Nonlinear scattering and mode conversion of Lamb waves at breathing cracks: An efficient numerical approach

Monitoring damage growth and topographical changes in plate structures using sideband peak count-index and topological acoustic sensing techniques

Some topographies in plate structures can hide cracks and make it difficult to monitor damage growth. This is because topographical features convert homogeneous structures to heterogeneous one and complicate the wave propagation through such structures. At certain points destructive interference between incident, reflected and transmitted elastic waves can make those points insensitive to the damage growth when adopting acoustics based structural health monitoring (SHM) techniques. A newly developed nonlinear ultrasonic (NLU) technique called sideband peak count - index (or SPC-I) has shown its effectiveness and superiority compared to other techniques for nondestructive testing (NDT) and SHM applications and is adopted in this work for monitoring damage growth in plate structures with topographical features. The performance of SPC-I technique in heterogeneous specimens having different topographies is investigated using nonlocal peridynamics based peri-ultrasound modeling. Three types of topographies - "X" topography, "Y" topography and "XY" topography are investigated. It is observed that "X" and "XY" topographies can help to hide the crack growth, thus making cracks undetectable when the SPC-I based monitoring technique is adopted. In addition to the SPC-I technique, we also investigate the effectiveness of an emerging sensing technique based on topological acoustic sensing. This method monitors the changes in the geometric phase; a measure of the changes in the acoustic wave's spatial behavior. The computed results show that changes in the geometric phase can be exploited to monitor the damage growth in plate structures for all three topographies considered here. The significant changes in geometric phase can be related to the crack growth even when these cracks remain hidden for some topographies during the SPC-I based single point inspection. Sensitivities of both the SPC-I and the topological acoustic sensing techniques are also investigated for sensing the topographical changes in the plate structures.

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 modeling with experimental verification investigating the effect of various nonlinearities on the sideband peak count-index technique

A newly developed nonlinear ultrasonic (NLU) technique called sideband band peak count-index (or SPC-I) measures the degree of nonlinearity in materials by counting the sideband peaks above a moving threshold line - larger the SPC-I values, higher is the material nonlinearity. In various published papers, the SPC-I technique has shown its effectiveness in structural health monitoring (SHM) applications. However, the effects of different types of nonlinear phenomenon on the sideband peak generation is yet to be investigated in depth. This work addresses this knowledge gap and investigates the effects of different types of nonlinearity on the SPC-I technique. Three types of nonlinearity (material nonlinearity, structural nonlinearity and contact nonlinearity) are investigated separately through numerical modeling. In this investigation the material nonlinearity and the contact nonlinearity are modeled by finite element method (FEM) using the commercial Abaqus/CAE software. The structural nonlinearity arising from stationary cracks is modeled using nonlocal peridynamics based peri-ultrasound modeling technique. Numerical modeling shows that the sideband peak values do not increase proportional to the input signal strength thus indicating nonlinear response, and different types of nonlinearities affect the SPC-I measurements differently. For the experimental verification a composite plate with impact-induced damage is considered for investigating the material nonlinearity and structural nonlinearity while a linear elastic aluminum plate is used to examine the contact nonlinearity between the transducers and the plate. The trends observed in the experimental observations matched with the numerical model predictions.

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.

Quantitative evaluation of crack based on the sparse decomposition of array Lamb wave propagation

Crack damage is one of the significant factors that may accumulate at the stress concentration area of engineering structures and cause catastrophic accidents. In this paper, we proposed a novel approach to identify the crack location and size by exploiting the reflections and diffractions of Lamb waves. The interaction mechanism between the crack and Lamb wave has been analyzed thoroughly, our analysis of the interaction between the crack and Lamb wave revealed that both reflections and diffractions carry valuable damage information that reflects the size and orientation of the crack. As the interaction coefficients between these two components and the crack are different, there are supposed to exist differences between them in the amplitude value. We implemented a threshold to classify the signals received from all paths into two groups: reflections and diffractions. Then we constructed an overcomplete dictionary of waveforms corresponding to different propagation distances to extract the damage information. Using sparse decomposition, the received signals were mapped to their corresponding propagation distances without the use of baseline signals. The diffractions allow us to determine the crack's tip points, while the reflections provide information about the edge points. The kinked crack's size and orientation were visualized based on the time-domain signals acquired in our experiment. We provided a comprehensive description of our algorithm and verified it through numerical simulation and experimental data. Our results show high agreement with actual cracks, demonstrating the efficacy of our proposed method.

