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Lamb wave method for quick inspection of impact-induced delamination in composite laminates
COMPOSITES SCIENCE AND TECHNOLOGY Composites Science and Technology 64 (2004) 1293–1300 www.elsevier.com/locate/compscitech
Lamb wave method for quick inspection of impact-induced delamination in composite laminates N. Toyama *, J. Takatsubo Smart Structure Research Center, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan Received 10 March 2003; received in revised form 8 September 2003; accepted 20 October 2003 Available online 16 December 2003
Abstract This paper proposes a new inspection technique using Lamb waves to detect impact-induced delamination in composite laminates. The technique, which consists of two line scans, is as follows. The first scan measures the arrival times of the transmitted S0 mode along the 0° direction to detect delamination and evaluate its size. The second scan measures the maximum amplitude of the earliest wave packet in a line, including the longest delamination, to locate its edge. We performed this technique on impacted CFRP cross-ply laminates. A remarkable decrease in the arrival times due to the delamination is detected, and the delamination length can be calculated based on a simple model for Lamb-wave propagation. Furthermore, the delamination edge is located as a sudden decrease in the amplitude. The technique enables detecting the delamination and evaluating its size and location using only the two scans. We demonstrated the validity and usefulness of this technique. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: A. Polymer matrix composites (PMCs); B. Impact behavior; C. Delamination; D. Non-destructive testing; D. Ultrasonics
1. Introduction Composite laminates are valuable structural components for aircraft and spacecraft because of their superior specific strength and stiffness. Composite structures in these safety-critical applications must be inspected frequently to ensure safety and reliability, and prevent catastrophic failure. Current inspection practices employ non-destructive evaluation (NDE) techniques such as X-ray or ultrasonic C-scan to identify internal damage. However, the use of these techniques for inspecting large structures is very time consuming and expensive. Therefore, a new NDE technique to detect damage quickly and reliably is necessary. Should any damage be found, the conventional method can then be applied to characterize the damage in detail. Internal damage from low-velocity impact is the most prevalent type of damage found in composite structures. *
Corresponding author. Tel.: +81-29-861-3025; fax: +81-29-8613126. E-mail address: [email protected] (N. Toyama). 0266-3538/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2003.10.011
This damage, in the form of matrix cracks, delamination and fiber breakage, is invisible to the naked eye and is easily induced from something as simple as a tool being dropped during maintenance. Of the various types of damage, delamination in particular causes a significant loss of compressive strength and stiffness. Therefore, numerous experimental and analytical techniques [1–6] have been developed to better understand the mechanisms and mechanics of impact damage in composite laminates. Ultrasonic Lamb waves are one of the techniques that have potential for long-range inspection because they can propagate a long distance. When a receiving transducer is positioned at a remote point on the structure, the signal received contains information about the integrity of the line between the transmitting and receiving transducers. Many studies have been conducted to detect damage in composite laminates using the Lamb wave method. Tang and Henneke [7], Dayal and Kinra [8], Seale et al. [9], and Toyama et al. [10] detected transverse cracks in CFRP cross-ply laminates as a reduction in Lamb wave velocity due to a loss of stiffness. Based on their studies, measuring Lamb wave velocity has the
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potential to quantitatively evaluate damage in composite laminates. Guo and Cawley [11,12] and Valdes and Soutis [13] detected delamination in CFRP laminates by a reflected wave at the delamination edge, and determined its location using the arrival time of the reflected wave. However, a reflected wave is often not clearly detectable because its amplitude is reduced due to scattering at the delamination edge. The dispersive nature of Lamb waves, as well as attenuation, creates more difficulty in distinguishing the reflected wave from the detected waveform. Tan et al. [14], Birt [15] and Bourasseau et al. [16] detected delamination in CFRP laminates and foam core sandwich structures based on attenuation of the transmitted Lamb wave. Their method is a simple and reliable method to detect damage. However, it is very difficult to quantitatively evaluate the delamination size using waveform changes, including attenuation. This paper develops a quick and quantitative inspection technique for impact-induced delamination in composite laminates. Based on previous studies on impact damage, we have designed a new method to detect and identify delamination, and evaluate its size and location using Lamb wave velocity and attenuation. The method consists of only two line scans. The first scan measures the distribution of the arrival times of the transmitted S0 mode along the 0° direction before and after impact; the second scan then measures the transition of the maximum amplitude of the earliest wave packet. We performed this technique on impacted CFRP cross-ply laminates, and compared the estimated delamination size and location with the data obtained by a conventional C-scan. 2. Principle of Lamb wave inspection Only the S0 mode and the A0 mode propagate in the frequency-thickness product range below 1 MHz mm. In this region, the S0 mode is almost non-dispersive, while the A0 mode is highly dispersive. The velocity of both modes is directly related to the properties of the materials; the S0 mode velocity has a higher dependence on the in-plane stiffness than the A0 mode. Furthermore, the S0 mode velocity is much higher than that of the A0 mode. The leading edge of the detected waveform is thus easily identified as the S0 mode. Since the S0 mode velocity is useful for detecting stiffness changes caused by damage, we focused solely on the S0 mode for this study. The S0 mode velocity in the low frequency-thickness product for the principal axis of the orthotropic laminate is simply expressed as [17]: sffiffiffiffiffiffiffi A11 ð1Þ V ¼ qh where A11 is the in-plane stiffness, q is the density and h is the thickness of the laminate.
