Contact Acoustic Nonlinearity Research Articles

Entire loosening stage monitoring of bolted joints via nonlinear electro-mechanical impedance spectroscopy

This article proposes a nonlinear electro-mechanical impedance spectroscopy (NEMIS) methodology for the entire loosening stage monitoring of bolted joints. Unlike the conventional electro-mechanical impedance spectroscopy (EMIS) implemented in the frequency domain, NEMIS utilizes a temporal interrogating signal to procure the developed nonlinear impedance spectrum. It can harness the structural resonance information akin to the conventional EMIS, while concurrently capturing the contact acoustic nonlinearity (CAN) features with only one solitary Piezoelectric Wafer Active Sensor (PWAS). To elucidate the underlying principles of NEMIS, a comparative analysis juxtaposing the conventional EMIS, nonlinear ultrasonic techniques, and the proposed NEMIS was conducted. Subsequently, a reduced-order analytical model was established to simulate the rough contact interfaces of the bolted joints under various looseness states. Parametric studies were carried out to demonstrate the resonance deviation and nonlinear features resulting from the bolt looseness. Ultimately, the experimental implementation of NEMIS for the entire loosening stage monitoring of the bolted joint was performed compared with the conventional EMIS method. It was proved that NEMIS could detect both the incipient bolt loosening at an embryo stage and severe loosening of the bolted joint at the terminal period, integrating the continuous monitoring capability of conventional EMIS and the sensitivity of nonlinear ultrasonic methodology. The quantification on the severity of bolt loosening was accomplished via both linear and nonlinear damage indices, exhibiting a consistent trend with the gradations of bolt looseness. The article culminates in a summary, concluding remarks, and suggestions for future work.

Nonlinear interaction of Lamb waves with fatigue cracks in metal plates under the condition of phase-velocity mismatching

Abstract Nonlinear Lamb waves have been widely acknowledged as an efficient method for evaluating material damage at an early stage. However, due to the dispersive and multimode natures of Lamb waves, nonlinear Lamb waves with exact/approximate phase-velocity matching have been employed in previous research solely for the evaluation of fatigue cracks. Second harmonic Lamb waves can be generated from the contact acoustic nonlinearity (CAN) induced by the “breathing” effect of fatigue cracks. This paper presents a verification of the second harmonic S0 mode Lamb waves due to fatigue crack CAN, despite the mismatch in phase velocity between this mode and the primary S0 mode Lamb waves. This verification is achieved through both simulation and experiment. Consequently, the generation of double-frequency Lamb waves by fatigue cracks under conditions of phase velocity mismatching is validated. Furthermore, the phase-velocity mismatching method is anticipated to exclude material nonlinearity in the detection of fatigue cracks. This method offers a potential for accurate detection and evaluation of fatigue cracks.

Nonlinear Lamb wave phased array for revealing micro-damage based on the second harmonic reconstruction

It is challenging but meaningful to detect and image the micro-damage in the early stages of engineering structure failure. The nonlinear ultrasonic technique has gained considerable attention for micro-damage detection, meanwhile, the Lamb wave phased array technique has become a practical tool for macro-damage imaging. The combination of these two techniques can pave a promising way for micro-damage imaging in plate-like structures. However, the research on nonlinear Lamb wave phased array imaging is complicated and not reported. The weak nature and hard extraction of the nonlinear features, such as the second harmonic generation, limits the application of the nonlinear Lamb wave phased array. A framework of nonlinear Lamb wave phased array for micro-damage imaging in the plate-like structure is developed. To maximize the second harmonic response of the recorded Lamb waves, two kinds of lead zirconate titanate (PZT) wafers are selected to compose the nonlinear phased array. Furthermore, focusing on the nonlinear feature extraction, the sparse representation approach is introduced for reconstructing the time-domain second harmonic generated by the micro-damage, from which a wealth of waveform information corresponding to the micro-damage can be extracted. The total focusing method (TFM) is used for micro-damage imaging based on the reconstructed second harmonic. Numerical simulation and experimental validation demonstrate the capability of the proposed framework to image the local contact acoustic nonlinearity represented by the barely visible closed fatigue crack with the nonlinear Lamb wave phased array.

