Dynamic characteristics of thermoplastic composite laminates

Dynamic characteristics of thermoplastic composite laminates I. LEE, B.N. KIM and K.N. KO0 (Korea Advanced Institute of Science and Technology, Korea) Received 16 June 1993; revised 9 July 1993

Dynamic characteristics of carbon fibre/polyetheretherketone (CF/PEEK) composites have been investigated by the impact test and the sinusoidal free vibration test. Using a cantilevered beam with rectangular cross-section, the natural frequencies and damping properties were measured. Also, dynamic tests for the cantilevered beam with a torsional bar have been performed to identify the shear modulus and damping in torsional motion. Results for the specific damping capacity given by the impact test are very close to those given by the sinusoidal vibration test. The elastic moduli from the impact test are slightly smaller than those from the tension test. The dynamic characteristics of angle-ply, cross-ply and quasi-isotropic laminates have been computed by the finite element method. For the purpose of verification, experimental tests were carried out by the impact test for these laminates. The experimental values are very close to the numerical values. In addition to CF/PEEKcomposites, experiments have been performed for CF/epoxy composites. The damping of CF/epoxy is much larger than that of CF/ PEEK. Key words: CF/PEEK; elastic moduli; impact test; specific damping capacity Dynamic characteristics of structures near the resonant frequency are very sensitive to their damping properties. Therefore, damping has a large influence on the response of the structures when repeated loads and impact loads act upon them. Since air damping is not present in outer space, the role of structural damping becomes very important for space structures. The damping of a matrix is much higher than that of a fibre due to the viscoelastic behaviour of the matrix, a common property in most composite materials except aramid composites. Depending upon the type of matrix, fibre-reinforced composites are classified into thermoset composites and thermoplastic composites. Many studies on damping have been carried out for thermoset composites. Recently, the development of thermoplastic composites having good fracture toughness has led to studies on their material properties and dynamic characteristics. Since Schuitz and TsaY first performed dynamic testing by sinusoidal free vibration, this experiment has been used for composite plates with various boundary conditions. Clary 2 studied the vibration characteristics of boron/epoxy panels in a free-free state, and Adams and Bacon 3-5 performed theoretical and experimental studies using a beam with a central mass. The previous investi-

gations are examples of measuring dynamic properties by use of the sinusoidal free vibration test. Lin e t al. 6 obtained the damping characteristics of carbon fibre-reinforced and glass fibre-reinforced plastics by the impact test. Suarez and co-workers7,s performed the extensional vibration test as well as the flexural vibration test to obtain the damping properties and studied how the frequency and the fibre orientation affect damping. In this paper, the dynamic properties of CF/PEEKthermoplastic composite, comprising AS4 carbon fibres (CF) and polyetheretherketone (PEEK) thermoplastic resin, are measured by use of both the impact test and the sinusoidal vibration test. In addition, experimental results obtained from the impact test are compared with numerical values predicted using the finite element method for laminates with various stacking sequences.

BASIC THEORIES The damping o f a material is defined in various ways depending on the testing method, all of them necessitating a dynamic test. The relations among various definitions are as follows:

0010~,361/94/040281-06 © 1994 Butterworth- Heinemann Ltd COMPOSITES. VOLUME 25. NUMBER 4. 1994 281

E* E*R -- tan 7 = 2 ( -

2 z co2_2~ . - co~

(1)

500

where r/ is the loss factor, @ is the specific damping capacity (SDC), E* and E* are the real part and the imaginary part of complex modulus, ?'is the loss angle, ( is the damping rate, COland (o2 are the frequencies of halfpower points and CO,is the resonant peak frequency.

4O0

1/ - 2Jr -

To obtain the damping characteristics by the sinusoidal free vibration test, a sinusoidal exciting force with resonant frequency is. applied to the specimen. After the steady-state sinusoidal force is suddenly removed, the decay rate of free oscillation may be measured by the logarithmic decrement: & = 1 In x0 n x,,

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E 0.5MPo

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0.5

i 5 min. I 5 min. I -F I

0

1.0

0.0

Tlrne

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Processing cycle for CF/PEEK

(2) 1

Ip = ~ bh(b 2 + M)

where x0 and x, are the amplitudes measured n cycles apart. For small damping, the darning rate ( m a y be approximated by: & ~"- 2tc

(3)

