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Nondestructive Testing and Evaluation

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Damage detection in composite structures withhigh-damping materials using time reversalmethod

Hang Xiao, Yanfeng Shen, Li Xiao, Wenzhong Qu & Ye Lu

To cite this article: Hang Xiao, Yanfeng Shen, Li Xiao, Wenzhong Qu & Ye Lu (2018) Damagedetection in composite structures with high-damping materials using time reversal method,Nondestructive Testing and Evaluation, 33:3, 329-345, DOI: 10.1080/10589759.2018.1476512

To link to this article: https://doi.org/10.1080/10589759.2018.1476512

Published online: 08 Jun 2018.

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https://doi.org/10.1080/10589759.2018.1476512

Damage detection in composite structures with high-damping materials using time reversal method

Hang Xiaoa, Yanfeng Shenb, Li Xiaoa, Wenzhong Qua and Ye Luc

adepartment of engineering Mechanics, Wuhan university, Wuhan, china; buniversity of Michigan-shanghai Jiao tong university Joint institute, shanghai Jiao tong university, shanghai, china; cdepartment of civil engineering, Monash university, Melbourne, australia

ABSTRACTThis paper presents a new damage detection technique for use in highly damped composite structures using the time reversal method with different excitation amplitudes. A Rayleigh damping model was used to numerically explore the influence of damping on the time-reversibility of Lamb waves. In the experimental investigation, high-damping absorptive materials were introduced between a sensing path on a composite plate. Excitations of different amplitudes were applied on transducers to generate different energy levels for interrogating waves. It was found that high damping broke down the time-reversibility of the Lamb waves. Both the damped and the damaged sensing paths had much higher damage indices than the pristine path under a large excitation. However, with the decrease in excitation amplitude, the damage indices of the damaged path obviously decreased, whereas those of the highly damped path remained almost constant. The proposed method can effectively detect damage in composite structures and avoid false alarms from the presence of high-damping materials.

1. Introduction

Due to the composites’ light weight and good mechanical performance, the application of the composite material in the load-carrying structural is significantly increased, especially in the aerospace and automotive industries [1]. Matrix cracking and delamination can occur when the composite structure is subjected to low-velocity impact. Such damage reduces compressive strength/stiffness, reduces the integrity and reliability of the structure, and therefore needs to be detected. The rapid development of structural health monitoring (SHM) technology has enabled us to effectively detect such kinds of damage in composite structures [2–7].

Ultrasonic guided waves have been identified as a class of powerful tools for SHM of large areas. The time reversal method using Lamb wave is a baseline-free method that is widely used in damage detection. For metallic or composite plate-like structures, the attenuation

KEYWORDSstructural health monitoring; damping effect; composite structure; time reversal method; excitation amplitude

ARTICLE HISTORYreceived 26 october 2017 accepted 25 april 2018

© 2018 informa uK limited, trading as taylor & Francis group

CONTACT Wenzhong Qu qwz@whu.edu.cn

NoNdestructive testiNg aNd evaluatioN2018, Vol. 33, No. 3, 329–345

mailto:qwz@whu.edu.cnhttp://www.tandfonline.comhttp://crossmark.crossref.org/dialog/?doi=10.1080/10589759.2018.1476512&domain=pdf

H. XIAO ET AL.

can be ignored when the waves transmit in the usual frequency range of interest. Thus, the assumption of time reversal invariance remains valid [8,9]. Roux et al. [10] experimentally studied the use of time-reversal mirror to solve multipath distortion in an ultrasonic wave-guide. Prada et al. [11] applied the iterative time reversal process in combination with the DORT(French acronym for decomposition of the time reversal operator) method to the detection of titanium billets. Gangadharan et al. [12] investigated the time reversal health monitoring technique and performed a damage detection experiment of the metallic struc-ture. They showed that the time reversal temporal recompression of dispersive Lamb waves remained effective. Lamberti et al. [13] numerically study the application of time reversal method in composite plate. They suggested that the time reversal-based technique could overcome the effects of material anisotropy and increase the effectiveness of SHM systems in detecting damage. A comprehensive theoretical analysis and experimental work focusing on the Lamb wave time reversal method in composites for damage detection was provided by Sohn’s group [14,15]. They demonstrate that the existence of damage can be detected by comparing the original excitation signal with the reconstructed signal. In an experimental study, Poddar et al. [16] discovered that the time-reversibility of the Lamb waves remained well although composites had inherent anisotropy. They investigated a GFRP woven-fabric laminate with various kinds of damage such as surface erosion and local impact. These types of damage were detected successfully without any baseline data (a signal obtained from the pristine structure) using the time-reversibility of Lamb waves.