Experimental Contact Acoustic Nonlinearity of Interfaces During Loading-Unloading Cycle: Combined Effects of Elastoplastic Nonlinear Spring, Crack-Clapping, and Adhesion

Experimental Contact Acoustic Nonlinearity of Interfaces During Loading-Unloading Cycle: Combined Effects of Elastoplastic Nonlinear Spring, Crack-Clapping, and Adhesion

Contact acoustic nonlinearity and damping properties of completely free vibrating curved and delaminated CFRP plates

This study reports an experimental investigation on the effect of plate curvature and circular inter-ply delamination on the completely free vibration properties of carbon fiber reinforced polymer (CFRP) plates. Impact tests on wire suspended plates were performed and variations in measured natural frequencies and modal damping are reported. Delamination clapping type contact acoustic nonlinearity (CAN) was observed in the presence of a series of higher harmonics in the vibration spectrum. These higher harmonics consisted of five to seven equally distanced peaks grouped in a frequency range of around the double of odd mode M (5,0). Modal damping was highly sensitive to delamination which caused a 33% average increase in damping loss factors. Odd mode M (3,0) was the most affected with an average increase of 51% in damping loss factor, explained by the delamination location relative to the wavelength of that mode shape. Natural frequencies were less sensitive to delamination, on average decreasing 1.0% in flat plates and increasing 3.1% in curved plates. The modal frequencies calculated from embedded fiber optic sensor (FOS) or electrical resistance strain gauge signals agreed with finite element modeling (FEM) to within a 3.1% difference for all modes considered. The damping loss factors deducted from suspended plate tests were consistent with complementary results from dynamic mechanical analysis (DMA). The measured delamination clapping CAN and its related influence on damping can serve to enhance structural health monitoring (SHM) methods.

Debonding detection of FRP-strengthened reinforced concrete using a novel amplitude modulated vibro-acoustic method

This paper presents a novel Amplitude Modulated Vibro-Acoustic (AMVA) method for debonding detection in reinforced concrete strengthened by fibre-reinforced polymer (FRP) composite laminates. This study also compares the behaviour of AMVA method with the conventional Vibro-Modulation (VM) method. The comparative analysis is based on sidebands measurements related to different debonding sizes. A theoretical framework is used to obtain the nonlinear parameter β of Contact Acoustic Nonlinearity (CAN), utilized in both AMVA and conventional VM methods to characterize varying debonding levels. In addition, the Sideband Peak Count (SPC) and Sideband Peak Count-Index (SPC–I) approaches are employed to evaluate damage levels by counting and comparing the number of sideband peaks above a moving threshold level. The results show that using SPC-I technique has a better behaviour to characterize damage levels since it is more accurate than SPC technique and it is easier to implement compared with calculating nonlinear parameters β. In addition, the AMVA method demonstrates greater sensitivity than conventional VM method, improving its capability to identify damage and making AMVA method as a promising tool for debonding detection in FRP strengthened concrete.

Analytical and numerical modeling of nonlinear lamb wave interaction with a breathing crack with low-frequency modulation

To characterize fatigue crack, an analytical calculation and finite element (FE) simulation of Lamb wave propagating through the region of a breathing crack in a two-dimensional(2D) isotropic plate were studied. Contact surface boundary conditions between the two surfaces of the vertical crack were considered to study contact acoustic nonlinearity (CAN) from the breathing contact crack in conjunction with the modal decomposition method, Fourier transform, and variational principle-based algorithm. Reflection and transmission coefficients in the fundamental frequency and second harmonic frequency were calculated and analyzed quantitatively. Different ratios of incident wave amplitude to crack width were studied to calculate CAN results related to micro-crack width. In addition, a low-frequency (LF) vibration(10 Hz) excitation was introduced to perturb the free surface vertical crack to close, and an interrogating Lamb wave(1 MHz) was used to study crack-related CAN in different conditions for interpreting the modulation mechanism. The contact boundary conditions between two surfaces of vertical crack were set which were dynamically changed due to the low frequency modulation. The clapping effects when the crack closed due to the modulation of the contact boundary conditions between the crack surfaces were studied and analyzed to get the quantitative correlation between CAN and LF modulation. The results obtained from the analytical model were compared with those from the FE simulation, showing good consistency. Knowledge of these effects is essential to correctly gauge the severity of surface cracks in the plate, which can be spotlighted in its application to quantitative evaluation of micro fatigue cracks in structural health monitoring(SHM).

