Nonlinear Ultrasonic Technique Research Articles

Monitoring fatigue cracks in riveted plates using a sideband intensity based nonlinear ultrasonic technique

Aluminum structures are routinely used in aircraft due to their lightweight and corrosion resistance properties. Multi-layered aluminum plates are generally joined by rivets forming regions which are prone to fatigue crack formation in an aircraft. Therefore, the detection and monitoring of fatigue cracks at rivet joints in aluminum structures are crucial for ensuring flight safety. In this study, piezoelectric sensors were utilized to generate and detect Lamb waves on aluminum plates with rivet joints to investigate the feasibility of a newly developed Sideband Peak Count (SPC) technique for detecting fatigue cracks around these joints. To overcome the limitations of existing SPC-I (Sideband Peak Count – Index) and SPI (Sideband Peak Intensity) techniques in capturing harmonic and modulating wave frequencies due to material nonlinearity, a comprehensive index, the Sideband Intensity Index (SII) is introduced. Comparative analysis with existing SPC-I and SPI techniques confirm the effectiveness of the SII technique. This investigation shows that the SII technique significantly improves the detection capability of initial fatigue cracks around rivet joints on aluminum plates. This study offers a more efficient method for detecting critical fatigue cracks in rivet joints.

Peri-ultrasound modeling to investigate the performance of different nonlinear ultrasonic techniques for damage monitoring in plate structures

Abstract Peri-ultrasound modeling which is based on nonlocal peridynamics is found and proven to be effective for modeling nonlinear waves propagating and interacting with damages in structures. This work presents the peri-ultrasound modeling to investigate the performance of three commonly used nonlinear ultrasonic (NLU) techniques – wave mixing, higher harmonic generation (HHG) and sideband peak count-index (or SPC-I) for monitoring damages (or cracks) in three-dimensional (3-D) plate structures. Cracks can be defined as “thin cracks” and “thick cracks” according to the horizon size mentioned in peridynamics. Peri-ultrasound modeling results reveal that the SPC-I results are consistent with other reported numerical modeling and experimental results available in the literature. However, the modulation indicator (MI) from wave mixing model only shows consistent trends for thin cracks but not for thick cracks and its reliability is affected by the initial excitation bandwidth. The relative acoustic nonlinearity factor β from HHG technique shows consistent trends for thick cracks but not for thin cracks. It can be concluded from the obtained parametric analysis results that the SPC-I technique is more robust and reliable for monitoring damages in engineering structures.

Early detection of steel tube welded joint failure using SPC-I nonlinear ultrasonic technique

Early detection of steel tube welded joint failure using SPC-I nonlinear ultrasonic technique

Experimental investigation on monitoring the evolution of fatigue microcracks in marine high-strength steel by nonlinear ultrasonic technique

ABSTRACT Due to harsh service conditions, fatigue damage is the main reason for numerous catastrophic accidents of ships and offshore constructions. This paper uses a nonlinear ultrasonic technique to monitor the evolution of fatigue microcracks in marine steel AH36. An experimental system was established and nonlinear ultrasonic inspections were conducted on the specimens with different fatigue degrees. The microstructural changes induced by fatigue loading were also studied by microscopic observation. The experimental results demonstrate that the normalised nonlinear parameters show a closed relation to the evolution of fatigue microcracks in steel AH36. Meanwhile, microscopic observation indicates that the microcrack generation mode and grain boundary cracking are the two mechanisms for microcrack generation. Both the generation and growth of the microcracks contribute to the rise of the nonlinear effect. Consequently, the nonlinear ultrasonic techniques provide a reliable and effective method for monitoring the evolution of fatigue microcracks in marine high-strength steel.

