SH ultrasonic guided waves for the evaluation of interfacial adhesion

Guided wave propagation in a double-layer plate with a nonlinear spring-interface

This article derives the solution to the guided wave fields in a double-layer plate consisting of two sublayers. It is assumed that the two sublayers are linearly elastic. They are bonded together at their interface by a nonlinear adhesive layer of infinitesimal thickness. This allows us to propose a nonlinear spring-interface model. Based on such an idealized model for the double-layer plate, guided wave fields in the plate are solved using the modified normal mode expansion method. It is found that the nonlinearity of the spring-interface can generate resonant guided waves in the double-layer plate. Specifically, when certain conditions are met, mixing of two primary guided waves will generate resonant guided waves whose frequencies are either the sum or difference of those of the two primary waves. Amplitudes of such resonant mixed waves are proportional to the compliance of the nonlinear spring-interface. As a special case, if the two primary waves have the same frequency, a resonant second harmonic guided wave may be generated. In addition, the conditions that generate resonant mixed waves are identified. We believe that the results of this work provide the theoretical foundation on which nondestructive evaluation techniques using nonlinear guided waves can be developed to nondestructively evaluate, for example, the bond strength of thin coating on a substrate.

Simulation-Based Inversion for the Characterization of Adhesively Bonded Joints Using Ultrasonic Guided Waves

Adhesively bonded structures are widely used to facilitate the manufacturing process and enhance the performance of critical components in the aerospace, automotive, and energy industries. The assessment of the bond layer using the propagation of ultrasonic guided waves has been extensively investigated in the literature using several different approaches. In this study, a finite element (FE) model was used to simulate the dispersion curves of the modes propagating in an aluminum/adhesive/aluminum bonded structure. The simulated dispersion curves were systematically compared with the experimental measurements to retrieve the shear modulus of the adhesive layer during its curing process. The optimization procedure was able to perform inversion with minimum prior knowledge of the adhesive layer properties. In general, the proposed FE-based forward model was able to match the experimental dispersion curves during curing. Notwithstanding some discrepancies observed in the early to intermediate state of curing, the predicted model parameters were in agreement within 6% of the values obtained by the reference methods. The optimal shear modulus was estimated at 1.55 GPa at the end of the curing, against a reference value of 1.47 GPa.

A constant-frequency ultrasonic phase method for monitoring imperfect adherent/adhesive interfaces

A primary mechanism of adhesive bond failure is a degradation of the adherent/adhesive interfacial stiffness from unwanted contamination or exposure to those environmental factors, which reduce adhesion quality. Substantial research has been conducted on the assessment of adhesively bonded structures and the detection of "kissing" bonds. Advanced ultrasonic assessment methods to interrogate bonded joints and measure interfacial stiffness using a distributed spring interface model have been developed. Amplitude-based ultrasonic methods have traditionally been used in adhesive bond quality assessment, but recent advancements in ultrasonic phase measurements allow for high measurement resolution with low-uncertainty. In this work, an ultrasonic phase technique for the monitoring of adhesively-bonded interfaces is demonstrated. Constant frequency measurements are obtained from the ultrasonic phase of the reflection coefficient from the adhesive bond with a glass adherent, where the degree of cure is controlled by exposure to ultraviolet light. A peak in the phase of the reflection coefficient, as predicted by the interfacial spring model, is measured experimentally. It is shown that the peak phase predicts the interfacial stiffness when some frequency dependent threshold value is crossed. With knowledge of the acoustic impedances of both materials at the interface, the interfacial stiffness is determined by an inverse algorithm involving measurements of ultrasonic phase shifts of bonded joint reflections. By monitoring the interface of bonded structures and coatings, this method permits a nondestructive inspection of bond strength from structural construction through its service life.

