Nonlinear Ultrasonic Method Research Articles

Decoding nonlinear ultrasonic time-frequency characteristics for fatigue crack quantification and localisation via CNN

ABSTRACT Early detection of fatigue cracks is crucial to guarantee the safe operation of engineering structures. Nonlinear ultrasonic technique (NUT) is widely used for closed crack characterisation as it breaks through the detection sensitivity limit upon closed defects that are usually invisible to linear ultrasonic techniques. The nonlinearity parameter is generally defined as the damage index (DI) to qualitatively detect these cracks. However, DI-based methods are underdetermined for quantifying and localising cracks in most circumstances. In this study, a deep learning method for intelligently decoding nonlinear ultrasonic time-frequency characteristics is developed to quantify and localise fatigue cracks. The nonlinear ultrasonic time-frequency spectrogram, which includes features characterising crack severity and location, is obtained by cleverly selecting the excitation frequency. The convolutional neural networks (CNNs) establish a mapping relationship between the nonlinear ultrasonic time-frequency characteristics and the crack length and location. It is worth mentioning that frequency-dependent convolutional kernels are proposed to more competitively decode nonlinear ultrasonic time-frequency characteristics. The results indicate that the CNNs with the frequency-correlation kernels are particularly robust and effective in both noiseless and noisy environments. The study demonstrated the potential of the proposed nonlinear ultrasonic time-frequency characteristic decoding method for accurate and efficient characterisation of damage.

Closed cracks characterization in a steel sample applying a pump probe waves ultrasonic method

Abstract Ultrasonic measurements are commonly used for crack sizing in industrial context, but due to potential partial crack closure, the crack depth can be underestimated. It could be of importance regarding the prediction of remaining service life and maintenance scheduling of industrial components. In the literature, nonlinear ultrasonic methods have proven efficient for this issue. Among them, a pump probe waves method is investigated here for possible use in an industrial context. In this paper, an industrial steel component with several partially closed fatigue cracks is studied. First, a three-point bending test associated with digital image correlation is performed with ultrasonic measurements to obtain reliable indications about the cracks closure state. A three-dimensional laser vibrometry experiment shows the possibility to open the crack using a pump wave. The pump probe waves method is conducted using a standard 45° shear wave transducer in echo mode as a probe. The results allow to discuss physical mechanism in play. It is also shown the possibility to detect the closed nature for all of the cracks even if the full opening state is not reached. Moreover, a coherent crack profile is found compared to mechanical test. The results are validated on a notched sample for which the nonlinear response is negligible. Industrial application as well as possible improvement are discussed.

Characterisation of coherent ultrasonic nonlinear imaging

Nonlinear ultrasonic imaging methods for non-destructive testing have shown sensitivity to early damage formation. Among those, the Fundamental wave Amplitude Difference (FAD) technique has been proposed in the literature as a nonlinearity mapping method for defect visualisation. It does so by calculating the residual between a low and high nonlinearity image, which is achieved by some modulation of the focal spot amplitude. This is realised either through different input voltages or alternating the element-wise firing scheme. This paper assesses the sensitivity of FAD through different techniques used for the generation of the low nonlinearity images, using both theoretical and experimental approaches. These techniques include (1) Different-Voltage FAD (DV-FAD); (2) Odd-Even FAD (OE-FAD) and; (3) Parallel–Sequential FAD (PS-FAD). Formulae are derived that allow the different firing sequences and image corrections to be compared. The FAD techniques are then experimentally evaluated against the theory, showing a 50% amplitude gain at the crack tip when comparing PS-FAD to OE-FAD and DV-FAD. Additionally, the instrument behaviour is assessed by considering the image correction required to improve the image contrast for the visualisation of the crack tip. Finally, it is shown that all FAD techniques are equivalent in terms of nonlinear detection but additional work is required in comparing the performance of other array controllers when using FAD.

Nonlinear Ultrasonic C-Scan Imaging for Contact-Type Defects in Diffusion-Bonded Joints-A Case Study.