This method does not require any signal processing procedure and the damping is obtained easily so long as the amplitude ratio is given in the time domain. To measure the elastic modulus, the resonant frequency is obtained from flexural tests of the composite beam by applying impact force and sinusoidal harmonic force. For a cantilevered beam, the Young's modulus of isotropic materials can be calculated using the Euler beam theory as follows: E-

48:n:2pf214 h2~z4

(4)

where p is the mass density, h is the thickness, l is the length of the specimen and ~ is the characteristic value of the cantilevered beam. Equation (4) refers to flexural tests for isotropic materials. For anisotropic materials, E~ is obtained from the flexural test of a 0 ° specimen in which the fibres are arranged in the longitudinal direction. E2 is obtained from the flexural test of a 90 ° specimen in which the fibres are in the transverse direction. Since the influence of transverse shear deformation and rotary inertia on the resonant frequency may be significant owing to the high Ei/Gi2 ratio for a 0 ° specimen, Equation (4) may lead to considerable errors for very thick beams. The length-to-thickness ratio of the composite beams in this work was taken to be higher than about 100, and the specimens for the flexural tests are considered to be thin beams. The shear modulus is measured using the torsional vibration test in this study. If the centre of mass is located in the axis of rotation and the warping of the cross-section is neglected, the shear modulus can be obtained as9: (5)

G = 47r2f2plp12 J/32

where Ip is the polar moment of inertia, J is the torsional constant of the cross-section and /3 is the characteristic value of the bar. For the specimen with thickness h and width b, Ip, J and/3 are defined as:

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COMPOSITES.

NUMBER 4. 1994

j-

b3h 3 3(b 2 + M)

/3- (2i-

l)Jr

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1,2,3,

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Equation (5) refers to torsional tests for isotropic materials. This equation can be applied to anisotropic materials but may have some errors since the torsional rigidity will involve contributions from Gl2 and G23 for rotation about an axis perpendicular to the fibre direction. EXPERIMENTAL DETAILS Specimen m a n u f a c t u r e

CF/PEEK laminates were fabricated according to the processing cycle shown in Fig. 1 in a hot press under the control of temperature and pressure. Because the crystalline structure of PEEK depends largely on the cooling rate, moderate conditions must be held during the cooling process. Laminates comprised eight plies of ICI APC-2 prepreg tape and test specimens were cut from these laminated plates. Dynamic material properties were measured for [0]Byand [9018T specimens. For the purpose of verification, [02/902] s cross-ply laminates, [452/- 452]s angle-ply laminates and [0/+45/90], quasi-isotropic laminates were manufactured. Also, H F G ~ CF/epoxy [0]By and [9018T thermoset composites were cured. Set - up

In this work, flexural and torsional vibration tests were performed to obtain the dynamic characteristics of CF/ PEEK. Young's modulus and material damping in the longitudinal and transverse directions were obtained from the flexural vibration test. Shear modulus and the damping related to shearing were obtained from the torsional vibration test. The flexural vibration test is performed both by applying an impulsive force with an impact hammer and by giving a sinusoidal force with a magnetic transducer. A diagram of the impact test set-up is given in Fig. 2. The excitation force from the impact hammer and the response displacement from the non-contacting capacitive probe are fed into a fast Fourier transform (FFT) analyser. The

placement increases suddenly and can be observed by the oscilloscope. After the steady-state vibration in resonance has been reached in some time, the function generator is turned off, resulting in the free vibration state. Triggering this response and using the logarithmic decrement, the damping is measured. To make the same condition in excitation, input power and initial displacement between the specimen and the probe are kept constant.

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The clamping effect can give rise to lowering of apparent moduli in the flexural tests, and increasing effective sample length and warping effect in torsion tests ~°. Therefore, there is a possibility of some errors in bending and torsion tests if the clamping effect is not considered.

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The torsional vibration test is performed by both the impact and sinusoidal torsion tests like the flexurai vibration test. If the torsional mode of the is obtained by hitting the [9018T specimen with the impact hammer, the resonant frequency and the damping can be obtained by STAR MODAL T M software. To measure the damping from the sinusoidal torsion test, the torsional bar is attached to the end of the specimen to give a large rotating moment of inertia and a low resonant frequency. A diagram of the sinusoidal torsion vibration test is shown in Fig. 4. Both ends of the torsional bar are excited by magnetic transducers. The displacement of the torsional bar is measured by the capacitive probe. The torsional damping is measured using logarithmic decrement.

