2.1. Lamb Wave Propagation in Aluminum Plate
Lamb waves was first used for structural health monitoring technology by the US general engineer Worlton [
22]. Transverse wave and longitudinal wave are two types of waves that exist only in an infinitely uniform, isotropic elastic medium. When the waves propagate in the aluminum alloy plate, a wave containing a large number of wave packets is formed, such waves are called Lamb waves [
23]. Lamb waves are dispersive waves.
Figure 1 is the group velocity dispersion curve of Lamb wave propagating in a 2 mm thick aluminium alloy plate. Lamb waves can be classified into two modes: symmetric (S) mode and anti-symmetric (A) mode. Each mode contains multi-order patterns, symmetric mode includes S0, S1, …, Sn, etc., anti-symmetric mode includes A0, A1, …, An, etc. In order to reduce the influence of the dispersion characteristics of the Lamb wave, the frequency-thickness product (
f·s) was chosen to be 0.1 MHz*mm in
Figure 1, so only A0 mode and S0 mode waves propagated in the aluminium alloy plate. The propagation speed of the S0 mode wave is much larger than the A0 mode wave, therefore, the first wave packet is the S0, and the second wave packet is the A0. The A0 mode wave was applied for piezoelectric element debonding given its higher energy and signal to noise ratio.
The number of cycles for each excitation pulse of the excitation signal is generally 3.5–13.5 cycles [
24]. The number of cycles should not be too large or too small, the more period will lead to crosstalk in different mode of wave packet, while small signal cycles carrid less energy. Besides, the wider the bandwidth, the signal will be susceptible to interference. In this study, five cycles of the sinusoidal narrowband signal modulated by Hanning window (as shown in
Figure 1) was selected as the excitation pulse [
25,
26], because the sinusoidal signal has periodicity, smoothness and peak time is faster than the parabolic shape, and the narrowband signal is easier to interpret than the broadband signal insignal analysis. The excitation frequency is set to be 50 kHz, as shown in
Figure 2. The input signal is 5 V and the maximum output voltage is 50 V, the high-speed elastic wave excitation module containing power amplifier fixed 10 times to amplify the input signal.
where A is the amplitude of the signal,
is the center excitation frequency, N is the number of excitation signal cycles, and
is the Heaviside step function.
SHM technology can be divided into active SHM and passive SHM; the active SHM is widely used to directly asses the structure health status. Piezoelectric elements are used to build a structural health monitoring network. There are two modes of damage monitoring using piezoelectric elements, one is pulse-echo mode and the other is active pitch-catch mode [
27,
28]. In this study, pitch-catch mode is used in debonding damage monitoring. The active Lamb wave signals were generated by driving actuators, then propagated in the structure and received by the sensors.
Figure 3 is a schematic diagram of the propagation of Lamb wave on the aluminum plate. There are four cases of piezoelectric element debonding.
Figure 3a shows that the excitation actuator and the receiving sensor are not debonded,
Figure 3b represents that only actuator is debonded,
Figure 3c shows that only receiving sensor is debonded,
Figure 3d shows that both the actuator and sensor are debonded.
Due to the positive piezoelectric effect and inverse piezoelectric effect, the piezoelectric materials can be made into piezoelectric sensors and actuators, which can be used to monitor the charge density on piezoelectric dielectrics and to change the structural deformation or stress state, the charge density on piezoelectric dielectrics is proportional to the external force. The constitutive equation of piezoelectric materials is as follows.
where
is the mechanical strain,
is the electric displacement,
is the electric field and
is the mechanical stress,
represent the dielectric constant under constant stress,
is the coefficient of flexibility under constant electric field,
and
is piezoelectric voltage constant.
On the receiving sensor, due to the debonding of piezoelectric components, the contact area between the piezoelectric sensor and the substrate decreases, irrespective of other factors that cause the charge density of piezoelectric sensors to change, which will result in thedecrease of the accumulated charges on the receiving sensor, leading to the decrease of the energy of the received signal and the signal amplitude.
