Contact Acoustic Nonlinearity Research Articles

Nonlinear Electro-Mechanical Impedance Spectroscopy for fatigue crack monitoring

This article presents a Nonlinear Electro-Mechanical Impedance Spectroscopy (NEMIS) methodology for fatigue crack monitoring. Different from the conventional Electro-Mechanical Impedance Spectroscopy (EMIS) implemented in the frequency domain, the proposed NEMIS employs a temporal chirp interrogating signal to obtain the impedance spectra, and simultaneously captures the Contact Acoustic Nonlinearity (CAN) features. To develop an insight into the mechanism behind the NEMIS method, a comparative investigation between the conventional EMIS and the two-phase NEMIS algorithm was conducted. Numerical studies were carried out on a 1-D transitional-bilinear CAN model to demonstrate the chirp-induced higher harmonics and nonlinear mixed-frequency response features. Furthermore, finite element (FE) simulations were conducted to demonstrate the feasibility of the NEMIS. A baseline-free damage index was subsequently developed to quantify the severity of the fatigue crack. Finally, experimental validation of the NEMIS method was performed. The experimental results validated the feasibility and accuracy of the chirp-based impedance spectra. It was also shown that NEMIS successfully captured the nonlinear impedance spectra, obtaining higher harmonics and wave modulation features to manifest the existence of the fatigue crack. Quantification on the severity of the crack was conducted via the nonlinear damage index, which presented a consistent, monotonic trend with the increasing severity of the fatigue crack. The experiment demonstrated the capability of NEMIS for detecting and quantifying fatigue cracks. The article finishes with summary, concluding remarks, and suggestions for future work.

Advanced numerical simulations considering crack orientation for fatigue damage quantification using nonlinear guided waves

A numerical study including a fatigue crack trajectory simulation was undertaken by means of separating morphing and adaptive remeshing technology (SMART) Crack Growth in ANSYS, on the basis of which the simulations of nonlinear ultrasonic waves for fatigue damage detection using the precise fatigue crack trajectory was achieved. The simulated crack trajectory was first validated by experimental results in terms of crack initiation angle and number of fatigue cycles and was subsequently utilised for crack quantification based on second harmonic method. The results revealed that the nonlinearity in terms of the trend and magnitude with respect to crack length in the advanced simulation is closer to that in the experimental results than the common simulation approach where damage was modelled as a straight line crack. Given that the influence of crack orientation on contact acoustic nonlinearity (CAN) was taken into consideration, the developed advanced simulation could further enhance the capability of numerical modelling for simulating the interaction between nonlinear guided waves and fatigue crack, facilitating the fundamental investigation of CAN mechanism.

Fourier spectral element for simulation of vibro-acoustic modulation caused by contact nonlinearity in the beam

The purpose of this research is to provide an efficient method for simulating the Vibro-acoustic modulation (VAM) effect in beam-type structures. Contact acoustic nonlinearity (CAN) can be induced by support loosening, which is a common defect in engineering systems. The appearance of sidebands caused by wave intermodulation is the basis of VAM based Structural Health Monitoring (SHM). The VAM simulation can be used for high level SHM, such as damage imaging, to provide some insights into the intermodulation mechanism and influencing factors. In this research, the Fourier spectral element method (FSEM) is used to simulate and investigate the VAM effect for the beam structures. The clamped support is represented by an elastic foundation that can be released by lowering its stiffness. The transducers, which contained three piezoelectric patches, two for high and low frequency actuation and one for sensing, were also incorporated in the numerical model. The Lagrange multiplier method and the node-to-node contact strategy were used to formulate the contact problem. The forward increment Lagrange multipliers approach was utilized for time integration. The results are consistent with the previous studies on beams with loosened supports. Furthermore, the FSEM results were compared to their FEM counterparts to assess the former’s efficacy. The impact of loosening intensity on VAM signals and damage metrics was investigated using the FSEM model. According to the results, the FSEM has a high convergence rate and accuracy, making it a good choice for improving VAM-based damage identification.