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After polishing the cross-section of the specimen, the fibre volume fraction was obtained by the area method and the line method. Although there was some difference among specimens due to processing conditions, the fibre volume fraction is about 65%.

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Fig. 3 Experimental set-up for sinusoidal vibration test

non-contacting capacitive probe does not require any additional mass-like accelerometer. If input force and output displacement signals are put into the FFT analyser, the frequency response function (FRF) is obtained by Fourier transform. Using the curve fitting process in the STAR MODAL T M software of Structural Measurement Systems, the resonant frequency and damping are obtained. A diagram of the sinusoidal flexural vibration test is shown in Fig. 3. The sinusoidai signal from the function generator is amplified by the power amplifier and input into the magnetic transducer, which transforms the electric signal into a magnetic force. Because the composite specimen does not have magnetism, a high-/1 disc (which is a ferromagnetic body) must be attached to the tip of the specimen. The response displacement is measured by the non-contacting capacitive type probe as in the impact test. In the vicinity of the resonant frequency, the dis-

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COMPOSITES . N U M B E R 4 . 1994

283

Table 1. Elastic modulus and specific damping capacity of CF/PEEK [0]st specimens in the longitudinal direction Impact test Specimen size, Ix bx t ( m m 3) 125.2 119.8 115.2 110.3 105.5

× x x x x

19.0 19.0 19.0 19.0 19.0

x x x x ×

1.07 1.07 1.07 1.07 1.07

Sinusoidal vibration test

Modulus, E1 (GPa)

SDC, I//1 (%)

Frequency, f(Hz)

SDC, ¢1 (%)

Frequency, f(Hz)

115.3 115.7 11 5.0 115.6 115.5

0.636 0.622 0.630 0.662 0.626

94.34 103.19 111.26 121.70 133.16

0.639 0.633 0.632 0.672 0.669

88.5 95.3 105.3 113.3 125.0

Table 2. Elastic modulus and specific damping capacity of CF/PEEK [90]st specimens in the transverse direction Impact test Specimen size, / x b x t ( m m 3) 125.0 120.0 11 5.0 11 0.0 105.0

x x x x x

19.5 19.5 19.5 19.5 19.5

× x x x x

1.06 1.06 1.06 1.06 1.06

Sinusoidal vibration test

Modulus, E2 (GPa)

SDC, ~2 (%)

Frequency, f(Hz)

SDC, ~2 (%)

Frequency, f(Hz)

9.54 9.48 9.48 9.37 9.44

2.169 2.226 2.163 2.157 2.123

26.80 28.98 31.55 34.27 37.73

2.140 2.1 26 2.134 2.071 2.138

25.0 27.0 29.4 31.9 35.2

Table 3. Shear modulus and specific damping capacity of CF/PEEK [0]sT specimens Impact test Specimen size, /x b x t ( m m 3) 125"(60) 120(55) 115(50) 110(45) 105(40)

× 19.5 x 1.06 x 19.5 × 1.06 x 19.5 × 1.06 x 1 9.5 x 1.06 x 19.5 x 1.06

Sinusoidal vibration test

Modulus, 612 (GPa)

SDC, ~P12(%)

Frequency, f(Hz)

SDC, i/)'12 (%)

Frequency, f(Hz)

5.61 5.60 5.61 5.61 5.65

2.299 2.330 2.341 2.370 2.345

410.36 427.15 446.35 466.65 490.79

2.241 2.279 2.339 2.21 2 2.303

22.5 23.8 25.7 28.2 31.3

*/= 125 for impacttest, 60 for sinusoidalvibrationtest Measurement of moduli

For the purpose of measuring the modulus and damping, [0]87 specimens and [9018T specimens were fabricated and tested; experimental results are shown in Tables 1-3. The reason for the variation of specimen size is that the temperature (390°C) and the pressure (2 MPa) in processing CF/PEEK are so high that it is difficult to obtain laminates with uniform thickness and aligned fibres. The elastic modulus of the CF/PEEK [0]8 T specimen is 115 GPa. The specific damping capacities of CP/PEEK were measured by both the impact test and the sinusoidal vibration test. The SDC of the CF/PEEK [018T specimen obtained from the sinusoidal vibration test is slightly higher than that obtained from the impact test. On the other hand, the natural frequencies of CF/PEEK [018x specimens from the sinusoidal vibration test are much lower than those from the impact test because the specimens used in the sinusoidal vibration test have an additional tip mass of high-p disc. The natural frequencies in the same test (sinusoidal or impact) are different depending on the specimen length, l.

