Surface/sub-surface crack-scattered nonlinear rayleigh waves: A full analytical solution based on elastodynamic reciprocity theorem

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).

Validation of zero-group-velocity feature guided waves in a welded joint

Extensive research has been conducted on zero-group-velocity (ZGV) Lamb waves in elastic plates, demonstrating significant progress in the field of nondestructive testing. However, there is a scarcity of studies focusing on ZGV modes in complex structures. In this paper, we present our research investigating the presence of ZGV feature guided waves (FGWs) in a welded joint. Our approach follows a similar methodology used to study ZGV Lamb waves in elastic plates. By employing two-dimensional (2D) finite element (FE) modeling, we analyze the response spectra of the welded joint when subjected to a force source, revealing the occurrence of resonance in the response spectra. To investigate resonance modes in the welded joint, we employ the three-dimensional (3D) time-step FE method. By applying spatial 2D and short-time Fourier transforms to the received time-domain signals, we analyze the frequency content and spatial distribution of the signals. This analysis allows us to verify the existence of non-propagation and propagation modes in the welded joint. The non-propagation mode refers to the presence of signals with a zero wavenumber, indicating that they do not propagate or travel along the welded joint. These signals are typically associated with local resonances or vibrations within the welded joint itself. On the other hand, the propagation mode corresponds to signals with nonzero wavenumbers, suggesting that they propagate or travel along the welded joint. Furthermore, by further analyzing the propagation mode in the welded joint, similar to the analysis of ZGV modes in solid plates, we have observed that it also exhibits ZGV characteristics based on the wavenumber-frequency spectra. To further analyze acoustic field distributions at resonance frequencies, we utilize the semi-analytical finite element method in conjunction with the perfectly matched layer method. The results obtained from this analysis are consistent with those obtained from the 2D FE method and 3D time-step FE method, thereby confirming that propagation modes with ZGV characteristics at resonance frequencies correspond to FGWs, which we refer to as ZGV-FGWs. Through this step-by-step analysis, we ultimately establish the existence of ZGV-FGWs in the welded joint. This study introduces fresh ideas and serves as a point of reference for future research on ZGV-FGWs in complex structures.

Surface breaking crack sizing method using pulse-echo Rayleigh waves

Surface cracks are common in various industries. Eddy current testing (ECT) is commonly used for crack sizing but necessitates complex calibration standards and a highly trained inspector. Moreover, for large-area inspections, it requires additional scanning arrangements. In recent years the wedge technique-based Rayleigh wave crack sizing method has attracted significant research interest due to its unidirectional excitability. However, Rayleigh wave features generated at crack tips are often weak and masked under noise, and they mostly attenuate before reaching the receiving probe due to the couplant between the wedge-test specimen interface. Consequently, sizing the crack depth is difficult using a pulse-echo setup. This work presents a wedge-free pulse-echo Rayleigh wave method for surface crack sizing using a conventional phased array transducer. Eliminating the wedge removes a couplant layer leading to lower attenuation, enabling the transducer to capture crack tip features. This allows the sizing of surface cracks in pulse-echo using the time-of-flight (ToF) information. Furthermore, leveraging the phased array system, an averaging technique employed to the time trace signals captured by the transducer elements effectively averages out the other wave modes generated at crack geometries by the scattering of Rayleigh waves. This significantly minimizes sizing errors and enhances the signal-to-noise ratio (SNR). The performance of the proposed method is demonstrated through finite element simulations and experiments. Experiments with electric discharged machined (EDM) notches on test specimen surface at various angles and depths mimicking surface-breaking cracks show accurate sizing within a 5% error. The proposed method offers flexibility in performing inspections using a wide frequency range and can be easily applied to different materials using any conventional phased array transducer. This enhances its adaptability for industrial applications in the characterization of surface cracks.

