A Novel Signal Compensation Algorithm for Piezoceramic Degradation in Damage Imaging for Structural Health Monitoring

Transcription

1 International Workshop on SMART MATERIALS, STRUCTURES & SHM NDT in Canada 2013 Conference & NDT for the Energy Industry October 7-10, 2013 Calgary, Alberta, CANADA A Novel Signal Compensation Algorithm for Piezoceramic Degradation in Damage Imaging for Structural Health Monitoring K. R. Mulligan, N. Quaegebeur, P. Masson GAUS, Dept. of Mechanical Engineering, Université de Sherbrooke, Sherbrooke, QC, J1K 2R1, CANADA Patrice.Masson@USherbrooke.ca ABSTRACT This paper describes a method for increasing the robustness of data gathered by leadzirconate-titanate (PZT) based Structural Health Monitoring (SHM) systems attached to structures under drop-weight impact loading. This method improves accuracy of SHM algorithms based on Time-of-Flight (ToF) by correcting the amplitude and phase of guided wave signals captured from the PZT transducers. Amplitude and phase correction is determined based on measurable changes of modal damping after impact at frequencies around PZT resonance. A Finite Element (FE) model is used to establish the influence of two bonding layer degradation failure modes on transducer modal damping: variation of bonding layer coverage area and variation of Young s modulus. The same model is also used to distinguish the effect of both bonding layer degradation failure modes on amplitude and phase for actuation and sensing of guided waves and calibration curves are developed for each failure mode. From this, a Signal Correction Factor (SCF) is developed for the dominant bonding layer degradation failure mode (i.e. variation of bonding layer coverage area) to compensate for the changes in amplitude and phase of guided waves generated and measured by degraded PZT transducers using the calibration curves. The benefits of the SCF are demonstrated below PZT resonance to improve damage imaging and localization using classical ToF methods. Keywords: SHM, bonding layer degradation, impact damage, damage imaging, EUSR, signal correction.

2 INTRODUCTION Impact damages including accidental tool drops, hail, high altitude ice dislodgment, and run-way debris (2-8 J, 3-5 m/s) occur during the maintenance, take-off, and landing operations of aircraft while influencing their day to day operations [1-3]. Piezoceramic (PZT) transducer based Structural Health Monitoring (SHM) systems used for injecting and receiving guided waves in structures are part of future strategies for detecting such damages [4]. Imaging techniques such as Embedded Ultrasonic Structural Radar (EUSR) provide a means for assessing structural damage in isotropic structures. Applying the algorithm to data gathered from a sparse array of PZT transducers, structural defects are localized with the time-of-flight (ToF) of guided wave modes transmitted and received between each transducer at given observation points using the delay and sum approach [5]. In close proximity to surface-bonded PZTs, impacts may degrade the bonding layer which forms the PZT-structural interface [6]. Degradation of the bonding layer from impacts is the result of tensile and shear stresses and respective strains on the surface of the host structure which propagate from the impact point to the bonding layer [7]. Degradation of the bonding layer from impact damage has been shown experimentally to cause alterations to traveling guided wave modes [6]. The amplitude, phase, frequency spectrum, and wave velocity of these modes are important parameters in damage imaging [8] as the goal is to assess only structural defects without the added effects of bonding layer degradation. A need is therefore expressed for monitoring transducer integrity in SHM. In response to this need, different methods have been proposed for monitoring transducer integrity including: modal analysis [9], mechanical response power (MRP) and Symmetric (SYM) indices [10], and changes in electrical admittance in the low frequency regime [11]. In modal analysis, damaged sensors are identified by analyzing the mean and variance of the residuals between numerical and measured first order structural modes. MRP and SYM are indices derived from a comparison of guided wave time-domain signals in low frequency near the driving frequency of an excitation PZT transducer and are insensitive to temperature variations. Although sensitive to temperature effects, measurement of the electrical admittance in low frequency (below 50 khz) using stationary excitation signals is the most common technique used for transducer monitoring. This method demonstrates that gradual upward shifts in admittance curves occur for increasing transducer debonding with respect to baseline admittance curves. These behavioral shifts are the result of changes in transducer capacitance which is derived from the low frequency admittance. Capacitance measurements for assessing gradual bonding layer degradation are able to detect debonded transducers but struggle to measure gradual degradations due to higher frequency PZT resonance modes shifting into the lower frequency regime as degradation increases [12]. More recent efforts to quantify the amount of bonding layer degradation for PZT transducers bonded to a host structure surface use metrics derived from measured electrical admittance curves in higher frequency regimes (above 500 khz). One such metric uses the modal damping of the first PZT resonance to measure gradual bonding layer degradation [6]. With a measurable metric that can assess the level of degradation, a link must then be established to associate a change in modal damping with effects on transmitted and received

