

The propagation of the A0and S0modes was modelledduring 70 s time interval. The obtained B-scan images of

the normal component of the particle velocity on the topsurface of the plate in the case of propagating A 0mode arepresented in Fig.5 and in the case of the S0 mode - in Fig.6.

The pattern of the A0 mode demonstrates that the phaseand the group velocities are different and the phasevelocity is smaller than the group velocity. At the distance40-60 mm small reduction of the amplitude of the A0modecan be observed. Probably it can be caused by thediffraction due to a limited length of the excitation zone.The S0mode of the Lamb waves is about five times fasterthan the A

0 mode and during the same modelling time

several times reflected by the plate edges. In Fig.6 the Bscan is zoomed in order to show only directly propagatingwaves (without reflections). The reflected waves werefiltered using 2D Fourier transform. It can be seen also thattogether with the S0 mode some the other much slowermode is generated. It can be assumed that it is the SHmode(Fig.6).

Fig.5. The B-scan image of the normal component of the particle

velocity on the surface of the plate in the case of generated A0mode

Fig.6. The B-scan image of the normal component of the particlevelocity on the surface of the plate in the case of generated S0mode

Analysis of the signals

The signals obtained by modelling were analysed

using the same method based on the zero-crossingtechnique and described in [1-4]. The obtained phasevelocities of the A0 mode at the different distances are

x

z

y

CFRP plate

Excitationzone

100 mm40 mm

x

z

y

CFRP plateExcitation

zone

100 mm40 mm

0 2 4 6 8 10 t, s

-0.8

-0.6

-0.4

-0.20

0.2

0.4

0.6

0.8

U(t)a.u

x, mm

t, s

80

60

40

20

0 10 20 30 40 50 60

t, s

x, mm

80

60

40

20

0 102 4 6 8 12 14 16 18


3/5


4/5


10

Fig.11. The phase velocities of the A0 mode Lamb wave in 0.2mm

thickness CFRP plate obtained using simulated signals andSAFE dispersion curve

Fig.12. The phase velocity of the S0mode of Lamb wave measured atdifferent distances using different zero-crossing points: 1-6 arethe numbers of zero-crossing point in the signal used for thedelay time estimation

The estimated equivalent frequencies of the S0 modedemonstrate increase versus distance also (Fig.13).However, comparing with the A0mode this dependency isdifferent, not so linear. On the other hand the variation ofthe equivalent frequency in the signal demonstratesopposite dependency with respect to with the A0 mode -the equivalent frequency increases for the later half periods

of the signal (Fig.14). Of course this dependency is not sostrongly expressed due to the very small dispersion of theS0mode in the frequency ranges under analysis. The smallincrease of the central frequency of the signal with thedistance can be observed also (Fig.15). The combination ofthe measured phase velocities and the equivalentfrequencies in one figure (Fig.16) gives the segment ofdispersion curve. In the case of the S0 mode somesystematic shift can be observed also the measuredvalues of the phase velocity are higher then the phasedvelocities obtained using the SAFE method. However theresults are distributed in more narrow frequency rangescomparing to the A0mode due to the week dispersion of

the S0mode phase velocity.

Fig.13. The equivalent frequencies of different half periods of thesignal: 1-5 are the numbers of the half period

Fig.14. Variations of the equivalent frequency of the different halfperiods in the case of the S0 mode signal at the distance50mm obtained using modelling signals.

Fig.15. The frequency spectrum of the S0mode: the solid line (1) thesignal is on the 1 mm distance and the dotted line (2) thesignal is on the 50 mm distance

1 2 3 4 5421

422

423

424

425

426

427

428

Number of half period in the signal

( )xf 5.0 ,kHz

S0

0 100 200 300 400 500 600 700 800 900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

U (f)

f, kHz

1 2

Analyzed frequencyrange is 400 kHz

300 350 400 450 500900

950

1000

1050

1100

1150

cA0,m/s

f, kHz

SAFE dispersion curve

Obtained using zero-crossing technique

20 30 40 50 60 70 80 90410

415

420

425

430

( )xf 5.0 ,

x, mm

1

2

3

45

20 30 40 50 60 70 80 909000

9500

10000

10500

11000

cph,

m/s

x, mm

1

2

3

4

5

6


5/5


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Fig.16. The phase velocities of S0 mode Lamb wave in 0.2mmthickness CFRP plate obtained using simulated signals andSAFE dispersion curve

Conclusions

In general the application of the phase velocitymeasurement technique applied for the anisotropic CFRP

plate demonstrated similar regularities as were obtained onthe isotropic aluminium plate. In both cases somesystematic mismatch between results obtained using the

proposed technique and the results obtained using SAFEmethod was observed.