We demonstrated that, in ½0=90n S cross-ply laminates [18], a Lamb wave propagated separately in the delaminated region because the interfacial continuity between the 0° and 90° layers was no longer retained. Based on this, the wave velocity in the delaminated region depends on the location, i.e., the interface at which the delamination initiates, and the size of the delamination in composite laminates. Multiple delaminations generally initiate at various interfaces for ½0=90nS and quasi-isotropic laminates under static or fatigue loading. Although we can detect the presence of the delamination as a change in the wave velocity, we cannot quantitatively evaluate the delamination length in such cases. As experimentally and analytically confirmed in the previous study on low-velocity impact damage [1–6], the major, nearly elliptical delamination is initiated at the bottom interface (the interface away from the impact side), and propagates in the fiber direction of the bottom layer for both cross-ply and quasi-isotropic laminates. Based on these results, when the wave propagates in the fiber direction of the bottom layer (defined as the 0° layer in this study), the wave propagates separately in the delaminated region, i.e., through the bottom 0° layer and the rest of the layers. The in-plane stiffness of the 0° layer is the highest, so the wave velocity increases in the delaminated region. The effect of the bending crack along the fiber direction in the bottom 0° layer on the wave velocity was regarded as small and neglected in this study. Considering the presence of a delamination with length L at the bottom interface, the difference in the transmitting time of the wave for L between intact and delaminated states is expressed as: 1 1 Dt ¼ 0 L ð2Þ Vi V where Vi and V 0 are the wave velocity of the intact laminate and the 0° layer. Hence L can simply be expressed as: L¼
V 0 Vi Dt V 0 Vi
ð3Þ
Consequently, we can quantitatively evaluate the length of the major delamination induced by low-velocity impact loading by measuring the arrival time of the transmitted wave along the 0° direction, and by using Eq. (3). This major delamination is of particular interest here and will be considered exclusively in this study.
3. Experimental procedures The material studied was T800H/3631 (CFRP) crossply laminates with stacking sequences of [0/903 ]S and [0/ 90]2S . These composite plates (300 mm 300 mm 1 mm) were fabricated with unidirectional prepregnated
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sheets by a hot-press machine in accordance with the manufacturerÕs recommended processes. The mechanical properties of the unidirectional laminate obtained by the tensile test are listed in Table 1. Fig. 1 illustrates the present method, which consists of two line scans for inspecting impact-induced delamination. The objective inspection area within the plate was 210 mm long and 200 mm wide. We generated a low-velocity impact using a vertical drop-weight impact machine to induce impact damage within the area. The machine, consisting of two vertical steel rods mounted on a heavy steel block, was similar to that was used by Aslan et al. [6]. The panels were impacted with a hemispherical impactor with a diameter of 15 mm. We set the total mass of the entire drop-weight to 1.5 kg, and the falling distance to 0.5 m. The first scan measures the distribution of the arrival times of the transmitted Lamb wave along the 0° direction before and after impact to detect and evaluate the size of the major delamination. The transmitter– receiver system is moved in a line parallel to the Y axis (90° direction) with a constant distance between the transducers (210 mm). A decrease in the arrival time after impact indicates the presence of delamination, and Table 1 Measured mechanical properties of unidirectional CFRP laminate Property
Values
Longitudional YoungÕs modulus, E1 (GPa) Transverse YoungÕs modulus, E2 (GPa) Longitudional shear modulus, G12 (GPa) PoissonÕs ratio, m12 Ply thickness (mm) Density, q (kg/m3 )
157.6 8.67 3.83 0.38 0.134 1571
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we calculate its length by Eq. (3) using the measured difference in the arrival times. However, the first scan cannot determine the X position of the delamination. Its precise location can be determined by the following second scan; the transmitter is positioned on the line corresponding to the maximum delamination length and the receiver is scanned along a line parallel to the X axis (0° direction) away from the transmitter. A sudden change in the maximum amplitude of the earliest wave packet then determines the X position of the delamination edge. These scans were initially performed in steps of 10 mm. When delamination was detected, additional measurements were performed to improve the estimation of the delamination width and location. We manually performed the scans on the impacted side of the plates. Fig. 2 illustrates the experimental set-up for Lamb wave generation and detection. A variable-angle-beam transducer consisting of a broadband transducer element (V414-SB, 0.5 MHz, Panametric) and a Perspex wedge (ABWX-2001, Panametric) was used as the ultrasonic transmitter to excite Lamb waves. In order to generate a pure S0 mode, the angles of incidence were determined by SnellÕs law as [8,14,15]: h ¼ sin1
VL VP
ð4Þ
where h is the angle of incidence, and VL and VP are the longitudinal wave velocity in the wedge (2720 m/s) and phase velocity of the S0 mode. An AE sensor (M304A, Fuji Ceramics) with a small diameter of 4 mm was chosen as a receiver. Both the transmitter and receiver were mounted on the surface of the laminate via a coupling gel. The excitation signal applied to the transmitter was 5 cycle of a 0.3 MHz tone burst enclosed in a Hamming window generated by an arbitrary function generator (33250A, Agilent), and amplified by a high-speed bipolar
Arbitrary function generator
High-speed amplifier
Impact
Transmitter
Receiver Major delamination
Trigger Digital oscilloscope Fig. 1. Schematic representation of the present line-scanning methods. The first scan measures the arrival time of the transmitted S0 mode along the 0° direction to detect and evaluate delamination size, and the second scan measures the maximum amplitude of the earliest wave packet in order to locate the longest delamination edge.
Amplifier
Arrival time Maximum amplitude Fig. 2. Schematic diagram for Lamb wave generation and detection.
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amplifier (HSA4011, NF). The detected signals were amplified (A1002, Fuji Ceramics) and transferred to a digital oscilloscope (TDS7054, Tektronix), which carried out 100 averages to improve the signal-to-noise ratio. An arbitrary function generator also transferred a trigger signal to the oscilloscope to set the initial time. The arrival time of the transmitted wave at the receiver was determined using the peak time of the first cycle of the earliest wave packet. Fig. 3 depicts a typical waveform detected at the receiver for ½0=903 S plate. The shape of the excitation signal was maintained, and we confirmed that the S0 mode was nearly non-dispersive in the present frequency-thickness product of 0.3 MHz mm. The arrows show the arrival time and maximum amplitude defined in this study. The peak amplitude of the first cycle used to measure the arrival time was lower than the entire signal, thus we magnified the leading part of the detected signal in the practical measurements. The S0 mode velocity was first measured before the inspection. To measure the time differences, we first mounted the AE sensor 30–150 mm apart from the transmitter in steps of 30 mm. A least-squares fit from a plot of time and distance was performed to obtain the wave velocity. The measured and predicted (from Eq. (1) using the values listed in Table 1) wave velocity is listed in Table 2. The predicted wave velocity was in good agreement with those measured for all laminates.