Scattering analysis of linear and nonlinear symmetric Lamb wave at cracks in plates

ABSTRACT This paper presents a detailed study on detecting defects in isotropic plates by studying scattering analysis of first and second harmonics of symmetric Lamb wave (S0 ) at cracks in aluminium plates induced by Contact Acoustic Nonlinearity (CAN) using experimental and 3D Finite Element (FE) simulation approaches. In this study, a set of models with different crack sizes and orientations are studied. The effects of crack size and crack orientation on scattering behaviour of first and second harmonics of Lamb waves are investigated . The results show that the Scattering Directivity Pattern (SDP) of Lamb wave around the cracks is significantly influenced by crack size and crack orientation. It is also shown that the largest amplitude of scattered S0 wave is acquired from forward scattering waves for linear waves while the largest amplitude of scattered S0 Lamb wave is obtained from backward scattering waves for nonlinear waves. Therefore, it is expected that pulse-echo sensor configuration enhances nonlinear wave damage detection while pitch-catch configuration may suit better when linear wave is used. It is shown that selecting proper propagation direction for incident wave and proper geometry and angle for monitoring points are the key factors to achieve successful damage detection in isotropic plates.

Damage detection and localization in loose bolted joints

In this paper damage detection and damage localization of imperfect bolted joints is studied numerically using three-dimensional explicit finite element simulations. The study is focused on using contact acoustic nonlinearity (CAN) due to interaction of asymmetric guide waves (A0) with imperfect joint surfaces for detecting and locating imperfect joints. Numerically obtained data are processed and it is shown that the CAN can detect and locate defects. The finite element model is used to study several case studies. It is demonstrated that finite element can predict propagation of guided waves in bolted joints. CAN is used for locating the loose bolt. It is demonstrated that FE model followed by signal processing approach used in this study can successfully and accurately detect and locate the imperfect joints. Overall, the findings of this study provide improved physical insights into using CAN for detecting and locating imperfect joints, which can be used to further advance damage detection techniques using nonlinear guided waves

Numerical Investigations Into Nonlinear Vibro-Ultrasonics and Surface Vibration Comparison Method for Detection of Defects in a Composite Laminate

Abstract This paper begins with a numerical study based on earlier experiments of nonlinear vibro-ultrasonic behavior of a composite laminate with a delamination defect upon sinusoidal linear sweep signal excitation. A methodology to model laminates with cross-ply layup is presented which can be extended to any layup if desired. In comparison to experiments where it is challenging to visualize the fine details of vibrations, simulations make it easier to visualize and help in optimizing the defect probing methods. The paper goes on to discuss with the help of numerical results that a separation gap between the delamination surfaces occurs to be a common cause for the failure of nonlinear vibro-ultrasonic methods to detect delamination defects. This constraint can often be overcome with application of higher excitation amplitudes as has been demonstrated in several experimental works. However, in this study, a new approach named surface vibration comparison method to probe delamination defects in the absence of contact acoustic nonlinearity is proposed as a proof-of-concept. The technique is then evaluated for detection of weak kissing bond defects in composite beam specimens. Both the experimental and simulation results show potential of the method as damage detection technique in thin composite structures.

Immunity of the second harmonic shear horizontal waves to adhesive nonlinearity for breathing crack detection

High-order harmonic guided waves are sensitive to micro-scale damage in thin-walled structures, thus, conducive to its early detection. In typical autonomous structural health monitoring (SHM) systems activated by surface-bonded piezoelectric wafer transducers, adhesive nonlinearity (AN) is a non-negligible adverse nonlinear source that can overwhelm the damage-induced nonlinear signals and jeopardize the diagnosis if not adequately mitigated. This paper first establishes that the second harmonic shear horizontal (second SH) waves are immune to AN while exhibiting strong sensitivity to cracks in a plate. Capitalizing on this feature, the feasibility of using second SH waves for crack detection is investigated. Finite element (FE) simulations are conducted to shed light on the physical mechanism governing the second SH wave generation and their interaction with the contact acoustic nonlinearity (CAN). Theoretical and numerical results are validated by experiments in which the level of the AN is tactically adjusted. Results show that the commonly used second harmonic S0 (second S0) mode Lamb waves are prone to AN variation. By contrast, the second SH0 waves show high robustness to the same degree of AN changes while preserving a reasonable sensitivity to breathing cracks, demonstrating their superiority for SHM applications.