Although time reversal-based Lamb wave method has provided remarkable achieve-ments in SHM of composite structures, very little work has been reported on the influence of the damping effect on the time reversal process in composite structures. This aspect is especially meaningful when high-damping materials are introduced for vibration/noise control purposes. High-damping materials or viscoelastic damping layers, that can be pasted onto structural surfaces, have been widely used as effective means of reducing structural vibration amplitude, controlling noise and increasing fatigue life [17–20]. When sur-face-bonded vibration absorptive materials are introduced, the time-reversibility of Lamb waves is destroyed, potentially leading to false alarms of the existence of genuine structural damage. Thus, damage detection using the time reversal method faces great difficulty and challenge for composite structures containing high-damping absorptive materials.

In this paper, detailed studies of the influence of damping on the time reversal procedure are carried out. We propose a new method as an improvement on the existing time reversal technique, applying different energy levels of Lamb wave excitation. The method enables the SHM system to distinguish damage and false alarms from high-damping materials. PZTs are used as transducers that excite and sense Lamb waves signals. Time reversal numerical models are presented using the multi-physics finite element method. Several numerical cases are considered: a pristine composite plate, a composite plate with physical damping, a composite plate with high-damping absorptive materials and a damaged composite plate. Then, time reversal experiments on a composite plate are performed to verify the proposed method.

2. Lamb wave time reversal method

This section describes the basic theory of time reversal method and its typical steps as shown in Figure 1. According to the concept, the procedure is as follows [21]:

330

NONDESTRUCTIVE TESTING AND EVALUATION

Step 1: An input signal VA(ω) is applied to piezo wafer A (PZT A). The Lamb waves generated in the structure propagate along the structure and picked up by PZT B acting as a sensor. The response signal is recorded as VB(ω).

Step 2: The time-reversed signal which means that the response signal VB(ω) components is flipped in the time domain is applied to PZT B.

Step 3: The position of the actuator and the sensor has been exchanged. PZT A receives the signal generated at PZT B with the time-reversed signal as the excitation signal.

Step 4: The reconstructed signal V �A(�) is obtained at PZT A by the operations of steps 1, 2, 3. Then the V �A(�) is time reversed and compared with the input signal VA(ω).

For a non-dissipative medium, the invariance of the time reversal operator of the wave equation constitutes the basic theory of the time reversal method. The acoustic displacement along the j axis, uj(r, t) with j = l, 2, or 3, is defined by the elastodynamic wave equation:

where �s and Cijkl are the density of the material and the stiffness tensor, respectively.A close observation of this equation shows that only the second derivative of time

appears in this partial differential wave equation, which is an important property of the time reversal method. This property is the foundation of the time reversal principle for the non-dissipative medium. As an immediate consequence, If uj(r, t) represents a solution of the elastodynamic equation, then uj(r,−t) is also a solution of the same equation [22]. This property is critical to the invariance of time reversal operator. More specifically, when an input signal VA(ω) is applied to PZT A, the response signal VB(ω) picked up by PZT B can be represented as follows:

where G(ω) is the frequency response function of the structure. Then, the response signal VB(ω) which has been time reversed is again excited in the structure by PZT B. According

(1)�s�2uj

�t2= Cijkl

�2uj

�xj�xk

(2)VB(�) = G(�)VA(�)

Figure 1. schematic of lamb wave time reversal procedure.

