Coda Wave Interferometry for the Measurement of Thermally Induced Ultrasonic Velocity Variations in CFRP

Laminates

Richard Livings1, 2, a), Vinay Dayal1, 2, b), and Dan Barnard2, c)

1Department of Aerospace Engineering, Iowa State University, 1200 Howe Hall, Ames, IA 50011 2Center for NDE, Iowa State University, 111 ASC II, 1915 Scholl Road, Ames, IA 50011

a)Corresponding author: rlivings@iastate.edu

b)vdayal@iastate.edu c)dbarnard@iastate.edu

Abstract. Ultrasonic velocity measurement is a well-established method to measure properties and estimate strength as well as detect and locate damage. Determination of accurate and repeatable ultrasonic wave velocities can be difficult due to the influence of environmental and experimental factors. Diffuse fields created by a multiple scattering environment have been shown to be sensitive to homogeneous strain fields such as those caused by temperature variations, and Coda Wave Interferometry has been used to measure the thermally induced ultrasonic velocity variation in concrete, aluminum, and the Earth’s crust. In this work, we analyzed the influence of several parameters of the experimental configuration on the measurement of thermally induced ultrasonic velocity variations in a carbon-fiber reinforced polymer plate. Coda Wave Interferometry was used to determine the relative velocity change between a baseline signal taken at room temperature and the signal taken at various temperatures. The influence of several parameters of the experimental configuration, such as the material type, the receiver aperture size, and fiber orientation on the results of the processing algorithm was evaluated in order to determine the optimal experimental configuration.---This work is supported by the NSF Industry/University Cooperative Research Program of the Center for Nondestructive Evaluation at Iowa State University.

INTRODUCTION

The concept of using a scattering medium as in interferometer was originally developed by seismologists [1-3] and was latter introduced into the NDE community [4, 5]. The comparison of several multiply scattered ultrasonic waves and the extraction of differential signal features makes Coda Wave Interferometry (CWI) very sensitive to the detection of small perturbations of the elastic wave propagation within scattering media. Several perturbation types (thermal loading [6-10], mechanical loading [11-13], and cracking/degradation [14-16]) have already been examined. The sensitivity of CWI has been demonstrated for rocks [17], concrete [6-16], and metals [18]. Many of these results are summarized in review articles [19, 20]. To date, little to no work using coda waves in fibrous polymer composites has been performed.

The high sensitivity of CWI to minute changes in the propagation medium not only allows for the detection of small stresses and nonlinearities, but also provides sensitivity to environmental changes such as a change in temperature between recording the baseline and secondary signals. Often, the changes of the differential signal feature (in this case a change in the relative velocity) caused by temperature changes can be as large as or larger than the changes caused by stresses or damage. It is therefore important to understand how a change in temperature can affect the differential features. The effect of temperature change on the calculated coda wave relative velocity is well known [9, 21] for effectively isotropic materials. It has not, however, been studied for other material models.

This study examines the thermally induced coda wave relative velocity variation in unidirectional Carbon Fiber Reinforced Polymer (CFRP) laminate that fits the transversely isotropic material model. The directional dependence

of the coda wave relative velocity is determined by comparing data collected at fiber orientations of 0, 45, and 90 degrees. Coda wave relative velocity extraction for isotropic (Plexiglas) and transversely isotropic (CFRP) materials is also compared. This is additionally a comparison of a non-scattering (or boundary reflection scattering only), nondispersive medium to a highly scattering, dispersive medium. The effect of phase cancellation across the transducer surface is examined by comparing the extracted coda wave relative velocity for three receivers with differing aperture sizes for both the isotropic and transversely isotropic materials.

THEORY

A coda wave is one in which the acoustic energy has pseudo-randomly diffused through the medium. The term coda wave was first used by Aki in the late 60’s and early 70’s [22, 23] to refer to the late arriving portion of seismic waves. For NDE applications the coda wave is composed of any multiply scattered and reflected wave modes that become superimposed at the transducer face as shown in Fig. 1. A coda wave can be considered as a late arriving elastic wave in which it is not possible to identify distinct wave modes, in contrast to a coherent wave that usually precedes it, see Fig. 2. Often called diffuse waves, coda waves do not require the equipartition of acoustic energy and thus follow a less restrictive definition than that given for diffuse fields.

(a) (b)

FIGURE 1. Example of a wave propagating with multiple scattering events for a) through transmission and b) one-sided pitch-catch.

FIGURE 2. Sample ultrasonic signal showing the ballistic and coda portions of the received waveform.