5
4. Experimental results 4.1. First scan results The experimental results of the distribution of the arrival times measured by the first scan are illustrated in Fig. 4. The scatter in the arrival times before impact was mainly due to the inhomogeneous nature of the laminates. Despite the scatter, remarkable decreases after impact were detected from the Y positions of 9.5 to 12 cm for ½0=903 S , and 10.5 to 11.5 cm for ½0=902S . These decreases indicate the presence of delamination, not matrix cracking or fiber breakage, which reduces the wave velocity. Thus, we were first able to detect and identify the delamination between the regions. Fig. 5 depicts a detected waveform at the Y position of 10.5 cm after impact for ½0=903 S . In comparison with the detected waveform before impact depicted in Fig. 3, the
62 61
Arrival time (µs)
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58 57
Before After
56
3
55
Arrival time
1
0
2
4
Delamination width 6
8
10
12
14
16
18
20
16
18
20
Y position (cm)
(a)
0
50
-1 -2 -3
49
-4 -5 40
60
80
100
120
Time (µs) Fig. 3. Waveform detected 210 mm from transmitter for ½0=903 S .
Arrival time (µs)
Amplitude (Voltage)
59
Maximum amplitude
4
2
60
48
47
Before After
46 Table 2 Measured and predicted S0 mode velocity for CFRP laminates Laminate
Measured (m/s)
Predicted (m/s)
½08 ½0=903 S ½0=902S
10,144 5420 7344
10,056 5427 7304
0 (b)
2
4
Delamination width 6
8
10
12
14
Y position (cm)
Fig. 4. Experimental results of the first scan; distribution of arrival time of transmitted S0 mode along the 0° direction before and after impact for: (a) ½0=903 S ; (b) ½0=902S .
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50
1.5
0.5
Maximum amplitude
Delamination length (mm)
Amplitude (Voltage)
1.0
Arrival time
0.0 -0.5 -1.0 -1.5 40
1297
60
80
100
4.2. Second scan results Based on the results from the first scan, we performed the second scan parallel to the X axis at only the Y position containing the major axis of the delamination. Experimental results of the transition of the normalized maximum amplitude of the earliest wave
20 10 0
0
2
4
6
8
10
12
14
16
18
20
14
16
18
20
Y position (cm)
(a)
Fig. 5. Waveform detected 210 mm from transmitter at the Y position of 10.5 cm after impact for ½0=903 S .
70
Delamination length (mm)
shape of the excitation signal was no longer maintained, and considerable attenuation in the earliest wave packet was observed. However, we could clearly observe a decrease in the arrival time after impact. In this study, we assumed the shape of the major delamination as an ellipse in both laminates. Based on this assumption, the minor axes of the major delamination were estimated from Fig. 4 as 25 mm for ½0=903 S , and 10 mm for ½0=902S . Fig. 6 depicts the calculated delamination length using the measured difference in the arrival times before and after impact. We used the predicted values of the Vi and V 0 for the right side of Eq. (3) in the calculations. The scatter in the intact regions was due to errors in the measurements. The detectable delamination length should be longer than the ranges of the scatter. We could therefore estimate the detectable delamination length to exceed about 10 mm based on the results shown in Fig. 6. The impact energy generated in this study induced the longer delamination, allowing us to estimate the longest delamination lengths, i.e., the major axes of the delamination and their linear locations, as 42 mm at the Y position of 10.5 cm for ½0=903 S , and 61 mm at the Y position of 11 cm for ½0=902S . From the first scan, we could detect and identify the delamination and estimate its size and linear location. The only unknown parameter was the X position of the delamination.
30
-10
120
Time (µs)
40
60 50 40 30 20 10 0 -10
(b)
0
2
4
6
8
10
12
Y position (cm)
Fig. 6. Distribution of delamination length calculated from the measured difference in arrival times obtained by the first scan for: (a) ½0=903 S ; (b) ½0=902S .
packet are provided in Fig. 7, which also includes the results at the Y position of 7 cm (intact regions) as a reference. The maximum amplitude gradually decreased due to attenuation in the intact regions. However, a sudden decrease was observed in the presence of the delamination, and the lower amplitude was maintained even beyond the delamination for both laminates. Tan et al. [14] offered several explanations for the amplitude reduction over the delamination, i.e., wave separation, mode conversion to the A0 mode, or wave scattering at the delamination edge. Based on their suggestions, the location of the sudden decrease in the amplitude indicates the front edge of the major axis of the delamination. We estimated the locations of the delamination edges as the X positions of 11 cm for ½0=903 S , and 10.5 cm for ½0=902S , from the results of the second scan. We quantitatively estimated the size and two-dimensional location of the delamination from the two scans.
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1.2
Y = 10.5 cm Y = 7 cm
Normalized amplitude
1.0 0.8 0.6 0.4
Delamination edge
0.2 0.0
0
2
4
6
8
10
12
14
16
18
20
X position (cm)
(a)
1.2
Y = 11 cm Y = 7 cm
Normalized amplitude
1.0 0.8 0.6
Delamination edge
0.4 0.2 0.0
(b)
0
2
4
6
8
10
12
14
16
18
20
X position (cm)
Fig. 7. Experimental results of the second scan; distribution of normalized maximum amplitude of the earliest wave packet at the Y positions of damaged and intact regions for: (a) ½0=903 S ; (b) ½0=902S .
4.3. Comparison with C-scan results We performed a conventional C-scan to validate the present method. The inspection area was 100 mm 100 mm, including the delamination, and was scanned in steps of 1 mm. Fig. 8 presents the C-scan image depicting the major impact-induced delamination at the bottom interface. We confirmed that the delaminations were nearly elliptical and that their major axes were parallel to the 0° direction in both laminates. The delaminations were 51 mm long and 28 mm wide for ½0=903 S , and 60 mm long and 12 mm wide for ½0=902S from the C-scan results. Additionally, we observed the cross-section of the impacted plates by an optical microscope to measure the real delamination length. We found a partially intact region of about 6 mm long between the delaminations at the bottom interface just under the impact point for ½0=903 S , which was hardly distinguishable from the C-scan image. Thus the real
Fig. 8. Conventional C-scan image depicting impact-induced delamination and evaluated size and location by the present method for: (a) ½0=903 S ; (b) ½0=902S .
major axis of the delamination length was 45 mm for ½0=903 S . In contrast, we did not observe such a partially intact region for ½0=902S , and the major axis was accurately estimated by the C-scan. Fig. 8 also includes the delamination size and location estimated by the present method. All estimates agreed well with the results obtained by C-scan and microscopic observation, and we demonstrated that the present method accurately evaluated the size and location of impact-induced delamination.