331

to the important property described above and the determined propagation path, the frequency response function G(ω) remains unchanged. Thus, the response signal V �A(�) received at PZT A is

It is noted that G(ω) is just a scalar in a non-dissipative medium. Therefore, V �A(�) and VA(ω) are similar in the frequency domain. Furthermore, the linear reciprocity of the system also exists when PZT transducers are used as the actuator and receivers. Thus, after normali-sation, the main peak shape of the reconstructed signal obtained in the non-damaged and non-dissipative material should match the original input signal well.

A breakdown in time-reversibility can be attributed to two main causes:

(1) A highly damped medium can have a frequency-dependent attenuation effect on Lamb waves. The elastodynamic wave equation contains a first-order time deriv-ative operator. Therefore, the invariance under a time reversal operation is lost.

(2) When there are some certain types of damage in the structure, the time reversal procedure will be affected by the nonlinear effect, and the linear reciprocity of the system is disrupted.

If either of these two scenarios occurs, G(ω) is no longer just a scalar and the invari-ance of time reversal operation would be lost. In other words, the main peak shape of the reconstructed signal and the original input signal would be different. The path containing the damaged or high-damping material can be identified by calculating the deviation of the two signals for each sensor pair path. However, high-damping materials usually exist as an additional structural feature incorporated for improved vibration control and they should be differentiated from physical damage.

The reconstructed signal and the original input signal can be represented as discrete points x =

{x1, x

2,… , xn

} and y =

{y1, y

2,… , yn

} in the time domain, respectively. After

normalisation, the deviation of the two signals is quantitatively measured by the correlation coefficient. The definition of the correlation coefficient is expressed as [23]

The damage index is defined as

It should be noted that, in the literature pertaining to composite structures, the reconstructed signal has matched the excitation signal well. That is because damping in these composite structures was quite weak, so it had marginal effects on the reconstructed signals compared to those from the damage. Very few investigations, however, have quantitatively studied the effects of high damping on the time reversal method due to the addition of acoustic/vibration absorptive materials. Further, very few studies of the time reversal method have considered the non-linear interaction between interrogating waves and various possible

(3)V �A(�) = G(�)VB(�) = G2(�)VA(�)

(4)�x,y =n

n∑i=1

xiyi −n∑i=1

xi

n∑i=1

yi

��n

n∑i=1

x2i − (n∑i=1

xi)2

��n

n∑i=1

y2i − (n∑i=1

yi)2

�

(5)DI = 1 − �x,y

H. XIAO ET AL.332

types of damage in composites. Damage types such as matrix cracking and delamination in composite plates may demonstrate different mechanical behaviours under various excita-tion amplitudes. Due to the initial close/open condition, a threshold excitation value exists, above which the nonlinear breathing mechanism begins to take effect. However, below the threshold excitation, the damage may appear to be linear region and the time-reversibility may still hold.

3. Numerical case studies of time-reversibility

In this section, a free boundary condition is adopted in all the simulations. More than eight finite element nodes per wavelength are guaranteed to ensure simulation accuracy. numerical case studies of time reversal procedures were carried out in a composite plate with dimensions 1000 × 1000 × 2 mm and a lay-up sequence of [90/±45/0]s (using multi-phys-ics finite element models). The material properties of the lamina are presented in Table 1.

Two square PZT transducers were surface-bonded 340 mm apart and were used as an actua-tor and a sensor for simulating the propagation process of the Lamb wave. Numerical simulations of the wave propagation were performed using the commercially available finite element code ANSYS. The PZT sensor and composite plate specimen were modelled using the coupling field element (SOLID5) and the eight-node layered solid element (SOLID46), respectively. In the finite element model of PZT, the electrode is simulated by the potential coupling of the nodes on the top and bottom surfaces. The material properties of the PZT had the following values:

(6)�Cp

�=

⎡⎢⎢⎢⎢⎢⎢⎢⎣

132 73 71 0 0 0

0 115 73 0 0 0

0 0 132 0 0 0

0 0 0 26 0 0

0 0 0 0 26 0

0 0 0 0 0 3

⎤⎥⎥⎥⎥⎥⎥⎥⎦

GPa

(7)��p

�=

⎡⎢⎢⎢⎣

8046 0 0

0 6597 0

0 0 8046

⎤⎥⎥⎥⎦× 10−12 CV

−1m

−1

(8)

�ep

�=

⎡⎢⎢⎢⎢⎢⎢⎢⎣

0 −4.1 0

0 14.1 0

0 −4.1 0

10.5 0 0

0 0 10.5

0 0 0

⎤⎥⎥⎥⎥⎥⎥⎥⎦

Cm−2

Table 1. Material properties of the lamina.

