- Email: [email protected]
Experimental analysis of porosity-induced ultrasonic attenuation and velocity change in carbon composites
Experimental analysis ultrasonic attenuation in carbon composites H. Jeong”
of porosity-induced and velocity change
and D. K. Hsu
Center for Nondestructive
Evaluation,
Iowa State University,
Ames, IA 50011,
USA
Accepted 3 1 December 1994 In this paper, ultrasonic measurement results are presented for analysing the wave propagation in carbon fibre reinforced plastics (CFRP) containing voids. The composite samples studied include laminates fabricated from unidirectional and woven fabric prepregs. The ultrasonic methods stress the utilization of spectral analysis and frequency dependence of the attenuation and phase velocity due to porosity. Morphological parameters of pores are found to play an important role in the proper interpretation of measured data. The measured attenuation shows approximately linear behaviour over the frequency range used. The corresponding phase velocity decreases substantially with increasing void content. In addition, the velocity in porous CFRP is found to be more dispersive than that in void-free composites. The relationship between the ultrasonic attenuation and dispersion is subsequently tested using the local form of the Kramers-Kronig relation. The linear relationship between the void content and the attenuation slope (da/do is found to hold, but the constant of proportionality is quite different for samples with different pore morphology. This morphology has a large effect on the dispersion of phase velocity. The fractional velocity decrease (AVIV,,) is correlated with the void content, and its dependence on the frequency and void shape is discussed. The present analysis will aid in the model development of wave propagation in porous composites for detecting and characterizing the porosity in these materiak. Keywords: carbon fibre Kramers-Kronig relations;
composites; attenuation
The presence of voids (or porosity) in composite laminates has noticeable effects on ultrasonic attenuation since voids are strong scatterers for elastic waveslP4. The correlation between attenuation and void content in carbon fibre reinforced composites is well known: greater void content causes increased attenuation and the increase is greater at higher frequencies. By manufacturing standards with known void contents, the void content of a particular system of composite can be quantitatively measurement procedures were evaluated. Recently, developed to obtain the ultrasonic attenuation as a function of frequency using broadband pulses, and correlation between the attenuation slope, or dx/dj-, and the void volume fraction has been established5*6. Little emphasis, however, has been given to the corresponding dispersion, which is a necessary consequence of the attenuation. When an elastic wave propagates in a porous composite material, the ultrasonic velocities generally depend on the void characteristics and the constituent material properties as well as on the frequency. *Present address: YuSeong,
DaeJon,
Agency Korea
for
0041-624X/95/$09.50 0 1995 SSDI 0041-624X(95)00023-2
Defense
Development,
PO Box
35,
pore morphology; wave slope; velocity change
propagation;
Considering the presence of voids in the matrix, increasing the void content decreases the longitudinal and shear wave velocities. This is due to a decrease of the effective elastic stiffnesses of the composite with increasing void content. Several investigators have attempted to use ultrasonic velocities as a measure of void content in carbon fibre reinforced plastics7.8. However, they assumed low frequencies, or equivalently, small void size; so that the frequency dependence of phase velocity (dispersion) was ignored. If the wavelength is of the same order of magnitude as a characteristic dimension of voids, one would expect a large frequency range over which the medium should show velocity dispersion. Dispersion effects are shown by the frequency dependent ultrasonic velocities. A pulse, being a superposition of many frequencies, will change its shape as it propagates through a dispersive medium. The ultrasonic attenuation and dispersion due to scattering are not independent according to Kramerss Kronig (K-K) relations’. The validity of this relationship rests only on the linear and causal properties of the system, which is true for a realistic model. The K-K relations have been successfilly applied by Beltzer and coworkers” for studying the wave attenuation and
- Elsevier Science B.V. All rights reserved Ultrasonics
1995 Vol 33 No 3
195
Porosity-induced
attenuation and velocity change: H. Jeong and D. K. Hsu
dispersion in fibrous composites. Recently, Gross and Zhang ” have extended this causal approach to wave propagation in solids containing cracks. When experimental results of both attenuation and phase velocity are available, their mutuai compatibility can be checked. Voids arising from trapped air during the fabrication process of CFRP are, in general, very complicated in nature. The size and shape of voids in CFRP have been described in several ultrasonic studies’*12. Stone and Clark found that the voids tend to be small and spherical at low porosity volume fractions (less than 1.5%) and at high volume fraction the interlaminar voids tend to be much larger and flattened and elongated in shape. Yuhas also found that the voids are roughly cigar-shaped and increase in size with increasing volume fraction. Since most composite materials for structural applications are of the laminated type, the morphological features also depend on the fibre layout of prepreg tapes. Thus, the wave propagation in porous composite laminates cannot be complete without detailed morphological knowledge of pores. In this paper, we investigate the effect of porosity on the ultrasonic attenuation and phase velocity of carbon fibre reinforced composites. Since voids bring about the large amount of attenuation due to scattering, ultrasonic measurements are made in an immersion tank using a substitution technique in the through-transmission mode. By introducing a complex wave-number, expressions are obtained for calculating the phase velocity and attenuation of longitudinal waves propagating normal to the plane of composite laminates. The frequency dependent velocity and attenuation are obtained from the spectral analysis of broadband pulses acquired without and with the sample in the propagation path. Morphological features of pores are examined using microscopy and image analysis, and the pore shape parameters are used to interpret the wave propagation characteristics in these samples. The phase velocity is also obtained from the measured attenuation data through the K-K relation given in its local form’. A quantitative correlation between void content and attenuation slope, as well as the fractional velocity decrease, is then established. The effect of void shape on the linear relationship between the attenuation slope and void content is investigated. In addition, the dependence of the fractional velocity decrease on the frequency and void shape
related to the frequency-dependent These relations can be written as k(w) = 244
12(o).
+ ia
(1)
The objective here is to derive expressions for V(o) and X(O) of the material with large attenuation and dispersion. Consider a composite laminate of thickness h immersed in water. In through-transmission testing, the sample velocity and attenuation can be obtained by specifying the waveform in the propagation path without and with the sample. The pulse transmitted through water alone is used as the reference signal, while the first transmitted pulse with the sample inserted between two transducers is used as the sample signal. Figure I shows the measurement configuration of a substitution method. A broadband longitudinal pulse u(x, t) propagating in the positive x direction can be expressed as a linear combination of all plane harmonic waves’3v’4, that is I i(kx -ml) do U(X,t) = JF,(o) e (2) 277I -1 where F,(o) is the Fourier transform of ~(0, t). It is assumed that water behaves in a non-attenuative, non-dispersive manner, i.e. the wave number k, is real and the phase velocity o, = o/k, is a constant. Referring to Figure la, the transmitted field of the reference signal at x = L can be written as 21c _z [F,(o)D,(o) u,(L, t) = J-
eiwLio*]eCiwrdo
(3)
s 3(
where D,(w) is the diffraction correction. The term inside
I
T
+L ’
=-I
a X t-
is discussed.
-+I-
Theory
When ultrasonic pulses, being a superposition of many different frequencies, propagate in porous composites, scattering by voids causes the attenuation and the
1
corresponding dispersion of waves. For the analysis of composite materials containing voids, we assume that
the solids comprise a linear system, and they are capable of supporting a one-dimensional plane wave of the form where k(w) is the effective wave-number and w e i(k(o)-‘-w’), is the circular frequency of the incident wave. To describe the above behaviour one can define a complex wave-number k(o), where the real part is a dispersive part related to the frequency-dependent phase velocity, L’(U)),while the imaginary part is an attenuative part
196
attenuation,
Ultrasonics
1995
Vol 33 No 3
R
b
Figure 1 Measurement configuration for the substitution method: (a) for reference waveform acquisition; (b) for sample waveform acquisition
Porosity-induced
attenuation and velocity change: H. Jeong and 0. K. Hsu
the bracket is the Fourier transform of u,(L, r) so that F(u,(L, t)) = F(o) = F,(w)D,(w) eiWLjV*
interface losses due to transmissions and is given as (4)
The specimen is now inserted in the water path and the signal due to the first transmission is recorded as the sample signal. We consider a relatively thick specimen such that all transmitted pulses of the sample can be clearly separated from each other in the time domain. Referring to Figure 16, and with Equation (l), the Fourier transform of the sample signal u,(L, t) can be expressed as F(u,(L, t)) = G(o) = F,,(w)T(w)D,(o) e-n,h eior(L-h)“‘N+h’r~l (5)
where qw) is the interface losses due to transmissions, D,(o) is the diffraction correction, and ~1,and u, are the frequency dependent attenuation and phase velocity of the sample, respectively. Then, from Equations (4) and (5) G(U) qo)~z(o) e-a& eioh(l/o>- l/r,,) -= (6) D,(o) F(o) Since the influence of diffraction on the phase shift of the ultrasonic signal is known to be small, one can disregard the phase correction due to diffraction in the calculation of phase velocity. The sample phase velocity can be obtained from the difference in the phase spectra of reference and sample waveforms. If the phase spectra of F(w) and G(w) are denoted as - 4, and - 4,, respectively, one can get - c#&o) + &(o) = -A&o)
04%v 1
= oh L[
i
(7)
to yield
vs(-)=(;_!g)-’
R-3)
T(o) =
4Z,Z,(w) IIZ, +
(14)
4k412
where Z, = pwv, and Z,(o) = p,o,(o) are the acoustic impedances of water and sample, respectively.