5. Discussion We will discuss the applicable ranges and advantages of the present method below. The specimen plates used
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in this study were 300 mm long, with the objective inspection length as 210 mm. The specimen length was the maximum due to the limitations of the hot-press machine (ranges longer than this could not be investigated). However, all the detected signals, even in the presence of the delamination, maintained a high signal-to-noise ratio despite considerable attenuation. Additionally, the higher amplitude was maintained after the delamination in ½0=902S , which is more important laminate in industrial applications. The inspection range could therefore be extended using this system. Furthermore, in this study we performed the first scan before impact, and determined the difference in the arrival times obtained in the same line before and after impact in order to eliminate the effect of the inhomogeneous nature of the laminates on evaluating the delamination length. We also calculated the major axes of the delamination using the arrival times in the intact state as the average values obtained by the measurements in the intact regions after the impact. The calculated lengths were 45 mm for ½0=903 S and 59 mm for ½0=902S , (nearly the same as those previously evaluated). Therefore, we were able to omit measurements before impact, which is important in practical use. As reported previously [14–16] and as depicted in this study in Fig. 5, a change in detected waveform (including attenuation) can clearly indicate the presence of damage located between the transducers. This simple technique is therefore very useful when it is necessary to quickly ascertain whether damage is present. However, identifying the type of damage, i.e., transverse crack, delamination, and/or fiber breakage, and evaluating delamination size are difficult. The present method of simply measuring the change in the arrival time can identify the impact damage found as a delamination and can evaluate its size. It is very important to note that the present method using only two line scans is simple and reliable, qualities required for quick inspection of a large surface area, as opposed to the point-by-point scan used in conventional C-scan technique. Considerable time saving can therefore be achieved while maintaining the ability to accurately evaluate the delamination.
6. Conclusions In this paper, we propose a quick and quantitative inspection technique using a Lamb wave method consisting of two line scans for detecting impact-induced delamination in composite laminates. We applied this technique on T800H/3631 (CFRP) cross-ply laminates with stacking sequences of ½0=903 S and ½0=902S . The first scan measured the distribution of the arrival times of the transmitted S0 mode along the 0° direction before
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and after impact. We were able to identify the major delamination and quantitatively evaluate its size and linear location. The second scan then measured the transition of the maximum amplitude of the earliest wave packet in a line including the major axis of the delamination. A sudden drop in the amplitude was clearly observed, and we were able to determine the location of the delamination edge. We could easily and quantitatively evaluate the size and two-dimensional location of the delamination using only two scans. A conventional C-scan validated this method, and we confirmed our method has great potential for quick inspection of impact-induced delamination in composite structures.
Acknowledgements This study was supported in part by the Ministry of Education, Culture, Sports, Science and Technology of Japan under Grant-in-Aid for Scientific Research (14750568).
References [1] Choi HY, Chang FK. A model for predicting damage in graphite/ epoxy laminated composites resulting from low-velocity point impact. J Compos Mater 1992;26:2134–69. [2] Choi HY, Downs RJ, Chang FK. A new approach toward understanding damage mechanisms and mechanics of laminated composites due to low-velocity impact: Part I – experiments. J Compos Mater 1991;25:992–1011. [3] Jih CJ, Sun CT. Prediction of delamination in composite laminates subjected to low velocity impact. J Compos Mater 1993;27:684–701. [4] Li CF, Hu N, Yin YJ, Sekine H, Fukunaga H. Low-velocity impact-induced damage of continuous fiber-reinforced composite laminates. Part I. An FEM numerical model. Composites, Part A 2002;33:1055–62. [5] Li CF, Hu N, Cheng JG, Fukunaga H, Sekine H. Low-velocity impact-induced damage of continuous fiber-reinforced composite laminates. Part II. Verification and numerical investigation. Composites, Part A 2002;33:1063–72. [6] Aslan Z, Kawakuzu R, Okutan B. The response of laminated composite plates under low-velocity impact loading. Compos Struct 2003;59:119–27. [7] Tang B, Henneke II EG. Lamb-wave monitoring of axial stiffness reduction of laminated composite plates. Mater Eval 1989;47: 928–34. [8] Dayal V, Kinra VK. Leaky Lamb waves in an anisotropic plate. II: Nondestructive evaluation of matrix cracks in fiber-reinforced composites. J Acoust Soc Am 1991;89:1590–8. [9] Seale MD, Smith BT, Prosser WH. Lamb wave assessment of fatigue and thermal damage in composites. J Acoust Soc Am 1998;103:2416–24. [10] Toyama N, Okabe T, Takeda N, Kishi T. Effect of transverse cracks on Lamb wave velocity in CFRP cross-ply laminates. J Mater Sci Lett 2002;21:271–3.
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[11] Guo N, Cawley P. The interaction of Lamb waves with delaminations in composite laminates. J Acoust Soc Am 1993;94:2240–6. [12] Guo N, Cawley P. Lamb wave reflection for the quick nondestructive evaluation of large composite laminates. Mater Eval 1994;52:404–11. [13] Valdes SHD, Soutis C. Real-time nondestructive evaluation of fiber composite laminates using low-frequency Lamb waves. J Acoust Soc Am 2002;111:2026–33. [14] Tan KS, Guo N, Wong BS, Tui CG. Experimental evaluation of delaminations in composite plates by the use of Lamb waves. Compos Sci Technol 1995;53:77–84.
[15] Birt EA. Damage detection in carbon-fibre composites using ultrasonic Lamb waves. Insight 1998;40:335–9. [16] Bourasseau N, Moulin E, Delebarre C, Bonniau P. Radome health monitoring with Lamb waves: experimental approach. NDT & E Int 2000;33:393–400. [17] Seale MD, Smith BT, Prosser WH, Zalameda JN. Lamb wave assessment of fiber volume fraction in composites. J Acoust Soc Am 1998;104:1399–403. [18] Toyama N, Kikushima Y, Takatsubo J. Effect of delamination on Lamb wave velocity in cross-ply laminates. J Mater Sci Lett 2002;21:1891–3.