Coda Wave Interferometry

Coda Wave Interferometry (CWI) was developed to detect small time-domain perturbations in the propagation medium that are normally undetectable using coherent waves by using a multiple scattering medium (scattering or reflections) as an interferometer [21]. The scattered waves repeatedly sample a region and accumulate small perturbations so that they become observable; this increases sensitivity when compared to coherent wave analysis [9].

The later the coda wave arrives the more pronounced the small perturbations become. Figure 3 shows the difference in the sensitivity to a small velocity perturbation between the early and late arrival portions of the received wave. Typical CWI is concerned with determining the relative time lag ∆t/t and the similarity between a baseline and post-perturbation waveforms. In the case of constant, homogeneous velocity perturbations, the relative time lag is the negative of the relative velocity, ∆V/V = - ∆t/t.

Estimation of the coda wave relative velocity variation is dependent on the propagation velocity and path of the different wave modes present. Monitoring the propagation for each individual mode is quite difficult to do since each scattering event will produce mode conversion. The superposition of these modes can be treated statistically, however [21], and the relative velocity variations can be calculated based on the propagation of acoustic energy and the mode conversion rates as (1) for constant velocity perturbations in an isotropic medium. For a Poisson medium, the relation reduces to (2). This indicates that the coda wave relative velocity can be determined by a change in moduli.

s

s

sp

p

p

p

sp

s

vv

vvv

vv

vvv

vv ∆

++

∆+

=∆

33

3

33

3

22

2 (1)

s

s

p

p

vv

vv

vv ∆

+∆

=∆ 91.009.0 (2)

Although the estimation of coda wave relative velocity is fairly straight forward in homogeneous, isotropic

materials, composite materials such as CFRP provide much more of a challenge. Wave modes in CFRP have different velocities in different directions, as shown in Fig. 4, and the thermally induced velocity change of each mode will also be different in all directions. This combined with the dispersive and attenuative nature of the material make analytical estimation of the relative velocity variation very difficult. It is likely, however, that the relative velocity change in the transverse direction will be larger than in the fiber direction due to dominance of matrix properties for transverse propagation and the increased sensitivity of the matrix moduli to thermal changes.

FIGURE 3. Ultrasonic waveforms collected from one-sided pit-catch UT on a 0.8 cm unidirectional CFRP plate subject to a 1.8 C temperature change. The two signals, h0 and h1, are collected before and after the temperature variation are the same in all three

plots with a) the entire recorded signal, and windowed signals at b) early propagation time, and c) late propagation time. The signals are transmitted and received with 1.25 cm, 1 MHz longitudinal transducers.

FIGURE 4. Velocity profiles for the three orthogonal wave modes in unidirectional CFRP. [recreated from Rokhlin, Chimenti,

and Nagy 2011]

Analysis Methodology

Three signal processing methods are widely used in literature to estimate the relative velocity variation produced by comparing collected signals before and after thermal loading: Cross-Spectral Moving-Window (also known as doublet) [3], Windowed Correlation [21], and Stretching [24]. A study by Hadziianou et al. [25] demonstrated that for pure, linear dilations, Stretching provides more stable and accurate results, especially in the presence of noise. The Stretching method was selected for this study based on the results of Hadziianou et al and the consideration that thermal loads produce almost pure dilation [26].

The Stretching method compares two time-domain signals, a baseline signal, h0(t), and a signal collected after a disturbance, h1(t), hereafter referred to as the measured signal. The measured signal is then dilated in time by dilation factor ε, giving h1(t(1-ε)). The similarity between the baseline and the dilated, measured signals is determined by the normalized cross-correlation coefficient evaluated at zero lag (4). A grid search is then used to find the dilation factor that maximizes the similarity between the baseline and dilated, measured signals: CC(εk) = Max(CC(εi)). If the velocity perturbation is linear, as it is for a homogeneous thermal load, then the relative velocity is proportional to the dilation factor εk: ∆v/v= - εk. The drawbacks of this technique are that it is computationally intensive since it involves a grid search and that its accuracy depends on the resolution of the dilation factor.

( )( )( ) ( )

( )( ) ( )∫∫∫

+

+=

dtthdtth

dtththCC

i

ii

21

20

10

1

1

ε

εε (3)

Both continuous time-domain signals are sampled with a sampling period of Ts such that hi[n] corresponds to the

sample at time t = nTs. The total number of samples is given as N. If the signals have been sampled using Nyquist criteria, then the continuous signal can be completely reconstructed using ideal bandlimited reconstruction (4).