Diffusion bonding technology is widely used in the connection of precision components, yet accurately and reliably detecting contact-type defects on the bond interface still remains a significant problem. Nonlinear ultrasonic methods have been proven to be sensitive to contact-type defects; however, the use of continuous wave or tone burst wave excitation limits its wider application. In this paper, dual-probe nonlinear ultrasonic testing with pulse wave excitation is proposed to detect contact-type defects in diffusion-bonded joints. A titanium alloy diffusion-bonded specimen with artificial defects was fabricated, and the corresponding detection device was designed based on the existing ultrasonic C-scan testing system. A C-scan imaging program based on nonlinear parameters was developed by extracting the fundamental and second harmonic waves of the reflection echo on the bond interface. The results demonstrated that the proposed detection scheme can obtain the nonlinear parameters of diffusion-bonded interfaces, and the nonlinear ultrasonic C-scan image of the bond interface is also obtained. The nonlinear parameter in the contact-type defects areas calculated from the bond interface echo is about 10 times (20 dB) higher than that in macro defects areas, whose gap is about 10 μm. The results indicate that the nonlinear ultrasonic methods seem to be more sensitive to contact-type defects and have a great potential to complement the insufficient detection capability of linear ultrasound for diffusion-bonded joints.

Research on nonlinear ultrasonic method for evaluating the mechanical properties of 3D printing aluminum alloy

Micro defects, such as pore and inclusions, inevitably appear in the forming process of three-dimensional (3D) printed materials, which would affect the mechanical properties of materials. Therefore, a nondestructive testing method is urgently needed to evaluate the effect of these micro defects on the mechanical properties of materials. In the present work, by using a nonlinear ultrasonic testing technology, mechanical test and characterization of material microstructure, the relationship between the relative acoustic nonlinearity parameter (RANP), tensile strength and material defect ratio of 3D printed aluminum alloy specimens under different scanning powers is investigated. The analysis results show that the greater the material defect ratio is, the smaller the tensile strength is and the greater the RANP is, and the RANP could be used to evaluate the strength of materials. Moreover, fatigue damage induced by high cycle fatigue loading test in the first stage of early performance degradation, the results of nonlinear ultrasonic testing show that the RANP presents an increasing trend as the fatigue load increases. By observing changes in material microstructure, it is found that the increasing acoustic nonlinearity parameter is due to the directional coarsening degree of the precipitated phase increasing, which shows that RANP is very sensitive to the change of material microstructure. The above results show that, the nonlinear ultrasonic testing technology can quantitatively evaluate and predict the mechanical performance and early performance degradation of 3D printing aluminum alloy.

Second harmonic generation for estimating state of charge of lithium-ion batteries

This study applied the nonlinear ultrasonic method, second harmonic generation, to precisely estimate the state of charge (SoC) in lithium-ion batteries. The second harmonic of the longitudinal wave is generated on a pouch cell battery at 5 MHz with a through-transmission setup. The relative nonlinear parameter β′ is determined by analyzing the amplitudes at the fundamental and second harmonic frequencies. To enhance the nonlinear parameter's measurement accuracy, multiple excitation amplitudes are employed. Two separate charge/discharge tests (four-cycle and eight-cycle) are conducted on the battery at a rate of C/10. The nonlinear parameter is measured periodically during the charge/discharge process, and temperature compensation is applied to the measurement. The correlation curves between the nonlinear parameter and the actual SoC align well for the four-cycle and eight-cycle tests, and a robust linear relationship is observed for both correlation curves. A linear model and a second-order polynomial model are applied to fit the correlation using all data points from both tests. The two models are employed to validate the SoC prediction on a second battery by using a four-cycle test. The results indicate that both models can predict the SoC with an accuracy of approximately 3%, whereas the polynomial model demonstrates smaller errors in the regions near 0% and 100% SoC. Therefore, the nonlinear parameter β′, measured through the second harmonic generation, can effectively predict lithium-ion battery SoC with an accuracy of less than 3%.

A nonlinear ultrasonic nondestructive testing method for microdefects of medical magnesium alloy coatings

ABSTRACT The microdefects of polylactic acid coating on medical magnesium alloy significantly reduce the corrosion resistance of magnesium alloy components, which is difficult to detect by conventional non-destructive testing methods. To address this issue, a nonlinear ultrasonic detection technique is proposed to detect polylactic acid coated specimens with different microdefects. Through electrochemical corrosion tests and nonlinear ultrasonic tests, it has been observed that the ultrasonic nonlinear coefficient β increases with the decrease of corrosion resistance. Furthermore, the microscopic test results show that the bubble microdefects caused by the uneven solidification of polylactic acid coating are the main source of ultrasonic nonlinearity. With the increase of microdefects, the β value of the specimen will increase. The correlation analysis reveals a strong relationship between β and parameters related to coating uniform coverage and electrochemical corrosion resistance, and the lowest correlation coefficient is 0.78. Therefore, using nonlinear ultrasonic non-destructive testing technology can effectively detect the microdefects of polylactic acid coating on magnesium alloys, and it also has a certain guiding role in the biological application of magnesium alloys.