Lamb wave method for quick inspection of impact-induced delamination in composite laminates N. Toyama *, J. Takatsubo Smart Structure Research Center, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan Received 10 March 2003; received in revised form 8 September 2003; accepted 20 October 2003 Available online 16 December 2003
Abstract This paper proposes a new inspection technique using Lamb waves to detect impact-induced delamination in composite laminates. The technique, which consists of two line scans, is as follows. The first scan measures the arrival times of the transmitted S0 mode along the 0° direction to detect delamination and evaluate its size. The second scan measures the maximum amplitude of the earliest wave packet in a line, including the longest delamination, to locate its edge. We performed this technique on impacted CFRP cross-ply laminates. A remarkable decrease in the arrival times due to the delamination is detected, and the delamination length can be calculated based on a simple model for Lamb-wave propagation. Furthermore, the delamination edge is located as a sudden decrease in the amplitude. The technique enables detecting the delamination and evaluating its size and location using only the two scans. We demonstrated the validity and usefulness of this technique. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: A. Polymer matrix composites (PMCs); B. Impact behavior; C. Delamination; D. Non-destructive testing; D. Ultrasonics
1. Introduction Composite laminates are valuable structural components for aircraft and spacecraft because of their superior specific strength and stiffness. Composite structures in these safety-critical applications must be inspected frequently to ensure safety and reliability, and prevent catastrophic failure. Current inspection practices employ non-destructive evaluation (NDE) techniques such as X-ray or ultrasonic C-scan to identify internal damage. However, the use of these techniques for inspecting large structures is very time consuming and expensive. Therefore, a new NDE technique to detect damage quickly and reliably is necessary. Should any damage be found, the conventional method can then be applied to characterize the damage in detail. Internal damage from low-velocity impact is the most prevalent type of damage found in composite structures. *
Corresponding author. Tel.: +81-29-861-3025; fax: +81-29-8613126. E-mail address: [email protected] (N. Toyama). 0266-3538/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2003.10.011
This damage, in the form of matrix cracks, delamination and fiber breakage, is invisible to the naked eye and is easily induced from something as simple as a tool being dropped during maintenance. Of the various types of damage, delamination in particular causes a significant loss of compressive strength and stiffness. Therefore, numerous experimental and analytical techniques [1–6] have been developed to better understand the mechanisms and mechanics of impact damage in composite laminates. Ultrasonic Lamb waves are one of the techniques that have potential for long-range inspection because they can propagate a long distance. When a receiving transducer is positioned at a remote point on the structure, the signal received contains information about the integrity of the line between the transmitting and receiving transducers. Many studies have been conducted to detect damage in composite laminates using the Lamb wave method. Tang and Henneke [7], Dayal and Kinra [8], Seale et al. [9], and Toyama et al. [10] detected transverse cracks in CFRP cross-ply laminates as a reduction in Lamb wave velocity due to a loss of stiffness. Based on their studies, measuring Lamb wave velocity has the
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potential to quantitatively evaluate damage in composite laminates. Guo and Cawley [11,12] and Valdes and Soutis [13] detected delamination in CFRP laminates by a reflected wave at the delamination edge, and determined its location using the arrival time of the reflected wave. However, a reflected wave is often not clearly detectable because its amplitude is reduced due to scattering at the delamination edge. The dispersive nature of Lamb waves, as well as attenuation, creates more difficulty in distinguishing the reflected wave from the detected waveform. Tan et al. [14], Birt [15] and Bourasseau et al. [16] detected delamination in CFRP laminates and foam core sandwich structures based on attenuation of the transmitted Lamb wave. Their method is a simple and reliable method to detect damage. However, it is very difficult to quantitatively evaluate the delamination size using waveform changes, including attenuation. This paper develops a quick and quantitative inspection technique for impact-induced delamination in composite laminates. Based on previous studies on impact damage, we have designed a new method to detect and identify delamination, and evaluate its size and location using Lamb wave velocity and attenuation. The method consists of only two line scans. The first scan measures the distribution of the arrival times of the transmitted S0 mode along the 0° direction before and after impact; the second scan then measures the transition of the maximum amplitude of the earliest wave packet. We performed this technique on impacted CFRP cross-ply laminates, and compared the estimated delamination size and location with the data obtained by a conventional C-scan. 2. Principle of Lamb wave inspection Only the S0 mode and the A0 mode propagate in the frequency-thickness product range below 1 MHz mm. In this region, the S0 mode is almost non-dispersive, while the A0 mode is highly dispersive. The velocity of both modes is directly related to the properties of the materials; the S0 mode velocity has a higher dependence on the in-plane stiffness than the A0 mode. Furthermore, the S0 mode velocity is much higher than that of the A0 mode. The leading edge of the detected waveform is thus easily identified as the S0 mode. Since the S0 mode velocity is useful for detecting stiffness changes caused by damage, we focused solely on the S0 mode for this study. The S0 mode velocity in the low frequency-thickness product for the principal axis of the orthotropic laminate is simply expressed as [17]: sffiffiffiffiffiffiffi A11 ð1Þ V ¼ qh where A11 is the in-plane stiffness, q is the density and h is the thickness of the laminate.
We demonstrated that, in ½0=90n S cross-ply laminates [18], a Lamb wave propagated separately in the delaminated region because the interfacial continuity between the 0° and 90° layers was no longer retained. Based on this, the wave velocity in the delaminated region depends on the location, i.e., the interface at which the delamination initiates, and the size of the delamination in composite laminates. Multiple delaminations generally initiate at various interfaces for ½0=90nS and quasi-isotropic laminates under static or fatigue loading. Although we can detect the presence of the delamination as a change in the wave velocity, we cannot quantitatively evaluate the delamination length in such cases. As experimentally and analytically confirmed in the previous study on low-velocity impact damage [1–6], the major, nearly elliptical delamination is initiated at the bottom interface (the interface away from the impact side), and propagates in the fiber direction of the bottom layer for both cross-ply and quasi-isotropic laminates. Based on these results, when the wave propagates in the fiber direction of the bottom layer (defined as the 0° layer in this study), the wave propagates separately in the delaminated region, i.e., through the bottom 0° layer and the rest of the layers. The in-plane stiffness of the 0° layer is the highest, so the wave velocity increases in the delaminated region. The effect of the bending crack along the fiber direction in the bottom 0° layer on the wave velocity was regarded as small and neglected in this study. Considering the presence of a delamination with length L at the bottom interface, the difference in the transmitting time of the wave for L between intact and delaminated states is expressed as: 1 1 Dt ¼ 0 L ð2Þ Vi V where Vi and V 0 are the wave velocity of the intact laminate and the 0° layer. Hence L can simply be expressed as: L¼
V 0 Vi Dt V 0 Vi
ð3Þ
Consequently, we can quantitatively evaluate the length of the major delamination induced by low-velocity impact loading by measuring the arrival time of the transmitted wave along the 0° direction, and by using Eq. (3). This major delamination is of particular interest here and will be considered exclusively in this study.