Application of the reciprocity principle to evaluation of mode-converted scattered shear horizontal (SH) wavefields in tapered thinning plates

The interaction of guided waves with wall thinning can be complex, depending on the thinning geometry and the frequency. At a high frequency-thickness, when a shear-horizontal (SH) guided wave mode impinges upon a tapered wall thinning region, there is mode conversion to other propagating SH modes, either in reflection or transmission, which heavily depends on the shape of the taper. In this paper, we have combined the reciprocity theorem of elastodynamics and the theory of multiple reflections, in order to analytically calculate the scattered SH wavefield in plates, due to the interaction with an arbitrary tapered thinning. The taper is discretized into several sections and the formulation is addressed in matrix notation, in order to tackle several modes which arise due to mode interconversion distributed within the taper. The method was validated with experimental and numerical data at linear tapered thinning, in the high-frequency-thickness regime. It was also applied to provide understanding of the reflection behaviour within smoother taper profiles, namely, raised-cosine and Blackman window tapers, and to visualize the propagating field of each mode. It is shown that for a linear taper profile, the reflection within the taper is virtually constant, which produces an interference pattern in the overall reflection from the whole taper. Such a mechanism is broken with smoother tapers, since they impose lower reflection close to the taper ends. The method proves itself useful for analytically investigating the scattering from arbitrary wall thinning when mode-conversion arises.

Laser ultrasonics in a multilayer structure: Plane wave synthesis and inverse problem for nondestructive evaluation of adhesive bondings

A laser ultrasonic method is proposed for the nondestructive evaluation of bonded assemblies based on the analysis of elastic plane waves reflected from the bonding interface. Plane waves are numerically synthesized from experimentally detected cylindrical waves. Several angles of incidence with respect to the bonding interface are achieved by varying the delay in the synthesis step. An inverse problem using these plane waves is then solved to identify the normal and transverse interfacial stiffnesses that model the mechanical coupling between two bonded media. The semi-analytic model developed and detailed in Hodé et al. [J. Acoust. Soc. Am. 150, 2065 (2021)] is used to create the database that contains simulated laser-generated ultrasounds required to solve the inverse problem. The developed method is first validated with semi-analytic simulated input data where Gaussian noise has been added. Next, the method is applied using signals acquired on an aluminum alloy plate and on assemblies (with and without adhesion defects) made of two aluminum alloy plates bonded by an aeronautical structural epoxy adhesive film. Differences between the identified values of interfacial stiffnesses distinguish the three samples and obtain quantitative values to characterize the adhesive bonding.

Quantifying adhesive thickness and adhesion parameters using higher-order SH guided waves

A method to quantify the interface shear stiffness, adhesive shear modulus and adhesive thickness in an aluminium-epoxy-aluminium joint is presented. Shear horizontal guided waves are considered to infer the properties. A numerical model that employs spring stiffness boundary conditions at the aluminium-epoxy interface was developed to generate dispersion curves. The sensitivity of the first four SH-like modes to epoxy thickness, interface shear stiffness, and adhesive shear modulus are analyzed. The dispersion analysis reveals that higher-order anti-symmetric modes are sensitive to all three parameters, whereas the symmetric modes are sensitive only to adhesive thickness. Hence to prevent false alarms that might arise while assessing the bond conditions, symmetric and anti-symmetric modes should be simultaneously generated. Periodic permanent magnet (PPM) electromagnetic acoustic transducers (EMATs) are used to generate and detect SH-like modes. Utilizing the constant wavelength property of PPM-EMATs, SH₂-like and SH₃-like modes are generated. Short-time Fourier transform (STFT) is used to separate the modes merged in the received time response. By overlaying the dispersion curves of SH₂-like mode on STFT, the thickness of epoxy is quantified. The dispersion curves of SH₃-like mode are generated using the measured thickness and overlaid on STFT to measure the interface shear stiffness and epoxy shear modulus. The proposed method is experimentally demonstrated on aluminium-epoxy-aluminium samples of different surface treatments. The study demonstrates a reliable nondestructive evaluation of adhesive bonds that reduces possible false alarms.

Air-Coupled, Contact, and Immersion Ultrasonic Non-Destructive Testing: Comparison for Bonding Quality Evaluation

The objective of this study is to compare the performance of different ultrasonic non-destructive testing (NDT) techniques for bonding quality evaluation. Aluminium-epoxy-aluminium single lap joints containing debonding in the form of release film inclusions have been investigated using three types of ultrasonic NDT methods: contact testing, immersion testing, and air-coupled testing. Apart from the traditional bulk wave ultrasound, guided wave testing was also performed using air coupled and contact transducers for the excitation of guided waves. Guided wave propagation within adhesive bond was numerically simulated. A wide range of inspection frequencies causing different ultrasonic wavelengths has been investigated. Average errors in defect sizing per ultrasonic wavelength have been used as a feature to determine the performance of each ultrasonic NDT technique. The best performance is observed with bulk wave investigations. Particularly, the higher frequencies (10–50 MHz) in the immersion testing performed significantly better than air-coupled testing (300 kHz); however, air coupled investigations have other advantages as contactless inspection. Whereas guided wave inspections show relatively lower accuracy in defect sizing, they are good enough to detect the presence of the debonding and enable to inspect long range. Even though each technique has its advantages and limitations, guided wave techniques can be practical for the preliminary in-situ inspection of adhesively bonded specimens.