( ) [ ]∑∞

−∞=

−=

n s

s

TnTtsincnhth (4)

A discreet signal can be perfectly reconstructed by evaluating (4) for specific time values giving ideal bandlimited interpolation (5). Since actual ultrasonic signals can be assumed to have zero amplitude for n<0 and n>N, a summation over the number of points in the signal is sufficient.

( )[ ] [ ] ( )∑=

−=

N

n s

s

TnTmtsincnhmth

0

ˆ (5)

Interpolation of the dilated signal is necessary in order to compare it to the baseline signal since the samples do

not otherwise line up and any further processing would be meaningless. For a dilated, discreet signal in the time domain, the sampling period becomes Ts(1+ε), therefore the interpolated signal is given by (6), where t(m)=t(n) for m=n.

( )[ ] ( )[ ] ( )( )∑

=

+

+−=

N

n s

s

TnTtsincnthmth

0 11ˆε

ε (6)

EXPERIMENTAL CONFIGURATION

Samples

Measurements were made on two samples; a 30x30x0.9 cm Plexiglas plate (isotropic) and a 30x31.8x 0.9 cm unidirectional CFRP plate (transversely isotropic) with the material properties summarized in Table 1. The Plexiglas plate, although simple in terms of material and geometry, is of interest because there is little to no internal scattering and minimal attenuation due to absorption. Therefore the development of coda waves will be due to reflections from the boundaries. By contrast, the CFRP plate is complex in terms of material with simple geometry: Development of coda waves will be due to multiple, strong Rayleigh scattering from the fiber-matrix interface in addition to the boundary reflections. The CFRP plate also exhibits high attenuation due to absorption, dispersive effects, and bulk wave velocities that vary with direction. The CFRP sample considered for this study was fabricated using 64 plies of Toray P2352W-19 unidirectional prepreg and was cured in a heated press. After fabrication, the laminate was examined for defects using immersion scanning. No defects were detected.

The specimens were subjected to thermal variations by heating them to 30˚C and allowing them to cool freely in an insulated enclosure (to slow down the specimen cooling rate) while monitoring the temperature with an Omega HH12 type-K thermocouple. Coda wave signals were collected periodically during the cool down of the specimens starting at 24˚C and continuing until room temperature was reached.

TABLE 1. Material properties of Toray P2352W-19 prepreg constituent parts. Density

(g/cm3)

Volume fraction

(%)

Tensile Modulus

(GPa)

Tensile Strength

(MPa)

Poisson’s Ratio

Acoustical Impedance

(MRayl) Plexiglas 1.19 100 3.10 72.39 0.35 2.43 Fiber (Toray T800S) 1.80 60 294 5880 0.3 26.70 Matrix* (Toray 3906-2B) 1.32 40 3.24 100 0.4 3.03

Laminate (from Toray) 100 154 2950 *Estimated properties

Ultrasonic Measurements

Three different transducers were used to collect the coda wave signals: a 12.7 mm Panametrics V103 p-wave transducer with 1MHz center frequency and -3dB bandwidth of 0.5-1.5 MHz, a 6.4 mm DWC B1025 acoustic emission transducer with a -3dB bandwidth of 0.05-2.0 MHz, and a 2 mm Valpey-Fisher pinducer with -3dB bandwidth of 0.001-10.0 MHz. These transducers were attached to the CFRP specimen using Crystalbond 555 (a water soluble wax with a flow point of 54˚C) at orientation of 0˚, 45˚, and 90˚ to the fibers with a radial separation of 8 cm from the transmitter. Figure 5 shows the locations of the transmitter and receivers for the CFRP plate. Both the transmitter and receiver were on the same side of the plate normal to the surface, thus there is no direct propagation between the two. A similar configuration was used for the pleixglas plate.

A conventional Panametrics 5052 PR ultrasonic pulser-receiver was used for a 300V spike mode excitation of a second 12.7 mm Panametrics V103 p-wave transducer as well as reception and waveform amplification. Primary amplification of the waveform came from a Panametrics 40dB constant gain ultrasonic preamp. Waveforms were digitized with a sampling frequency of 10MHz using a Lecroy LT342 Waverunner digital oscilloscope with 8-bit resolution. The recorded waveform was averaged 200 times and successive windows were taken to maximize the volts per division and hence the resolution. Waveforms were then transferred via GPIB to a computer for storage and later processing. Figure 6 shows a schematic of the ultrasonic system configuration.