E11(GPa) E22(GPa) E33(GPa) G12(GPa) G23(GPa) G13(GPa) υ12 υ23 υ13 ρ(kg/m3)

152 9.5 9.5 4.2 3.4 4.2 0.3 0.38 0.3 1540

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where [Cp], [ɛp] and [ep] is the stiffness matrix, dielectric matrix and piezoelectric matrix, respectively. The density of the PZT material is assumed to be ρ = 7500 kg/m3.

To study the effect of damping on the time reversal procedure, a reasonable and feasible damping model should be chosen. In contrast to metals, composite structures generally exhibit higher damping capacity, primarily because of the viscoelasticity of the polymeric matrix. The damping effect is particularly noticeable especially when high damping materials for vibration/noise control are introduced in this paper. For the study of composite damping model, a large number of theoretical and experimental studies have been carried out to characterise the damping properties of the composite [24]. Such as strain energy method [25] and complex modulus approach [26]. These methods/models attempt to explain the physics of energy dissipation and characterise it with parameters. Theoretically, they will also break down the invariance of time reversal operation compared to linear viscoelastic models, whose equations of motion can be expressed as:

where q(t) is a generalised coordinate. Therefore, in order to simplify the calculation, a Rayleigh damping model is used in the simulation, which is a linear combination of the mass matrix and the stiffness matrix:

where αM and βK are the mass and stiffness damping factors, respectively.The lower frequency is affected by the mass damping factor αM, while the higher The

lower frequency is affected by the mass damping factor αM, while the higher frequency is affected by the mass damping factor βK. Since the frequency of the signals used in this study is in the high frequency range (>10 kHz), the effect of αM on the system is negligible compared to βK. Therefore, in this paper, the value of factor αMwas given as zero, and βK was 1.18 × 10–7, obtained by experimental measurement. In detail, an input signal is excited at a PZT actuator and two PZT sensors, at arbitrary reference positions x1 and x2, are used to receive Lamb wave signals in the composite plate. In this experiment, two PZT sensors with a distance of 66.7 mm are set in the composite plate, and the group velocity C and attenuation coefficients α are calculated from the received signals of the two PZT sensors. The attenuation coefficient α of the viscoelastic medium could be expressed as [27]

where A1 and A2 are the amplitudes of Lamb waves at positions x1 and x2, respectively. The group velocity C could be expressed as

where t1and t2 are the arrival times of Lamb waves at positions x1and x2. The relationship between damping ratio and attenuation coefficient can be expressed as

(9)[M]q̈(t) + [C]q̇(t) + [K]q(t) = 0

(10)[C] = �M[M] + �K [K]

(11)� =ln

(A

1

A2

)

x2− x

1

(12)C =x2− x

1

t2− t

1

(13)� =��

C

H. XIAO ET AL.334

So βK could be computed by

where ω = 2πf is the angular frequency at frequency f, which we used in the experiment is 100 kHz.

To study the effect of damage on the time-reversibility, a numerical model with damage was constructed where no damping effect was involved. A rectangular delamination region of 32 mm × 32 mm between two PZT transducers was simulated by nonlinear spring ele-ments (COMBIN39). In reality, it is physically impossible for elements of the top and bot-tom sub-laminates to penetrate into each other within the delamination region. Therefore, non-linear spring elements were inserted between the delamination contact surface nodes, contributing no stiffness upon node separation and a contact force upon node penetration. According to the theory of the penalty method for contact analysis, the simulation results would approximate the accurate physical contact phenomenon when the amount of pene-tration was reasonably small. The configuration diagram is shown in Figure 2.