A tunable bidirectional SH wave transducer based on antiparallel thickness-shear (d15) piezoelectric strips

Guided wave based defects inspection is very promising in the field of structural health monitoring (SHM) and nondestructive testing (NDT) due to its less dissipation and thus long distance coverage. In comparison with the widely used Lamb waves, shear horizontal (SH) waves are relatively simple but less investigated probably due to the traditional notion that SH waves were usually excited by electromagnetic acoustic transducers (EMAT). In this work, we proposed a tunable method to excite single-mode bidirectional SH waves in plates using antiparallel thickness-shear (d₁₅) piezoelectric strips (APS). The proposed SH wave driving mechanism here is similar to that by using the periodic permanent magnetics (PPM) based EMAT with the period of strips equal to half of the wavelength. Both finite element simulations and experiments were conducted to validate this transducer in excitation of bidirectional SH waves. Results show that the Lamb waves excited by single piezoelectric strip can be suppressed very well. The radiation angle of the excited bidirectional SH wave can be reduced by extending the strip length, increasing the driving frequency or using more strips. Moreover, the APS transducer can selectively excite SH₁ wave and suppress the SH₀ wave at 174 kHz and 273 kHz in a 10 mm-thick aluminum plate. Considering its simple structure, flexible design and low excitation energy, the APS SH wave transducer is expected to be widely used in near future.

Wave Frequency Effects on Damage Imaging in Adhesive Joints Using Lamb Waves and RMS

Structural adhesive joints have numerous applications in many fields of industry. The gradual deterioration of adhesive material over time causes a possibility of unexpected failure and the need for non-destructive testing of existing joints. The Lamb wave propagation method is one of the most promising techniques for the damage identification of such connections. The aim of this study was experimental and numerical research on the effects of the wave frequency on damage identification in a single-lap adhesive joint of steel plates. The ultrasonic waves were excited at one point of an analyzed specimen and then measured in a certain area of the joint. The recorded wave velocity signals were processed by the way of a root mean square (RMS) calculation, giving the actual position and geometry of defects. In addition to the visual assessment of damage maps, a statistical analysis was conducted. The influence of an excitation frequency value on the obtained visualizations was considered experimentally and numerically in the wide range for a single defect. Supplementary finite element method (FEM) calculations were performed for three additional damage variants. The results revealed some limitations of the proposed method. The main conclusion was that the effectiveness of measurements strongly depends on the chosen wave frequency value.

Effect of interfacial adhesion on the ultrasonic interaction with adhesive joints: A theoretical study using spring-type interfaces

The effect of interfacial properties on the reflection and transmission characteristics of ultrasonic waves at adhesively bonded joints is theoretically investigated. An adhesive joint is modeled as a double-interface model, namely, a homogeneous layer coupled to adherends by two spring-type interfaces with different interfacial stiffnesses. For the normal incidence of a one-dimensional longitudinal wave, theoretical results are obtained and validated by finite element simulation. When the thickness of the adhesive layer is sufficiently small compared to the wavelength, the amplitude reflection and transmission coefficients show monotonic dependence on frequency, which can be explained by the theoretical relation of the double-interface model to a single spring-type interface model. The reflection and transmission behavior is invariant if the values of the two interfacial stiffnesses are interchanged. For a relatively thick adhesive layer, on the other hand, the reflection coefficient shows local minima at multiple frequencies. As one interfacial stiffness decreases, the local minimum frequencies decrease and the local minima increase. If the values of the two interfacial stiffnesses are interchanged, the reflection coefficient remains invariant but the reflection waveform shows different features. The obtained reflection and transmission characteristics are discussed in light of the characterization of the interfacial adhesion.