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.

Determination of the softening point and temperature interval of asphalt mixture for the healing process based on the contactless nonlinear ultrasonic method

The softening point and gradient healing have significant engineering significance for the self-healing of asphalt mixtures. This study introduces a novel approach utilizing a contactless ultrasonic system in conjunction with the Second Harmonic Generation (SHG) technique to determine the softening point and monitor the gradient healing process of asphalt mixtures. Three distinct fracture patterns resulting from temperature variations are accurately characterized through simulation using the Discrete Element Method (DEM). The ultrasonic nonlinear parameter β, reflecting different crack interfaces, proves to be a highly effective alternative for characterizing asphalt fractures, outperforming traditional methods such as bearing force and wave velocity. In experimental analysis, variations in the healing index highlight the significant influence of asphalt mixture fracture patterns on healing efficiency. The observed decrease in ultrasound amplitude signifies the transition of the asphalt binder from a solid to a liquefied state, accompanied by an increase in the nonlinear parameter indicating enhanced plasticity. The softening point is precisely determined when the Rayleigh surface wave disappears. The cumulative healing process is visualized through the continuous decrease in the nonlinear parameter. To further enhance the understanding of the asphalt self-healing process, the internal temperature gradient field is characterized using the proposed energy difference method. A correlation between the nonlinear parameter and the depth of the temperature interval is established, providing a non-destructive method for evaluating the distribution of the temperature interval. This innovative approach significantly accelerates the development of non-destructive testing in the field of asphalt self-healing.

Quantification of tiny damage variation in asphalt mixture during the low-temperature thermal cycle

The performance evaluation of asphalt materials during low-temperature thermal cycles remains a challenge, particularly in quantifying the early tiny damage development and recovery processes. To address this issue, a high-sensitivity nonlinear ultrasonic method - the second harmonic generation (SHG) technique in the form of Rayleigh surface waves, is proposed to investigate these behaviors in asphalt mixture. The decrease in thermal contraction value and stiffness modulus with cycles verifies the damage behavior at the macro level. Turning points in crack length, crack density, and nonlinear parameter during the thermal cycle indicate the generation of cracks from − 20 ℃ to − 30 ℃ during the cooling process. The decrease of crack length and crack density in the heating phase demonstrates the recovery of asphalt. The nonlinear ultrasonic parameter β'(c) caused by crack is successfully separated from the total nonlinear parameter β', and the recovery index (RI)is defined to quantify the recovery behavior. Both of them are highly consistent with crack length and crack density. While the sensitivity index (SI) of nonlinear parameter is hundreds or thousands of times greater than other measurements of damage development. Furthermore, a qualitative correlation between the nonlinear parameters and plastic strain has been established. This breakthrough widens the scope of studying low-temperature weak damage in asphalt mixtures, moving beyond the confines of crack analysis.

Tube-to-tube impact wear damage mechanism and nonlinear ultrasonic detection method of alloy 690 tubes

Tube-to-tube impact wear is one of the prime reasons that cause the failure of alloy 690 tubes in nuclear steam generators. Therefore, it is of great importance to study the tube-to-tube impact wear damage mechanism and damage detection method of alloy 690 tubes. In this paper, the tube-to-tube impact wear experiments are conducted on alloy 690 tubes under different impact loads and cycle numbers. The impact wear damage mechanism of alloy 690 tubes is revealed by analyzing the macro and micro morphologies as well as metallographic structures of the wear scar. A nonlinear ultrasonic wave mixing (NUWM) method is proposed for damage detection of alloy 690 tubes. A detection device is developed to implement the NUWM method. A nonlinear modulation index is used to assess the damage degree of alloy 690 tubes. Experimental results indicate that, for an impact load lower than 100 N and a cycle number smaller than 2 × 105, the tube damage is mainly in forms of the surface plastic deformation and delamination. For a higher impact load or a larger cycle number, the fatigue cracking is the main tube damage mode. With increasing the impact load or cycle number, the tube damage degree increases, leading to an increase of the nonlinear modulation index. Therefore, the NUWM method is effective for detecting and assessing the damage of alloy 690 tubes.