3 guided wave modes. The Signal Correction Factor (SCF) presented in [6] and [13] is used to adjust the amplitude and phase of measured guided wave modes based on experimental measurements of degradation using transparent materials. The choice of using transparent materials is to validate modal damping as a capable metric in assessing degradation. Accurate estimations of the level of degradation under the PZT especially in non-transparent structures is however difficult to assess experimentally, such that this approach has limited applicability. This causes difficulties in inducing an accurate amount of degradation to build experimental modal damping versus degradation curves and the amplitude and phase correction curves that follow. The SCF is validated by comparing adjusted signals obtained from transducers with degraded bonding layers with healthy reference signals. In this paper, an approach to develop a practical SCF in non-transparent materials is presented. A simple numerical model of a PZT transducer bonded to a simple structure is used to assess a physical degradation under damaging conditions and associated changes to guided wave signals. Numerical modal damping, amplitude, and phase calibration curves are derived from the model with gradual degradation of the bonding layer for two degradation modes: bonding layer coverage area and bonding layer Young s modulus degradation. A novel SCF is proposed based on combining physical modal damping measurements with these numerical calibration curves and validated experimentally using damage imaging by EUSR [5] on an isotropic aluminum plate with a damage induced using a drop-weight impact system. Piezoelectric debonding process METHODS Bonding layer degradation modes due to impacts. Impacts have been shown to damage the bonding layer between a PZT transducer and a host structure but failure modes associated with impacts to the bonding layer have not yet been explicitly studied [11]. As PZT transducers may debond completely from structural surfaces when standardized impact energies are used, understanding such failure modes is important [14]. Much work has already been done on failure modes of the bonding layer in bonded joints that are initiated by impacts [15], showing that failure occurs at the extremities of the adherends and gradually propagates from the extremities of the joint. These findings indicate a potential that in the presence of increasing impact energies, the bonding layer is prone to two failure modes including: a reduction in bonding layer coverage area through structural deformation and delamination due to shearing motion [16] and because of the shearing motion, the bonding layer Young s modulus for ductile bonding layers (such as epoxy) is affected. The second failure mode occurs as a result of the bonding layer becoming more brittle due to increased maximum stress and a decreased strain rate [17]. These two degradation modes are therefore investigated in the case of bonded PZTs. Metrics to monitor the piezoelectric debonding process. For SHM system health verification, variations in the electrical admittance Y(ω) pzt have been shown to play a meaningful role in the detection of transducer debonding due to environmental and mechanical loading [11]. One way to measure the electrical admittance spectrum is by

4 sending voltage bursts U Generated to the PZT and measuring simultaneously voltage and current I generated using the circuit shown in Fig. 1 (a). The capacitance metric is derived as the slope of the electrical admittance curve in low frequency (below 50 khz) [11]. Upward shifts in this slope with respect to a pristine measurement correspond to increases in capacitance which designates bonding layer degradation [11]. This rule however does not always hold true for gradual bonding layer degradation due to the influence of PZT resonance shifting from high frequency into the low frequency domain [6]. Fig 1 - Electrical admittance measurement circuit (a) and LCR model for an unloaded PZT that accounts for multiple resonances and damping (b). The modal damping metric has been developed as an improvement to the capacitance metric [6]. To extract the modal damping from the electrical admittance curves, the theoretical electrical admittance can be estimated using a lumped parameter model as presented in Fig. 1 (b). Classically, low frequency admittance is modeled using a resistor and capacitance (RC) in series circuit. However, in order to model PZT mechanical resonances, the addition of a parallel inductor, capacitor, and resistor (LCR) circuit in series with the initial RC circuit as indicated in Fig. 1 (b) is required with: series resistance R s, electrostatic capacitance C s, mechanical elastic compliance, mechanical mass, and mechanical damping represented electrically as C p, L p, and R p respectively, where R s and R p account for energy dissipation [18]. The constants R s, C s, C p, L p, and R p of the lumped parameter model are determined by minimizing the distance between the modeled and measured electrical admittance for both the real and imaginary parts using the least squares minimization algorithm. A refined and more accurate method for minimizing the lumped parameter model is to use the modal resonance frequencies ω i and damping parameters ξ i directly and model the electrical admittance curve using Eq. 1: To account for higher order resonances of the PZT which could occur with debonding, n series LCR circuits can be added as in Fig. 1 (b) in parallel where n is the total number of resonances that influence the PZT response. For a limited frequency range of interest, using non-stationary signal excitations, a single mode approach can provide a reasonable estimate of the modal damping.