Reflection and transmission characteristics of Lamb waves at an adhesive lap joint of plates

The reflection and transmission characteristics of Lamb waves at an adhesive single lap joint of plates are examined theoretically by the hybrid finite element method. The adhesive joint is modeled by a linear spring-type interface, which is characterized by normal and tangential stiffnesses. For the incidence of the lowest-order antisymmetric (A0) Lamb mode in a low frequency range, it is shown that the reflection and transmission coefficients of the A0 mode take local maxima and minima at multiple frequencies. This behavior results from the interference of waves originating from the lowest-order antisymmetric guided wave mode in the overlap region. The peak frequencies of the transmission coefficient increase monotonically with increasing tangential stiffness, but are almost invariant with the normal stiffness of the adhesive joint. Furthermore, time-domain numerical simulation using the finite element method is carried out to discuss the theoretical results. As a result, for the A0 mode incidence, the reflection and transmission waveforms of the A0 mode from the lap joint are found to show long-oscillation tails. The spectral analysis for the obtained waveforms shows that these tails are necessary to identify the frequencies at which the reflection and transmission coefficients take local maxima and minima.

Swept-frequency ultrasonic phase evaluation of adhesive bonding in tri-layer structures

As modern aerospace and automotive designs continually strive for higher performance, and thus rely on advanced composite structures where adhesive bonding is a preferred method of joining, the need for a robust quantitative nondestructive bond strength measurement method has increased. As such, advanced nondestructive evaluation methods have been researched for increased sensitivity to weak interfacial bonding and ultimately to detect "kissing" bonds. In this work, a phase-based method for interrogating bonded joints and detecting weak adhesion is developed by using swept-frequency phase measurements of ultrasonic waves reflected from an adhesive joint and modeling adhesive interfaces as a distributed spring system. The method's sensitivity to bond strength is explored by ultrasonic phase evaluation of tri-layer joints with bond quality varied by controlling ultraviolet light exposure and extracting interfacial stiffness constants of the bonds. Mechanical tensile tests found each joint failed adhesively, allowing a linear correlation to be drawn between interfacial stiffness and tensile strength, consistent with previous theoretical research. The ultrasonic phase measurement method identifies intermediate bond strengths, rather than simply detecting good or bad bonds. This technique has the potential for the verification of bond quality in lightweight aerospace and automotive designs utilizing advanced composite structures with adhesive attachments.

Debonding Detection in Hidden Frame Supported Glass Curtain Walls Using the Nonlinear Ultrasonic Modulation Method with Piezoceramic Transducers

Debonding defects are common and they are the main reason for the failure of hidden frame supported glass curtain walls, which are widely used as an external enclosure and decorative structure. In this paper, a debonding detection method for hidden frame supported glass curtain walls is developed based on nonlinear ultrasonic modulation and piezoceramic transducers. First, the excitation frequency was determined according to the response characteristics. Then, empirical mode decomposition (EMD) was applied to extract the feature components. After discrete Fourier transform (DFT), the nonlinear coefficients were calculated to evaluate the debonding defect. Finally, the experimental setup was established and a series of experiments were carried out to verify the feasibility and effectiveness of the nonlinear ultrasonic modulation method. The nonlinear harmonics detection method was also investigated and it was compared with the nonlinear ultrasonic modulation method. The detection effect at different temperatures and impact were studied. The results showed that the nonlinear coefficient increases with the debonding length. The mean squared error (MSE) of the nonlinear ultrasonic modulation method was improved by 41% compared with the nonlinear harmonics method. The nonlinear ultrasonic modulation method can successfully detect debonding defects in hidden frame supported glass curtain walls at different temperatures and impact.

A semi-analytical approach for SH guided wave mode conversion from evanescent into propagating

Conversion of evanescent shear horizontal (SH) guided waves into propagating is presented in this paper. The conversion is exemplified by a time-harmonic SH evanescent displacement prescribed on a narrow aperture at an edge of a semi-infinite isotropic plate. The conversion efficiency in terms of the amplitude of the propagating SH mode converted from evanescent can be expressed in a very simple compact form. The magnitude of the conversion efficiency can be quantified through a derived semi-analytical form based on the complex reciprocity theorem in conjunction with a two-dimensional (2-D) finite element analysis (FEA). Through power conversion analysis, it can be shown that the power flow generated into the plate due to evanescent incident is complex valued. It is theoretically proved that the real part of the complex power flow is associated with the propagating SH modes, while the imaginary part is confined due to the evanescent modes at the plate edge. The conversion efficiency and converted modes are dependent on the geometric configuration of the aperture as well as the selection of the excitation frequency.