Experiments Both the phase velocity and attenuation measurements are made with the same experimental set-up. Two nominally identical broadband transducers are set up in an immersion tank to face each other and are separated by a distance of typically 15 cm. The transducers used are 6.35 mm (l/4”) diameter unfocussed probes with nominal centre frequencies of 10 MHz. To get the broadband pulse, one transducer is excited by a spike voltage pulse produced by a Panametrics 5052PR pulser/receiver and the other is connected to the receiver. The signal from the receiving transducer is acquired by digital sampling in a LeCroy 9400 digital oscilloscope, averaged over one-hundred times to increase the S/N ratio, and transferred to file storage in a computer, where further processing is performed. The ultrasonic pulse transmitted through water, in the absence of the composite sample, is digitized and recorded as the reference signal. The composite sample is then inserted between the transducers so that it is perpendicular to the sound beam. The first ultrasonic pulse is then digitized and recorded as the sample signal. A rectangular window is often used to obtain the first arrival sample signal only. Frequency spectral analysis of these signals using fast Fourier transform (FFT) algorithms then allows the calculation of the velocity and attenuation as a function of frequency within the bandwidth of the transducers.
or Phase velocity
(9) Once the sample phase velocity has been calculated, it is possible to calculate To), D,(o) and D2(o) in Equation (6), and finally the sample attenuation as
where 1.1 represents the magnitude spectra. D,(o) and D,(w) are diffraction corrections Reference 15 as 2nv L
D,(w)= Do 2 [ wa2
Do
1
given by
b(w) = ATAN2(Im H(o), Re H(w))
(11)
= D,, ((L - h)u, + hv,) 2
1
ma2
(12)
where the function D,(s) is given by D&)=
1 -exp(
-i F)[.J,,(T)
+ iz(:)]
As shown in Equation (7), the sample phase velocity is obtained by calculating the phase difference A4 between the sample signal and the reference signal. This phase difference, to within an uncertainty of *Zrrrn, I~Ibeing an integer, can be obtained by performing a deconvolution of the two signals. The phase uncertainty of an integer multiple of 27~arises because of the following reasons. If we let H(w) = G(w)/F(o), the phase spectrum of H(tu) is calculated by the relation
(13)
Here, .I, and J1 refer to Bessel functions of the first kind, and a is the transducer radius. T(o) represents the
(15)
Since the ATAN
function keeps the phase in the interval routines are often used to obtain the continuous phase spectrum. The routine simply inserts a 2n radians (or 360”) correction whenever there is a jump of more than rc radians. Thus, the phase uncertainty of +2nm may arise at low frequencies because the spectral contents of the ultrasonic pulse do not extend all the way to zero frequency. Thus, the continuous phase spectra may always contain spurious 2~ errors that lead to wrong phase velocity results. This error can be eliminated by using the nearly linear behaviour of the phase spectrum. First, using the data points (A4i, .fi) with frequencies ,I; in the usable (- 7c,n), phase unwrapping
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1995
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Porosity-induced
80
-
60
-
0
attenuation
and velocity
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H. Jeong
sample FFT data and the reference FFT data are corrected for diffraction (beam spreading) effects. After the necessary corrections, the attenuation is then obtained by taking the difference of the logarithms of the magnitude spectra of the two signals and dividing the result by the sample thickness”. The attenuation in Equation (10) contains the background attenuation of the void-free sample. (The reference signal in the experiment is the pulse propagated through water alone, not through a known void-free reference coupon.) It has been found that the background attenuation is very small in comparison with the porosity-induced attenuation, as long as the porosity level is not too low.
2
4 Frequency
6
8
10
(MHZ)
Figure 2 Comparison of phase spectra before and after -277 correction: before -2x correction (dashed curve); correct phase spectrum after 2n addition (solid curve)
bandwidth of the transducer, the ):-axis intercept is calculated from the least squares fit to the data and compared with +Znnz. If there is a -2~ error in the phase, for instance, the calculated intercept will be close in value to -2~. The correct A&f) is then obtained by adding 2~. The phase spectra before and after -271. correction are shown in Figure 2. This scheme provided accurate phase velocity even in samples with very high porosity and proved more effective than the method proposed in Reference 16, where the correct value of ITI is determined by comparing the phase spectral velocity and the approximate velocity from the time-of-flight approach. The phase difference A4 between the sample signal and the reference signal was usually found with respect to a common window. It is often necessary to shift the reference or sample signal by say. t,, to fit the signal of interest into the digitizing window. The phase velocity equation (Equation (9)) is then modified to account for the time delay of the digitizing window as shown below. Considering the window time delay t, and the phase velocity in water as a function of temperature T, we arrive at the following expression for the sample phase velocity
(16) The sound wave-speed in water was assumed to be a constant. In practice, the wave velocity in water varies as a function of temperature. The temperature of the water bath was measured with 0.1 -C accuracy, and the velocity in water at the temperature of the experiment is computed using the equation in Reference 17. Attenuation
To compute the attenuation given in Equation (lo), the frequency spectrum of the through-sample pulse is corrected for interfacial transmission losses and both the
198
Ultrasonics
and D. K. Hsu
1995
Vol 33 No 3
Materials
and microstructures
Three groups of composite specimens were used in this study. These samples were fabricated specifically to contain various amounts of porosity. Samples Al, A2, A4 and A5 are 16-ply unidirectional carbon/epoxy laminates containing, respectively, 6.5 1, 2.04, 1.14 and 0.2% of voids by volume according to acid digestion tests conducted by the manufacturer. Each of the acid digestion results represents an average from four locations on the panel. Samples Bl, B2, B4 and B5 are 16-ply quasi-isotropic carbon/epoxy laminates with a [ +45/O/90],, lay-up and containing, respectively, 4.05, 2.82. 1.25 and 0.34% voids by volume. The second group of specimens consists of four 8-ply carbon/epoxy laminates of woven prepregs with a coarse weave pattern. Samples Dl, D2, D3 and D5 contain 5.09, I .58,3.4 I and 0.01% void volume fractions, respectively. The third group of samples are five coupons of woven carbon/polyimide laminates. These coupons consist of six plies of 8-harness satin weave. Samples 6240-4, -7, -8, -10 and -13 contain, respectively, 1.2, 2.9, 5.4, 9.0 and I 1.2% void contents. The thicknesses of the specimens in these groups vary from about 2 mm for samples of low porosity to 2.5 mm for high porosity samples. These samples contain the fibre volume fraction of approximately 60-65% as determined by acid digestion tests. Microstructural
examination
Optical microscopy and image analysis were used to obtain statistical data on the pore morphology in the above samples. A de-ply method was also applied to examine the pore distribution at the interfaces between the plies. Detailed experimental procedures and results on the morphological study can be found in References 6 and 19. The pores in the unidirectional laminates tend to occur at the ply interfaces and to be elongated along the adjacent fibre directions. Thin slices cut parallel to the fibre direction often reveal needle-like voids several millimetres in length or longer, depending on the void content. The porosity volume fraction is dominated by the larger needle-like or strip crack-like pores. Most of the voids, especially the larger ones, do not have a circular cross-section. The orientation of the longer (width) axis of the generally elliptic pore cross-section tends to follow
Porosity-induced
18
I
I
I
I
I
attenuation
H. Jeong
and 0. K. Hsu
of occurrence measurement
voids
Results 3.41%
change:
logical features as size, shape and location will aid the interpretation of the ultrasonic results.