Ordinary state-based peri-ultrasound modeling to study the effects of multiple cracks on the nonlinear response of plate structures

Since it is almost impossible to carry out a comprehensive parametric investigation experimentally for internal cracks with different geometry and orientation, a good numerical modeling and simulation technique is necessary to have a clear understanding of the physics of wave propagation and its interaction with cracks. Such investigation is helpful for structural health monitoring (SHM) with ultrasonic techniques. This work presents a nonlocal peri-ultrasound theory based on ordinary state-based (OSB) peridynamics for modeling elastic wave propagation in three-dimensional (3-D) plate structures containing multiple cracks. A relatively new and promising nonlinear ultrasonic technique called Sideband Peak Count - Index (or SPC-I) is adopted to extract the nonlinearity generated from the interactions between elastic waves and multiple cracks. Effects of three main parameters - the distance between the acoustic source and the crack, the crack spacing and the number of cracks are investigated using the proposed OSB peri-ultrasound theory together with the SPC-I technique. For each of these three parameters investigation, different crack thicknesses were considered - 0 mm (crack-free), 1 mm (thin crack), 2 mm (intermediate thickness) and 4 mm (thick crack); thin and thick cracks are defined after comparing the crack thickness value with the horizon size mentioned in the peri-ultrasound theory. It is found that for obtaining consistent results the acoustic source should be placed at least one wavelength away from the crack and crack spacings also play an important role on the nonlinear response. It is concluded that the nonlinear response diminishes when the cracks become too thick, and thin cracks show higher nonlinearity than that of thick cracks and no cracks. Finally, the proposed method which is combining the peri-ultrasound theory and SPC-I technique is used for monitoring cracks' evolution process. The numerical modeling results are compared with the experimental findings reported in the literature. Consistent qualitative trends in SPC-I variations predicted numerically and obtained experimentally are observed, thus it gives confidence in the proposed method.

Robust and quantitative characterization of aircraft icing with mode and frequency selective ultrasonic guided wave

The aircraft flight safety and efficiency are largely affected by the aircraft icing, whose characterization is of great significance to guiding the de-icing operation. This study targets a robust and quantitative characterization of icing with ultrasonic guided wave (UGW) of selective frequency-mode pair. Firstly, the frequency domain finite element (FDFE) model is developed to quantitatively analyze the reflection, transmission, and mode conversion of UGW with icing aluminum plate of different lengths and thickness, in order to pick the UGW with appropriate frequency-mode pair sensitive to icing. With the candidate UGW frequency-mode pair, the time domain finite element (TDFE) analysis is further performed to validate the effectiveness of FDFE and to optimize the pulse duration cycle for icing detection. Finally, based on the performed FDFE and TDFE analysis, experimental icing characterization is carried out with the UGW of the selected frequency-mode pair. Results show that the selected UGW at (1239 kHz, mode A1) with ice (0.5 mm thick) has achieved a high detection sensitivity based on the time-of-flight and good robustness against the random error, showing the great potential for the application of UGW to aircraft icing characterization.

Sideband peak count-index technique for monitoring multiple cracks in plate structures using ordinary state-based peri-ultrasound theory

This work presents a peri-ultrasound theory based on ordinary state-based peridynamics for modeling elastic waves propagating in three-dimensional (3-D) plate structures and interacting with multiple cracks. A recently developed nonlinear ultrasonic technique called sideband peak count-index (or SPC-I) is adopted for monitoring one or more cracks with thickness values equal to 0 mm (crack-free), 1, 2, and 4 mm. Three separate scenarios-one crack, two cracks, and four cracks in 3-D plate structures-are investigated. These cracks can be classified as thin and thick cracks depending on the horizon size, which is mentioned in peri-ultrasound theory. Computed results for all three cases show larger SPC-I values for thin cracks than for thick cracks and the case of no cracks. This observation is in line with the previously reported results in the literature and proves that the state-based peri-ultrasound theory can capture the expected nonlinear response of elastic waves interacting with multiple cracks without changing the cracks' surface locations artificially, and this is always needed in most of the other numerical methods. The proposed state-based peri-ultrasound theory is more flexible and reliable for solving 3-D problems, and the out-of-plane wave field can be obtained for engineering analysis.