Plane Wave SH₀ Piezoceramic Transduction Optimized Using Geometrical Parameters

Structural health monitoring is a prominent alternative to the scheduled maintenance of safety-critical components. The nondispersive nature as well as the through-thickness mode shape of the fundamental shear horizontal guided wave mode (SH0) make it a particularly attractive candidate for ultrasonic guided wave structural health monitoring. However, plane wave excitation of SH0 at a high level of purity remains challenging because of the existence of the fundamental Lamb modes (A0 and S0) below the cutoff frequency thickness product of high-order modes. This paper presents a piezoelectric transducer concept optimized for plane SH0 wave transduction based on the transducer geometry. The transducer parameter exploration was initially performed using a simple analytical model. A 3D multiphysics finite element model was then used to refine the transducer design. Finally, an experimental validation was conducted with a 3D laser Doppler vibrometer system. The analytical model, the finite element model, and the experimental measurement showed excellent agreement. The modal selectivity of SH0 within a 20∘ beam opening angle at the design frequency of 425 kHz in a 1.59 mm aluminum plate was 23 dB, and the angle of the 6 dB wavefront was 86∘.

Study of guided wave propagation on a plate between two solid bodies with imperfect contact conditions

In this work, fundamental symmetric Lamb wave S0 mode is characterized in terms of its velocity variation as function of the interfacial conditions between solid bodies in contact. Imperfect contact conditions are numerically and experimentally determined by using ultrasonic Lamb wave propagation parameters. For the study, an experimental system was used, formed by two solid aluminum rods (25.4mm in diameter) axially loading a thin aluminum plate to control contact interfacial stiffness. The axially applied load on the aluminum plate was varied from 0MPa to 10MPa. Experimental Lamb wave signals were excited on the plate through two longitudinal contact transducers (1MHz of central frequency) using a pitch-catch configuration. Numerical simulations of contact conditions and Lamb wave propagation were performed through Finite Element Analysis (FEA) in commercial software, ANSYS 15®. Simulated Lamb wave signals were generated by means of a 5 cycles tone burst signals with different frequency values. Results indicate a velocity change in both, experimental and simulated Lamb wave signals as function of the applied load. Finally, a comparison between numerical results and experimental measurements was performed obtaining a good agreement.

Efficient simulation of elastic guided waves interacting with notches, adhesive joints, delaminations and inclined edges in plate structures

This paper presents an approach to model transmission and reflection phenomena of elastic guided waves in plates. The formulation is applied to plate structures containing notches, inclined edges, delaminations or (adhesive) joints. For these cases, only the thickness direction of the structure needs to be discretized at several locations, while the direction of propagation is described analytically. Consequently, the number of degrees of freedom is very small. Semi-infinite domains can be modeled, in which case the radiation condition is fulfilled exactly. Traction boundary conditions are introduced on the plate surface without requiring a mesh along the surface. Results are validated against conventional finite element implementations, showing the accuracy of the proposed approach and a reduction of the computational costs by typically 2-3 orders of magnitude.

A Reference-Free and Non-Contact Method for Detecting and Imaging Damage in Adhesive-Bonded Structures Using Air-Coupled Ultrasonic Transducers

Adhesive bonded structures have been widely used in aerospace, automobile, and marine industries. Due to the complex nature of the failure mechanisms of bonded structures, cost-effective and reliable damage detection is crucial for these industries. Most of the common damage detection methods are not adequately sensitive to the presence of weakened bonding. This paper presents an experimental and analytical method for the in-situ detection of damage in adhesive-bonded structures. The method is fully non-contact, using air-coupled ultrasonic transducers (ACT) for ultrasonic wave generation and sensing. The uniqueness of the proposed method relies on accurate detection and localization of weakened bonding in complex adhesive bonded structures. The specimens tested in this study are parts of real-world structures with critical and complex damage types, provided by Hyundai Heavy Industries^® and IKTS Fraunhofer^®. Various transmitter and receiver configurations, including through transmission, pitch-catch scanning, and probe holder angles, were attempted, and the obtained results were analyzed. The method examines the time-of-flight of the ultrasonic waves over a target inspection area, and the spatial variation of the time-of-flight information was examined to visualize and locate damage. The proposed method works without relying on reference data obtained from the pristine condition of the target specimen. Aluminum bonded plates and triplex adhesive layers with debonding and weakened bonding were used to examine the effectiveness of the method.