I
16 5.09%
and velocity
voids
and discussion
Attenuation 3 shows the measured attenuation of a longitudinal wave propagating normal to the laminate plane over the frequency range I to 9 MHz. Results are presented for four woven carbon/epoxy laminates (D series). The results of Figure 3 show that the attenuation increases with frequency and, at a given frequency, it is higher for laminates with more voids. The attenuation curve also shows approximately linear behaviour with frequency and its slope increases with void content. The attenuation slope (da/df) was calculated from the linear fit to the data over the frequency used, and is presented in the figure caption. It is noted that the attenuation due to scattering by voids in this frequency range is proportional to f, while it is generally known to be proportional to p for the Rayleigh scattering process by spherical scatterers. The attenuation of the almost void-free sample (0.01% porosity sample) is small compared with other porous samples in the group. The samples in the other two groups showed similar behaviour, but the magnitudes of attenuation and attenuation slope were different as discussed further below.
Figure 1.58%
voids Ii
0.01%
voids -I
01
’
I
I
I
I
I
I
0
2
4
6
8
10
12
14
Frequency
(MHZ)
Figure 3 Attenuation curves of the woven carbon/epoxy laminates. They show approximately linear behaviour with frequency. The attenuation and the attenuation slope are higher for laminates with more voids. The attenuation slopes (da/df) obtained from the linear fit to the data are 1.606, 1.03, 0.655 and 0.165 cm-’ MHz-’ for 5.09,3.41,1.58 and 0.01% porosity samples, respectively
the ply interface. The voids in the quasi-isotropic laminates show generally similar behaviour except that they are elongated along the fibre directions in the laminate plane. The dimension of pore cross-section in these samples has a large variation. The width b ranges from several micrometres to hundreds of micrometres while the height II ranges from a few micrometres to tens of micrometres, so that the average aspect ratio (u/b) falls between 0.3 and 0.45. The width and height of the pore cross-section show a log normal distribution. Results from the de-ply method showed a considerable networking of the pores at the ply interfaces. The de-ply method also confirmed that the voids occur mostly at the ply interfaces. The voids in both the woven carbon/polyimide and carbon/epoxy laminates tend to be localized in the resin rich pockets. However, their overall shape and size distributions are slightly different. In the carbon/polyimide samples, most of the voids are spherical and their sizes have a large variation from a few micrometres for small voids to a few hundred micrometres for larger voids, giving rise to average diameters of about 30-80 pm. On the other hand, in the carbon/epoxy samples, some of the voids tend to be small and spherical, while the other voids have flat and elliptic cross-sections. The different pore morphology in these woven composite samples can be attributed to the prepreg structure; the weave pattern of the carbon/epoxy laminates is coarser. To summarize, the pore morphology in the carbon fibre composites appears to be most strongly influenced by the prepreg lay-up, although there can be a number of causes including the constituent material properties and the curing process. Understanding such morpho-
Phase velocity Shown in Figure 4 are the corresponding
phase velocities of the woven carbon/epoxy laminates. The velocities measured with 10 MHz transducers agreed well with the results obtained with 5 MHz transducers. The velocity data obtained with the phase spectral method were compared with the toneburst measurements made at different frequencies. The agreement was very good. The void-free sample is very slightly dispersive over the frequency range used. This almost non-dispersive behaviour of a void-free composite sample agrees with the point-by-point toneburst measurement results of Williams et a1.20. Results in Figure 4 show that the phase velocity of a porous composite material is always smaller than that of the void-free sample and, for a given frequency, the velocity decrease is higher for laminates with more voids. The velocity dispersion becomes greater as the frequency decreases. Measurements were also made in the unidirectional and quasi-isotropic laminates (A and B series), and woven carbon/polyimide laminates (6240 series). The correlation of decreasing velocity with increasing porosity was also observed, but the velocity dispersion and the rate of velocity decrease were different as discussed further below. Kramers-Kronig
retation
It is well known that ultrasonic attenuation and phase velocity are related by the Kramers-Kronig (K-K) relations’. In the general K-K relations, it is required that the attenuation be known over all frequencies in
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1995
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Porosity-induced
3200
attenuation and velocity change: H. Jeong and D. K. Hsu
I
I
I
I
I
In Figure 5, phase velocities of Figure 4, as determined experimentally, are compared with those obtained from Equation (17) for the woven carbon/epoxy composites. In the calculation of the phase velocity, the linear fit to the attenuation curve (Figure 3) was used and a reference frequency o0 at 3 MHz was taken. These results show that the local approximation of the K-K relation holds in porous composites where the velocity dispersion and attenuation are quite large.
I
: $
3000
A .z ” 0
u > g
0 i:
Effect of void shape on the attenuation slope
2800
2600
0
2
4
6 Frequency
8
IO
12
14
(MHZ)
Figure 4 Phase velocities of the woven carbon/epoxy laminates. The velocity decrease is higher for laminates with more voids at a given frequency. The velocity dispersion of the 0.01% sample is very small, while the other porous samples show increasing dispersion with decreasing frequency
3200
I
I
I
I
In order to correlate the measured void content with the attenuation, the slope of the attenuation curve was calculated by a linear fit to the attenuation data. The measured attenuation slope (da/df) is plotted as a function of void content (based on the acid digestion) in Figure 6. Results are presented for the three groups of samples. In each group, the data points define an approximate straight line. It is noted that, at a given void content, the attenuation slope is the largest in the unidirectional and quasi-isotropic laminates, and the lowest in the woven carbon/polyimide laminates. This difference can be explained through the void shapeeultrasound interaction. The voids are flatter and longer in the unidirectional and quasi-isotropic laminates and are thus very effective in blocking the’sound energy. On the other hand, the voids tend to be more spherical in the woven carbon/polyimide laminates. The attenuation and the attenuation slope are therefore lower in the woven composites for the same amount of porosity content. This observation is consistent with the dependence of scattering cross-section on the void shape’; the slope of the scattering cross-section of the flat ribbon-like crack is higher than that of the circular void in the intermediate ‘ka’ range. Based on the comparison between the attenuation slope and the porosity volume fraction determined by acid digestion, the void content (in percent) may be predicted by the following relationship dz void content = constant x df
2600 0
I
I
I
I
2
4
6
8
Frequency
1
(MHZ)
Figure 5 Comparisons between the measured phase velocities (solid curves) and the calculated velocities through the K-K relation of Equation (17) (discrete points). For a(w), linear fits to the attenuation curves of Figure 3 were used, and the reference frequency was taken to be m,, = 3 MHz
order to calculate the phase velocity, and vice versa. A simpler form of the K-K relation, known as the local approximation, relates the phase velocity u,(o) and the attenuation LX,(O)over a finite frequency range’ 1 1 2 o r,(o’) -=--~ dw’ r&4 u,(WJ 7cs W,, w’* where u,(wO) and u,(o) are respectively velocities at frequencies w,, and o.
200
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1995
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(18)
4-
0
2
4
6 Void
content
8
10
12
14
(%)
(17) the sample
Figure 6 Attenuation slope (da/do versus void content determined by acid digestion. Comparisons between: 0. unidirectional and quasi-rsotropic laminates; 0, woven carbon/epoxy laminates; & woven carbon/polyimide laminates
Porosity-induced
g
i!i 0
v,
attenuation
and velocity
change:
H. Jeong
and 0. K. Hsu
12 10
_
I
.-o 0 3
8
: =: 0
6
2
4
,x .-
F
2
a0 0 I
I
I
I
I
I
I
0
2
4
6
8
10
12
Porosity
by acid
digestion
Figure 7 Comparisons between the predicted the relation void = constant x (dz/df) and measured by acid digestion. The constant 2, 3 three groups of samples, i.e. 0, unidirectional laminates; l , woven carbon/epoxy laminates; polyimide laminates
14
(%)
elliptic voids approaches 1 (circular cylinder) to 0 (thin ribbon). Another observation can be made on the dependence of the fractional velocity decrease on the frequency. Since the phase velocity of the samples in each group becomes more dispersive as the frequency becomes lower, the velocity decreases more at lower frequencies as manifested by overlapping Figures 8a and 8h. Furthermore, the unidirectional and quasi-isotropic laminates containing flat, elliptic voids show a more rapid decrease rate in A V/V, than the other two groups of samples where the voids are more spherical. This implies that composites with flat, elliptic voids are more dispersive for a given void content.