Spectral finite element method for efficient simulation of nonlinear interactions between Lamb waves and breathing cracks within the bi-potential framework

Nonlinear ultrasonic guided waves are of great importance in structural health monitoring, since they have both the large-area inspection capability of guided waves and the desirable sensitivity to incipient defects from nonlinear ultrasonic features. Efficient numerical methods play a key role in investigating the nonlinear features of guided waves. In this work, a time domain spectral finite element method (TDSFEM) combined with the bi-potential contact theory is developed to capture the nonlinear interactions between guided waves and breathing cracks. The bi-potential approach has better accuracy than the conventional penalty method, since there is no any user-defined parameter for computation in the former method while the latter one requires a user-experience-based penalty factor. In addition, a semi-explicit algorithm is proposed to integrate the wave equation, which can take full advantage of the diagonal mass matrix of TDSFEM while not sacrificing numerical stability. Numerical verifications against ANSYS show that the computational efficiency of the bi-potential method-based TDSFEM is much higher than that of the FEM via the penalty method. Numerical case studies are then performed to investigate the nonlinear interactions between Lamb waves and breathing cracks. Results show that the proposed method can successfully capture the classical nonlinear features, such as higher harmonic generation and zero frequency (DC) response. Moreover, the influence of the length and gap of a breathing crack on the contact acoustic nonlinearity (CAN) is investigated. As an efficient numerical approach, the bi-potential method-based TDSFEM may be a good tool for investigating the CAN.

Feasibility investigation of rail monitoring by wheel-mounted acoustic emission technology using two-dimensional analytical contact acoustic nonlinearity model

In an attempt to analyze the feasibility of a rail monitoring scheme with a wheel-mounted acoustic emission measurement method, a two-dimensional analytical spring model was proposed to interpret the interactions between acoustic waves and stationary wheel–rail contact interfaces. The spring model represents the coupling strength of the interfaces with their stiffness. It accommodates the environmental information of contact stiffness and the acoustic source information, such as the feature frequency and the incident angle in the analysis of interface transmissibility. The fractal dimension of the interface is introduced into the spring model to interpret the effect of the axle load on the interface stiffness and the variation in transmissibility. Discrete Rayleigh integration is further combined to obtain the directivity of the interface and estimate the acoustic field intensity in the entire wheel. A wheel–rail contact rig was designed to simulate the actual contact conditions in a railway. Experimental data acquired from this test rig were utilized to validate the model, with regard to the interfacial stiffness in normal incidence and amplitudes of the transmitted waves in oblique incidence. After verifying the reliability of the model, the acoustic field intensity in the wheel was visualized under the assumed environmental conditions. Finally, a discussion is presented to determine a proper angular separation for the wheel-mounted sensor system, and substantiate the feasibility of the system.