5 Assessment of the modal damping as a metric for debonding Simulation setup. A numerical model is used to assess the influence of bonding layer degradation on the modal damping of a bonded PZT for two bonding layer failure modes: coverage area and Young s modulus degradation. To do this, a numerical model is developed as shown in Fig. 2 using commercial FEM software COMSOL (v. 4.2). An axisymmetric 2D model of a 5 mm circular PZT attached to an isotropic aluminum plate using a 0.5 mm thick epoxy bonding layer is chosen for simplicity and calculations are performed in the frequency domain to reduce computation time. The properties of the aluminum plate and the epoxy bonding layer are shown in Tab. 1. Absorbing regions are used to avoid boundary reflections from the edges of the structure. Item Material Thickness (mm) Young s modulus (GPa) Poisson s ratio Density (kg/m 3 ) PZT PZT 5A Aluminum plate 6061-T Bonding layer Epoxy Table 1 - Properties of the PZT transducer, aluminum plate, and bonding layer. Fig 2 - Schematic of the FE model mesh used for computation (a) and 3D reconstruction of the displacement field (b). The model is meshed using triangular elements for a total number of degrees of freedom (DoF) such that a maximum mesh size of 0.1 mm is ensured and that at least 10 nodes exist per minimum resolvable wavelength. A voltage of 1V is simulated at the upper electrode of the PZT and current is estimated at the same electrode to extract the electrical admittance. The modal damping is then estimated using the LCR model. The A 0 and S 0 guided wave modes are also estimated in the far-field region of the plate by summing and taking the difference of the out-of-plane displacement at both the top and bottom surface of the structure. Due to the reciprocity principle, there is no need for a 3D pitch-catch model to investigate the effects of degradation on sensing [19]. Simulation of adhesive coverage area degradation. The influence of bonding layer coverage is estimated by changing the adhesive coverage degradation from 0 % (perfectly bonded) to 100 % (debonded) by steps of 0.1 %. This procedure is selected based on results reported in [15] showing that bonding layer failure initially occurs at the extremities of the adherends

6 and gradually propagates inward. The results for the bonding layer coverage area degradation are presented in Fig. 3. Fig. 3 - Numerical results for the effects of bonding layer coverage area degradation on the real (a) and imaginary (b) parts of the electrical admittance. The real and imaginary parts of the electrical admittance versus bonding layer coverage area degradation below 1 MHz are presented in Fig. 3. From the figure, the amplitude of the real part at PZT resonance gradually increases with a reduction in bonding layer coverage area up to 88% higher than that of the perfectly bonded PZT. This increase is associated with a reduction in the modal damping of the PZT and a shift in the PZT resonance frequency towards low frequency with bonding layer degradation. This result indicates that with bonding layer degradation, there is a reduction in the constraining effects of the PZT. This appears as a reduction in stiffness in the bonding layer coupled to the PZT which in turn results in a lower transfer of the generated displacement from the PZT to the structure [11]. Simulation of adhesive Young s modulus degradation. The above simulations are repeated for different bonding layer Young s modulus in order to assess the second bonding layer failure mode. For this purpose, the bonding layer Young s modulus is decreased by increments of 1% from a perfectly healthy state. The results for the Young s modulus failure mode are presented in Fig. 4. Fig 4 - Numerical results for the effects of bonding layer Young's modulus degradation against the real (a) and imaginary (b) parts of the electrical admittance. In the real and imaginary parts of the admittance, presented in Fig. 4, a shift on the first PZT resonance peak from 530 khz (perfectly bonded) to 400 khz (nearly debonded) is observed as in the case of the bonding layer coverage area degradation mode. This shift is associated with a decrease in the bonding layer stiffness. Unlike the bonding layer coverage area degradation, a secondary peak is not visible. The results in Fig. 4 (a) and (b) show that changes to the bonding layer Young s modulus have little effect on the electrical admittance and thus the modal damping, until large degradation is incurred.