3. Experimental procedures The material studied was T800H/3631 (CFRP) crossply laminates with stacking sequences of [0/903 ]S and [0/ 90]2S . These composite plates (300 mm 300 mm 1 mm) were fabricated with unidirectional prepregnated
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sheets by a hot-press machine in accordance with the manufacturerÕs recommended processes. The mechanical properties of the unidirectional laminate obtained by the tensile test are listed in Table 1. Fig. 1 illustrates the present method, which consists of two line scans for inspecting impact-induced delamination. The objective inspection area within the plate was 210 mm long and 200 mm wide. We generated a low-velocity impact using a vertical drop-weight impact machine to induce impact damage within the area. The machine, consisting of two vertical steel rods mounted on a heavy steel block, was similar to that was used by Aslan et al. [6]. The panels were impacted with a hemispherical impactor with a diameter of 15 mm. We set the total mass of the entire drop-weight to 1.5 kg, and the falling distance to 0.5 m. The first scan measures the distribution of the arrival times of the transmitted Lamb wave along the 0° direction before and after impact to detect and evaluate the size of the major delamination. The transmitter– receiver system is moved in a line parallel to the Y axis (90° direction) with a constant distance between the transducers (210 mm). A decrease in the arrival time after impact indicates the presence of delamination, and Table 1 Measured mechanical properties of unidirectional CFRP laminate Property
Values
Longitudional YoungÕs modulus, E1 (GPa) Transverse YoungÕs modulus, E2 (GPa) Longitudional shear modulus, G12 (GPa) PoissonÕs ratio, m12 Ply thickness (mm) Density, q (kg/m3 )
157.6 8.67 3.83 0.38 0.134 1571
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we calculate its length by Eq. (3) using the measured difference in the arrival times. However, the first scan cannot determine the X position of the delamination. Its precise location can be determined by the following second scan; the transmitter is positioned on the line corresponding to the maximum delamination length and the receiver is scanned along a line parallel to the X axis (0° direction) away from the transmitter. A sudden change in the maximum amplitude of the earliest wave packet then determines the X position of the delamination edge. These scans were initially performed in steps of 10 mm. When delamination was detected, additional measurements were performed to improve the estimation of the delamination width and location. We manually performed the scans on the impacted side of the plates. Fig. 2 illustrates the experimental set-up for Lamb wave generation and detection. A variable-angle-beam transducer consisting of a broadband transducer element (V414-SB, 0.5 MHz, Panametric) and a Perspex wedge (ABWX-2001, Panametric) was used as the ultrasonic transmitter to excite Lamb waves. In order to generate a pure S0 mode, the angles of incidence were determined by SnellÕs law as [8,14,15]: h ¼ sin1
VL VP
ð4Þ
where h is the angle of incidence, and VL and VP are the longitudinal wave velocity in the wedge (2720 m/s) and phase velocity of the S0 mode. An AE sensor (M304A, Fuji Ceramics) with a small diameter of 4 mm was chosen as a receiver. Both the transmitter and receiver were mounted on the surface of the laminate via a coupling gel. The excitation signal applied to the transmitter was 5 cycle of a 0.3 MHz tone burst enclosed in a Hamming window generated by an arbitrary function generator (33250A, Agilent), and amplified by a high-speed bipolar
Arbitrary function generator
High-speed amplifier
Impact
Transmitter
Receiver Major delamination
Trigger Digital oscilloscope Fig. 1. Schematic representation of the present line-scanning methods. The first scan measures the arrival time of the transmitted S0 mode along the 0° direction to detect and evaluate delamination size, and the second scan measures the maximum amplitude of the earliest wave packet in order to locate the longest delamination edge.
Amplifier
Arrival time Maximum amplitude Fig. 2. Schematic diagram for Lamb wave generation and detection.
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amplifier (HSA4011, NF). The detected signals were amplified (A1002, Fuji Ceramics) and transferred to a digital oscilloscope (TDS7054, Tektronix), which carried out 100 averages to improve the signal-to-noise ratio. An arbitrary function generator also transferred a trigger signal to the oscilloscope to set the initial time. The arrival time of the transmitted wave at the receiver was determined using the peak time of the first cycle of the earliest wave packet. Fig. 3 depicts a typical waveform detected at the receiver for ½0=903 S plate. The shape of the excitation signal was maintained, and we confirmed that the S0 mode was nearly non-dispersive in the present frequency-thickness product of 0.3 MHz mm. The arrows show the arrival time and maximum amplitude defined in this study. The peak amplitude of the first cycle used to measure the arrival time was lower than the entire signal, thus we magnified the leading part of the detected signal in the practical measurements. The S0 mode velocity was first measured before the inspection. To measure the time differences, we first mounted the AE sensor 30–150 mm apart from the transmitter in steps of 30 mm. A least-squares fit from a plot of time and distance was performed to obtain the wave velocity. The measured and predicted (from Eq. (1) using the values listed in Table 1) wave velocity is listed in Table 2. The predicted wave velocity was in good agreement with those measured for all laminates.