void contents using the void contents and 4 was used for and quasi-isotropic 0, woven carbon/
where should sample groups. The void (18) together with those compared in Figure
be different between different contents deduced from Equation measured by acid digestion are 7, where the proportionality
LF constant is used depending on the void
0
2
4
a
6
Void
8
content
IO
12
14
(%)
shape. Effect of voidshape
on the fractional
velocity decrease
To make a quantitative correlation between the velocity change and the void content, the fractional velocity decrease AVIV,, (expressed in percent) with respect to the velocity V, in a void free sample was plotted against the void content. The velocity of the void-free sample was taken from the lowest void specimens in the first and second group of samples. The void-free velocity of the third group of samples (6240 series) was found from the linear fit to the velocity data at each frequency. Fi~guw 8a shows the fractional velocity decrease versus void content at 6 MHz. As a comparison, the same plot was also made for a frequency of 4 MHz, as shown in Figurr 86. A review of the results at different frequencies reveals that regardless of frequencies the velocity decrease is the highest in the unidirectional samples and the lowest in the woven carbon/polyimide
E
20
I
I
I
I
I
e, :: a~
/
16-
b al
Tl
x
.c ::
a, >
8
0
6 .+” 0
I= b
0
2
4
6 Void
8
content
10 (%)
Figure 8 Fractional velocity decrease versus vord content: (a) at 6 MHz; (b) at 4 MHz. Comparisons between: 0, unidirectional and quasi-isotropic laminates; 0, woven carbon/epoxy laminates; LL woven carbon/polyimide laminates. At both frequencies, the unidirectional and quasi-isotropic laminates show a higher velocity decrease than the other groups of samples. As the frequency decreases, the fractional velocity decrease becomes larger
Ultrasonics
1995
Vol 33 No 3
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attenuation and velocity change: H. Jeong
Porosity-induced
I
I
I
I
I
I
I
I
0
2
4
6
8
10
12
14
Porosity
by
acid
digestion
(%)
Figure 9 Comparisons between the predicted void contents using the relation void =constant x (AVIV) and the void contents measured by acid drgestion. The constant 0.3.0.5 and 0.6 was used for three groups of samples, i.e. 0. unidirectional and quasiisotropic laminates; 0, woven carbon/epoxy laminates; A, woven carbon/polyimide laminates
The effect of void shape on dispersion may also be appreciated from the attenuation results through the K-K relation. Equation (17) can be further approximated as” Au, = v,(w) - II,
W%) = ___ 71
“J x&-J) dw’ __ s W, of2
(19)
The amount of dispersion Av, is, in general, dependent on z(w)/w’ so that the higher attenuation or the attenuation slope will bring about more dispersion. Since the unidirectional and quasi-isotropic laminates show the highest attenuation (slope) for a given void content, the dispersion of these samples will also be the highest in a given frequency range. Based on the correlation between the fractional velocity change and the void content, the void content can also be obtained by the relationship void content
= constant
AV x V
and D. K. Hsu
posites containing porosity. The measurements yielded the frequency dependent attenuation and phase velocity over the range of approximately 1 to 10 MHz. The relationship between attenuation and dispersion was tested using the local form of the KramerssKronig relation and found to hold in porous composite materials. The attenuation was found to be linearly dependent on the frequency, and its magnitude and slope were larger for laminates with more voids. The ultrasonic velocity decreases with increasing void content and the velocity dispersion increases as the frequency decreases. The void shape had a great effect on the constant that relates the void content and the attenuation slope da/df. It is therefore important to use prior knowledge about the laminate structure and the pore morphology in estimating the void content from the attenuation slope. The fractional velocity decrease (AV/V,) of the porous composite samples was found to be dependent both on the void shape and the frequency. The samples with the flat. elliptic voids gave a higher fractional velocity decrease than the samples with more spherical voids at all frequencies tested. Moreover, the samples with the flat, elliptic voids showed a stiffer decrease rate in A V/V, for a given void content. It is hoped that the experimental results obtained in this work will help the model development of wave propagation in porous carbon fibre composites for characterizing voids.
Acknowledgment This work was supported State University, USA.
References I
2 3 4
(20)
In this case. however, the constant depends not only on the void shape but also on the frequency. The void contents deduced from Equation (20) are compared with those obtained by acid digestion in Figure 9, where the predicted void contents were calculated from the values of fractional velocity change at 4 MHz (Figure 8b) using the constants of 0.3. 0.5 and 0.6 for the three groups of samples, respectively. Because of the velocity dispersion in the porous composite samples, different values of the constant should be used to estimate the void contents from the velocity data at other frequencies.
5
6
7
x 9
IO
Conclusions
II
An ultrasonic spectroscopic broadband through-transmission
202
Ultrasonics
1995
method was applied to measurements in com-
Vol 33 No 3
by the Center for NDE at Iowa
12
Stone, D.E.W. and Clarke, B. Ultrasonic attenuation as a measure of void content in carbon-fiber reinforced plastics Non-De~slr Test (1975) 8 1377145 Martin, B.C. Ultrasonic attenuation due to voids in fiberreinforced plastics NDT In/ (1976) 9 2422246 Hale, J.M. and Ashton, J.N. Ultrasonic attenuation in voided fiber-reinforced plastics NDT I~I/ (1988) 21 321-326 Daniel, I.M., Wooh, S.C. and Komsky, I. Quantitative porosity characterization of composite materials by means of ultrasonic attenuation measurements .I Nor~tles/r Ecu/ (1992) II t-8 Nair, SM., Hsu, D.K. and Rose, J.H. Porosity estimation using the frequency dependence of the ultrasonic attenuation J Nornlestr Ertrl ( 1989) 8 13-26 Hsu, D.K. Ultrasonic measurements of porosity in woven graphite polyimide composites. In Rerien, of Proyrexs if7 &w~/itatice .YoJJtk~,.v/,JJc’J;~~’ fi’~~.(J/w~ioJ~, Vol. 7B (Eds Thompson, D.O. and Chimenti, D.E.) Plenum Press. New York, USA (1988) 1063~1068 Martin, B.G. Ultrasonic wave propagation in fiber-reinforced solids containing voids J Appl P/JJY (1977) 48 3368-3373 Reynolds, W.N. and Wilkinson, S.J. The analysis of tiberreinforced porous composite materials by the measurement of ultrasonic wave velocities L~l~rcwonic.v (1978) 16 1599163 O’Donnell, M., Jaynes, E.T. and Miller, J.G. General relationships between ultrasonic attenuation and dispersion J -Ic~o~r.r/SOC AUJ (1978) 63 1935-1937 Beltzer, A.I. and Brauner, N. SH waves of an arbitrary frequency in random fibrous composites via the K-K relations J MK/J Phy.~ SO/id\ ( 1985) 33 471-487 Gross, D. and Zhang, Ch. Wave propagation in damaged solids Int J Solids Structures (1992) 29 1763-l 779 Yuhas, D.E., Vores, C.L. and Roberts, R.A. Variations in backscatter attributed to porosity. In Reuiew @’ Proyress in
Porosity-induced
attenuation and velocity change: H. Jeong and 0. K. Hsu
Hughes,
Handley, SM., between frequency porosity in laminates.
Quantitative
D.E.) Plenum 13
1275-1284 Sachse, W. Pao, Y.-H. velocities of
New York,
(1986)
the determination phase and waves in J Appl 49
Qurmtitcrtire
D.O.
Notldestructire
Chimenti,
D.E.)
