The anisotropic propagation of ultrasonic guided waves in composite materials and implications for practical applications

An Optimal Shaped Sensor Array Derivation

In Structural Health Monitoring (SHM) applications, the Direction of Arrival (DoA) estimation of Guided Waves (GW) on sensor arrays is often used as a fundamental means to locate Acoustic Sources (AS) generated by damages growth or undesired impacts in thin-wall structures (e.g., plates or shells). In this paper, we consider the problem of designing the arrangement and shape of piezo-sensors in planar clusters in order to optimize the DoA estimation performance in noise-affected measurements. We assume that: (i) the wave propagation velocity is unknown, (ii) the DoA is estimated via the time delays of wavefronts between sensors, and (iii) the maximum value of the time delays is limited. The optimality criterion is derived basing on the Theory of Measurements. The sensor array design is so that the DoA variance is minimized in an average sense by exploiting the Calculus of Variations. In this way, considering a three-sensor cluster and a monitored angles sector of 90°, the optimal time delays-DoA relations are derived. A suitable re-shaping procedure is used to impose such relations and, at the same time, to induce the same spatial filtering effect between sensors so that the sensor acquired signals are equal except for a time-shift. In order to achieve the last aim, the sensors shape is realized by exploiting a technique called Error Diffusion, which is able to emulate piezo-load functions with continuously modulated values. In this way, the Shaped Sensors Optimal Cluster (SS-OC) is derived. A numerical assessment via Green's functions simulations shows improved performance in DoA estimation by means of the SS-OC when compared to clusters realized with conventional piezo-disk transducers.

Guided wave skew velocity correction in anisotropic laminates

Guided ultrasonic wave propagation in anisotropic structures results in directional dependency of velocity and wave skewing effects that can impact the accuracy of damage detection. Phase and group velocities of the A₀ guided wave mode, propagating in a unidirectional carbon fiber reinforced laminate, were investigated experimentally and through finite element analysis. A correction for the significant offset in phase and group velocities due to wave skewing effects is illustrated for both point and short line sources, achieving good agreement with theoretical calculations assuming planar wave fronts. The influence of the line excitation length on velocity measurements is discussed.

Guided wave propagation and skew effects in anisotropic carbon fiber reinforced laminates

Guided ultrasonic waves provide a promising structural health monitoring (SHM) solution for composite structures as they are able to propagate relatively long distances with low attenuation. However, the material anisotropy results in directionally dependent phase and group velocities, in addition to energy focusing, wave skewing, and beam spreading phenomena. These effects could lead to inaccurate damage localization if not accounted for. In this contribution, the guided wave propagation behavior (A0 mode) for a highly anisotropic, unidirectional carbon fiber reinforced polymer laminate is systematically investigated through both finite element analysis and non-contact laser measurements and compared to theoretical predictions. The directional dependency of phase and group velocity measured for a point and line source shows good agreement with theoretical predictions, once a correction for wave skew effects is applied. Wave skew angles were evaluated from the experimental and numerical wave propagation in multiple directions and matched theoretical predictions based on the phase slowness curve. Significant guided wave beam spreading from a line source was observed and quantified from both experiments and simulations and compared with theoretical predictions using the anisotropy factor. The impact of anisotropic guided wave propagation behavior on SHM is discussed.

Influence of Composite Thickness on Ultrasonic Guided Wave Propagation for Damage Detection

In this paper, the propagation properties of ultrasonic guided waves (UGWs) in different-thickness composites (i.e., 2, 4 and 9 mm) were critically assessed, and their effectiveness for damage detections and localisations under varying temperatures was demonstrated. A diagnostic film with phased-array lead zirconate titanate (PZT) transducers based on the ink-jet printing technique was used in the experiments. Initially, the dispersion curves for these composites were compared. Next, the effects of the composite thickness on the A₀ and S₀ mode amplitudes and the group velocity were investigated by active sensing. Next, the behaviours of UGWs under varying temperatures in different-thickness plates were also investigated. Finally, surface-mounted artificial damage and impact damage were detected and located in different composites.

Adaptive instantaneous frequency ridge extraction based on target tracking for frequency-modulated signals

The instantaneous frequency (IF) is an important feature for the analysis of non-stationary signals. However, extracting multiple IF ridges, crossing IF ridges, and discontinuous IF ridges simultaneously is still a challenging task. To solve this problem, an adaptive IF ridge extraction method is proposed. This method regards the IF ridge values at each time point as targets to be tracked. The tracking targets are defined as three states: survival, death, and birth. Firstly, the potential peaks in the time-frequency representation are found to reduce the noise effect. Secondly, an adaptive penalty function is constructed to determine the target state and track the ridge target. Thirdly, the crossing ridges are separated base on the slope information. This method is capable of simultaneously extracting multiple IF ridges, crossing IF ridges, and discontinuous IF ridges. The performance of the proposed method is investigated by a simulated signal and two experimental signals.