Characterization on vermicular graphite rate and tensile strength in vermicular graphite cast iron based on nonlinear ultrasonic technique

Ultrasonic techniques have been widely used to detect the percentage of vermicular graphite, defects, etc. in vermicular graphite cast iron. The linear ultrasonic velocity method is the main ultrasonic method for characterizing vermicular graphite rate and tensile strength in the current study, however, it is often easy to misjudge the vermicular graphite rate due to its insignificant variation. This study explores the feasibility of using the nonlinear ultrasonic technique (NUT) to characterize the vermicular graphite rate and tensile strength. Based on the longitudinal critically refracted (LCR) wave detection model, an experimental study to detect the vermicular graphite rate and tensile strength of vermicular graphite cast iron is carried out using the nonlinear ultrasonic harmonic method, and compared with the ultrasonic velocity method. The experiment results show that the relative nonlinear parameter of the LCR wave decreases along with the increase of vermicular graphite rate and increases along with the increase of tensile strength, and it has higher detection sensitivity and resolution than ultrasonic velocity by analyzing the obtained data. The increase in the acoustic nonlinearity parameter (ANP) is related to the increase in the number of grain boundaries in the microstructure. Therefore, the relationship among microstructure, ANP, and mechanical properties of vermicular graphite cast iron can be established, and it’s promising that a new approach might be developed for quickly detecting the vermicular graphite rate and corresponding tensile strength with the NUT.

Far-end delamination characterization of CFRP laminates using nonlinear ultrasonic spectra of scaling subtracted vibration response

The application of nonlinear ultrasonic techniques for the near-end damage characterization of carbon fiber reinforced polymers (CFRP) has proven to be successful and extensive. However, the nonlinear ultrasonic response is weak and may be overwhelmed by the linear component of signals if the damage is located at the far-end. In this paper, the scaling subtraction method (SSM) is adopted to filter out the nonlinear ultrasonic signature aimed at the better characterization of far-end delaminations in CFRP laminates. A three-dimensional finite element model is constructed first to validate the feasibility of separation effect of SSM. Then the experimental study is conducted for a delaminated CFRP plate using laser scanning Doppler vibrometer (LSDV) response measurements. Results show that the far-end delamination can be detected and localized clearly since the nonlinear features can be accurately separated from the surface vibration response by using SSM. Moreover, the far-end delamination size is qualitatively analyzed by using the maximum response amplitude (MRA) of the higher harmonics of SSM signals, and a positively correlated trend is shown as the delamination size increases. This work demonstrates the applicability and potential of SSM technique for the comparative assessment of far-end defect information in composites.

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.

Numerical model of nonlinear elastic bulk wave propagation in solids for non-destructive evaluation

Nonlinear ultrasonic techniques can be difficult and non-intuitive to understand due to the range of wave mixing combinations available between similar or different wave modes. To overcome this, a numerical model that uses a Finite Difference Time Domain (FDTD) scheme, without a staggered grid system, to solve the nonlinear elastic bulk wave equations in two dimensions is proposed in this paper, with the purpose of better understanding nonlinear ultrasonic techniques. Both material and geometrical nonlinearities are considered and a stress-type boundary condition is used to model the excitation. The energy transfer between frequency bands is shown and the amplitude trend of the harmonics are validated against available theories. It is then used to simulate the nonlinear ultrasonic field generated by a finite-size element of an array in a solid to better understand its behaviour. An array-element directivity at the second harmonic frequency is shown. Since the FDTD model does not account for attenuation, a correction using a ray-based approach is applied to the simulated result for direct comparison against experimental measurements. The field obtained from a typical array used in non-destructive testing is then simulated to characterise its behaviour. Experimental comparison of the nonlinear displacement fields for different focal positions showed good agreement, further validating the FDTD model. This FDTD model opens opportunities to virtually experiment and design appropriate nonlinear ultrasonic array inspections whilst isolating and understanding contribution from material nonlinearity.

Non-destructive evaluation of corrosion in steel liner plates embedded in concrete using nonlinear ultrasonics

Nuclear containment structures employ a leak-tight steel liner to avoid any unwanted particle release into the exterior environment. The steel liner can be embedded in concrete which creates large continuous areas where the steel plate is in direct contact with surrounding concrete. The impact of the aging of concrete structures due to the presence of structural discontinuities, such as the presence of foreign matter and a delamination gap at the embedded steel–concrete interface, is investigated for small laboratory-scale specimens manufactured with a novel inlay technique by nonlinear ultrasonic evaluation. A Total Damage Index (TDI) which combines several parameters related to acoustic wave distortion into a single damage index to rank the specimens is introduced. The findings in this work indicate that severe corrosion, the presence of foreign matter, and delamination gap in the steel–concrete interface can be detected using nonlinear ultrasonic techniques based on higher-harmonic analysis and modulation intensity using continuous ultrasonic probe excitation and an impactor to modulate the signal. The results obtained using the TDI are consistent with attenuation, a conventional parameter used in corrosion detection.