7 Modal Damping (%) Influence of degradation on modal damping. The above numerical results indicate that bonding layer coverage area degradation is the dominant failure mode. Using the electrical admittance curves obtained numerically, the modal damping is extracted for each degradation step in Fig. 3 by minimizing the LCR model and presented in Fig. 5. Up to 15% bonding layer coverage area degradation, the modal damping increases which could suggest a change of stress and strain at the edges of the PZT, leading to non-classical stress and strain profiles between the PZT, bonding layer, and the structure [20]. This is followed by an almost linear decrease in modal damping between 20% and 80% degradation FEM Per f ec t l y B on de d Fre e -Fr ee Dam ag e d PZT Adhesive Coverage Degradation (%) Fig 5 - Modal damping versus bonding layer coverage area degradation obtained from FE model (solid) and experimentally (shapes). Implementation of a Signal Correction Factor (SCF) Formulation. The numerical results describe changes to the modal damping metric that can be used as a means to estimate the amount of bonding layer degradation under a PZT bonded to a host structure. Following this, changes in amplitude and phase associated with bonding layer degradation of the A 0 and S 0 guided wave modes can also be extracted from the numerical study as presented in Fig. 6 to compensate for bonding layer degradation. A Signal Correction Factor (SCF) is therefore proposed and assessed in the following. Variations in a guided wave signal s(t) measured after degradation by a transducer within a SHM system, are caused by degradation of the host structure Δs damaged (t) and degradation of the transducer bonding layer Δs degraded (t). The measured signal s (t) can then be described as the sum of the two components caused by damage on top of a pristine signal s(t) as shown in Eq. 3 in the time domain and Eq. 4 in the frequency domain: Derived from the modal damping metric, the SCF represents a transfer function in the frequency domain F(ω) which adjusts the amplitude A(ω) and phase of the measured signal spectrum S (ω) to compensate for bonding layer degradation: The parameters A(ω) and (ω) are determined from the numerical displacement amplitude and phase calibration curves (Fig. 6) based on the assessment of the amplitude A degraded (ω) and phase degraded(ω) at a specific frequency and amount of bonding layer

8 degradation with respect to the reference (0% degradation). Applying the SCF to Eq. 4 and taking the inverse Fourier transform of Eq. 6, produces a time domain signal related to propagation delay only: Fig 6 - Numerical results for the effects of bonding layer coverage area degradation against the amplitude of the A 0 (a) and S 0 (b), and the unwrapped phase of the A 0 (c) and S 0 (d) guided wave modes. Experimental assessment of the SCF to damage imaging and localization. In order to investigate the applicability of the SCF for damage imaging, experimental validation is proposed on an aluminum plate with setup shown in Fig. 7. Four 5 mm diameter with 0.5 mm thick PZT transducers are separated by a distance of 20 cm, and fixed to a 1.54 mm thick aluminum sheet (60 cm x 60 cm) using epoxy. The bonding layer beneath one transducer is degraded by impact damage using a drop-weight impact system with standard impact energy of 8.9 J. The damage location is selected to be in close proximity (~6.4 cm) to one transducer such that degradation does not affect other transducers in the array. Absorbing tape at the plate edges is used to prevent edge reflections. The baseline modal damping metric is extracted from electrical admittance measurements. Guided wave measurements are acquired using a 5.5 cycle burst at 125 khz and 450 khz in order to selectively generate A 0 and S 0 modes prior to damage initiation. Pitch and catch baseline measurements of the 12 paths between each transducer are gathered in a round-robin fashion. Baseline guided wave measurements are taken without the presence of damage such that pristine and damage signals are subtracted before post-processing using the EUSR imaging algorithm. After subtraction and correction using the SCF the measured time signals contain only time traces scattered by the reflectors (damage). The acquisition of the receiving transducers is controlled using a high impedance NI PCI bit DAQ board. The signals are recorded at a fixed sampling frequency of 6 MHz with a low-pass filter set at 1.5 MHz and averaged 100 times in order to increase the signal-to-noise ratio.