Numerical study of nonlinear interaction of the guided wave due to breathing type debonding in stiffened panel

Abstract The common tool for assessment of breathing-type debonding in metallic or composite structures is nonlinear guided wave-based technique. The past studies show that with debonding size, the strength of the nonlinearity does not exhibit strictly increasing or decreasing trends, or that the monocity is valid up to a certain size limit of debonding. This paper presents the study of non-linear interaction of guided waves in the debonding interface of a metallic stiffened panel. The study attempts to establish a relationship between the contact energy generated by the contact acoustic nonlinearity (CAN) at the debonding interface and the associated nonlinearity strength for various debonding sizes at various excitation frequencies. A numerical model of the stiffened panels is developed in three-dimensional finite element (FE) and validated with experiments for the study of interaction of nonlinear guided waves. The validated FE model is used to conduct studies on nonlinear interactions in debonding. The outcome of this study contributes to a better understanding of how guided waves can be used to effectively assess the debonding in metallic stiffened panels by considering non-linear interactions at the debonding interface. The study also provides insights into a more accurate and consistent quantification of the debonding using higher harmonic signals and contact energy produced by non-linear interactions.

Enhancement of Contact Acoustic Nonlinearity Effect in a Concrete Beam Using Ambient Vibrations

Abstract Contact acoustic nonlinearity (CAN) is generated when oscillating crack faces open and close while a wave passes through it. However, reliably assessing the nonlinear effect due to micro-scale defects is challenging, especially in concrete structures, due to their large size, high attenuation, and low signal-to-noise ratio. However, concrete facilities vibrate due to ambient excitations such as vehicle movement, wind, and water flow. These ambient vibrations can be utilized in amplifying CAN. For example, a vehicle can be moved at a particular velocity over a bridge to amplify a particular natural mode of vibration. This paper illustrates a method of enhancing contact acoustic nonlinearity with the help of ambient vibrations of the structure. A finite element model of a concrete beam with a thin crack is developed. The base of the beam was oscillated at 100 Hz. Meanwhile, a 200 kHz ultrasonic excitation was applied on the beam to monitor its propagation through the crack. The closing and opening of the crack generate the nonlinear behavior of the ultrasonic pulse. A considerable increment of nonlinearity was observed demonstrating the efficacy of the proposed method. The time windows for the nonlinear zone have been identified. A laboratory experiment has been performed to demonstrate the proposed method in reinforced concrete beams. This investigation demonstrates that CAN can be utilized in monitoring concrete structures when ambient vibrations are taken into account.

Tension evaluation of prestressed strand based on combined features of nonlinear ultrasonic mixing

The estimation of prestressed strand stress levels is of great significance in ensuring the structurally reasonable performance of post-tensioned concrete structures, cable-stayed bridges, and arch bridges. This paper proposes a method to evaluate the remaining tensile stress on the strand through the ultrasonic mixing technique. The relationship between the strand tension and the nonlinear harmonics is established based on the theory of contact acoustic nonlinearity, and the acoustic nonlinear parameters at different tension levels are investigated by finite element analysis and step-loading experiments. The results show that the nonlinear parameters follow a power-law decrease with the increase in the tensile stress. To overcome the shortage of decreasing sensitivity of theoretical nonlinear parameters in monitoring early loosening, support vector regression is introduced to utilize complex high-order nonlinear generations in stress evaluation. With this approach, the accuracy of early-stage stress evaluation based on wave mixing has been remarkably improved.