Apparent anisotropy of adhesive bonds with weak adhesion and non-destructive evaluation of interfacial properties

The present research attempts to non-destructively characterize mechanical properties, which are representative of the interfacial adhesion and bond line cohesion of adhesively bonded assemblies, using an ultrasonic method. Eight bonded samples made of two aluminium substrates and of an epoxy-based adhesive layer were manufactured: four in which the adhesive is fully cured (100%) and four in which crosslinking is partial (80%). For each level of curing, four different surface treatments were applied to the aluminium substrates before assembling, in order to vary the quality of adhesion. Ultrasonic plane wave transmission coefficients (UPWTC) were either measured in a water tank, or simulated using the well-known stiffness matrix method that micmics the experiments, to produce input data for the inverse problem. This latest consists in the evaluation of the elastic properties of either the adhesive bond or the interphases between both substrates and the adhesive layer. If the interphases are of nominal quality, the values of the inferred properties of the adhesive bond match those previously measured on individual epoxy samples, whether the epoxy is fully or partially cured. However, when interphases are not of nominal quality level, the optimized bond moduli reveal an apparent anisotropy, although the epoxy layer is known to be isotropic. This apparent anisotropy is explained by an analytical rule of mixture, thus giving confidence in the proposed ultrasonic technique, which is then suggested as a potential way to detect weaknesses of interphases. Finally, the optimization of the interphases elastic properties is carried out. The measured normal and shear stiffnesses are shown to decrease as the interphases get degraded. All ultrasonically-measured parameters (apparent anisotropy of the bond and interfacial stiffnesses) vary monotonically with the bonds strength, which was measured via mechanical tests. The proposed UPWTC method was shown to have a strong potential to distinguish between adhesive and cohesive weaknesses of bonded joints, and to estimate corresponding mechanical properties.

The Feasibility of Structural Health Monitoring Using the Fundamental Shear Horizontal Guided Wave in a Thin Aluminum Plate

Structural health monitoring (SHM) is emerging as an essential tool for constant monitoring of safety-critical engineering components. Ultrasonic guided waves stand out because of their ability to propagate over long distances and because they can offer good estimates of location, severity, and type of damage. The unique properties of the fundamental shear horizontal guided wave (SH₀) mode have recently generated great interest among the SHM community. The aim of this paper is to demonstrate the feasibility of omnidirectional SH₀ SHM in a thin aluminum plate using a three-transducer sparse array. Descriptions of the transducer, the finite element model, and the imaging algorithm are presented. The image localization maps show a good agreement between the simulations and experimental results. The SH₀ SHM method proposed in this paper is shown to have a high resolution and to be able to locate defects within 5% of the true location. The short input signal as well the non-dispersive nature of SH₀ leads to high resolution in the reconstructed images. The defect diameter estimated using the full width at half maximum was 10 mm or twice the size of the true diameter.

Damage detection in bent plates using shear horizontal guided waves

Study of the interaction of shear horizontal guided mode with defects in the bend region of an isotropic top hat stiffener is presented. Compared with the SH0 wave in a plate, the shear mode in the bend is dispersive and its wavefield characteristics are affected by the curvature of the bend. The scattering studies showed that the sensitivity of the wave to outer surface cracks in the bend increases with increasing frequency compared to inner surface cracks. Further numerical simulations demonstrated that the shear mode is sensitive to the delamination in the bend due to non-zero transverse shear stress. Results of finite element modeling were validated by experiments and reasonably good agreements were obtained.

Transmission of Lamb waves and resonance at an adhesive butt joint of plates

The transmission behavior of Lamb waves and the possible occurrence of resonance at an adhesive butt joint of plates are studied experimentally. To this purpose, two 2.5-mm thick aluminum alloy plates are bonded at their edges using cyanoacrylate-based adhesive. Bonded plate specimens with different joint conditions are prepared by changing the bonding procedure. The measurements are performed for the transmission characteristics of the lowest-order symmetric (S0) and antisymmetric (A0) Lamb modes for the frequency range of 0.4-0.6MHz below the cut-off frequency of the higher-order modes. The experimental results show that the transmission coefficients of the S0 and A0 modes exhibit different frequency-dependent characteristics depending on the joint condition. Furthermore, for the incidence of the S0 mode at the center frequency of 1MHz, the transmitted S0 mode in weakly bonded specimens shows a long oscillation tail due to the resonance effect. The experimental results are discussed in the light of the theoretical results based on the spring-type interface model. The interfacial stiffnesses identified from the transmission coefficients are shown to be correlated with the bonding condition of the joint and give reasonable estimates of the resonance frequencies of weakly bonded specimens.