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COMPOSITES . NUMBER 4 . 1994

The elastic modulus and the specific damping capacity of CF/PEEK [9018Tspecimens are given in Table 2. The elastic modulus in the transverse direction (E2) is much less than that in the fibre direction (E0, as expected. The SDC in the transverse direction (~/2) is much higher than that in the fibre direction (~/~). The SDC of CF/PEEK [9018v specimens obtained from impact test is very close to that obtained from the sinusoidal vibration test. The shear modulus and specific damping capacity of CF/ PEEK [018T specimens are given in Table 3. The shear modulus G~2 is about 5.6 GPa. The SDC obtained from the impact test is close to that from the sinusoidal vibration test. Table 4 summarizes the above results and also presents the dynamic properties of CF/epoxy. Young's modulus by the impact test is slightly lower than that by the static tension test based on ASTM D3039-76 for E~ and E2, and ASTM D3039 for G~2 (Reference 11). While the modulus by the tension test is measured by applying tensile stress without compressive stress, the modulus by the impact test is obtained by simultaneous action of tensile and compressive stresses. Furthermore, the

Table 4. Material properties of CF/PEEK and CF/epoxy CF/PEEK Material property

CF/epoxy

Tension test

Impact test

Sinusoidal vibration test

Impact test

130.0 10.3 5.45 0.33

114.0 9.42 5.63 1575

-

148.9 9.52 6.29 1548

~1 (%) ~2 (%)

-

~12 ( % )

--

0.626 2.147 2.320

0.651 2.105 2.227

0.586 3.717 5.588

E1 (GPa) E2 (GPa) GlZ (GPa) v12 p (kg m -3)

Table 5. Resonant frequency and specific damping capacity of CF/PEEK [02/902], laminates Resonant frequency (Hz) Specimen size, / x b x t (mm 3)

SDC, ~0 (%)

Mode no

FEM

Exp

FEM

Exp

125 x 19.7 x 1.08

1B 1T

89.65 460.17

91.72 456.31

0.646 2.126

0.626 1.955

120 x 19.7 x 1.08

1B 1T

92.78 481.66

98.53 474.49

0.646 2.117

0.631 1.954

115 x 19.7 x 1.08

1B 1T

105.92 505.25

106.31 494.14

0.646 2.1 08

0.649 1.978

Table 6. Resonant frequency and specific damping capacity of CF/PEEK [452/-45z], laminates Resonant frequency (Hz) Specimen size, / × b × t ( m m 3)

SDC, ~k (%)

Mode No

FEM

Exp

FEM

Exp

135 × 19.6 x 1.11

1B 2B

34.55 220.24

35.38 220.79

1.864 1.847

1.865 2.048

130 × 19.6 x 1.11

1B 2B

37.31 237.77

37.82 235.61

1.872 1.856

1.932 1.91 6

125 x 19.6 x 1.11

1B 2B

40.41 257.47

41.19 255.79

1.868 1.852

1.903 2.037

120 × 1 9.6 × 1.11

1B 2B

43.91 279.72

45.44 281.43

1.864 1.847

1.865 2.048

clamping effect and dimensional instability due to high temperature and pressure in processing can cause some errors in both results. Shear modulus by the impact test is higher than that by the tension test. If Equation (5) is used o evaluate the shear modulus, the estimated value from the impact test becomes higher than the actual modulus because of several assumptions involved in Equation (5). The damping of CF/epoxy in the transverse direction (¢2) is much higher than that of CF/PEEK due to the property of the matrix.

Verification using laminates with various stacking sequences Experimental results were compared with those of the finite element method based on the first-order shear deformable theory 12. The finite element analysis of crossply, angle-ply and quasi-isotropic laminates was per-

formed by utilizing the measured dynamic material properties: El, E2 and G~2 from the impact test, v12 from the tension test and G23 computed by the following equation: G23 -

E) 2(1 +-v:3)

v23 ~ 0.5

(7)

The damping value by the finite element method is obtained from the specific damping capacity which is defined as the ratio of the energy dissipated during a cycle to maximum strain energy. Experimental values were obtained from the impact test. Numerical and experimental values for the resonant frequency and SDC of laminates with various stacking sequences are given in Tables 5-7. In these tables, 1B and 2B represent the first and the second bending mode and 1T represents the first torsional mode. The variation between the two values is about 3% in the resonant