5
4. Experimental results 4.1. First scan results The experimental results of the distribution of the arrival times measured by the first scan are illustrated in Fig. 4. The scatter in the arrival times before impact was mainly due to the inhomogeneous nature of the laminates. Despite the scatter, remarkable decreases after impact were detected from the Y positions of 9.5 to 12 cm for ½0=903 S , and 10.5 to 11.5 cm for ½0=902S . These decreases indicate the presence of delamination, not matrix cracking or fiber breakage, which reduces the wave velocity. Thus, we were first able to detect and identify the delamination between the regions. Fig. 5 depicts a detected waveform at the Y position of 10.5 cm after impact for ½0=903 S . In comparison with the detected waveform before impact depicted in Fig. 3, the
62 61
Arrival time (µs)
1296
58 57
Before After
56
3
55
Arrival time
1
0
2
4
Delamination width 6
8
10
12
14
16
18
20
16
18
20
Y position (cm)
(a)
0
50
-1 -2 -3
49
-4 -5 40
60
80
100
120
Time (µs) Fig. 3. Waveform detected 210 mm from transmitter for ½0=903 S .
Arrival time (µs)
Amplitude (Voltage)
59
Maximum amplitude
4
2
60
48
47
Before After
46 Table 2 Measured and predicted S0 mode velocity for CFRP laminates Laminate
Measured (m/s)
Predicted (m/s)
½08 ½0=903 S ½0=902S
10,144 5420 7344
10,056 5427 7304
0 (b)
2
4
Delamination width 6
8
10
12
14
Y position (cm)
Fig. 4. Experimental results of the first scan; distribution of arrival time of transmitted S0 mode along the 0° direction before and after impact for: (a) ½0=903 S ; (b) ½0=902S .
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50
1.5
0.5
Maximum amplitude
Delamination length (mm)
Amplitude (Voltage)
1.0
Arrival time
0.0 -0.5 -1.0 -1.5 40
1297
60
80
100
4.2. Second scan results Based on the results from the first scan, we performed the second scan parallel to the X axis at only the Y position containing the major axis of the delamination. Experimental results of the transition of the normalized maximum amplitude of the earliest wave
20 10 0
0
2
4
6
8
10
12
14
16
18
20
14
16
18
20
Y position (cm)
(a)
Fig. 5. Waveform detected 210 mm from transmitter at the Y position of 10.5 cm after impact for ½0=903 S .
70
Delamination length (mm)
shape of the excitation signal was no longer maintained, and considerable attenuation in the earliest wave packet was observed. However, we could clearly observe a decrease in the arrival time after impact. In this study, we assumed the shape of the major delamination as an ellipse in both laminates. Based on this assumption, the minor axes of the major delamination were estimated from Fig. 4 as 25 mm for ½0=903 S , and 10 mm for ½0=902S . Fig. 6 depicts the calculated delamination length using the measured difference in the arrival times before and after impact. We used the predicted values of the Vi and V 0 for the right side of Eq. (3) in the calculations. The scatter in the intact regions was due to errors in the measurements. The detectable delamination length should be longer than the ranges of the scatter. We could therefore estimate the detectable delamination length to exceed about 10 mm based on the results shown in Fig. 6. The impact energy generated in this study induced the longer delamination, allowing us to estimate the longest delamination lengths, i.e., the major axes of the delamination and their linear locations, as 42 mm at the Y position of 10.5 cm for ½0=903 S , and 61 mm at the Y position of 11 cm for ½0=902S . From the first scan, we could detect and identify the delamination and estimate its size and linear location. The only unknown parameter was the X position of the delamination.
30
-10
120
Time (µs)
40
60 50 40 30 20 10 0 -10
(b)
0
2
4
6
8
10
12
Y position (cm)
Fig. 6. Distribution of delamination length calculated from the measured difference in arrival times obtained by the first scan for: (a) ½0=903 S ; (b) ½0=902S .
packet are provided in Fig. 7, which also includes the results at the Y position of 7 cm (intact regions) as a reference. The maximum amplitude gradually decreased due to attenuation in the intact regions. However, a sudden decrease was observed in the presence of the delamination, and the lower amplitude was maintained even beyond the delamination for both laminates. Tan et al. [14] offered several explanations for the amplitude reduction over the delamination, i.e., wave separation, mode conversion to the A0 mode, or wave scattering at the delamination edge. Based on their suggestions, the location of the sudden decrease in the amplitude indicates the front edge of the major axis of the delamination. We estimated the locations of the delamination edges as the X positions of 11 cm for ½0=903 S , and 10.5 cm for ½0=902S , from the results of the second scan. We quantitatively estimated the size and two-dimensional location of the delamination from the two scans.
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1.2
Y = 10.5 cm Y = 7 cm
Normalized amplitude
1.0 0.8 0.6 0.4
Delamination edge
0.2 0.0
0
2
4
6
8
10
12
14
16
18
20
X position (cm)
(a)
1.2
Y = 11 cm Y = 7 cm
Normalized amplitude
1.0 0.8 0.6
Delamination edge
0.4 0.2 0.0
(b)
0
2
4
6
8
10
12
14
16
18
20
X position (cm)
Fig. 7. Experimental results of the second scan; distribution of normalized maximum amplitude of the earliest wave packet at the Y positions of damaged and intact regions for: (a) ½0=903 S ; (b) ½0=902S .
4.3. Comparison with C-scan results We performed a conventional C-scan to validate the present method. The inspection area was 100 mm 100 mm, including the delamination, and was scanned in steps of 1 mm. Fig. 8 presents the C-scan image depicting the major impact-induced delamination at the bottom interface. We confirmed that the delaminations were nearly elliptical and that their major axes were parallel to the 0° direction in both laminates. The delaminations were 51 mm long and 28 mm wide for ½0=903 S , and 60 mm long and 12 mm wide for ½0=902S from the C-scan results. Additionally, we observed the cross-section of the impacted plates by an optical microscope to measure the real delamination length. We found a partially intact region of about 6 mm long between the delaminations at the bottom interface just under the impact point for ½0=903 S , which was hardly distinguishable from the C-scan image. Thus the real
Fig. 8. Conventional C-scan image depicting impact-induced delamination and evaluated size and location by the present method for: (a) ½0=903 S ; (b) ½0=902S .
major axis of the delamination length was 45 mm for ½0=903 S . In contrast, we did not observe such a partially intact region for ½0=902S , and the major axis was accurately estimated by the C-scan. Fig. 8 also includes the delamination size and location estimated by the present method. All estimates agreed well with the results obtained by C-scan and microscopic observation, and we demonstrated that the present method accurately evaluated the size and location of impact-induced delamination.