Contact acoustic nonlinearity and local damage resonance for the detection of kissing bonds in structural adhesive joints

Adhesively bonded joints are susceptible to contamination of surfaces during manufacture and environmental deterioration in real operating conditions. These may cause the generation of so-called “kissing bonds” that can dramatically alter the strength of the joint leading to premature failure. Nonlinear acousto-ultrasonic (AU) techniques have shown great potential for monitoring kissing bonds with piezoelectric sensors permanently installed on the structural joint, thus enabling online and in-situ inspection. This paper investigated the combined contact acoustic nonlinearity (CAN) and local damage resonance (LDR) effects in the presence of kissing bonds in adhesive joints. Experimental nonlinear AU tests showed the formation of LDR frequency down-shifts and “jumps” of the fundamental damage resonance in adhesively bonded aluminium joints, with the kissing bond located internally to the overlapping region between the two adherends. These results were supported by a theoretical model based on the solution of the nonlinear Duffing's equation, under the assumption that the debonded region is a damped nonlinear harmonic oscillator subject to harmonic forcing. The Harmonic Balance Method was used to solve the nonlinear differential problem, showing the generation of frequency down-shifts via the dependence of the ratio between the excitation and LDR frequencies with the amplitude of the fundamental damage resonance. Additionally, two-dimensional finite element simulations using a reduced order model based on the Craig-Bampton technique were carried out to support experimental AU tests for the identification of the LDR frequency and the generation of nonlinear resonance effects. Good agreement between analytical, numerical, and experimental results revealed that a monitoring approach combining CAN and LDR is an extremely efficient and sensitive tool for ensuring integrity and safety of structural adhesive joints.

Detection and evaluation of heat damage in reinforced concrete beams using linear and nonlinear guided waves

This study utilizes the linear and nonlinear features of guided waves (GWs) for detecting and evaluating heat damage in reinforced concrete (RC) beams. The RC beams with embedded sensors attached at rebar ends are experimentally studied using longitudinal GW at 200 kHz after heating the specimens in a furnace from 100°C to 300°C. For the studies investigating the effect of heat damage on the RC beams beyond 300°C, the rebar ends are exposed outside the concrete so that the longitudinal transducers can be attached there. These specimens are then experimentally studied using GW with an excitation frequency of 100 kHz. In this study, the RC beams are prepared as fully bonded and debonded specimens. The experimental study shows that heat damage in the RC beams causes debonding between rebar and concrete enabling GW signal to generate second harmonics. The experimental study also discussed the linear features of GW, which shows that the amplitude of the GW signal increases with elevated temperatures in the RC beams. To distinguish material nonlinearity and contact nonlinearity, two types of nonlinear parameters are defined in this study. The nonlinear parameter due to the contact acoustic nonlinearity effect in the RC beams is defined as β, whereas the nonlinear parameter due to material nonlinearity is defined as β m . The study shows that β m is negligible in comparison to β at relevant heated temperatures. With the increase in temperature, the nonlinear parameter β is significantly increased at elevated temperatures. The peak amplitude of the nonlinear parameter β is observed at the maximum heated temperature 800°C for both bonded and debonded specimens.

Modeling for nonlinear acoustic imaging of an isolated crack via standing waves in a 2D solid

This paper is concerned with numerical modeling for nondestructive imaging of defects in solids via standing waves excited by a periodic sinewave signal. The stationary solution, purely sinusoidal in an intact sample, contains higher harmonics when damage is present. These harmonics are generated by contact acoustic nonlinearity and form their own standing waves whose intensity maximum usually indicates the position of damage, in a way similar to resonant vibrometry experiments. The key point of the developed numerical tool that describes those wave phenomena is a model of planar damage (crack, delamination) considered here as an inner contact with rough surfaces and friction. The corresponding boundary conditions are given by the previously developed contact model based on the Method of Memory Diagrams (MMD) capable of automating the account for hysteretic frictional effects. Combination of the MMD for boundary conditions and a finite element formulation for waves in a volume (MMD-FEM model) provides a complete description which represents a numerical code applied here for nonlinear standing waves simulations. We present a number of examples obtained for idealized 2D geometry and reveal conditions in which both position and extent of damage are clearly seen as well as cases where only partial detection is possible.