Nonlinear ultrasonic techniques to quantify oxidation damage in carbon/carbon composite material

This research applies linear and nonlinear ultrasonic (NLU) techniques to quantify oxidation damage in a carbon/carbon (C/C) composite material cut from an automotive friction disc ring. The oxidation as a result of gasification of carbon at high temperatures (T >∼ 500 °C) is a major degradation mechanism in C/C composites. This is the first research to successfully use a dry-contact mediator wedge setup for nonlinear ultrasonic applications, enabling repeatable in-situ Rayleigh wave measurements on slow wave velocity materials where submersion is impractical. The samples are subjected to thermal damage by exposure to a high temperature atmosphere over multiple holding times, and the oxidation damage is visualized using scanning electron microscopy (SEM). The sample mass is recorded and both linear (velocity and attenuation) and nonlinear (β′) ultrasonic measurements are performed after each holding time. Superior sensitivity to early stage oxidation affirms the suitability of nonlinear Rayleigh wave measurements for the quantification of thermally induced oxidation damage in C/C composites, while the double mediator wedge setup is well suited for high attenuation, slow wave velocity materials, demonstrating potential applicability for in-situ condition monitoring. The results show that a systematic oxidation starts after 3 min of exposure to the temperature in this C/C composite. The oxidation induced fiber–matrix debonding, matrix defects (appearing to be microcracking), and void growth are consistently detected by the Rayleigh wave velocity and acoustic nonlinearity. In addition to the higher sensitivity, the nonlinearity parameter has the capability of selectively measuring the strength related damage such as the observed fiber–matrix debonding, while the wave velocity can detect the oxidation voids. A combined use of these two parameters can provide useful information on the microstructural evolution in C/C composites subjected to high temperatures.

Bolt Axial Stress Detection and Prediction Based on the Nonlinear Ultrasonic Technique

Bolt Axial Stress Detection and Prediction Based on the Nonlinear Ultrasonic Technique

In-situ nonlinear ultrasonic technique for monitoring damage in ultra-high performance fibre reinforced concrete (UHPFRC) during direct tensile test

This paper aims to employ the nonlinear ultrasonic technique for the in-situ monitoring of Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) structures subject to tensile loads. The UHFPRC, characterized by specific mechanical properties of high compressive and tensile strength, provides the basis for this investigation. Particularly, the nonlinear parameter β of the nonlinear ultrasonic technique is extracted by formulating a theoretical model that accounts for the interaction of contacting rough surfaces under tensile loads. The experimental findings substantiate that β provides enhanced sensitivity and feasibility for evaluating crack conditions compared to the measurements obtained through conventional Linear Variable Differential Transformers (LVDT). Furthermore, this study explores the potential application of β to estimate tensile load condition by: i) establishing an estimation equation grounded in the relationship between tensile load and displacement (kN-mm); ii) incorporating β into this estimation equation to calculate the anticipated tensile load; and iii) comparing real and estimated tensile loads. The analysis outcomes reveal that estimated tensile loads are in good agreement with the actual loads. Although the estimation equation is based on the findings of this study, it underscores the potential applicability of β for estimating the load conditions in various structures.

Evaluation of high-temperature degradation of platen superheater tube in thermoelectric power plant using nonlinear surface ultrasonic waves

The operating conditions of Korean standard coal-fired thermal power plants involve high temperatures, with steam reaching approximately 540 °C. To support the life management of platen superheater (PSH) tubes, which operate under the highest temperature and pressure conditions among boiler tubes, various methods have been used. These methods include visual inspection, thickness measurement, and hardness measurement, which are typically used to conduct lifespan diagnosis on facilities that have been operating for more than 100,000 h or 20 y. This study examined the applicability of a nonlinear ultrasonic technique to evaluate the degradation damage of a PSH tube composed of X20CrMoV12.1 steel in a thermal power plant. The specimens of a PSH tube made of X20CrMoV12.1 steel that has been operating for approximately 20 y (160,000 h) in a Korean standard thermal power plant was obtained from three points, and the nonlinear surface ultrasonic wave was measured. Then, the results of the nonlinear ultrasound, microstructure analysis, and tensile test were compared. Based on where the boiler tube specimen was located, a strong correlation was observed between the ultrasonic nonlinearity parameter and changes in the tensile and yield strengths. These results confirm that the nonlinear ultrasonic method can be used to evaluate the changes in the mechanical properties affected by boiler tube degradation.