Wavefield imaging of nonlinear ultrasonic Lamb waves for visualizing fatigue micro-cracks

The traditional nonlinear ultrasonic technique, as typified by the second-harmonic generation and the frequency mixing response, can be employed to identify and characterize the micro-damage. However, the research on micro-damage characterization using nonlinear Lamb wave imaging technique remains an ongoing challenge and is rarely reported. A method called standardized amplitude difference is proposed for nonlinear feature enhancement, and further for fatigue crack imaging based on the wavefield data. Wavefield data contain abundant information on the spatial and temporal variation of propagating waves in the damaged structure. The nonlinearity index β' of the signal difference under the high and low incident wave amplitudes is calculated for fatigue crack imaging. Two scanning methods, including local scanning and global scanning, are introduced to image the fatigue crack tip and visualize the wave field of the harmonics respectively. The experimental validation, based on the imaging results of an aluminum alloy plate specimen with a barely visible fatigue crack and a steel plate with a blind hole, manifests that the proposed method can be used to enhance and extract the nonlinear features and suppress the fundamental frequency, so as to improve the signal-to-noise ratio (SNR) of the micro-damage imaging results.

Methodologies for modeling and identification of breathing crack: A review

Swift development of technology for monitoring complex structures demands major attention on the precision of damage detection methods. The early detection of any type of deterioration or degradation of structures is of paramount importance to avoid sudden catastrophic failure. It warns users about the impending state of the system. At the initiation of a crack or some other system faults, the system may generate a time-varying state of crack under ambient vibration. It represents the nonlinear breathing phenomena of crack. An assessment of this degree of nonlinearity can be utilized for the detection, localization, and quantification of breathing cracks. Appropriate modeling of such cracks is thus necessary to capture distinctive nonlinear features. Recognizing this importance, various methods of modeling and nonlinear system identification which have been employed in the past for the detection of breathing crack are reviewed. The present study also explores some of the available vibration as well as acoustic-based damage identification techniques, chronologically connecting their evolutions. It summarizes the advantages and limitations of the methods to inspect potential future applications. The future scopes drawn from this review are highlighted to pave the path of wide-spread applications of nonlinear features of crack.

Modeling ultrasonic wave fields scattered by flaws using a quasi-Monte Carlo method: Theoretical method and experimental verification

The modeling and visualization of wave fields scattered by flaws can be helpful in terms of guiding the testing and evaluation of flaws using an ultrasonic nondestructive method. In this work, the ultrasonic scattering of wave fields from flaws with different shapes is modeled using a quasi-Monte Carlo (QMC) method and measured through experiments for verification. The incident wave fields generated by a transducer can be modeled using the Rayleigh integral expression and calculated using the QMC method. When the size of the flaw is much larger than the wavelength, the incident wave over the lit portion of flaw can be treated as the source for the scattering of wave fields, and these wave fields can also be modeled using the proposed QMC method. In this paper, water is treated as the material and an embedded solid component is considered as the flaw. Numerical examples and results are presented for flaws with different shapes and sizes, and the properties of these scattering wave fields are analyzed and discussed. Experiments are performed to measure the scattering wave fields using a needle transducer, and it is shown that the results agree with the simulations, thus verifying the proposed modeling method. The work presented here can assist in understanding the wave-flaw interaction and can help in optimizing ultrasonic nondestructive testing.

Fatigue crack detection in edges of thin-walled structures with corners using the fundamental mode of edge waves

Non-destructive detection and evaluation of fatigue cracks is critical to maintain safety and effective operation of high-value assets working under cyclic loading. However, this can be difficult in the case of the corners of the structural elements, especially at inaccessible locations. In this article, the propagation of the fundamental symmetric mode of edge wave (ES₀) along structural features such as sharp and rounded corners are investigated using experimental and numerical methods. The ultimate aim of this study is to demonstrate that the ES₀ is a promising for defect detection in geometries with corners. The outcomes of this study show that ES₀ wave is able to propagate through sharp and rounded corners and provides a way to inspect difficult-to-reach locations. Further, the numerical simulations indicate that the radius-to-wavelength ratio above 3 has no significant impact on the wave amplitude when the ES₀ propagates through the rounded corner. The results also demonstrate that the presence of fatigue crack leads to generation of the second harmonic of the ES₀ wave mode, and this phenomenon can be utilised in the development of fatigue crack detection and characterization procedures.