For all of the configurations, the waveform collection starts and ends at 0 µs and 1500 µs respectively. This window length is sufficient to capture most of the energy in the ultrasonic field from the Plexiglas specimen and is more than sufficient for the CFRP specimen. The choice of collection length is to ensure that the elastic waves have had enough time to interact with the sample and become sufficiently diffused. Note that an arrival time of 1500 µs is equivalent to a longitudinal wave traveling ~4,500 mm in Plexiglas and ~4,500-15,000 mm in CFRP (depending on direction), which is at least 15 times (for Plexiglas) the largest dimension of the plate.

(a) (b)

FIGURE 1. Illustrations of the unidirectional CFRP plate showing the sample dimensions and the transducer placement locations.

(a) (b)

FIGURE 2. Experimental configuration for one-sided pitch-catch ultrasonic transmission with a) photo of the configuration and b) schematic of the configuration.

Error Analysis

The error involved in the determination of the coda wave relative velocity is not just a matter of accurate time and distance measurement. Since the coda wave samples a large volume and consists of the superposition of many wave modes, the error analysis becomes nontrivial very quickly. It has been shown previously by several authors that errors in the determination of coda wave relative velocity can be introduced by transducer positioning error, variation in the

transducer coupling, and errors introduced by the processing algorithm. The positioning and coupling errors are negated by coupling the sensors to the specimen semi-permanently during the tests. The combined algorithm errors and measurement errors can be estimated by taking repeated measurements at a constant temperature.

The temperature measurement error is a combination of the sensor error and the thermocouple error, where Esensor = 0.3% of measurement + 1˚C and Ethermocouple = max(0.4% of measurement, 1.1˚C) [www.omega.com]. Since the error of the thermal couple wire is a calibration constant, it is only necessary when determining absolute temperature. When considering relative temperature measurements the wire calibration does not affect the measurement and the measurement error is due solely to the sensor error. This was confirmed experimentally by using two separate thermocouple wires simultaneously with the same sensor. When measuring temperature differences (as we are in this study) the cold junction compensation (CJC) error, which normally dominates the sensor error, becomes insignificant as long as the sensor itself is held at near constant temperature. The error in consecutive temperature measurements is therefore given as Etemperature = 0.3% of measurement.

RESULTS AND DISCUSSION

Figure 7 shows the results from the one-sided pitch-catch propagation through the Plexiglas specimen. The raw signals and spectra (Fig. 7a) are highly dependent on the receiver type. Similar, periodic amplitude spikes are observed in the raw signals which correspond to a spectral peak around 0.5 MHz and are likely due to the plate thickness. The overall structure of the signals is quite different however as can be seen by the differences in the spectra. The distribution of spectral energy decreases in frequency as the receiving transducer face increases in diameter, though similar spectral peaks are present in all three spectra. The maximum signal to noise ratios are also similar for the 12.5, 5.25, and 2 mm receivers with ratios of 62, 59, and 60 dB respectively. Significant differences in S:N occur at late times where the 12.5 mm receiver has the best ratio at 30 dB, the 2 mm has 23 dB, and the 6.25 mm has 12 dB. The S:N ratio is determined by taking the ratio of the signal amplitude to the amplitude at very late times when only the system noise is present (see Fig. 2).

Thermally induced relative velocity variations from the Plexiglas specimen are shown in Fig. 7b. The relative velocity variations are very similar for the 12.5 and 6.25 mm receivers with a few outliers. The results from the 2 mm receiver is also very similar to the other two for temperatures close to room temperature, but deviates from the other two with increasing temperature change. This deviation can be attributed to the higher uniformity of the signal yielding multiple instances of highest correlation. The deviation can be corrected by examining the results and manually selecting the correct maximum correlation. The three transducer-receiver pairs behave as expected for an isotropic, homogeneous material with thermal loading (i.e. they all yielded very similar results). Little to no evidence of phase cancellation was observed for the different receivers.

(a) (b)

FIGURE 3. Results of waveforms collected from one-sided pitch-catch UT on 0.9 cm Plexiglas plate. Signal was transmitted with a 1.25 cm, 1 MHz P-wave transducer and a spike excitation and was received with the three transducers at the 0˚ orientation; the transducer pairs separated by 8 cm. a) is the raw waveforms and spectra; b) is the thermally induced relative velocity variation

vs. receiver type.