J.G. and ultrasonic In o/ Vol. 78 Press. New
E.I. A attenuation Progre.rs
Thompson, USA (1987)
(1978)
14
15
Pialucha, T., C.C.H. and method for measurement of 27 270-279 Thompson, R.B. Gray, T.A. ultrasonic scattering Nondestructive
16
D.O. and 567-586 D.K. Progress
water
Evaluation,
D.E.) Plenum and due to
in
(1976) 35
diffraction corrections In RecPlr Pruyress it? 2A (Eds New York, (1983)
H. Ultrasonic in composite Nondeswuctive
D.O. and (1989) 1567-1573 W. and
17
P. Amplitude velocity Ultrasonics
Evaluation,
D.E.) Plenum
change and In Review 8B (Eds New York,
20
21
23 K.H. Sound
in pure
sea
Hsu, D.K. Uhl, K.M. morphological study porosity defects carbon-epoxy composites. Review o/’ in Quautiratire Eruluutiotr. Vol. (Eds Thompson, and Chimenti, Plenum Press. York, USA 1175-1184 Williams, J.H., NayebHashemi, and Lee, Ultrasonic attenuation velocity in graphite fiber J Nun&s/r (1980) 1 Zhao, Y.H. Weng, G.J. elastic moduli ribbon-reinforced composites Appl MW/I 57 158-l Hill, R. of mechanical of fibre-strenthened I. elastic J Me& So/i& (1964) 199-2 12 Z. On behavior of reinforced materials arbitrary transverse geometry J P/~Jx Solid7 13 119-134
Ultrasonics 1995 Vol 33 No 3
203
of porosity-induced and velocity change
and D. K. Hsu
Center for Nondestructive
Evaluation,
Iowa State University,
Ames, IA 50011,
USA
Accepted 3 1 December 1994 In this paper, ultrasonic measurement results are presented for analysing the wave propagation in carbon fibre reinforced plastics (CFRP) containing voids. The composite samples studied include laminates fabricated from unidirectional and woven fabric prepregs. The ultrasonic methods stress the utilization of spectral analysis and frequency dependence of the attenuation and phase velocity due to porosity. Morphological parameters of pores are found to play an important role in the proper interpretation of measured data. The measured attenuation shows approximately linear behaviour over the frequency range used. The corresponding phase velocity decreases substantially with increasing void content. In addition, the velocity in porous CFRP is found to be more dispersive than that in void-free composites. The relationship between the ultrasonic attenuation and dispersion is subsequently tested using the local form of the Kramers-Kronig relation. The linear relationship between the void content and the attenuation slope (da/do is found to hold, but the constant of proportionality is quite different for samples with different pore morphology. This morphology has a large effect on the dispersion of phase velocity. The fractional velocity decrease (AVIV,,) is correlated with the void content, and its dependence on the frequency and void shape is discussed. The present analysis will aid in the model development of wave propagation in porous composites for detecting and characterizing the porosity in these materiak. Keywords: carbon fibre Kramers-Kronig relations;
composites; attenuation
The presence of voids (or porosity) in composite laminates has noticeable effects on ultrasonic attenuation since voids are strong scatterers for elastic waveslP4. The correlation between attenuation and void content in carbon fibre reinforced composites is well known: greater void content causes increased attenuation and the increase is greater at higher frequencies. By manufacturing standards with known void contents, the void content of a particular system of composite can be quantitatively measurement procedures were evaluated. Recently, developed to obtain the ultrasonic attenuation as a function of frequency using broadband pulses, and correlation between the attenuation slope, or dx/dj-, and the void volume fraction has been established5*6. Little emphasis, however, has been given to the corresponding dispersion, which is a necessary consequence of the attenuation. When an elastic wave propagates in a porous composite material, the ultrasonic velocities generally depend on the void characteristics and the constituent material properties as well as on the frequency. *Present address: YuSeong,
DaeJon,
Agency Korea
for
0041-624X/95/$09.50 0 1995 SSDI 0041-624X(95)00023-2
Defense
Development,
PO Box
35,
pore morphology; wave slope; velocity change
propagation;
Considering the presence of voids in the matrix, increasing the void content decreases the longitudinal and shear wave velocities. This is due to a decrease of the effective elastic stiffnesses of the composite with increasing void content. Several investigators have attempted to use ultrasonic velocities as a measure of void content in carbon fibre reinforced plastics7.8. However, they assumed low frequencies, or equivalently, small void size; so that the frequency dependence of phase velocity (dispersion) was ignored. If the wavelength is of the same order of magnitude as a characteristic dimension of voids, one would expect a large frequency range over which the medium should show velocity dispersion. Dispersion effects are shown by the frequency dependent ultrasonic velocities. A pulse, being a superposition of many frequencies, will change its shape as it propagates through a dispersive medium. The ultrasonic attenuation and dispersion due to scattering are not independent according to Kramerss Kronig (K-K) relations’. The validity of this relationship rests only on the linear and causal properties of the system, which is true for a realistic model. The K-K relations have been successfilly applied by Beltzer and coworkers” for studying the wave attenuation and
- Elsevier Science B.V. All rights reserved Ultrasonics
1995 Vol 33 No 3
195
Porosity-induced
attenuation and velocity change: H. Jeong and D. K. Hsu
dispersion in fibrous composites. Recently, Gross and Zhang ” have extended this causal approach to wave propagation in solids containing cracks. When experimental results of both attenuation and phase velocity are available, their mutuai compatibility can be checked. Voids arising from trapped air during the fabrication process of CFRP are, in general, very complicated in nature. The size and shape of voids in CFRP have been described in several ultrasonic studies’*12. Stone and Clark found that the voids tend to be small and spherical at low porosity volume fractions (less than 1.5%) and at high volume fraction the interlaminar voids tend to be much larger and flattened and elongated in shape. Yuhas also found that the voids are roughly cigar-shaped and increase in size with increasing volume fraction. Since most composite materials for structural applications are of the laminated type, the morphological features also depend on the fibre layout of prepreg tapes. Thus, the wave propagation in porous composite laminates cannot be complete without detailed morphological knowledge of pores. In this paper, we investigate the effect of porosity on the ultrasonic attenuation and phase velocity of carbon fibre reinforced composites. Since voids bring about the large amount of attenuation due to scattering, ultrasonic measurements are made in an immersion tank using a substitution technique in the through-transmission mode. By introducing a complex wave-number, expressions are obtained for calculating the phase velocity and attenuation of longitudinal waves propagating normal to the plane of composite laminates. The frequency dependent velocity and attenuation are obtained from the spectral analysis of broadband pulses acquired without and with the sample in the propagation path. Morphological features of pores are examined using microscopy and image analysis, and the pore shape parameters are used to interpret the wave propagation characteristics in these samples. The phase velocity is also obtained from the measured attenuation data through the K-K relation given in its local form’. A quantitative correlation between void content and attenuation slope, as well as the fractional velocity decrease, is then established. The effect of void shape on the linear relationship between the attenuation slope and void content is investigated. In addition, the dependence of the fractional velocity decrease on the frequency and void shape
related to the frequency-dependent These relations can be written as k(w) = 244
12(o).
+ ia
(1)
The objective here is to derive expressions for V(o) and X(O) of the material with large attenuation and dispersion. Consider a composite laminate of thickness h immersed in water. In through-transmission testing, the sample velocity and attenuation can be obtained by specifying the waveform in the propagation path without and with the sample. The pulse transmitted through water alone is used as the reference signal, while the first transmitted pulse with the sample inserted between two transducers is used as the sample signal. Figure I shows the measurement configuration of a substitution method. A broadband longitudinal pulse u(x, t) propagating in the positive x direction can be expressed as a linear combination of all plane harmonic waves’3v’4, that is I i(kx -ml) do U(X,t) = JF,(o) e (2) 277I -1 where F,(o) is the Fourier transform of ~(0, t). It is assumed that water behaves in a non-attenuative, non-dispersive manner, i.e. the wave number k, is real and the phase velocity o, = o/k, is a constant. Referring to Figure la, the transmitted field of the reference signal at x = L can be written as 21c _z [F,(o)D,(o) u,(L, t) = J-
eiwLio*]eCiwrdo
(3)
s 3(
where D,(w) is the diffraction correction. The term inside
I
T
+L ’
=-I
a X t-
is discussed.
-+I-
Theory
When ultrasonic pulses, being a superposition of many different frequencies, propagate in porous composites, scattering by voids causes the attenuation and the
1
corresponding dispersion of waves. For the analysis of composite materials containing voids, we assume that
the solids comprise a linear system, and they are capable of supporting a one-dimensional plane wave of the form where k(w) is the effective wave-number and w e i(k(o)-‘-w’), is the circular frequency of the incident wave. To describe the above behaviour one can define a complex wave-number k(o), where the real part is a dispersive part related to the frequency-dependent phase velocity, L’(U)),while the imaginary part is an attenuative part
196
attenuation,
Ultrasonics
1995
Vol 33 No 3
R
b
Figure 1 Measurement configuration for the substitution method: (a) for reference waveform acquisition; (b) for sample waveform acquisition
Porosity-induced
attenuation and velocity change: H. Jeong and 0. K. Hsu
the bracket is the Fourier transform of u,(L, r) so that F(u,(L, t)) = F(o) = F,(w)D,(w) eiWLjV*
interface losses due to transmissions and is given as (4)
The specimen is now inserted in the water path and the signal due to the first transmission is recorded as the sample signal. We consider a relatively thick specimen such that all transmitted pulses of the sample can be clearly separated from each other in the time domain. Referring to Figure 16, and with Equation (l), the Fourier transform of the sample signal u,(L, t) can be expressed as F(u,(L, t)) = G(o) = F,,(w)T(w)D,(o) e-n,h eior(L-h)“‘N+h’r~l (5)
where qw) is the interface losses due to transmissions, D,(o) is the diffraction correction, and ~1,and u, are the frequency dependent attenuation and phase velocity of the sample, respectively. Then, from Equations (4) and (5) G(U) qo)~z(o) e-a& eioh(l/o>- l/r,,) -= (6) D,(o) F(o) Since the influence of diffraction on the phase shift of the ultrasonic signal is known to be small, one can disregard the phase correction due to diffraction in the calculation of phase velocity. The sample phase velocity can be obtained from the difference in the phase spectra of reference and sample waveforms. If the phase spectra of F(w) and G(w) are denoted as - 4, and - 4,, respectively, one can get - c#&o) + &(o) = -A&o)
04%v 1
= oh L[
i
(7)
to yield
vs(-)=(;_!g)-’
R-3)
T(o) =
4Z,Z,(w) IIZ, +
(14)
4k412
where Z, = pwv, and Z,(o) = p,o,(o) are the acoustic impedances of water and sample, respectively.