Optimal Array Design and Directive Sensors for Guided Waves DoA Estimation

The estimation of Direction of Arrival (DoA) of guided ultrasonic waves is an important task in many Structural Health Monitoring (SHM) applications. The aim is to locate sources of elastic waves which can be generated by impacts or defects in the inspected structures. In this paper, the array geometry and the shape of the piezo-sensors are designed to optimize the DoA estimation on a pre-defined angular sector, from acquisitions affected by noise and interference. In the proposed approach, the DoA of a wave generated by a single source is considered as a random variable that is uniformly distributed in a given range. The wave velocity is assumed to be unknown and the DoA estimation is performed by measuring the Differences in Time of Arrival (DToAs) of wavefronts impinging on the sensors. The optimization procedure of sensors positioning is based on the computation of the DoA and wave velocity parameters Cramér-Rao Matrix Bound (CRMB) with a Bayesian approach. An efficient DoA estimator is found based on the DToAs Gauss-Markov estimator for a three sensors array. Moreover, a novel directive sensor for guided waves is introduced to cancel out undesired Acoustic Sources impinging from DoAs out of the given angles range. Numerical results show the capability to filter directional interference of the novel sensor and a considerably improved DoA estimation performance provided by the optimized sensor cluster in the pre-defined angular sector, as compared to conventional approaches.

Modeling the Effect of Anisotropy in Ultrasonic-Guided Wave Tomography

Most of the existing ultrasonic-guided wave tomography approaches to map structural changes in plate-like waveguides are based on the assumption of an isotropic material model. However, there are many other engineering applications that are made of anisotropic materials and structures. Applying these techniques on such structures becomes complicated due to the anisotropic wave propagation behavior. The main challenge is to develop a suitable forward model that describes the wave propagation in such material, thereby enabling accurate reconstruction of the material properties. The present study proposes an anisotropic formulation of the acoustic forward model to map velocity variations induced by defects in anisotropic plates. The anisotropic behavior of the waves along the plate is simulated by implementing approximate anisotropic parameters. The velocity reconstruction is based on a full-waveform inversion algorithm, and its performance is investigated in the case of different degrees of anisotropy of the plate material and the defect. The results suggest that the method is highly suitable for imaging velocity changes due to defects. This is found to be the case when the defect has a similar anisotropic structure to the surrounding plate material. The validation experiment is performed on a multilayered composite plate with a circular defect of stiffness reduction using A₀ mode, showing a very good performance of the reconstruction algorithm.

Ultrasonic Guided Wave Testing on Cross-Ply Composite Laminate: An Empirical Study

Structural health monitoring comprises a set of techniques to detect defects appearing in structures. One of the most viable techniques is based on the guided ultrasonic wave test (UGWT), which consists of emitting waves throughout the structure, acquiring the emitted waves with various sensors, and processing the waves to detect changes in the structure. The UGWT of layered composite structures is challenging due to the anisotropic wave propagation characteristics of such structures and to the high signal attenuation that the waves experience. Hence, very low amplitude signals that are hard to distinguish from noise are typically recovered. This paper analyzes the propagation of guided waves along a cross-ply composite laminate following an empirical methodology. The research compares several implementations for UGWT with piezoelectric wafer active sensors. The reference for comparison is set on a basic mode, which considers the application of nominal voltage to a single sensor. The attenuation and spreading of the waves in several directions are compared when more energy is applied to the monitored structure. In addition, delayed multiple emission is also considered in multisensor tests. The goal of all the UGWT configurations is to transmit more energy to the structure such that the echoes of the emission are of greater amplitude and they ease the signal processing. The study is focused on the realization of viable monitoring systems for aeronautical composite made structures.

Analysis of Wave Patterns Under the Region of Macro-Fiber Composite Transducer to Improve the Analytical Modelling for Directivity Calculation in Isotropic Medium

Analytical modelling is an efficient approach to estimate the directivity of a transducer generating guided waves in the research field of ultrasonic non-destructive testing of the large and complex structures due to its short processing time as compared to the numerical modelling and experimental techniques. The wave patterns or the amplitude variations along the region of ultrasonic transducer itself depend on its behavior, excitation frequency, and the type of propagating wave mode. Depending on the wave-pattern of a propagating wave mode, the appropriate value of the amplitude correction factor must be multiplied to the amplitudes of the excitation signal for the accurate evaluation of directivity pattern of the ultrasonic transducers generating guided waves in analytical modelling. The objective of this work is to analyse the wave patterns under the region of macro-fiber composite (MFC) transducer to improve the accuracy of a previously developed analytical model for the prediction of directivity patterns. Firstly, the amplitude correction factor based on the wave patterns under the region of P1-type MFC (MFC-2814) transducer at two different frequencies (80 kHz, 3 periods and 220 kHz, 3 period) glued on 2 mm Al alloy plate has been estimated analytically in the case of an asymmetric (A0) guided Lamb wave. The validation of analytically estimated amplitude correction factor is performed by a proposed experimental method that allows analyzing the behaviour of MFC transducer under its region by gluing MFC on bottom surface and scanning the receiver on the top surface of the sample. Later on, the estimated amplitude correction factor is included in the previously developed 2D analytical model for the improvement in the directivity patterns of the A0 mode. The modified analytical model shows a significant improvement in the directivity pattern of the A0 wave mode in comparison to the results obtained by the previous model without considering the proper wave patterns. The results reveal that errors between the directivity estimated by the present modified 2D analytical model and experimental investigation are reduced by more than 58% in comparison to the previously developed analytical model.