Advances in nonlinear ultrasonic detection of microcracks

<p indent="0mm">A large number of key components are widely operated under extreme conditions of high temperature and high pressure in power, nuclear energy, aerospace and other important industrial fields. Microdefects are inevitably generated in these key components during the process of manufacturing. Due to the periodic loading and thermal stress, microcracks are generally initiated from these microdefects at the location with stress concentration. It has been found that the initiation and propagation of fatigue microcracks usually occur prior to 70%–90% of fatigue life. It is difficult to observe the evidence before the formation of macrocracks, which may result in catastrophic accidents. Thus, the risk of sudden failure of key components increases greatly. Therefore, the accurate detection of microcracks is crucial for guaranteeing the safe operation of key components. Based on the diffraction, reflection and transmission, traditional ultrasonic testing method is merely validated to effectively detect macroscopic defects within half a wavelength. The nonlinear ultrasonic testing method is found to be sensitive to microcracks, as high order harmonics, sub-harmonics, DC components and frequency mixing waves can be generated due to the strong nonlinear interaction microcracks and ultrasonic waves. With the outstanding effectiveness to detect microcracks, the nonlinear ultrasonic testing method has attracted much attention in recent years. In this work, the research on detection of microcracks using nonlinear ultrasonic testing method is systematically reviewed in terms of theoretical models, numerical simulations and experimental measurements. Firstly, according to the breathing effect and sliding mechanism of microcrack surfaces, we present several theoretical models of nonlinear interaction between ultrasonic waves and microcracks, namely contact acoustic nonlinearity (CAN), bi-linear stiffness model, nonlinear spring model, Hertz contact theory, and rough contact surface model. The advantages and disadvantages of these theoretical models are discussed comparatively. Two mechanisms are mainly considered for the nonlinear interaction of microcracks and ultrasonic waves, namely the macroscopic opening and closing of crack surfaces and the microscopic contact of rough microcracks surfaces. Secondly, we introduce numerical simulation studies on the nonlinear ultrasonic generation induced by microcracks. The applicability is analyzed for several simulation methods, such as finite element method, spectral finite element method, finite difference method, boundary element method and local interaction simulation approach, and the generation and propagation of nonlinear ultrasonic waves are analyzed as well. The effect of microcrack geometries on the nonlinear ultrasonic waves is then summarized. The microcrack geometries are considered mainly clouding the microcrack length, width, depth, density and direction. Furthermore, we present the experimental measurements on the generation of nonlinear ultrasonic waves induced by microcracks and on the localization and imaging of microcracks based on the nonlinear ultrasonic waves. The generation of high order harmonics, sub-harmonics, DC components and frequency mixing waves was observed in the specimens with microcracks. The nonlinear ultrasonic detection is presented to evaluate fatigue microcracks with various microcrack length, width, depth, density and direction. Based on this phenomenon, nonlinear ultrasonic mixing method, transducer array imaging method and nonlinear ultrasonic phased array method are introduced to localize the microcracks. Finally, further studies on evaluation of microcracks using nonlinear ultrasonic waves are proposed, including the comprehensive physical model for actual microcracks in engineering components, robust detection method, and quantitative evaluation of microcracks and service life.

Debonding detection at adhesive joints using nonlinear Lamb waves mixing

Many engineering structural elements make use of adhesively bonded joints due to its lighter weight, load distribution and transmission mechanisms. The safety of the structure relies greatly on the condition of the adhesive joint. In this paper, the detection of debonding at the adhesive joint is investigated using a nonlinear Lamb wave mixing approach. The method relies on the presence of combined harmonics as indicative of material nonlinearity due to dislocations or anharmonicity in intact specimens or contact nonlinearity produced by the defects. In this study, experiments and three-dimensional finite element simulations were conducted and demonstrated that the presence of combined frequency wave due to contact acoustic nonlinearity is effective for indicating debonding. The effect of the debonding width was investigated and the debonding width was found to correlate well with the combined harmonic energy generated due to debonding. The findings presented in this study provides physical insights into the effect of debonding mechanisms at adhesive joints in related to the nonlinear Lamb wave mixing approach, and can be used to further develop the debonding detection techniques using wave mixing.

Modeling of vibro-acoustic modulation induced by non-linear contact in the Euler-Bernoulli beam using the Fourier spectral element

Exploiting the nonlinear nature of structural damage through piezoelectric patches is one of the latest concepts of early detection of damage. Support loosening as one of the prevalent defects in engineering systems is a source of contact acoustic nonlinearity. Vibro-acoustic modulation has proven to be a promising method for revealing structural nonlinearity characteristics. Requiring a large number of cycles to be solved in the time domain to reach the steady-state before evaluating the results in the frequency domain, makes using existing computational methods such as finite element method to model this phenomenon very expensive. This paper is concerned with a novel numerical method called Fourier spectral element to investigate the vibro-acoustic modulation in the Euler-Bernoulli beam caused by contact nonlinearity. Three piezoelectrics were attached to the beam as the probe, pump and sensor. The numerical outcomes are compared against the experimental results to check the validity of the developed method. The results show that the Fourier spectral element not only provides a high convergence rate but is also capable of simulating the phenomenon of modulation with sufficient accuracy.

Nonlinear Guided-Wave Mixing for Condition Monitoring of Bolted Joints.

Bolted joints are fundamental to numerous structural components in engineering practice. Nevertheless, their failure or even their loosening can lead to insufficient performance and reduced structural safety. This study presents a theoretical development and experimental investigation into nonlinear guided-wave mixing for integrity monitoring of bolted joints in plates. Combinational harmonics generated due to nonlinear Lamb wave mixing and contact acoustic nonlinearity at the bolted joints were used to evaluate the applied torque level in the joint. The area of the power spectral density in the region of the sum combinational harmonic bandwidth is found to be highly correlated to the applied torque level at the joint. Moreover, the effect of the number of cycles and thus the time duration of the excitation is investigated. The results show that the combinational harmonics remain robust for different numbers of cycles in detecting bolt loosening. The findings presented in this study also provide physical insight into the phenomena of nonlinear Lamb wave mixing for evaluating applied torque in bolted joints, and the results help further advance the use of nonlinear guided waves for damage detection.