The Lamb waves were excited by applying voltage to the top nodes of the actuator. A 100 Vpp, 50 kHz, and 3.5-cycle Hann-windowed sinusoidal tone burst signal was used as the excitation, as illustrated in Figure 3. Four different cases were studied: (1) no damping was considered; (2) βK took the measured value 1.18 × 10

–7; (3) βK adopted four times the measured value to represent a high-damping situation; (4) a rectangular delamination region was considered to simulate a damaged case.

In Figure 4, the variation of the amplitude of the normalised signal with respect to the propagation distance of the wave under three different damping situations is plotted. As shown in Figure 4, when βK took four times the measured value, the attenuation of Lamb waves was much greater than that of both the no damping and the physical damping cases, indicating that the effect of additional high damping on the propagation of Lamb waves cannot be ignored.

Comparisons of the reconstructed signals with the original signal are shown in Figure 5. The difference between the two signals can be clearly observed. Further, The correlation coefficients between the reconstructed signal and the original signal were quantitatively

(14)�k =2�C

�2

Figure 2. the configuration diagram in the finite element simulations (mm). t and B represent the top and bottom interfaces of the delamination, and k represents the nonlinear spring constant.

NONDESTRUCTIVE TESTING AND EVALUATION 335

calculated in these four cases by Equation (4) as 98, 96, 91 and 92%, respectively, with the corresponding damage indices 0.02, 0.04, 0.09 and 0.08.

It was, therefore, concluded that the damage index was the lowest (0.02) when damping was not considered. Further, the damage index changed little (0.04) when a measured βK

Figure 3. excitation signal.

Figure 4. variation of normalised amplitude under different damping conditions.

H. XIAO ET AL.336

of Rayleigh damping was introduced, that is the foundation of the applicability of the time reversal method in composite structures. As βK was increased to four times of the measured value, the damage index increased significantly (0.09), reaching a much higher value than in the previous two cases. When the delamination damage was included, the damage index also reached a very high value (0.08). These numerical simulation results showed that damping had an adverse impact similar to that of damage on the time-reversibility of Lamb waves. When only the inherent composite damping value was considered，the high damping effect was negligible. However, additional high damping caused a false alarm, because the damage index under high damping could be comparable to that introduced by damage. As a result, the time reversal method could face additional difficulty when the damping properties of a composite material were high or when vibration/acoustic absorption materials were added.

Another interesting phenomenon was found when the excitation amplitude decreased to 20 Vpp in the simulation. For the first three cases without delamination damage, the normalised main peak shape of reconstructed signals was almost same as that of 100 Vpp with the same corresponding damage indices. In contrast, there was a noticeable deviation between the main peak shapes of reconstructed signals under two different excitation ampli-tudes when there was a delamination, as shown in Figure 6. Moreover, it was calculated that the damage index was 0.03 under 20 Vpp excitation, which was comparable to that of no-damping case (0.02) and significantly lower than that under 100 Vpp excitation (0.08).

Figure 5. comparisons of the reconstructed signals with the original signal for the four cases: (a) pristine with no damping effect; (b) pristine with physical damping (βK = 1.18 × 10

–7); (c) pristine with additional high damping (βK = 4 × 1.18 × 10

–7); (d) damaged plate with delamination.

NONDESTRUCTIVE TESTING AND EVALUATION 337

This phenomenon indicated that only the damage index in the damaged case was sensitive to variation of the amplitude of excitation.

Therefore, to overcome the difficulty when the effects of high damping are considered, we propose a varying amplitude interrogation based time reversal technique that is exper-imentally demonstrated in the next section.

4. Experimental investigation

The experimental investigation aimed to verify the simulation results, as well as to show the applicability of the proposed time reversal method with different excitation amplitudes for the detection of damage in composites with high-damping materials.