A study on the wave propagation on weld joints by the use of feature-guided wave mixing

The concentration of the wave energy around certain features such as bends, stiffeners, and welds in plate-like structures has been identified as feature-guided waves (FGW). In practice, these features can be useful for assessing defects in or near them. The propagation characteristics of FGW propagating along a feature such as a welded joint have been extensively studied. However, most of them are based on the linear acoustic response of materials that generally results in the amplitude and phase variations of the input signal. Compared to linear methods, nonlinear ultrasonic techniques have shown to be effective in characterizing the microstructural changes in engineering materials. In this paper, a wave mixing method is employed to investigate the nonlinear acoustic response of FGWs propagating in a welded joint. The dispersion characteristics of weldguided modes are first revealed via the eigenfrequency analysis of an unbounded welded plate by using the finite element method. The nonlinear response of FWGs is studied through 3D finite element (FE) simulations. A pair of a weld-guided modes of different frequencies are identified and allowed to mix within the welded joint to generate second-order harmonic waves. The current study reveals that the mixing of FGWs could be effectively used for the evaluation of material nonlinearity in welded joints.

Ordinary state-based peri‑ultrasound modeling for monitoring crack propagation in plate structures using sideband peak count-index technique

This work presents a nonlocal theory based on ordinary state-based (OSB) peridynamics for numerical modeling of crack propagation under loadings and peri‑ultrasound modeling for elastic wave propagation that interacts with generated cracks in 3-D plate structures. Propagating cracks in plate structures for two types of loading – tensile and shear are considered. For both loading cases, at six different times after the start of the loading the analysis is carried out to investigate how the results vary for these six different stages of crack propagation. An ultrasonic excitation is applied at a point on the surface of the plate to generate guided waves propagating through the plate structure and interacting with generated cracks at different stages of crack formation. The out-of-plane velocity fields are recorded at the receiving material point for further analysis. A relatively new and promising nonlinear ultrasonic (NLU) technique called sideband peak count-index (or SPC-I) is adopted to extract the nonlinear response due to the generated cracks. Results show that when the crack propagation is at its early stage the SPC-I value first increases, and then decreases with time at the advanced stages of crack propagation. This is because for both types of loading (tensile or shear) the newly generated cracks are small cracks (or micro-cracks) in the beginning and then they evolve into macro-cracks under increasing loadings. The observation for SPC-I trends is consistent with other numerical modelings and experimental observations reported in the literature, and such qualitative matching gives confidence in the proposed method. The proposed method combining the peri‑ultrasound modeling and SPC-I technique presented in this paper can provide a new insight for monitoring crack propagation and give some guidance for experimental structural health monitoring (SHM) applications.

The Variation of Precipitated Phase Investigated with the Usage of Nonlinear Ultrasonic Technique

The Variation of Precipitated Phase Investigated with the Usage of Nonlinear Ultrasonic Technique

Monitoring Elastoplastic Deformation in Ductile Metallic Materials Using Sideband Peak Count-Index Technique

Abstract Ductile metallic materials such as aluminum alloy, brass, and steel are widely used in engineering structures. Monitoring elastoplastic deformation in these materials is important for structural health monitoring (SHM) to ensure the safety of structures made of metallic materials. This article presents a newly developed and promising nonlinear ultrasonic (NLU) technique called sideband peak count-index (or SPC-I) for monitoring the early stages of elastoplastic deformation in ductile metallic alloy Al6061. Experimental results presented in this article show that the elastic range of the Al6061 SPC-I values shows slight changes due to the inherent inhomogeneities (imperfect grain boundaries or dislocations at the grain boundaries under loadings) of Al6061. Then the SPC-I value changes rapidly as the material enters the plastic range zone. Compared to the linear ultrasonic (LU) parameters (wave velocity and attenuation changes), the SPC-I shows a noticeable advantage (higher sensitivity) for monitoring the early stages of the elastoplastic deformation in these ductile metallic specimens investigated in this study. It is concluded that the SPC-I technique is useful for monitoring deformations in ductile metallic materials, especially in their plastic zone. This work extends the applicability of the SPC-I technique for monitoring elastoplastic deformations in metallic specimens that have not been reported in earlier works and can provide some guidelines for SHM related to elastoplastic deformation in metallic structures.