Online nonlinear ultrasound imaging of crack closure during thermal fatigue loading

A thermal fatigue surface crack (6 mm deep × 23 mm wide) in a thick austenitic stainless steel plate is opened and closed with thermal heating and cooling cycles. This closing and opening of the crack is recorded with using fundamental wave amplitude difference (FAD) technique with 5 MHz 64 element phased array probe. In addition, the contact pressure and crack opening state at different time intervals were estimated using finite element (FE) simulation. In combination with the nonlinear output from the FAD and FE simulation gave insight at which level the contact pressure or the distance between crack faces prevents the contact acoustic nonlinearity (CAN) from happening. Predictably, no clear nonlinear response was recorded at crack face locations experiencing high contact pressure and on the locations where the crack could be considered fully open, as predicted by the FE simulation. Therefore, the FAD technique can be utilized within the constraints quantified in the paper.

Contact acoustic nonlinearity effect on the vibro-acoustic modulation of delaminated composite structures

In recent years, Vibro-Acoustic Modulation (VAM) techniques for structural health monitoringhave received increasing attention. For such techniques, the sidebands and higher-order harmonics generated by double/single sinusoidal excitations are utilized to identify a series of damages. Currently, most VAM investigations are experimental, mainly involving signal processing, while few studies have paid attention to the mechanics of VAM generation. This paper presents a comprehensive investigation which studies the effects of Contact Acoustic Nonlinearity (CAN) on VAM for delaminated composite structures. The paper includes theoretical analysis, simulations, and experiments. Considering both a nonlinear contact constitutive model and the clapping/rubbing discontinuity, an approximate solution for nonlinear motional equation was established by using Fourier series expansion. A modified Greenwood-Williamson (GW) model for physical contact was implemented into the commercial finite element software ABAQUS by a UINTER subroutine, which described the contact behaviors between rough surfaces. The calculated signal responses from the delaminated composite plates were compared to experimental results. A good agreement was qualitatively and quantitatively achieved with acceptable error. Particularly, some specific features of higher-order sidebands existing in the experiment were identified. Results showed that the combined effect of the nonlinear contact constitutive model and the clapping/rubbing mechanism caused odd–even order differences. The asymmetry between the sidebands indicates the existence of amplitude and frequency modulations, which can be used to extract nonlinear damage indexes. These indexes are capable of characterizing the degree and range of damage.

Debonding detection in rebar-reinforced concrete structures using second harmonic generation of longitudinal guided wave

Nonlinear features of ultrasonic guided waves (GWs) is studied for debonding detection and location estimation in rebar reinforced concrete structure. The study shows that the presence of debonding between steel rebar and concrete surface produces breathing phenomenon causing contact acoustic nonlinearity (CAN), which generates second harmonics. Time-frequency analysis is used to estimate the location of debonding in this study. At a particular frequency, embedded rebar has much greater number of wave modes in bare rebar. To avoid unnecessary complexity, only longitudinal GW modes for bare and embedded rebar are excited and received to detect and locate debonding. To precisely determine the wave mode at excited frequency and frequency of second harmonics, frequency-wavenumber analysis is performed using 2D-Fast Fourier Transform of time-space data. Three-dimensional explicit finite element simulations are performed for various case studies and the model is validated by experimentally measured data. The results of this study show that the proposed method is practically viable and beneficial for debonding detection and location estimation in reinforced concrete structures.