COMPOSITES . N U M B E R 4 . 1994

285

Table 7. Resonant frequency and specific damping capacity of CF/PEEK [O/+ 45/90], laminates Specimen size, / x b x t (mm 3)

Resonant frequency (Hz)

SDC, ~p (%)

Mode no

FEM

Exp

FEM

Exp

125 x 1 9.8 x 1.07

1B 2B

76.78 487.71

77.06 478.94

0.776 0.782

0.805 0.698

120 x 1 9.8 x 1.07

1B 2B

83.32 529.15

83.17 518.32

0.776 0.782

0.809 0.743

11 5 x 1 9.8 x 1.07

1B 2B

90.74 576.07

90.27 564.00

0.775 0.783

0.811 0.728

frequency and about 5% in the SDC. Among [02/902]s, [452/- 452]s and [0/+ 45/90]s specimens, the [452/- 452], specimen has the highest damping and the lowest natural frequency in the first bending mode. The [02/902]s specimen has the lowest damping and highest natural frequency in the first bending mode. The damping in the first torsional mode of the [02/902]~ specimen is almost 3.27 times higher than that in the first bending mode. CONCL USIONS

Through the dynamic testing of CF/PEEK, a database has been established to help redress the current lack of data on material properties of thermoplastic composites compared with thermoset composites. Damping properties obtained from the impact test and from the sinusoidal vibration test are in a good agreement; however, the modulus determined from the impact test is slightly different from that determined from the tension test. The discrepancy may be explained by the clamping effect, the different stress condition in bending such as tension and compression, and dimensional instability stemming from processing difficulties. The natural frequency and specific damping capacity from the finite element method based on first-order shear deformable theory are very close to the experimental results. Because of the property of the matrix, ~2 and ~#12of CF/epoxy are much larger than those of CF/PEEK. REFERENCES 1 Schultz, A.B. and Tsai, S.W. 'Dynamic moduli and damping ratios in fiber-reinforced composites' J Composite Mater 2 (1968) pp 368-379 2 Clary, R.R. 'Vibration characteristics of unidirectional filamentary composite material panels' Composite Materials Testing and

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3 4 5 6

7 8

9 l0 11

12

Design, A S T M STP 497 (American Society for Testing and Materials, Philadelphia, 1972) pp 415-438 Adams, R.D. and Bacon, D.G.C. 'Measurement of the flexural damping capacity and dynamic Young's modulus of metals and reinforced plastics' J Phys D: Appl Phys 6 0973) pp 27-41 Adams, R.D. and Bacon, D.G.C. 'The dynamic properties of unidirectional fiber-reinforced composites in flexure and torsion' J Composite Mater 7 (1973) pp 53~7 Adams, R.D. and Bacon, D.G.C. "Effect of fiber orientation and laminate geometry on the dynamic properties of CFRP' J Composite Mater 7 (1973) pp 402-428 Lin, D.X., Ni, R.G. and Adams, R.D. 'Prediction and measurement of the vibrational and damping parameters of carbon and glass fibre-reinforced plastics plates' J Composite Mater 18 (1984) pp 132-152 Suarez, S.A., Gibson, R.F., Sun, C.T. and Chaturvedi, S.K. 'The influence of fiber length and orientation on damping and stiffness of polymer composite materials' Exptl Mech 26 (1985) pp 175-184 Suarez, S.A. and Gibson, R.F. 'Improved impulse-frequency response techniques for measurement of dynamic mechanical properties of composite materials' J Testing and Eva115 (1987) pp 114-121 Blevins, R.D. Formulas for Natural Frequency and Mode Shape (Van Nostrand Reinhold Co, New York, 1979) Read, B.E. and Dean, G.D. The Determination of Dynamic Properties of Polymers and Composites (Halsted Press, New York, 1978) Hong, C.S., Lee, I., Ira, S.Y., Lee, K.Y., Earmme, Y.Y. and Song, J.H. 'Fabrication and mechanical characterization of high toughness thermoplastic composite laminates' KOSEF CR 89-04-05-02 (Korea Science and Engineering Foundation, 1992) Koo, K.N. and Lee, I. 'Vibration and damping analysis of composite laminates using shear deformable finite element' AIA.4 J 31 (1993) pp 728~35

AUTHORS

The authors are with the Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea. Correspondence should be addressed to Professor Lee.