9 Fig 7 Schematic (a) and picture (b) of the experimental setup of an aluminum plate for EUSR imaging. Results for compensation in imaging. The imaging results for the A 0 and S 0 modes with the bonding layer coverage area of one transducer degraded by 8% are presented in Fig. 8 (a,c) without the SCF and in Fig. 8 (b,d) with the SCF. The actual damage location is indicated in the figures using a dashed circle. In Fig. 8 (a) high amplitudes for damage index (DI) are observed at the damage location however the maximum DI is located almost 10 cm from the actual damage location. This DI represents phantom damage, leading to false positives in the damage detection procedure. In Fig. 8 (b) following adjustment, the maximum DI is found exactly on the actual damage location. Some phantom damage is still observed for the A 0 mode due to its dispersive nature at the excitation frequency (125 khz). In Fig. 8 (c) high amplitudes for DI are observed near the damage location with the maximum situated relatively close. Phantom damages are still observed and the DI at the damage location is dispersed. In Fig. 8 (d) following adjustment, the maximum DI is found exactly on the actual damage location and no phantom damage is observed as the S 0 mode is non dispersive at the excitation frequency (450 khz). Fig 8 EUSR imaging results for the A 0 mode at 125 khz (a) and S 0 mode at 450 khz (c) modes with 8% bonding layer coverage degradation and EUSR imaging results with SCF applied to the A 0 (b) and S 0 (d) modes.

10 CONCLUSION The present paper demonstrates a SCF that compensates for bonding layer degradation of surface-bonded PZT transducers of a SHM system. Electrical admittance curves for a surface-bonded PZT are obtained in simulation using a FE model to simulate the degradation of the transducer bonding layer. Modal damping is extracted from the measured electrical admittance curves as a metric for estimating gradual bonding layer degradation. Guided wave signal transmission is simulated using the FE model to investigate the effect of bonding degradation on amplitude and phase for actuation and sensing. The numerical results show that bonding layer coverage area degradation dominated as the failure mode for surface bonded PZT transducer. A SCF is developed capable of adjusting the amplitude and phase of guided wave signals generated or measured by PZT transducers with bonding layer coverage area degradation. The SCF is demonstrated below PZT resonance on improving damage imaging results in the imaging algorithm when a single transducer of a sparse array is damaged due to close proximity drop-weight impacts causing mild and severe degradation. The SCF proves useful for improving the accuracy of the damage imaging results allowing an extension of the service life of the SHM system. REFERENCES 1. W. J. Staszewski, S. Mahzan and R. Traynor, "Health monitoring of aerospace composite structures-active and passive approach," Composites Science and Technology, vol. 69, no , pp , G. A. Schoeppner and S. Abrate, "Delamination threshold loads for low velocity impact on composite laminates," Composites: Part A: Applies Science and Manufacturing, vol. 31, no. 9, pp , J. Tomblin, T. Lacy, B. Smith, S. Hooper, A. Vizzini and S. Lee, "Review of damage tolerance for composite sandwich airframe structures. Technical Report DOT/FAA/AR- 99/49," Federal Aviation Administration, Washington, DC, August L. B. Vogelesang and A. Vlot, "Development of fibre metal laminates for advanced aerospace structures," Journal of Materials Processing Technology, vol. 103, no. 1, pp. 1-5, V. Giurgiutiu and J. J. Bao, "Embedded-ultrasonics structural radar for in situ structural health monitoring of thin-wall structures," Structural Health Monitoring, vol. 3, no. 2, pp , K. R. Mulligan, N. Quaegebeur, P.-C. Ostiguy, P. Masson and S. Létourneau, "Comparison of metrics to monitor and compensate for piezoceramic degradation in structural health monitoring," Structural Health Monitoring, vol. 12, no. 2, pp , N. K. Gupta, M. A. Iqbal and G. S. Sekhon, "Experimental and numerical studies on the behavior of thin aluminum plates subjected to impact by blunt- and hemispherical-nosed projectiles," Impact Engineering, vol. 32, no. 1, pp , N. Quaegebeur, P. Masson, D. Langlois-Demers and P. Micheau, "Dispersion-based imaging for structural health monitoring using sparse and compact arrays," Smart Materials and Structures, vol. 20, no. 1, pp , 2010.

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