Experiments Both the phase velocity and attenuation measurements are made with the same experimental set-up. Two nominally identical broadband transducers are set up in an immersion tank to face each other and are separated by a distance of typically 15 cm. The transducers used are 6.35 mm (l/4”) diameter unfocussed probes with nominal centre frequencies of 10 MHz. To get the broadband pulse, one transducer is excited by a spike voltage pulse produced by a Panametrics 5052PR pulser/receiver and the other is connected to the receiver. The signal from the receiving transducer is acquired by digital sampling in a LeCroy 9400 digital oscilloscope, averaged over one-hundred times to increase the S/N ratio, and transferred to file storage in a computer, where further processing is performed. The ultrasonic pulse transmitted through water, in the absence of the composite sample, is digitized and recorded as the reference signal. The composite sample is then inserted between the transducers so that it is perpendicular to the sound beam. The first ultrasonic pulse is then digitized and recorded as the sample signal. A rectangular window is often used to obtain the first arrival sample signal only. Frequency spectral analysis of these signals using fast Fourier transform (FFT) algorithms then allows the calculation of the velocity and attenuation as a function of frequency within the bandwidth of the transducers.
or Phase velocity
(9) Once the sample phase velocity has been calculated, it is possible to calculate To), D,(o) and D2(o) in Equation (6), and finally the sample attenuation as
where 1.1 represents the magnitude spectra. D,(o) and D,(w) are diffraction corrections Reference 15 as 2nv L
D,(w)= Do 2 [ wa2
Do
1
given by
b(w) = ATAN2(Im H(o), Re H(w))
(11)
= D,, ((L - h)u, + hv,) 2
1
ma2
(12)
where the function D,(s) is given by D&)=
1 -exp(
-i F)[.J,,(T)
+ iz(:)]
As shown in Equation (7), the sample phase velocity is obtained by calculating the phase difference A4 between the sample signal and the reference signal. This phase difference, to within an uncertainty of *Zrrrn, I~Ibeing an integer, can be obtained by performing a deconvolution of the two signals. The phase uncertainty of an integer multiple of 27~arises because of the following reasons. If we let H(w) = G(w)/F(o), the phase spectrum of H(tu) is calculated by the relation
(13)
Here, .I, and J1 refer to Bessel functions of the first kind, and a is the transducer radius. T(o) represents the
(15)
Since the ATAN
function keeps the phase in the interval routines are often used to obtain the continuous phase spectrum. The routine simply inserts a 2n radians (or 360”) correction whenever there is a jump of more than rc radians. Thus, the phase uncertainty of +2nm may arise at low frequencies because the spectral contents of the ultrasonic pulse do not extend all the way to zero frequency. Thus, the continuous phase spectra may always contain spurious 2~ errors that lead to wrong phase velocity results. This error can be eliminated by using the nearly linear behaviour of the phase spectrum. First, using the data points (A4i, .fi) with frequencies ,I; in the usable (- 7c,n), phase unwrapping
Ultrasonics
1995
Vol 33 No 3
197
Porosity-induced
80
-
60
-
0
attenuation
and velocity
change:
H. Jeong
sample FFT data and the reference FFT data are corrected for diffraction (beam spreading) effects. After the necessary corrections, the attenuation is then obtained by taking the difference of the logarithms of the magnitude spectra of the two signals and dividing the result by the sample thickness”. The attenuation in Equation (10) contains the background attenuation of the void-free sample. (The reference signal in the experiment is the pulse propagated through water alone, not through a known void-free reference coupon.) It has been found that the background attenuation is very small in comparison with the porosity-induced attenuation, as long as the porosity level is not too low.
2
4 Frequency
6
8
10
(MHZ)
Figure 2 Comparison of phase spectra before and after -277 correction: before -2x correction (dashed curve); correct phase spectrum after 2n addition (solid curve)
bandwidth of the transducer, the ):-axis intercept is calculated from the least squares fit to the data and compared with +Znnz. If there is a -2~ error in the phase, for instance, the calculated intercept will be close in value to -2~. The correct A&f) is then obtained by adding 2~. The phase spectra before and after -271. correction are shown in Figure 2. This scheme provided accurate phase velocity even in samples with very high porosity and proved more effective than the method proposed in Reference 16, where the correct value of ITI is determined by comparing the phase spectral velocity and the approximate velocity from the time-of-flight approach. The phase difference A4 between the sample signal and the reference signal was usually found with respect to a common window. It is often necessary to shift the reference or sample signal by say. t,, to fit the signal of interest into the digitizing window. The phase velocity equation (Equation (9)) is then modified to account for the time delay of the digitizing window as shown below. Considering the window time delay t, and the phase velocity in water as a function of temperature T, we arrive at the following expression for the sample phase velocity
(16) The sound wave-speed in water was assumed to be a constant. In practice, the wave velocity in water varies as a function of temperature. The temperature of the water bath was measured with 0.1 -C accuracy, and the velocity in water at the temperature of the experiment is computed using the equation in Reference 17. Attenuation
To compute the attenuation given in Equation (lo), the frequency spectrum of the through-sample pulse is corrected for interfacial transmission losses and both the
198
Ultrasonics
and D. K. Hsu
1995
Vol 33 No 3
Materials
and microstructures
Three groups of composite specimens were used in this study. These samples were fabricated specifically to contain various amounts of porosity. Samples Al, A2, A4 and A5 are 16-ply unidirectional carbon/epoxy laminates containing, respectively, 6.5 1, 2.04, 1.14 and 0.2% of voids by volume according to acid digestion tests conducted by the manufacturer. Each of the acid digestion results represents an average from four locations on the panel. Samples Bl, B2, B4 and B5 are 16-ply quasi-isotropic carbon/epoxy laminates with a [ +45/O/90],, lay-up and containing, respectively, 4.05, 2.82. 1.25 and 0.34% voids by volume. The second group of specimens consists of four 8-ply carbon/epoxy laminates of woven prepregs with a coarse weave pattern. Samples Dl, D2, D3 and D5 contain 5.09, I .58,3.4 I and 0.01% void volume fractions, respectively. The third group of samples are five coupons of woven carbon/polyimide laminates. These coupons consist of six plies of 8-harness satin weave. Samples 6240-4, -7, -8, -10 and -13 contain, respectively, 1.2, 2.9, 5.4, 9.0 and I 1.2% void contents. The thicknesses of the specimens in these groups vary from about 2 mm for samples of low porosity to 2.5 mm for high porosity samples. These samples contain the fibre volume fraction of approximately 60-65% as determined by acid digestion tests. Microstructural
examination
Optical microscopy and image analysis were used to obtain statistical data on the pore morphology in the above samples. A de-ply method was also applied to examine the pore distribution at the interfaces between the plies. Detailed experimental procedures and results on the morphological study can be found in References 6 and 19. The pores in the unidirectional laminates tend to occur at the ply interfaces and to be elongated along the adjacent fibre directions. Thin slices cut parallel to the fibre direction often reveal needle-like voids several millimetres in length or longer, depending on the void content. The porosity volume fraction is dominated by the larger needle-like or strip crack-like pores. Most of the voids, especially the larger ones, do not have a circular cross-section. The orientation of the longer (width) axis of the generally elliptic pore cross-section tends to follow
Porosity-induced
18
I
I
I
I
I
attenuation
H. Jeong
and 0. K. Hsu
of occurrence measurement
voids
Results 3.41%
change:
logical features as size, shape and location will aid the interpretation of the ultrasonic results.