Microcrack localization using nonlinear Lamb waves and cross-shaped sensor clusters

Using the nonlinear interaction effect between ultrasonic Lamb waves and microcracks to detect and locate microcracks has the advantages of fast detection speed and high sensitivity. In this paper, a method for microcrack localization based on cross-shaped sensor clusters in a plate is proposed by combining nonlinear ultrasonic Lamb wave technology and time difference of arrival (TDOA) technology. The antisymmetric (A0) mode at low frequency is chosen as the primary Lamb wave to simplify the complication of the dispersion and multi-mode properties of Lamb waves. The selected mode pair (A0-s0) weakens the influence of the cumulative growth effect of higher harmonics induced by the inherent material nonlinearity on the microcrack characteristic signals. Pulse inversion technique and cross correlation function are used to extract the TDOAs of the nonlinear characteristic signals including microcrack information. The cross-shaped sensor clusters approach proposed for the first time can achieve reliable and fast microcrack localization without being affected by the duration of the excitation signal, and a priori knowledge of group velocities of primary wave modes or generated harmonics. Experimental and numerical results validate the proposed method in isotropic and anisotropic plates. This paper provides a new idea for nonlinear ultrasonic nondestructive evaluation and structural health monitoring of microcracks in plates.

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.

Low-frequency Lamb wave mixing for fatigue damage evaluation using phase-reversal approach

Fatigue damage is difficult to detect and evaluate non-destructively, specifically at its early stages (before the macro-crack formation). In this study, fatigue damage is evaluated based on the growth rate of the combinational harmonics generated by mixing of two fundamental symmetric mode (S₀) of Lamb waves in the low frequency range. The incorporation of the phase reversal approach to the wave mixing method could potentially improve the evaluation of the combinational and second harmonics and avoid the influence of other undesirable harmonics. A series of parametric case studies are carried out using the three-dimensional (3D) finite element (FE) method to investigate the effects of the excitation frequencies and time delay of the incident waves in wave mixing on the transient response of a weakly-nonlinear material. The numerical results and experimental results show that the sum combinational harmonic and second harmonics are sensitive to weak material nonlinearities. Further experiments on damaged samples by cyclic loading demonstrate that the sum combinational harmonic has much better sensitivity to the progressive fatigue damage than the the second harmonics. In general, the outcomes of this study indicate that the damage evaluation of early stage fatigue damage is feasible and effective with the wave mixing method using the S₀ waves generated at low frequency, and the phase-reversal approach improves considerably the quality of experimental results in the fatigue damage evaluation.

High-Selectivity imaging of the closed fatigue crack due to thermal environment using surface-acoustic-wave phased array (SAW PA)

Crack closure can cause the underestimation or misdetection of fatigue cracks in ultrasonic testing (UT). Fatigue-crack closure due to an environmental factor, i.e., high temperature, was found in eddy current testing (ECT), which is used to inspect the vicinity of surfaces. However, its effect and countermeasures have yet to be examined in UT. In this study, we examined the fatigue-crack closure induced by heat processing using a surface-acoustic-wave phased array (SAW PA). SAW PA is a phased-array imaging method using Rayleigh waves, which can sensitively visualize defects in the vicinity of surfaces. As a result, the intensity of crack responses visualized by SAW PA markedly decreased after the heat processing of a fatigue-crack specimen. Furthermore, we demonstrated that the combination of SAW PA with a crack opening method, global preheating and local cooling (GPLC), and a load difference phased array (LDPA) is useful for the high-selectivity imaging of closed fatigue cracks. We also discussed a possible mechanism of the fatigue-crack closure induced by heat processing.