4.1. Experimental set-up and procedure

The experimental set-up is shown in Figure 7. The dimensions of the carbon fibre composite plate to be interrogated are 380 mm by 310 mm by 2 mm, with two arrays of PZT actuators/sensors (#1–#8) bonded on the plate surface. The laminate was fabricated from T300 carbon fibre-epoxy prepreg, with approximately 60% in weight of fibre. The quasi-isotropic plates stacked in the sequence of [0/45/–45/90]2S contained 16 layers of the laminate. A 2.5 mm by 5  mm damage region near the midpoint of paths #2 to #5 was created by hammer impact. Fire clay was pasted between sensors #4 and #8 to simulate high-damping absorp-tive materials. The schematic diagram of the plate with a PZT array, damage position, and damping material is shown in Figure 8. To achieve clear separation of directly propagating waves and waves reflected from the boundary on the composite plate, sufficient distance is

Figure 6. comparisons of the reconstructed signals with the original signal under different excitation amplitudes in the damaged case.

H. XIAO ET AL.338

preserved from the sensor to the boundary, and the proper time window is chosen to get directly propagating waves signal. a 3.5-cycle Hann-windowed sinusoidal tone burst signal of 100 kHz was used as the excitation. An arbitrary function generator (Agilent 33522A) was used to excite the PZT actuator after being amplified by a TEGAM2350 amplifier. An Agilent D50-X3014A oscilloscope was used to collect the wave signals. It should be noted that due to the direct and inverse PZT effects, each PZT wafer could serve as both an actuator and a sensor.

In the high amplitude excitation tests, an excitation signal with 100 Vpp was applied to actuators #1 to #4 sequentially. The other four sensors #5 to #8 recorded the signals simul-taneously. The recorded signals were reversed in the time domain. These signals were then

Figure 7. experimental set-up.

Figure 8. geometry of plate showing the damage position, the PZt arrays and damping material (mm).

NONDESTRUCTIVE TESTING AND EVALUATION 339

applied to the corresponding sensors after being amplified to 100 Vpp, and those sensors (#5 to #8) now functioned as actuators. The previous actuators (#1 to #4) were used as receivers to record the Lamb waves sent back towards them. The same procedure was repeated for the low amplitude excitation tests, with the much lower excitation amplitude of 20 Vpp.

4.2. Experimental results and discussion

Repeated experiments with 100 and 20 Vpp excitations showed that the maximum value of the damage index in the undamaged paths was less than 0.02. According to Equations (4) and (5), the increase in the damage index value reflects the increase in the deviation of the original input signal from the reconstructed signal, indicating that the possibility of the existence of the damage along the wave path is increased. A threshold of the damage index is set in advance to distinguish the effect of the damage for excluding the influence of other factors (such as the inherent composite damping). A damage index value that exceeds the threshold is likely to indicate a damaged situation. So the threshold of the damage index value of this study could be as 0.03. Detailed analysis was focused on the following three different paths: undamaged path, path with fire clay and path with impact damage.

As shown in Figure 8, the impact damage is distant from the sensing path between sen-sors #4 and #7, which might represent an undamaged wave path. Comparisons of the time reversal reconstructed signal with the excitation signal under 100 and 20 Vpp excitations are shown in Figure 9(a) for the pristine path (#4 to #7). The correlation coefficients calculated by Equation (4) with two different excitation amplitudes were both 99%, corresponding to a damage index of 0.01. This result shows that, at these two different levels of excitation, the distant damage had negligible effect on the Lamb wave propagation in this pristine path. Any damping effect in this path inherently from the composite material was too weak to affect the time reversal reconstructed signal. It is also evident that, although this sensing path was close to the location of the fire clay, no significant wave scattering is observed, indicating that the presence of fire clay did not play a role as damage to break the time-re-versibility of the Lamb waves.

In the case of path #4 to #8, additional high-damping material was present. Comparisons of the time reversal reconstructed signals with the original input signal under 100 and 20 Vpp excitations are shown in Figure 9(b). The correlation coefficients under the two differ-ent amplitudes of excitation are both 91%, corresponding to a damage index of 0.09. It can be observed that for different levels of excitation, high damping had a significant effect on Lamb wave time reversal reconstruction, yielding a much higher damage index that could lead to a false alarm although actually no damage was present in this path.