2.2. Monitoring System Setup for Debonding Tests
The Integrated Structural Health Monitoring Scanning System (SHM-ISS-4.0A), which was provided by Nanjing SMART Monitoring Technology Co., Ltd. was used to excite and receive signals when the PZT elements are in different percentages of debonding. As shown in
Figure 4, the entire PZT debonding monitoring system is composed of SHM-ISS-4.0A system (including data acquisition program and SMART piezoelectric element monitoring equipment, the equipment is composed of high speed elastic wave excitation and response module, high speed elastic wave excitation response channel scanning module, as well as various interfaces and heat dissipation devices), signal terminal board and 2024-T3 aluminum alloy plate with different degrees of debonding piezoelectric pieces. The system integrates various functions such as structural state analysis, damage characteristic parameters, it is a highly integrated structural health monitoring system that is suitable for both industrial field applications and scientific research. So in this study, the system can be used to extract the characteristic parameters of amplitude and phase shift of monitoring signals.
The debonding monitoring system of the piezoelectric sensor utilizes the active monitoring method of pitch catch mode, and the response variable takes the amplitude and phase difference of the signal received by the sensors. The schematic diagram of the piezoelectric element debonding monitoring system is shown in
Figure 5. In the signal excitation module, the sinusoidal modulation wave generates a specific excitation signal through a function generator. The excitation signal is amplified by a power amplifier, and thenLamb wave is generated by the inverse piezoelectric effect of the piezoelectric actuator. Lamb wave propagates to the sensor through the structure. The sensor receives stress wave through piezoelectric effect. Then the data are collected through the data acquisition module. In this system, parameters can be set by system controller and monitored by structural health monitoring software.
2.3. Extraction of Characteristic Parameters
As shown in
Figure 6, the dotted line represents the healthy signal when the piezoelectric discs are full bonded on the aluminum plate, the solid line represents the damage signal when the debonding area of actuator is 20%. The comparison of the sensing signals obtained by different excitation frequencies for partial debonding and full bonded piezoelectric elements shows that when the frequency thickness product (f·d) is 0.1 MHz*mm (the thickness of aluminum plate is 2 mm), the A0 mode signal is more sensitive to the change of debonding area. Therefore, 50 kHz and A
0 mode are chosen as the excitation frequency and signal mode to monitor the signal changes of piezoelectric sensors under different debonding area conditions.
Figure 7 is a schematic diagram of the time window of the A0 mode wave packet intercepting the Lamb wave, the black line represents the excitation signal and the red line represents the received signal. T
0 is the duration of the excitation signal propagation, and TOF is the flight time of the signal from an actuator to a sensor, the measurement standard for the extraction of TOF is based on the arrival time of the maximum peak of A0 mode Lamb wave.
In order to investigate the degradation trends of PZT actuator/sensor under different percentages of debonding, the method of extracting characteristic parameters of the signal was performed. [
29,
30] There are two main characteristic parameters ofLamb wave signal during the debonding process of actuator/sensor, one is normalized amplitude, which corresponding to the energy of the Lamb wave, the other is phase angle offset ofreceiving signal, which represents the propagation path of Lamb wave [
31]. During the debonding process of the piezoelectric sensor, the energy and propagation path will change, which leads to the changes of normalized amplitude and phase angle offset respectively.
To simplify the calculation, the absolute value of the physical system was changed into relative value. The amplitude of the acquired Lamb wave signal is normalized as following formula:
In Equation (4), x represents the normalized amplitude, represents the amplitude of the wave packet signal in the ith case, and represents the amplitude of the wave packet in the reference signal (the initial state of the piezoelectric element).
The phenomenon of partial debonding or even shedding of the PZT discs may occur in actual environment, such as vibration, which may lead to the change of propagation distance of Lamb wave, i.e. the phase angle offset. The formula for calculating the relative phase angle shift is as follows:
In the Equation (5), represents the time corresponding to the maximum amplitude of wave packet in the i-th case, and denotes the time corresponding to the maximum amplitude of the wave packet of the reference signal (in the initial state of the piezoelectric element).