The raw baseline signals collected from the CFRP specimen for each transmitter-receiver pair and each orientation as shown in Fig. 8 while the corresponding spectra are shown in Fig. 9. It is immediately apparent that the signals are receiver and angle dependent. Figure 8 and 9 show that the signals change drastically with orientation. The 0˚ arrives and dies out very quickly while the 45˚ and 90˚ signals arrive latter (with the 90˚ arrive ~10µs after the 45˚ signal) and last much longer. The spectral content also changes drastically with receiver orientation, which is shown by the distribution of spectral energy decreasing with increasing receiver angle. This is likely to be due to fiber- and matrix-dominated properties similar to those observed by Vary [27]. The high attenuation in CFRP allows for lower frequency (slower) wave modes to travel farther. The attenuation properties can be easily seen when inspecting a thick vs thin composite with direct propagation.

In direct propagation, the fiber direction has a higher effective modulus, thus the fiber direction has a higher propagation velocity (Fig. 4) which allows higher frequencies to travel farther before being attenuated out. On the other hand, the transverse direction is matrix dominated, has a lower effective modulus, and a lower propagation velocity which allows for higher frequencies to be attenuated out before they can travel very far. The indirect propagation used in this study shows similar trends to direct propagation, which is unexpected. This indicates that high frequencies prefer the fiber direction and low frequencies prefer the transverse direction. It is interesting to note that the 45˚ orientation is much more similar to the 90˚ orientation than the 0˚. Since the indirect signals demonstrate this preferential behavior, we can predict that we should observe large relative velocity variations in the 45˚ and 90˚ orientations due to the larger moduli variation in the matrix than in the fibers.

FIGURE 4. Typical ultrasonic waveforms collected from one-sided pitch-catch UT on 0.9 cm unidirectional CFRP plate. Signal was transmitted with a 1.25 cm, 1 MHz P-wave transducer and a spike excitation. The transducers were 8 cm apart. The columns

indicate the receiver type used and the rows indicate the angle of the transmitter-receiver pair to the fibers.

TABLE 2. Ultrasonic receiver characteristics and signal-to-noise ratios from waveforms collected from one-sided pitch-catch UT on a 0.9 cm unidirectional CFRP plate. The signal is transmitted with a 1.25 cm, 1 MHz P-wave transducer with spike excitation. The transmitter and receivers are separated by 8 cm, and the angle indicates the

angle of the transmitter-receiver pair to the fibers. Size (mm) BW (MHz) S:N (dB) (Maxium, at 2.5 µs) 0˚ 45˚ 90˚ P-wave 12.5 0.5-1.5 (62, 30) (54, 30) (54, 32) AE 6.25 0.05-2.0 (59, 22) (49, 30) (52, 34) Pinducer 2 0.001-10.0 (60, 23) (60, 23) (50, 29)

FIGURE 5. Typical ultrasonic spectra collected from one-sided pitch-catch UT on 0.9 cm unidirectional CFRP plate. Signal was

transmitted with a 1.25 cm, 1 MHz P-wave transducer and a spike excitation. The transducers were 8 cm apart. The columns indicate the receiver type used and the rows indicate the angle of the transmitter-receiver pair to the fibers.

The signals and spectra from Figs. 8 and 9 show the effect of the receiver on the signal. Similar trends can be

observed between the signals and spectra from the CFRP specimen and those from the Plexiglas specimen. The signal changes with receiver, but the main signal features are present in all signals and the main features become obscured with decreasing aperture size. Contrary to the Plexiglas results, the distribution of spectral energy from the CFRP sample decreases in frequency with aperture size and becomes more diffuse for the 45˚ and 90˚ fiber angles. Similar structures are present in the 12.5 and 6.25 mm receiver spectra. The diffusing of the 2 mm spectrum indicates that the transducer may have an issue with self-noise.

Table 2 gives the characteristics of the receivers used in this study along with the measured maximum and late time signal to noise ratios. The best overall S:N ratio is produced by the 12.5 mm receiver followed by the 6.25 mm and finally the 2 mm. Late time S:N ratios are roughly the same regardless of the receiver or orientation. Phase cancellation is a concern mentioned in some literature, but its importance in experiment has not been measured. Phase cancellation should reduce with aperture size, which would make the 2 mm receiver ideal, but all three receivers have thus far given near equal performance.

The thermally induced relative velocity variations measured from the CFRP sample are plotted in Figs. 10 and 7. Linear trends are observed which indicate that, as with isotropic materials, the thermal loading of transversely isotropic (or slightly orthotropic) materials also produces nearly pure dilation of acoustic waves.