I
16 5.09%
and velocity
voids
and discussion
Attenuation 3 shows the measured attenuation of a longitudinal wave propagating normal to the laminate plane over the frequency range I to 9 MHz. Results are presented for four woven carbon/epoxy laminates (D series). The results of Figure 3 show that the attenuation increases with frequency and, at a given frequency, it is higher for laminates with more voids. The attenuation curve also shows approximately linear behaviour with frequency and its slope increases with void content. The attenuation slope (da/df) was calculated from the linear fit to the data over the frequency used, and is presented in the figure caption. It is noted that the attenuation due to scattering by voids in this frequency range is proportional to f, while it is generally known to be proportional to p for the Rayleigh scattering process by spherical scatterers. The attenuation of the almost void-free sample (0.01% porosity sample) is small compared with other porous samples in the group. The samples in the other two groups showed similar behaviour, but the magnitudes of attenuation and attenuation slope were different as discussed further below.
Figure 1.58%
voids Ii
0.01%
voids -I
01
’
I
I
I
I
I
I
0
2
4
6
8
10
12
14
Frequency
(MHZ)
Figure 3 Attenuation curves of the woven carbon/epoxy laminates. They show approximately linear behaviour with frequency. The attenuation and the attenuation slope are higher for laminates with more voids. The attenuation slopes (da/df) obtained from the linear fit to the data are 1.606, 1.03, 0.655 and 0.165 cm-’ MHz-’ for 5.09,3.41,1.58 and 0.01% porosity samples, respectively
the ply interface. The voids in the quasi-isotropic laminates show generally similar behaviour except that they are elongated along the fibre directions in the laminate plane. The dimension of pore cross-section in these samples has a large variation. The width b ranges from several micrometres to hundreds of micrometres while the height II ranges from a few micrometres to tens of micrometres, so that the average aspect ratio (u/b) falls between 0.3 and 0.45. The width and height of the pore cross-section show a log normal distribution. Results from the de-ply method showed a considerable networking of the pores at the ply interfaces. The de-ply method also confirmed that the voids occur mostly at the ply interfaces. The voids in both the woven carbon/polyimide and carbon/epoxy laminates tend to be localized in the resin rich pockets. However, their overall shape and size distributions are slightly different. In the carbon/polyimide samples, most of the voids are spherical and their sizes have a large variation from a few micrometres for small voids to a few hundred micrometres for larger voids, giving rise to average diameters of about 30-80 pm. On the other hand, in the carbon/epoxy samples, some of the voids tend to be small and spherical, while the other voids have flat and elliptic cross-sections. The different pore morphology in these woven composite samples can be attributed to the prepreg structure; the weave pattern of the carbon/epoxy laminates is coarser. To summarize, the pore morphology in the carbon fibre composites appears to be most strongly influenced by the prepreg lay-up, although there can be a number of causes including the constituent material properties and the curing process. Understanding such morpho-
Phase velocity Shown in Figure 4 are the corresponding
phase velocities of the woven carbon/epoxy laminates. The velocities measured with 10 MHz transducers agreed well with the results obtained with 5 MHz transducers. The velocity data obtained with the phase spectral method were compared with the toneburst measurements made at different frequencies. The agreement was very good. The void-free sample is very slightly dispersive over the frequency range used. This almost non-dispersive behaviour of a void-free composite sample agrees with the point-by-point toneburst measurement results of Williams et a1.20. Results in Figure 4 show that the phase velocity of a porous composite material is always smaller than that of the void-free sample and, for a given frequency, the velocity decrease is higher for laminates with more voids. The velocity dispersion becomes greater as the frequency decreases. Measurements were also made in the unidirectional and quasi-isotropic laminates (A and B series), and woven carbon/polyimide laminates (6240 series). The correlation of decreasing velocity with increasing porosity was also observed, but the velocity dispersion and the rate of velocity decrease were different as discussed further below. Kramers-Kronig
retation
It is well known that ultrasonic attenuation and phase velocity are related by the Kramers-Kronig (K-K) relations’. In the general K-K relations, it is required that the attenuation be known over all frequencies in
Ultrasonics
1995
Vol 33 No 3
199
Porosity-induced
3200
attenuation and velocity change: H. Jeong and D. K. Hsu
I
I
I
I
I
In Figure 5, phase velocities of Figure 4, as determined experimentally, are compared with those obtained from Equation (17) for the woven carbon/epoxy composites. In the calculation of the phase velocity, the linear fit to the attenuation curve (Figure 3) was used and a reference frequency o0 at 3 MHz was taken. These results show that the local approximation of the K-K relation holds in porous composites where the velocity dispersion and attenuation are quite large.
I
: $
3000
A .z ” 0
u > g
0 i:
Effect of void shape on the attenuation slope
2800
2600
0
2
4
6 Frequency
8
IO
12
14
(MHZ)
Figure 4 Phase velocities of the woven carbon/epoxy laminates. The velocity decrease is higher for laminates with more voids at a given frequency. The velocity dispersion of the 0.01% sample is very small, while the other porous samples show increasing dispersion with decreasing frequency
3200
I
I
I
I
In order to correlate the measured void content with the attenuation, the slope of the attenuation curve was calculated by a linear fit to the attenuation data. The measured attenuation slope (da/df) is plotted as a function of void content (based on the acid digestion) in Figure 6. Results are presented for the three groups of samples. In each group, the data points define an approximate straight line. It is noted that, at a given void content, the attenuation slope is the largest in the unidirectional and quasi-isotropic laminates, and the lowest in the woven carbon/polyimide laminates. This difference can be explained through the void shapeeultrasound interaction. The voids are flatter and longer in the unidirectional and quasi-isotropic laminates and are thus very effective in blocking the’sound energy. On the other hand, the voids tend to be more spherical in the woven carbon/polyimide laminates. The attenuation and the attenuation slope are therefore lower in the woven composites for the same amount of porosity content. This observation is consistent with the dependence of scattering cross-section on the void shape’; the slope of the scattering cross-section of the flat ribbon-like crack is higher than that of the circular void in the intermediate ‘ka’ range. Based on the comparison between the attenuation slope and the porosity volume fraction determined by acid digestion, the void content (in percent) may be predicted by the following relationship dz void content = constant x df
2600 0
I
I
I
I
2
4
6
8
Frequency
1
(MHZ)
Figure 5 Comparisons between the measured phase velocities (solid curves) and the calculated velocities through the K-K relation of Equation (17) (discrete points). For a(w), linear fits to the attenuation curves of Figure 3 were used, and the reference frequency was taken to be m,, = 3 MHz
order to calculate the phase velocity, and vice versa. A simpler form of the K-K relation, known as the local approximation, relates the phase velocity u,(o) and the attenuation LX,(O)over a finite frequency range’ 1 1 2 o r,(o’) -=--~ dw’ r&4 u,(WJ 7cs W,, w’* where u,(wO) and u,(o) are respectively velocities at frequencies w,, and o.
200
Ultrasonics
1995
Vol 33 No 3
(18)
4-
0
2
4
6 Void
content
8
10
12
14
(%)
(17) the sample
Figure 6 Attenuation slope (da/do versus void content determined by acid digestion. Comparisons between: 0. unidirectional and quasi-rsotropic laminates; 0, woven carbon/epoxy laminates; & woven carbon/polyimide laminates
Porosity-induced
g
i!i 0
v,
attenuation
and velocity
change:
H. Jeong
and 0. K. Hsu
12 10
_
I
.-o 0 3
8
: =: 0
6
2
4
,x .-
F
2
a0 0 I
I
I
I
I
I
I
0
2
4
6
8
10
12
Porosity
by acid
digestion
Figure 7 Comparisons between the predicted the relation void = constant x (dz/df) and measured by acid digestion. The constant 2, 3 three groups of samples, i.e. 0, unidirectional laminates; l , woven carbon/epoxy laminates; polyimide laminates
14
(%)
elliptic voids approaches 1 (circular cylinder) to 0 (thin ribbon). Another observation can be made on the dependence of the fractional velocity decrease on the frequency. Since the phase velocity of the samples in each group becomes more dispersive as the frequency becomes lower, the velocity decreases more at lower frequencies as manifested by overlapping Figures 8a and 8h. Furthermore, the unidirectional and quasi-isotropic laminates containing flat, elliptic voids show a more rapid decrease rate in A V/V, than the other two groups of samples where the voids are more spherical. This implies that composites with flat, elliptic voids are more dispersive for a given void content.