Reflection and transmission coefficients of the SH0 mode in the adhesive structures with imperfect interface

Compared with body waves, ultrasonic guided waves can provide more local characteristic information about the interface in the defect detection of adhesive structures. In the paper, the expressions of the reflection and transmission coefficients of the lowest SH mode (SH0) in multilayered plate-like adhesive structure were deduced on the basis of wave propagation controlling equations and tangential stiffness coefficient KT was contained in the expressions. Then, the expressions were compared with the previous results to verify their applicability and correctness. Then, aluminum/epoxy resin/aluminum adhesive structures were used to explore the effects of the changes in incident angle, frequency-thickness product and tangential stiffness coefficient on SH wave propagation characteristics in adhesive structures with different interface quality (perfect, weak bonding, and slip/debonding interfaces). The results showed that the propagation mode of SH wave in adhesive structures was mainly determined by the incident angle, frequency, adhesive layer thickness and tangential stiffness coefficient. With the increase in the frequency-thickness product, multi-order resonance is generated in the reflection and transmission coefficient curves of SH wave under the perfect and weak bonding interfaces. If proper values of the incident angle of acoustic waves and frequency-thickness product are selected, the perfect, weak bonding, and slip/debonding interfaces can be differentiated from each other, but the slip and debonding interfaces cannot be distinguished from each other. The study provides theoretical contribution to the detection of multilayered plate-like adhesive structure by SH wave.

A remark on the computation of shear-horizontal and torsional modes in elastic waveguides

When modeling the propagation of elastic guided waves in plates or cylinders, Finite Element based numerical methods such as the Scaled Boundary Finite Element Method (SBFEM) or the Semi-Analytical Finite Element (SAFE) Method lead to an eigenvalue problem to be solved at each frequency. For the particular case of shear horizontal modes in a homogeneous plate or torsional modes in a homogeneous cylinder, the problem can be drastically simplified. The eigenvalues become simple functions of the frequency, while the eigenvectors are constant. The current contribution discusses how this behavior is represented in the numerical formulation and derives the expressions for the eigenvalues and eigenvectors as well as the dynamic stiffness matrix of infinite elastic waveguides.

Investigation of interfacial stiffnesses of a tri-layer using Zero-Group Velocity Lamb modes

Zero-Group Velocity (ZGV) Lamb waves are studied in a structure composed of two plates bonded by an adhesive layer. The dispersion curves are calculated for a Duralumin/epoxy/Duralumin sample, where the adhesion is modeled by a normal and a tangential spring at both interfaces. Several ZGV modes are identified and their frequency dependence on interfacial stiffnesses and on the bonding layer thickness is numerically studied. Then, experiments achieved with laser ultrasonic techniques are presented. Local resonances are measured using a superimposed source and probe. Knowing the thicknesses and elastic constants of the Duralumin and epoxy layers, the comparison between theoretical and experimental ZGV resonances leads to an evaluation of the interfacial stiffnesses. A good agreement with theoretical dispersion curves confirms the identification of the resonances and the parameter estimations. This non-contact technique is promising for the local evaluation of bonded structures.

Use of shear horizontal waves to distinguish adhesive thickness variation from reduction in bonding strength

The capability of shear horizontal (SH) guided waves, to evaluate geometrical imperfections in a bonding layer, is investigated. SH waves are used in a three-layer structure in which the adhesive layer has variable thickness. It is proven that the SH waves are adapting to the local thickness of the adhesive layer (adiabatic waves). This is particularly useful in case of small thickness variations, which is of technical interest. The influence of thickness and stiffness of the adhesive layer on the wavenumbers are investigated. The selected SH2 mode is proven to be very sensitive to the adhesive layer thickness variation in the given frequency range and considerably less sensitive to the adhesive stiffness variation. This property is due to its specific displacement field and is important in practical applications, such as inspection techniques based on SH waves, in order to avoid false alarms.