Depth profiling of residual stress distribution in surface treated metallic structures using nonlinear ultrasonics

Robotic hammer peening (RHP) is a cold-working technique to improve the fatigue life of metallic structures by inducing compressive residual stress in the near-surface region. Measuring the depth profiling of residual stress distribution plays an important role in process design towards the advanced manufacturing of metallic structures. This study investigates the use of the nonlinear ultrasonic method to measure the residual stress profiles through the frequency-dependent penetration depth approach. Stainless steel specimens were treated with varying RHP intensities, and their morphological evolutions were characterized with a step-profilometer. The amplitudes of the second and third harmonic components of the longitudinal critically refracted (LCR) and Rayleigh waves were measured and analyzed. The effect of the surface roughness on the acoustic nonlinearity parameters before and after polishing at various peening intensities was briefly discussed. The results show a large variation in the acoustic nonlinearity parameter at the surface layer, indicating the potential of the proposed nonlinear ultrasonics for the measurement of depth profiling of residual stress.

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.

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.

Motion magnification-based nonlinear ultrasonic signal enhancement and its application to remaining fatigue life estimation of a steel padeye

In this study, a nonlinear ultrasonic signal enhancement method based on phase-based motion magnification was proposed. First, a two-dimensional (2D) video was constructed from a one-dimensional time-domain ultrasonic signal with an automatically selected pixel scale. The constructed 2D video was spatially decomposed into multiple sub-bands with different spatial scales. The subtle motions of the nonlinear responses of interest were enhanced by phase denoising and magnification in each sub-band. Then, the magnified 2D video was reconstructed by collapsing all the amplified sub-bands. Finally, a magnified ultrasonic signal was extracted from the magnified 2D video for further nonlinear ultrasonic analysis. The proposed method was validated with a group of synthetic signals at different noise levels, and applied in the estimation of the remaining fatigue life of a steel padeye with improved accuracy.

Synthetic generation of vibroacoustic modulation signals for structural health monitoring

The vibroacoustic modulation (VAM) is a nonlinear ultrasonic testing method that utilizes the modulation of a high-frequency/low-amplitude probe wave with a low-frequency/high-amplitude pumping vibration, resulting in high sensitivities to damages in the structure. However, applying the method outside of the laboratory as a structural health monitoring system for actual structures is challenging, since the amplitude and frequency of the ambient vibrations – which is ideally utilized as pumping vibration – fluctuates over time. To circumvent this, we present a synthetic generation of the VAM signal using only the probe measurements , acquired at two (or more) stress levels of the structure when a steady state is reached. We could show that only 16 values (8 measured values of only two stress levels with a sampling frequency of 1/20 of the Nyquist frequency) are required to generate the often calculated Modulation Index with a mean deviation of 0.97% to the expected dynamic measured values for glass fiber reinforced composites and 1.86% for the aluminum specimens, which is negligible compared to a typical increase of the Modulation Index of 10–30 dB in case of severe damage. Even undersampled measurements at each stress level can be used without sacrificing accuracy, which reduces the sensing requirements for the sensor nodes. Moreover, this method decouples VAM from the actual need for a constant recurrent frequency and amplitude of the natural vibration in order to reliably compare measurements throughout the lifetime. Hence, this work aims to open the possibility of ultimately applying VAM to assess the structural health of complex structures.

Non-linear ultrasonic testing of the long-period stacking ordered phase volume fraction in magnesium alloys

The content of the long-period stacking ordered (LPSO) structure strengthening phase has an important influence on the tensile strength, compressive strength, ductility and other mechanical properties of magnesium (Mg) alloys. Therefore, effective detection of the volume fraction of the LPSO phase plays an important role in understanding the properties of the alloy. Focused on the problem that the accuracy of the non-destructive testing method for the LPSO phase precipitates with micron or nanometer scale is not sufficient, this paper studies the non-linear ultrasonic testing of the Mg alloy LPSO phase volume fraction. Based on the non-linear ultrasonic testing theory, the non-linear ultrasonic simulation of the simulation models with different LPSO phase contents was carried out using finite element simulation. The relationship between the volume fraction of the LPSO phase and the non-linear coefficient of ultrasonic simulation was studied and a non-linear ultrasonic testing system was established to test the Mg alloy specimens with different LPSO phase volume fractions. The results show that the non-linear ultrasonic testing method is sensitive to changes in the LPSO phase volume fraction. Thus, this method is an effective way to detect the LPSO phase volume fraction.