In the case of path #2 to #5, an impact damage region is introduced. Comparisons of the time reversal reconstructed signals with the original input signal under 100 and 20 Vpp excitations are shown in Figure 9(c). The correlation coefficient under 100 Vpp excitation is 92%, corresponding to a damage index of 0.08, which means that the damage has a very evident influence on the Lamb wave propagation under a high amplitude of excitation. In the case of low excitation amplitude (20 Vpp), however, the correlation coefficient becomes 98%, corresponding to a damage index of 0.02, indicating that the damage has a relatively weak influence on the Lamb wave time-reversibility under a low amplitude of excitation.

Figures 10 and 11 show comparisons of reconstructed signals in these three different paths at low and high excitation amplitudes, respectively. It can be seen that under both

H. XIAO ET AL.340

low and high amplitude excitations, the attenuation of reconstructed signals on the highly damped path was severe, where the main peak shapes obviously deviated from those of the intact paths. In contrast, both the main peak shape and the amplitude of the reconstructed signal in the damaged path showed relatively small deviations from those of the intact paths under low amplitude excitation, whereas the deviation increased significantly under high amplitude excitation.

Figure 12 presents the comparison of damage indices in these three paths at different excitation amplitudes. It is apparent that the damage indices in the intact path are very low under different amplitudes of excitation. When high excitation amplitude was used, both the high-damping path and the damaged path show high damage indices. Under low ampli-tude excitation, however, the damage index in the damping path remains almost the same, whereas the damage index decreases significantly in the damaged path. This phenomenon is due to the fact that the wave-delamination nonlinear interaction depends strongly on the wave amplitude. Low amplitude waves may not be able to trigger the clapping/kissing nonlinear acoustic mechanism, whereas high amplitude waves can induce these nonlinear effects and break down the time-reversibility of Lamb waves. In the damping case, regard-less of the amplitude of excitation applied, high damping always disrupts the invariance of

Figure 9. comparisons of the reconstructed signals with the original signal under different excitation amplitudes for three paths (a) Path #4 to #7 which is an intact path. (b) Path #4 to #8 which is a damping path. (c) Path #2 to #5 which is a damaged path.

NONDESTRUCTIVE TESTING AND EVALUATION 341

time reversal and thus the time reversal reconstructed signal shows a large deviation from the original signal.

Figure 10. comparisons between the reconstructed signals in the three different paths under 20 vpp excitation.

Figure 11. comparisons between the reconstructed signals in the three different paths under 100 vpp excitation.

H. XIAO ET AL.342

Therefore, a high damage index may not necessarily indicate the existence of damage in the structure because the damage index can be attributed to high-damping materials as well. Thus, in highly damped composite plates or with additional damping materials, comparison of damage indices under different amplitudes of excitation is necessary to effectively detect damage and avoid false alarms. It should be noted that fibre orientation in composite laminates can have an effect on the Lamb wave amplitude. However, as the influence of orientation is not sensitive to the variation of excitation amplitude that is similar to the damping effect, the proposed method is also applicable to anisotropic composites.

5. Conclusions

In this study, we identified two aspects that break down the time-reversibility of Lamb waves: (1) nonlinear interaction between guided waves and structural damage; (2) high-damping materials. We proposed a new method to differentiate these two cases using a varying excita-tion amplitude method. It was found that under different excitation amplitudes, both the damage indices in the pristine path were low. However, the high-damping path presented high damage indices for both high and low excitation amplitude cases, indicating that the damping effect was insensitive to the change in excitation amplitude. The damage index in the damaged path was found to be very high under a high amplitude of excitation, and it decreased significantly as the amplitude decreased below a certain threshold. As a result, impact damage in high-damping composite plates can be effectively detected by comparing damage indices under different amplitudes of excitation so as to avoid the adverse influence of the damping effect.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

The research was supported by the National Natural Science Foundation of China [grant number 51378402].

Figure 12. comparison of damage indices.

NONDESTRUCTIVE TESTING AND EVALUATION 343

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NONDESTRUCTIVE TESTING AND EVALUATION 345

Abstract1. Introduction2. Lamb wave time reversal method3. Numerical case studies of time-reversibility4. Experimental investigation4.1. Experimental set-up and procedure4.2. Experimental results and discussion

5. ConclusionsDisclosure statementFundingReferences