On the emergence of the second harmonic shear horizontal wave in presence of tangential prestress

Nonlinear ultrasonic techniques have significant advantages in characterizing incipient defects of materials. The classical nonlinear ultrasonic theory indicates that a primary longitudinal wave can generate a second harmonic longitudinal wave due to the material nonlinearity (MN) or contact acoustic nonlinearity (CAN). However, in both MN and CAN, a second harmonic shear horizontal (SH) component generated from a normally-incident SH wave has not been reported. In this work, a time domain spectral finite element method combined with the bi-potential contact theory is extended to simulate the CAN problems with prestresses. Numerical verifications are performed to show the robustness and accuracy of the developed method. After that, the nonlinear interactions between the SH wave and frictional interfaces under complex prestresses are investigated. It is found for the first time that when there are tangential prestresses at the frictional interfaces or crack surfaces, a primary SH wave of normal incidence can generate the second harmonic SH wave. A theoretical model is then proposed to interpret this new phenomenon. It is found that the even SH wave harmonics result from the asymmetric sliding of the frictional interface induced by the tangential prestresses. This asymmetric sliding mechanism can be compared with the breathing behavior of a crack caused by an incident longitudinal wave. The findings of this work could enrich the understanding of contact acoustic nonlinearity behavior of the SH wave and promote the development of related nondestructive evaluation techniques.

Understanding contact acoustic nonlinearity through coupled synchrotron x-ray imaging and dynamic acoustoelastic measurements under stress

Dynamic acoustoelastic testing (DAET) is a vibro-acoustic technique, which has been used to measure acoustic nonlinearity in disparate solid media. DAET is a pump-probe approach, where the strain pump-induced changes in the elastic properties of the medium are monitored by a pair of ultrasonic probes at frequencies much higher than that of the strain pump. In a fractured/cracked medium, the measured changes in the elastic properties are attributed to fracture breathing (opening/closing) or shearing caused by the low-frequency pumping. In a set of unprecedent experiments, we use time-lapse synchrotron x-ray imaging in tandem with quasi-static loading/unloading and DAET to visualize the fast dynamics mechanisms in four different materials systems under various stress levels. These include two samples with localized CAN: fractured Westerly granite and Berea sandstone and two samples of granular media with distributed CAN: glass beads and sand. The synchrotron x-ray images are analyzed to obtain true contact areas and changing strain fields under stress. The ultrasonic signals are analyzed in relation to the changes in contact areas during both the quasi-static and dynamic loading to examine the state-of-the-art understanding of ultrasonic transmission in fractured media as well as acoustoelasticity and dynamic acoustoelasticity.

Microcrack inspection in a functionally graded plate structure using nonlinear guided waves

The nonlinear guided wave technique based on contact acoustic nonlinearity (CAN) has been considered one of the best approaches for characterizing microcracks or fatigue cracks in structures. Through various mode selections, nonlinear guided wave testing has higher sensitivity that is suitable for detecting micro-defects at a very early stage. However, in most of the previous studies, this technique has been implemented in homogeneous materials such as aluminium, steel and layered composites. In recent years, functionally graded material (FGM) has received a great deal of attention because of its exceptional mechanical properties. Monitoring and evaluating the microstructural changes of FGM are essential for safety. In this study, the nonlinear interaction of the guided waves with a microcrack in an FGM plate is investigated numerically. The results showed that the generation of higher harmonics provides a sensitive means for detecting microcracks in FGM plates. Besides, the dependence of relative nonlinear parameters on microcrack length, sensor location and crack locations is studied through comprehensive finite element simulations. The study reveals that the nonlinear ultrasonic technique can be used effectively to detect microcracks in FGM plate structures.