Detection of interface flaws in Concrete-FRP composite structures using linear and nonlinear ultrasonics based techniques

Timely and appropriate retrofitting of existing structures holds paramount importance to ensure the structural integrity and sustainability. Fiber Reinforced Polymer (FRP) composites with high corrosion resistance, strength and durability, have been increasingly used in recent years for retrofitting of concrete infrastructure. The effectiveness of retrofitting is primarily dependent on the appropriate integrity at the interface between FRP and concrete substrate. Presence of any interface flaw can jeopardize the structural performance. In the present study, investigations are carried out to detect the early stage flaws at the FRP-concrete interface using ultrasonic waves. Artificial flaws of different size are introduced in the adhesive (epoxy) layer of carbon based FRP composite concrete beam. Rayleigh waves (at different frequencies) are generated for measuring the response from different FRP composite-concrete specimens. The specimens consist of three different types of materials, namely, concrete, epoxy and FRP. Two different input excitation frequencies, i.e., 75 KHz and 250 KHz, are tried out during the experimental investigations. The output signals are processed using different linear and nonlinear ultrasonic methods. Numerical simulations are also performed to better understand the wave signals’ interactions with the multi-layer composite medium. The results showed that the linear ultrasonic methods are not able to provide a consistent information on presence and extent of flaws. Nonlinear ultrasonic methods showed significantly better performance for characterizing both small and large flaws considered in this investigation. Sensitivity analysis reveals that relatively new and promising nonlinear ultrasonic technique, namely, the Sideband Peak Count-Index (SPC-I) performs remarkably well for detection of flaws in FRP-concrete interface.

Nickel-Based Superalloy Inconel 718, Relation between Non-Linear Ultrasonic and Microstructure Changes under the Creep Damages.

Nickel-based superalloy, Inconel 718, has high temperature strength effected by γ"(Ni3Nb) phase at approximately 973 K. It has been found that the creep damage of Inconel 718 was induced by γ"phase disappearance. In the study, we applied the nonlinear ultrasonic method, nonlinear three-wave interaction, for evaluation of the creep damages and the microstructural degradation in γ" phase for Inconel 718 at 973 K, 310MPa. In the nonlinear three-wave interaction method, two intersecting ultrasonic waves produced a scattered wave when the resonance condition was satisfied. The amplitude in resonant scattering wave was measured. We analyzed the relation between the microstructural change and nonlinear acoustic characterizations by the electromagnetic acoustic resonance (EMAR) throughout the creep life, and the nonlinearity corresponded to change of the dislocation density. This was supported with X-ray diffraction, EBSD and SEM observation.

In situ nonlinear Rayleigh wave technique to characterize the tensile plastic deformation of stainless steel 316L

The acoustic nonlinearity parameter β is sensitive to dislocation parameters, which continuously change during plastic deformation. Dislocation-based damage in structures/components is the source of the failure; thus, β has been studied as a metric for non-destructive evaluation. This work consists of two parts: the development of an in situ experimental setup for nonlinear Rayleigh wave measurements, and characterization of the dependence of β on applied stress at different levels of initial plastic strain. First, we introduce an experimental setup and methods for repeatable in situ nonlinear ultrasonic measurements. Details on design considerations and measurement schemes are provided. In the second part, β was measured in situ during an incremental monotonic tensile test. The measured β monotonically decreases with plastic strain, but it is relatively insensitive to the applied stress during elastic deformation. This result highlights three aspects of the evolution of β, which have not been sufficiently emphasized in prior work: the apparent insensitivity of β to the applied stress during elastic deformation, decreasing β with plastic deformation, and the saturation of β. We attribute the trend of decreasing β to a scaling of β with monopole loop length during plastic deformation, which depends on initial microstructure. The saturation of β at 1.8% coincides with a planar-to-wavy transition of dislocation structures. The in situ nonlinear ultrasonic experimental method presented in this work is significant as the in situ results can provide broader insights on β and dislocation-based damage evolution than ex situ measurements alone.