Scattered Ultrasonic Guided Waves Characterized by Wave Damage Interaction Coefficients: Numerical and Experimental Investigations

The present paper comprehensively investigates the complex interaction between ultrasonic guided waves and local structural discontinuities, such as damages, through highly sensitive features: so-called wave damage interaction coefficients (WDICs). These WDICs are unique for each structural discontinuity and depend solely on their characteristics for a given structure and condition. Thus, they can be particularly useful for advanced assessment of lightweight structures in the context of non-destructive evaluation and structural health monitoring. However, the practical application of WDICs entails significant difficulties due to their sensitivity and complex patterns. Therefore, this study attempts to guide researchers and practitioners in the estimation of WDICs from numerical simulations and physical experiments. Detailed investigations are made for an aluminum host plate modified by artificial structural discontinuities, i.e., surface-bonded steel sheets. The numerical simulations are performed to predict WDICs and study sensitivities using a sophisticated finite element model. The experimental setup uses piezoelectric transducers to excite guided waves in the host plate. A single scanning laser Doppler vibrometer measures the scattered guided waves caused by the surface-bonded steel sheets, and the resulting WDICs with possible influences are investigated. In both cases, the orientation and thickness of the attached steel sheets were varied to create 12 different damage scenarios. In general, the comparison between numerical and experimental WDICs show good agreement. This underpins the applicability of the general methodology for simulating and measuring WDICs over all scenarios. Furthermore, the WDIC scattering patterns reveal a clear dependency of the peaks in the back-scattered reflections for both the numerical and experimental amplitude coefficients on the damage orientation, basically following the law of reflection. However, some discrepancies between both studies were observed. Numerical sensitivity analysis identified the adhesive layer as one reason for such differences. Additionally, misalignment errors in the experimental measurements were also found to affect WDICs. Therefore, an improved baseline subtraction method is proposed, which clearly enhances the experimental WDICs. Finally, an experimental sensitivity study of WDICs for selected sensing radii revealed only a minor influence. All these investigations were made for the amplitude as well as the phase representation of WDICs. Thus, these findings may open the way to future research and development of techniques employing WDICs for advanced applications of non-destructive evaluation and structural health monitoring.

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.

Multi-Dimensional Uniform Initialization Gaussian Mixture Model for Spar Crack Quantification under Uncertainty

Guided Wave (GW)-based crack monitoring method as a promising method has been widely studied, as this method is sensitive to small cracks and can cover a wide monitoring range. Online crack quantification is difficult as the initiation and growth of crack are affected by various uncertainties. In addition, crack-sensitive GW features are influenced by time-varying conditions which further increase the difficulty in crack quantification. Considering these uncertainties, the Gaussian mixture model (GMM) is studied to model the probability distribution of GW features. To further improve the accuracy and stability of crack quantification under uncertainties, this paper proposes a multi-dimensional uniform initialization GMM. First, the multi-channel GW features are integrated to increase the accuracy of crack quantification, as GW features from different channels have different sensitivity to cracks. Then, the uniform initialization method is adopted to provide more stable initial parameters in the expectation-maximization algorithm. In addition, the relationship between the probability migration index of GMMs and crack length is calibrated with fatigue tests on prior specimens. Finally, the proposed method is applied for online crack quantification on the notched specimen of an aircraft spar with complex fan-shaped cracks under uncertainty.

Use of Bispectrum Analysis to Inspect the Non-Linear Dynamic Characteristics of Beam-Type Structures Containing a Breathing Crack

A breathing crack is a typical form of structural damage attributed to long-term dynamic loads acting on engineering structures. Traditional linear damage identification methods suffer from the loss of valuable information when structural responses are essentially non-linear. To deal with this issue, bispectrum analysis is employed to study the non-linear dynamic characteristics of a beam structure containing a breathing crack, from the perspective of numerical simulation and experimental validation. A finite element model of a cantilever beam is built with contact elements to simulate a breathing crack. The effects of crack depth and location, excitation frequency and magnitude, and measurement noise on the non-linear behavior of the beam are studied systematically. The result demonstrates that bispectral analysis can effectively identify non-linear damage in different states with strong noise immunity. Compared with existing methods, the bispectral non-linear analysis can efficiently extract non-linear features of a breathing crack, and it can overcome the limitations of existing linear damage detection methods used for non-linear damage detection. This study’s outcome provides a theoretical basis and a paradigm for damage identification in cracked structures.