void contents using the void contents and 4 was used for and quasi-isotropic 0, woven carbon/
where should sample groups. The void (18) together with those compared in Figure
be different between different contents deduced from Equation measured by acid digestion are 7, where the proportionality
LF constant is used depending on the void
0
2
4
a
6
Void
8
content
IO
12
14
(%)
shape. Effect of voidshape
on the fractional
velocity decrease
To make a quantitative correlation between the velocity change and the void content, the fractional velocity decrease AVIV,, (expressed in percent) with respect to the velocity V, in a void free sample was plotted against the void content. The velocity of the void-free sample was taken from the lowest void specimens in the first and second group of samples. The void-free velocity of the third group of samples (6240 series) was found from the linear fit to the velocity data at each frequency. Fi~guw 8a shows the fractional velocity decrease versus void content at 6 MHz. As a comparison, the same plot was also made for a frequency of 4 MHz, as shown in Figurr 86. A review of the results at different frequencies reveals that regardless of frequencies the velocity decrease is the highest in the unidirectional samples and the lowest in the woven carbon/polyimide
E
20
I
I
I
I
I
e, :: a~
/
16-
b al
Tl
x
.c ::
a, >
8
0
6 .+” 0
I= b
0
2
4
6 Void
8
content
10 (%)
Figure 8 Fractional velocity decrease versus vord content: (a) at 6 MHz; (b) at 4 MHz. Comparisons between: 0, unidirectional and quasi-isotropic laminates; 0, woven carbon/epoxy laminates; LL woven carbon/polyimide laminates. At both frequencies, the unidirectional and quasi-isotropic laminates show a higher velocity decrease than the other groups of samples. As the frequency decreases, the fractional velocity decrease becomes larger
Ultrasonics
1995
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201
attenuation and velocity change: H. Jeong
Porosity-induced
I
I
I
I
I
I
I
I
0
2
4
6
8
10
12
14
Porosity
by
acid
digestion
(%)
Figure 9 Comparisons between the predicted void contents using the relation void =constant x (AVIV) and the void contents measured by acid drgestion. The constant 0.3.0.5 and 0.6 was used for three groups of samples, i.e. 0. unidirectional and quasiisotropic laminates; 0, woven carbon/epoxy laminates; A, woven carbon/polyimide laminates
The effect of void shape on dispersion may also be appreciated from the attenuation results through the K-K relation. Equation (17) can be further approximated as” Au, = v,(w) - II,
W%) = ___ 71
“J x&-J) dw’ __ s W, of2
(19)
The amount of dispersion Av, is, in general, dependent on z(w)/w’ so that the higher attenuation or the attenuation slope will bring about more dispersion. Since the unidirectional and quasi-isotropic laminates show the highest attenuation (slope) for a given void content, the dispersion of these samples will also be the highest in a given frequency range. Based on the correlation between the fractional velocity change and the void content, the void content can also be obtained by the relationship void content
= constant
AV x V
and D. K. Hsu
posites containing porosity. The measurements yielded the frequency dependent attenuation and phase velocity over the range of approximately 1 to 10 MHz. The relationship between attenuation and dispersion was tested using the local form of the KramerssKronig relation and found to hold in porous composite materials. The attenuation was found to be linearly dependent on the frequency, and its magnitude and slope were larger for laminates with more voids. The ultrasonic velocity decreases with increasing void content and the velocity dispersion increases as the frequency decreases. The void shape had a great effect on the constant that relates the void content and the attenuation slope da/df. It is therefore important to use prior knowledge about the laminate structure and the pore morphology in estimating the void content from the attenuation slope. The fractional velocity decrease (AV/V,) of the porous composite samples was found to be dependent both on the void shape and the frequency. The samples with the flat. elliptic voids gave a higher fractional velocity decrease than the samples with more spherical voids at all frequencies tested. Moreover, the samples with the flat, elliptic voids showed a stiffer decrease rate in A V/V, for a given void content. It is hoped that the experimental results obtained in this work will help the model development of wave propagation in porous carbon fibre composites for characterizing voids.
Acknowledgment This work was supported State University, USA.
References I
2 3 4
(20)
In this case. however, the constant depends not only on the void shape but also on the frequency. The void contents deduced from Equation (20) are compared with those obtained by acid digestion in Figure 9, where the predicted void contents were calculated from the values of fractional velocity change at 4 MHz (Figure 8b) using the constants of 0.3. 0.5 and 0.6 for the three groups of samples, respectively. Because of the velocity dispersion in the porous composite samples, different values of the constant should be used to estimate the void contents from the velocity data at other frequencies.
5
6
7
x 9
IO
Conclusions
II
An ultrasonic spectroscopic broadband through-transmission
202
Ultrasonics
1995
method was applied to measurements in com-
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by the Center for NDE at Iowa
12
Stone, D.E.W. and Clarke, B. Ultrasonic attenuation as a measure of void content in carbon-fiber reinforced plastics Non-De~slr Test (1975) 8 1377145 Martin, B.C. Ultrasonic attenuation due to voids in fiberreinforced plastics NDT In/ (1976) 9 2422246 Hale, J.M. and Ashton, J.N. Ultrasonic attenuation in voided fiber-reinforced plastics NDT I~I/ (1988) 21 321-326 Daniel, I.M., Wooh, S.C. and Komsky, I. Quantitative porosity characterization of composite materials by means of ultrasonic attenuation measurements .I Nor~tles/r Ecu/ (1992) II t-8 Nair, SM., Hsu, D.K. and Rose, J.H. Porosity estimation using the frequency dependence of the ultrasonic attenuation J Nornlestr Ertrl ( 1989) 8 13-26 Hsu, D.K. Ultrasonic measurements of porosity in woven graphite polyimide composites. In Rerien, of Proyrexs if7 &w~/itatice .YoJJtk~,.v/,JJc’J;~~’ fi’~~.(J/w~ioJ~, Vol. 7B (Eds Thompson, D.O. and Chimenti, D.E.) Plenum Press. New York, USA (1988) 1063~1068 Martin, B.G. Ultrasonic wave propagation in fiber-reinforced solids containing voids J Appl P/JJY (1977) 48 3368-3373 Reynolds, W.N. and Wilkinson, S.J. The analysis of tiberreinforced porous composite materials by the measurement of ultrasonic wave velocities L~l~rcwonic.v (1978) 16 1599163 O’Donnell, M., Jaynes, E.T. and Miller, J.G. General relationships between ultrasonic attenuation and dispersion J -Ic~o~r.r/SOC AUJ (1978) 63 1935-1937 Beltzer, A.I. and Brauner, N. SH waves of an arbitrary frequency in random fibrous composites via the K-K relations J MK/J Phy.~ SO/id\ ( 1985) 33 471-487 Gross, D. and Zhang, Ch. Wave propagation in damaged solids Int J Solids Structures (1992) 29 1763-l 779 Yuhas, D.E., Vores, C.L. and Roberts, R.A. Variations in backscatter attributed to porosity. In Reuiew @’ Proyress in
Porosity-induced
attenuation and velocity change: H. Jeong and 0. K. Hsu
Hughes,
Handley, SM., between frequency porosity in laminates.
Quantitative
D.E.) Plenum 13
1275-1284 Sachse, W. Pao, Y.-H. velocities of
New York,
(1986)
the determination phase and waves in J Appl 49
Qurmtitcrtire
D.O.
Notldestructire
Chimenti,
D.E.)
J.G. and ultrasonic In o/ Vol. 78 Press. New
E.I. A attenuation Progre.rs
Thompson, USA (1987)
(1978)
14
15
Pialucha, T., C.C.H. and method for measurement of 27 270-279 Thompson, R.B. Gray, T.A. ultrasonic scattering Nondestructive
16
D.O. and 567-586 D.K. Progress
water
Evaluation,
D.E.) Plenum and due to
in
(1976) 35
diffraction corrections In RecPlr Pruyress it? 2A (Eds New York, (1983)
H. Ultrasonic in composite Nondeswuctive
D.O. and (1989) 1567-1573 W. and
17
P. Amplitude velocity Ultrasonics
Evaluation,
D.E.) Plenum
change and In Review 8B (Eds New York,
20
21
23 K.H. Sound
in pure
sea
Hsu, D.K. Uhl, K.M. morphological study porosity defects carbon-epoxy composites. Review o/’ in Quautiratire Eruluutiotr. Vol. (Eds Thompson, and Chimenti, Plenum Press. York, USA 1175-1184 Williams, J.H., NayebHashemi, and Lee, Ultrasonic attenuation velocity in graphite fiber J Nun&s/r (1980) 1 Zhao, Y.H. Weng, G.J. elastic moduli ribbon-reinforced composites Appl MW/I 57 158-l Hill, R. of mechanical of fibre-strenthened I. elastic J Me& So/i& (1964) 199-2 12 Z. On behavior of reinforced materials arbitrary transverse geometry J P/~Jx Solid7 13 119-134
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