It is interesting to note that unlike the Plexiglas results, the receivers demonstrate different sensitivities for each of the orientations (Fig. 6a, b, and c) with the variance of the sensitivities decreasing with increasing fiber angle (Table 3). Thus the sensitivity of coda wave relative velocity to thermal changes is affected by both the receiver type and the fiber orientation. A comparison of the effect of fiber angle for each of the receivers is shown in Fig. 7a, b, and c where it is clear that the fiber angle has a dramatic effect on the receiver sensitivity, with the 12.5 mm receiver showing the maximum variance in sensitivity while the 2 mm receiver shows the least. This demonstrates that the pinducer is nearly insensitive to fiber orientation while the 12.5 mm receiver is the most sensitive. Also notable is that the 12.5 mm receiver at a 0˚ fiber angle is most sensitive to thermal changes.

Our expectation of phase cancellation can partially explain the observed differences in receiver sensitivity at various fiber angles. As observed in Fig. 4 and 9 the scattered waves that travel along the fibers experience a higher velocity and less visco-elastic absorption, thus allowing higher frequency modes to propagate farther than in the

transverse direction. Phase cancellation should be more prevalent as the ratio of aperture diameter the wavelength increases. Also, our prediction of increased relative velocity change with increasing fiber angle can be observed in the results from the 6.25and 2 mm receivers (Fig. 11). The 12.5 mm receiver does not show this trend as the results for the 0˚ fiber angle is likely greatly affected by phase cancellation.

(a) (b) (c)

FIGURE 6. Thermally induced relative velocity variations vs. receiver type (1 MHz P-wave, AE, and Pinducer) for a) 0˚, b) 45˚, and c) 90˚ transmitter-receiver pair orientations. Signal is transmitted in a 0.8 cm unidirectional CFRP plate in one-sided pitch-catch mode with a 1.25 cm, 1 MHz P-wave transducer and a spike excitation. Transmitter and receivers are separated by 8 cm.

(a) (b) (c)

FIGURE 7. Thermally induced relative velocity variations vs. fiber angle (0˚, 45˚, and 90˚) for a) 1.25 cm, 1 MHz P-wave, b) 6.25 mm AE, and c) 2 mm Pinducer receivers Signal is transmitted in a 0.8 cm unidirectional CFRP plate in one-sided pitch-

catch mode with a 1.25 cm, 1 MHz P-wave transducer and a spike excitation. Transmitter and receivers are separated by 8 cm.

TABLE 3. Slopes of the linear trend lines in Fig. 7b, Fig. 10, and Fig. 11. The trend lines were determined by using a least squares linear fit.

Plexiglas CFRP 0˚ 0˚ 45˚ 90˚ P-wave -0.2039 -0.2261 -0.0180 -0.0796 AE -0.2103 -0.0687 -0.1797 -0.1009 Pinducer -0.1200 -0.1096 -0.1346 -0.1293

CONCLUSION

The effect of receiver aperture size on the measurement of the thermally induced ultrasonic coda wave relative velocity has been examined for both Plexiglas (isotropic with little to no scattering) and CFRP (transversely isotropic with significant scattering). The effect of fiber angle for CFRP has also been examined. In the isotropic and the

transversely isotropic materials, the aperture affects the received waveform by obscuring the signal features and making it more uniform with decreasing aperture size. The effect on the spectra is to change the spectral energy distribution center frequency (increasing for the Plexiglas and decreasing for the CFRP) with decreasing aperture size.

Although the waveform and spectra are affected by the aperture size, the relative velocity variation measurement was not affected for the Plexiglas sample. The aperture size had a dramatic effect on the relative velocity measurement for the CFRP sample by causing a variance in the ∆V/V vs. T sensitivities for all orientations. The minimum variance was observed for the 2 mm receiver, which is an indication of the presence of phase cancellation for the other receivers.

Fiber orientation also had a dramatic effect on the relative velocity measurement, again by a causing a variance in the ∆V/V vs. T sensitivities for the three receivers. The variance decreases with increasing fiber orientation which indicates the presence of fiber- and matrix-dominated properties that need to be further studied.

At this point, it is difficult to say which receiver is optimal, or why the aperture size and receiver orientation have such a great effect on the relative velocity measurement in CFRP but not in Plexiglas. Currently there is no good scattering or coda wave model for composite materials, or for non-isotropic materials. Future work includes further examination of coda wave propagation and formation in CFRP materials as well as an investigation into the scattering properties of CFRP and phase cancellation.

ACKNOWLEDGMENTS

This material is based on work supported by the NSF Industry/University Cooperative Research Program of the Center for Nondestructive Evaluation at Iowa State University.

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