The most reliable property which enables to identifydifferent modes is distribution of the equivalentfrequencies in the signal.

The results demonstrated also that the phase velocitydispersion curve is reconstructed in wider frequency ranges

if the mode under analysis possesses stronger dispersion inthat frequency ranges. So, contrarily to other techniquesthe proposed method is more suitable for measurements inthe frequency ranges with a stronger dispersion.

References

1. Maeika L., Draudvilien L., ukauskas E. Influence of thedispersion on measurement of phase and group velocities of Lambwaves. Ultrasound. 2009. Vol.64. No.4. P.18-21.

2. Maeika L., Draudvilien L. Analysis of the zero-crossingtechnique in relation to measurements of phase velocities of theLamb waves. Ultrasound. 2010. Vol.65. No.2. P.7-12.

3. Draudvilien L., Maeika L. Analysis of the zero-crossingtechnique in relation to measurements of phase velocities of the S 0mode of Lamb waves. Ultrasound. 2010. Vol.65. No.3. P.11-14.

4. Maeika L., Draudvilien L., Vladiauskas A., Jankaukas A.Comparison of modelling and experimental results of the phasevelocity measurements of Lamb wave in aluminium plate.

Ultrasound. 2010. Vol.65. No.3. P.15-19.5. Raiutis R., Kays R., ukauskas E., Maeika L. Vladiauskas A.

Application of ultrasonic guided waves for non-destructive testing ofdefective CFRP rods with multiple delaminations. NDT & EInternational Volume 43, Issue 5, July 2010, Pages 416-424.

6. Takahiro Hayashi, Won-Joon Song, Joseph L. Rose. Guided wavedispersion curves for a bar with an arbitrary cross-section, a rod andrail example. Ultrasonics Volume 41, February 2003, Pages 175-183

7. Marzani A., Viola E., Bartoli I., Lanza di Scaleea F., Rizzo P. Asemi-analytical finite element formulation for modeling stress wavepropagation in ax symmetric damped waveguides, Journal of Soundand Vibration 2008, 318 (3), 488-505.

8. Hayashi T. Guided wave animation using semi-analytical finiteelement method, 16th WCNDT 2004world conference on NDT;2004. P.18.

DraudvilienL., Maeika L., ukauskas E.

Perjimo per nulmatavimo metodo tyrimas matuojant nukreiptjbangfazingreit, signalui sklindant plona anglies pluoto (CFRP)ploktele

Rezium

Viena i pagrindini srii, kurioje nukreiptosios bangos gali btitaikomos, yra kompozicins mediagos. Jos daniausiai turi anizotropinisavybi. Siekiant vertinti fazinio greiio matavimo metodo, pagrstosignalo perjimo per nullaiko momento nustatymu, galimybes tokiomsmediagoms tirti, buvo atlikti matavimai. Tam naudoti baigtinielementmetodu gauti kompozicine mediaga sklindanios bangos signalai.Tyrimo metu buvo modeliuojamas nukreiptj bang A0 ir S0 modsklidimas 100 x 40 mm matmen, 0,2 mm storio anglies pluoto (CFRP)

ploktele. Bangoms adinti buvo naudojamas prastas ultragarsinineardomjbandym400 kHz Gauso gaubtins signalas. Tyrimai parod,kad nukreiptj bang fazinio greiio matavimo duomen analizsmetodas galina atkurti skirting mod dispersini kreivi segmentusnagrinjamame dani diapazone ir identifikuoti sklindani Lembobangmodas.

Pateikta spaudai 2010 12 10

400 410 420 430 4408000

8500

9000

9500

10000

10500

11000

cS0,m/s

f, kHz

Obtained zero-crossing points

SAFE dispersion curve

Investigation of the Zero-crossing Technique in Measurement of Phase Velocities of the Guided Wave...

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