Nonlinear ultrasonic detection of closed cracks in metal plates with phase-velocity mismatching

In this paper, nonlinear Lamb waves with phase-velocity mismatching are proposed to detect accurately closed cracks by excluding the intrinsic material nonlinearity. Simulations and experimental studies were conducted to analyze double frequency Lamb waves (DFLWs) induced by the closed cracks and the intrinsic material nonlinearity. The results show that DFLWs induced by the material nonlinearity are negligible as compared with that caused by the contact acoustic nonlinearity (CAN) of the closed cracks. The closed cracks can be accurately detected using the proposed method, and the acoustic nonlinearity parameter increases monotonically with the crack evolution. The findings of this study provide a feasible method for detection and characterization of closed cracks.

Theoretical and experimental investigations on control parameters of piezo-based vibro-acoustic modulation health monitoring of contact acoustic nonlinearity in a sandwich beam

Contact-type defects are prevalent in composite constructions and sandwich panels due to failure mechanisms such as bolt loosening and delamination. Contact acoustic nonlinearity is a manifestation of such defects that nonlinear health monitoring systems can detect. Vibro-acoustic modulation (VAM) is a well-established technique for the early detection of nonlinear defects in structures. It employs bi-tone excitation to reveal damage-induced nonlinearity, which results in the appearance of sidebands in the response spectrum. The objective of this research is to use PZT-based excitation to monitor bolt loosening in a sandwich beam in real-time. To address the limited capacity of the PZT transducers to excite the nonlinear mechanism, a sensitivity analysis (SA) for input factors of VAM testing was conducted to improve damage detection using the results. The Morris approach is used to investigate the sensitivity of VAM damage metrics derived analytically in the frequency domain. To reduce the number of tests required for the experimental SA, the response surface methodology (RSM) is applied. The analysis of variance and Fischer's statistics are used to calculate the SA of experimental damage indices. In RSM computations, the discrete influence of excitation frequencies on the modulation sidebands is addressed. For reliable SA of experimental results, the effect of background noise is taken into account. The findings of this study may be applied to the selection of appropriate damage metrics in real-world applications of VAM health monitoring systems, as well as the effective tuning of input control parameters to maximize damage detectability.

Residual opening of fatigue cracks due to the wake of plasticity

The concept of a breathing crack and the clapping mechanism, when a crack periodically opens and closes subject to a cyclic or harmonic excitation, are widely utilised in studies concerning contact acoustic nonlinearity (CAN) and nonlinear phenomena. The investigation of these phenomena is particularly important for the development of reliable non-destructive fatigue crack detection techniques. The aim of the current contribution is to demonstrate the characteristic behaviour of a fatigue crack under excitation loading using a simple analytical model that accounts for the wake of plasticity behind the crack tip, which leads to the plasticity-induced fatigue crack closure phenomenon. It is believed that incorporation of these features and more realistic behaviour of fatigue cracks can help to improve the methods for the detection of nonlinear phenomena associated with CAN. The results of the present work indicate that ultrasonic inspections based on the CAN using a bilinear stiffness model may underestimate the length of the detected crack(s) due to the plasticity-induced crack closure phenomenon. Despite many modelling assumptions, the present work can serve as a starting point for the development of accurate models for different crack geometries and load histories. The latter may help to develop effective nondestructive techniques for detection and identification of fatigue cracks and prevention of fatigue failures.

Nonlinear ultrasonic evaluation of damaged concrete based on mixed harmonic generation

Nonlinear wave mixing provides a potential method to evaluate localized micro-damage in structures. The wave mixing technique has some unique advantages over the nonlinear ultrasonic technique based on the higher harmonic generation, such as frequency selectivity, which can separate harmonic components generated due to instrumentation. In this paper, we numerically studied the frequency mixing response induced by the nonlinear interaction of two primary Rayleigh waves in a concrete material. The nonlinearity considered in the present study is due to crack-wave interaction, which is often called contact acoustic nonlinearity (CAN). A limited number of experimental studies were conducted on concrete prisms to evaluate surface cracks. Both numerical and experimental results illustrate the generation of the second- and third-order combined harmonics, which can be utilized to detect and localize subsurface cracks in concrete structures. The newly discovered third-order combined harmonics, which result from the mutual interaction between the primary Rayleigh waves and their induced second-harmonic waves, can be exploited to characterize micro-damage in various applications.