Microcrack localization using a collinear Lamb wave frequency-mixing technique in a thin plate

A novel Lamb wave frequency-mixing technique is proposed for locating microcracks in a thin plate, which does not require the resonance condition of Lamb wave mixing and can accurately locate the microcracks through only one-time sensing. Based on the bilinear stress-strain constitutive model, a two-dimensional finite element (FE) model is built to investigate the frequency-mixing response induced by the interaction between two primary Lamb waves and a microcrack. When twoprimary Lamb waves of A0 and S0 modes with different frequencies excited on the same side of the plate simultaneously impinge on the examined microcrack, under the modulation of the contact acoustic nonlinearity, the microcrack itself can be deemed as the secondary sound source and it will radiate the Lamb waves of new combined frequencies. Based on the timeof flight of the generated A0 mode at difference frequency, an indicator named normalized amplitude index (NAI) is defined to directly locate the multi-microcracks in the given plate. It is found that the number and location of the microcracks can be intuitively visualized by using the NAI based frequency-mixing technique. It is also demonstrated that the proposed frequency mixing technique is a promising approach for the microcrack localization.

Identification of fatigue crack under vibration by nonlinear guided waves

This study identified fatigue cracks in a steel joint under vibration by nonlinear guided waves based on second harmonic generation. Piezoelectric transducers were utilised to excite S1 Lamb wave mode in experiment and the nonlinear ultrasonic testing was performed at different crack lengths. The contact acoustic nonlinearity (CAN) was measured in experiments and quantified by a nonlinear index to evaluate fatigue crack. Finite element method was utilised to verify the experimental results and they were in good consistence. The simulation was divided into two stages where the first stage was to model the vibration responses of the specimen and the second stage was to simulate the nonlinear ultrasonic testing to characterise the fatigue crack with the effect of vibration. A percent reduction in nonlinearity was proposed to evaluate the crack length based on the difference of nonlinear index measured at static and vibration conditions. It is observed that percent of reduction in nonlinearity increased with crack growth. The outcomes of this study can further advance the fatigue crack identification and qualification based on second harmonic generation under practical working condition of structures.

Experimental Verification of Contact Acoustic Nonlinearity at Rough Contact Interfaces.

When a longitudinal wave passes through a contact interface, second harmonic components are generated due to contact acoustic nonlinearity (CAN). The magnitude of the generated second harmonic is related to the contact state of the interface, of which a model has been developed using linear and nonlinear interfacial stiffness. However, this model has not been sufficiently verified experimentally for the case where the interface has a rough surface. The present study verifies this model through experiments using rough interfaces. To do this, four sets of specimens with different interface roughness values (Ra = 0.179 to 4.524 μm) were tested; one set consists of two Al6061-T6 blocks facing each other. The second harmonic component of the transmitted signal was analyzed while pressing on both sides of the specimen set to change the contact state of the interface. The experimental results showed good agreement with the theoretical prediction on the rough interface. The magnitude of the second harmonic was maximized at a specific contact pressure. As the roughness of the contact surface increased, the second harmonic was maximized at a higher contact pressure. The location of this maximal point was consistent between experiments and theory. In this study, an FEM simulation was conducted in parallel and showed good agreement with the theoretical results. Thus, the developed FEM model allows parametric studies on various states of contact interfaces.

A hybrid spectral/finite element method for accurate and efficient modelling of crack-induced contact acoustic nonlinearity

We propose a 2D hybrid spectral/finite element scheme for numerically resolving crack-induced contact acoustic nonlinearity in solid structures. While the high-order spectral element method (SEM) is much more efficient than the classical low-order finite element method (FEM), the fact that spectral elements are relatively large renders the SEM ineffective in discretizing microscopic cracks. The classical FEM, on the other hand, is good at modelling complex geometries. However, the computation of large-scale structures by the classical FEM can be extremely expensive. In this work, the coupling between high-order spectral elements and low-order finite elements is formulated by the Lagrange multipliers method. The nonlinear contact between crack surfaces is modelled using a penalty method. The aim of the proposed hybrid method is to simultaneously reduce the degrees of freedom (DOFs) in systems and ensure high numerical accuracy. A comprehensive mesh convergence study has been conducted to demonstrate the high convergence rate of the proposed method in modelling ultrasonic wave propagation, and its capability to converge for weak crack-induced contact acoustic nonlinearity. Through a series of numerical experiments on generation and propagation of nonlinear ultrasonic wave modes, the proposed method has been shown to possess a high accuracy and geometric flexibility, and require significantly less computational resources than the classical FEM. The proposed hybrid method will provide an efficient, accurate and robust numerical approach for studying crack-induced contact acoustic nonlinearity which nowadays is being widely exploited by non-destructive testing applications.