Bidirectional, Bimodal Ultrasonic Lamb Wave Sensing in a Composite Plate Using a Polarization-Maintaining Fiber Bragg Grating

Lamb wave (LW) is well suited for structural health monitoring (SHM) in advanced composites. However, characteristic differences between the symmetric modes and the anti-symmetric modes often add complexity to SHM systems. The anisotropic nature of composite materials, on the other hand, necessitates direction-sensitive sensing. In this paper we report the experimental demonstration of bidirectional (0° and 90°), bimodal (S0 and A0) LW measurement within the frequency range of 20–140 kHz using a polarization-maintaining fiber Bragg grating (PM-FBG) sensor attached to a composite laminated plate. By selectively interrogating the fast and/or the slow axis of the PM-FBG, we show that not only can the sensor respond to LWs propagating along both directions, but the response can also be used to differentiate the two directions. Moreover, the fast axis of the sensor is able to respond to both the S0 and the A0 modes when the sensor is aligned with the wave propagation direction, whereas single S0 mode response can be achieved with the slow axis operating perpendicularly to the wave propagation direction. Such diverse responses indicate the potential of PM-FBGs as versatile multi-parameter SHM detectors, which can effectively address the challenges posed by material anisotropicity and LW mode diversity.

Defect Estimation in Non-Destructive Testing of Composites by Ultrasonic Guided Waves and Image Processing

The estimation of the size and location of defects in multi-layered composite structures by ultrasonic non-destructive testing using guided waves has attracted the attention of researchers for the last few decades. Although extensive signal processing techniques are available, there are only a few studies available based on image processing of the ultrasonic B-scan image to extract the size and location of defects via the process of ultrasonic non-destructive testing. This work presents an image processing technique for ultrasonic B-scan images to improve the estimation of the location and size of disbond-type defects in glass fiber-reinforced plastic materials with 25-mm and 51-mm diameters. The sample is a segment of a wind turbine blade with a variable thickness ranging from 3 to 24 mm. The experiment is performed by using a low-frequency ultrasonic system and a pair of contact-type piezoceramic transducers kept apart by a 50-mm distance and embedded on a moving mechanical panel. The B-scan image acquired by the ultrasonic pitch-catch technique is denoised by utilizing features of two-dimensional discrete wavelet transform. Thereafter, the normalized pixel densities are compared along the scanned distance on the region of interest of the image, and a −3 dB threshold is applied to the locations and sizes the defects in the spatial domain.

Identification and Characterization of Defects in Glass Fiber Reinforced Plastic by Refining the Guided Lamb Waves

In this paper, the disbond-type defect presented on glass fiber reinforced plastic material is analyzed by refining the guided Lamb wave signals. A segment of wind turbine blade is considered as a test sample. The low-frequency ultrasonic measurement system is used for the non-destructive testing of the test sample using guided waves. The P-1 type macro-fiber composite transducer as a transmitter and contact-type piezoceramic transducer as a receiver are used for the testing of a sample. The disbond type defect having a diameter of 81 mm is detected from the experimental results. To improve the accuracy in locating and sizing the defects and estimation of the time of flight and phase velocity of ultrasonic guided waves in defective region, signal processing algorithm is developed by utilizing the promising properties of various ultrasonic signal processing techniques such as wavelet transform, amplitude detection, two-dimensional Fast-Fourier transform, Hilbert transform and variational mode decomposition. The discrete wavelet transform is used to denoise the guided wave signals and then, the size and location of defects are estimated by amplitude detection. The reflected wave signals from the opposite edge of the sample are removed by applying the two-dimensional Fast-Fourier transform to the experimental B-scan signal. Afterwards, variational mode decomposition and Hilbert transform are used for the phase velocity and time-delay estimation by comparing the instantaneous amplitudes of the defective and defect-free signal. The validation and the demonstration of reproducibility of the algorithm is performed by extracting the features of a 51 mm defect from another experimental B-scan.

Anisotropic effects on ultrasonic guided waves propagation in composite bends

Ultrasonic guided waves have proven to be attractive to the long-range testing of composite laminates. As complex-shaped composite components are increasingly incorporated in high-performance structures, understanding of both anisotropic and geometric effects on guided waves propagation is needed to evaluate their suitability for the non-destructive testing (NDT) of such complex structures. This paper reports the Semi-Analytical Finite Element (SAFE) simulations revealing the capability of energy confinement carried by two types of guided modes in 90° carbon fiber/epoxy (CF/EP) bends. Existence of the phenomenon is cross-validated by both 3D Finite Element (FE) modeling and experimental measurements. The physics of such energy trapping effect is explained in view of geometric variation and anisotropic properties, and the frequency effect on the extent of energy concentration is discussed. Finally, the feasibility of using such confined guided waves for rapid inspection of bent composite plate structures is also discussed.