5. Discussion We will discuss the applicable ranges and advantages of the present method below. The specimen plates used
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in this study were 300 mm long, with the objective inspection length as 210 mm. The specimen length was the maximum due to the limitations of the hot-press machine (ranges longer than this could not be investigated). However, all the detected signals, even in the presence of the delamination, maintained a high signal-to-noise ratio despite considerable attenuation. Additionally, the higher amplitude was maintained after the delamination in ½0=902S , which is more important laminate in industrial applications. The inspection range could therefore be extended using this system. Furthermore, in this study we performed the first scan before impact, and determined the difference in the arrival times obtained in the same line before and after impact in order to eliminate the effect of the inhomogeneous nature of the laminates on evaluating the delamination length. We also calculated the major axes of the delamination using the arrival times in the intact state as the average values obtained by the measurements in the intact regions after the impact. The calculated lengths were 45 mm for ½0=903 S and 59 mm for ½0=902S , (nearly the same as those previously evaluated). Therefore, we were able to omit measurements before impact, which is important in practical use. As reported previously [14–16] and as depicted in this study in Fig. 5, a change in detected waveform (including attenuation) can clearly indicate the presence of damage located between the transducers. This simple technique is therefore very useful when it is necessary to quickly ascertain whether damage is present. However, identifying the type of damage, i.e., transverse crack, delamination, and/or fiber breakage, and evaluating delamination size are difficult. The present method of simply measuring the change in the arrival time can identify the impact damage found as a delamination and can evaluate its size. It is very important to note that the present method using only two line scans is simple and reliable, qualities required for quick inspection of a large surface area, as opposed to the point-by-point scan used in conventional C-scan technique. Considerable time saving can therefore be achieved while maintaining the ability to accurately evaluate the delamination.
6. Conclusions In this paper, we propose a quick and quantitative inspection technique using a Lamb wave method consisting of two line scans for detecting impact-induced delamination in composite laminates. We applied this technique on T800H/3631 (CFRP) cross-ply laminates with stacking sequences of ½0=903 S and ½0=902S . The first scan measured the distribution of the arrival times of the transmitted S0 mode along the 0° direction before
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and after impact. We were able to identify the major delamination and quantitatively evaluate its size and linear location. The second scan then measured the transition of the maximum amplitude of the earliest wave packet in a line including the major axis of the delamination. A sudden drop in the amplitude was clearly observed, and we were able to determine the location of the delamination edge. We could easily and quantitatively evaluate the size and two-dimensional location of the delamination using only two scans. A conventional C-scan validated this method, and we confirmed our method has great potential for quick inspection of impact-induced delamination in composite structures.
Acknowledgements This study was supported in part by the Ministry of Education, Culture, Sports, Science and Technology of Japan under Grant-in-Aid for Scientific Research (14750568).
References [1] Choi HY, Chang FK. A model for predicting damage in graphite/ epoxy laminated composites resulting from low-velocity point impact. J Compos Mater 1992;26:2134–69. [2] Choi HY, Downs RJ, Chang FK. A new approach toward understanding damage mechanisms and mechanics of laminated composites due to low-velocity impact: Part I – experiments. J Compos Mater 1991;25:992–1011. [3] Jih CJ, Sun CT. Prediction of delamination in composite laminates subjected to low velocity impact. J Compos Mater 1993;27:684–701. [4] Li CF, Hu N, Yin YJ, Sekine H, Fukunaga H. Low-velocity impact-induced damage of continuous fiber-reinforced composite laminates. Part I. An FEM numerical model. Composites, Part A 2002;33:1055–62. [5] Li CF, Hu N, Cheng JG, Fukunaga H, Sekine H. Low-velocity impact-induced damage of continuous fiber-reinforced composite laminates. Part II. Verification and numerical investigation. Composites, Part A 2002;33:1063–72. [6] Aslan Z, Kawakuzu R, Okutan B. The response of laminated composite plates under low-velocity impact loading. Compos Struct 2003;59:119–27. [7] Tang B, Henneke II EG. Lamb-wave monitoring of axial stiffness reduction of laminated composite plates. Mater Eval 1989;47: 928–34. [8] Dayal V, Kinra VK. Leaky Lamb waves in an anisotropic plate. II: Nondestructive evaluation of matrix cracks in fiber-reinforced composites. J Acoust Soc Am 1991;89:1590–8. [9] Seale MD, Smith BT, Prosser WH. Lamb wave assessment of fatigue and thermal damage in composites. J Acoust Soc Am 1998;103:2416–24. [10] Toyama N, Okabe T, Takeda N, Kishi T. Effect of transverse cracks on Lamb wave velocity in CFRP cross-ply laminates. J Mater Sci Lett 2002;21:271–3.
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[11] Guo N, Cawley P. The interaction of Lamb waves with delaminations in composite laminates. J Acoust Soc Am 1993;94:2240–6. [12] Guo N, Cawley P. Lamb wave reflection for the quick nondestructive evaluation of large composite laminates. Mater Eval 1994;52:404–11. [13] Valdes SHD, Soutis C. Real-time nondestructive evaluation of fiber composite laminates using low-frequency Lamb waves. J Acoust Soc Am 2002;111:2026–33. [14] Tan KS, Guo N, Wong BS, Tui CG. Experimental evaluation of delaminations in composite plates by the use of Lamb waves. Compos Sci Technol 1995;53:77–84.
[15] Birt EA. Damage detection in carbon-fibre composites using ultrasonic Lamb waves. Insight 1998;40:335–9. [16] Bourasseau N, Moulin E, Delebarre C, Bonniau P. Radome health monitoring with Lamb waves: experimental approach. NDT & E Int 2000;33:393–400. [17] Seale MD, Smith BT, Prosser WH, Zalameda JN. Lamb wave assessment of fiber volume fraction in composites. J Acoust Soc Am 1998;104:1399–403. [18] Toyama N, Kikushima Y, Takatsubo J. Effect of delamination on Lamb wave velocity in cross-ply laminates. J Mater Sci Lett 2002;21:1891–3.