Monitoring prestress in plates by sideband peak count-index (SPC-I) and nonlinear higher harmonics techniques

Propagating guided waves in a homogeneous, isotropic, prestressed, hyperelastic plate show nonlinear characteristics that depend on the state of initial prestress. These nonlinear phenomena include higher harmonic generation, occurring when Lamb wave modes of different frequencies (omega _a and omega _b) are allowed to mix within the material generating secondary waves at frequencies 2omega _a,2omega _b, text {and},omega _apm omega _b. Further, if prescribed internal-resonance conditions are satisfied, the amplitude of secondary waves increases in space, providing a response quantity which is dependent on prestress and easy to be observed. Using the finite element method, in this paper we investigate the time and space evolution of higher harmonics arising in one-way wave mixing. The influence of prestress on the response is elucidated, observing the nonlinear parameter beta . It is further shown that the nonlinear ultrasonic technique called sideband peak count-index (SPC-I) can provide an effective monitoring tool for prestress.

Fatigue damage quantitative evaluation of carbon fiber composites at different stress ratios based on nonlinear ultrasonic

In order to investigate the fatigue behavior of carbon fiber composites and the influence of different stress levels on their fatigue damage characteristics, the fatigue experiments of carbon fiber composites under different stress ratios are carried out. The nonlinear ultrasonic technique is used to online detect the fatigue damage process of carbon fiber composites, the relative nonlinear coefficient β under different stress ratios and different measuring positions is analyzed with the fatigue loading period. The experimental results indicate the relative nonlinear coefficient increases significantly and the rising trend accelerates when the fatigue life of specimen reaches 50%, it is the most sensitive to the change of material microstructure by comparing other parameters and can be used as the characteristic parameter to evaluate the fatigue damage of materials. In addition, the fatigue damage factor D is proposed by analyzing the relationship between the relative nonlinear coefficient and the damage degree of materials, the nonlinear ultrasonic quantitative analysis is carried out and the fatigue damage prediction model based on the relative nonlinear coefficient is established to characterize the severity of fatigue damage of materials. Therefore, the nonlinear ultrasonic quantitative evaluation method for carbon fiber composites is established, it provides a new method and data support for quantitative evaluation of fatigue damage degree of materials by nonlinear ultrasonic method.

Monitoring of crack healing in geopolymer concrete using a nonlinear ultrasound approach in phase-space domain

Ultrasonic testing is a robust non-destructive evaluation method frequently employed in the health monitoring of concrete structures. Cracking in concrete can be one of the most critical problems, and its healing is important for structural safety. The current study proposes the evaluation of crack healing in geopolymer concrete (GPC) using different linear and nonlinear ultrasonic techniques. In this regard, a notched GPC beam was constructed at the laboratory and geopolymer grout was applied as a repair material. Ultrasonic pulse velocity (UPV) and signal waveform tests were performed at several stages before and after grouting the notch. Nonlinear wave signals were processed in the phase-space domain for qualitative health monitoring of GPC. Furthermore, feature extraction was applied to phase-plane attractors using fractal dimension for quantitative assessment. The sideband peak count-index (SPC-I) method was also utilized to assess the ultrasound waves. The results indicate that the phase-space analysis of ultrasound can successfully represent the healing progress inside the GPC beam. At the same time, the fractal dimension can be used as a healing index. Ultrasound signal attenuation demonstrated high sensitivity to crack healing. The SPC-I technique exhibited an inconsistent trend at the early stage of healing. However, it provided a clear indication of repair at the advanced stage. Although the linear UPV method was found sensitive to the grouting at the initial stages, it demonstrated insufficient capability to monitor the healing process fully. Therefore, the phase-space-based ultrasonic method and the attenuation parameter could be employed as reliable techniques for the robust monitoring of progressive healing in concrete.