Nonlinear Ultrasonic Technique Research Articles

A Preliminary Numerical Study on the Interactions Between Nonlinear Ultrasonic Guided Waves and a Single Crack in Bone Materials With Motivation to the Evaluation of Micro Cracks in Long Bones

Fatigue damage in a bone occurs in the form of micro-scale cracks with the lengths as small as to a few microns. The evaluation of cracks in bones has recently been a hot topic. However, the current most frequently used method is based on traditional linear ultrasound, which is just sensitive to gross damages rather than micro cracks. Nonlinear ultrasonic technique, which is capable of detecting micro-scale damages, has been widely used in metallic structures. However, few study has been directed to employing second harmonic generation of nonlinear ultrasound to evaluate fatigue damages in bones. In this study, a preliminary study is conducted on the interactions between nonlinear guided waves and a single crack in bone materials motivating to the evaluation of micro cracks in long bones. Considering the symmetry, asymmetry, location, orientation, length and width of the crack in bone materials, their influences on second harmonic responses are discussed in detail. Our results are presented as follows. Firstly, not only the primary S0 but also A0 mode Lamb wave generates the second harmonic component of S0 mode after interacting with a symmetric crack. Secondly, along the thickness direction, the primary S0 mode Lamb wave possesses almost the same detection sensitivity, no matter where the crack is located. Thirdly, the amplitudes of S0 mode second harmonic component are increased slightly when the oblique angle of the crack is set from 0°to 45°, while the amplitudes increase dramatically when the oblique angle changes to 67.5° and 90°. Lastly, the second harmonic amplitude and the relative acoustical nonlinear parameter are increased with the length of the crack, while they possess a monotonically decreasing relationship with the width of the crack. Our preliminary studies will provide priori knowledge when using nonlinear ultrasonic guided waves for detecting micro-scale cracks in long bones in future clinical inspections.

Micro-crack detection of nonlinear Lamb wave propagation in three-dimensional plates with mixed-frequency excitationyg**Project supported by the National Natural Science Foundation of China (Grant Nos. 61571222, 61602235, and 11474160) and the Six Talent Peaks Project of Jiangsu Province, China.

We propose a nonlinear ultrasonic technique by using the mixed-frequency signals excited Lamb waves to conduct micro-crack detection in thin plate structures. Simulation models of three-dimensional (3D) aluminum plates and composite laminates are established by ABAQUS software, where the aluminum plate contains buried crack and composite laminates comprises cohesive element whose thickness is zero to simulate delamination damage. The interactions between the S0 mode Lamb wave and the buried micro-cracks of various dimensions are simulated by using the finite element method. Fourier frequency spectrum analysis is applied to the received time domain signal and fundamental frequency amplitudes, and sum and difference frequencies are extracted and simulated. Simulation results indicate that nonlinear Lamb waves have different sensitivities to various crack sizes. There is a positive correlation among crack length, height, and sum and difference frequency amplitudes for an aluminum plate, with both amplitudes decreasing as crack thickness increased, i.e., nonlinear effect weakens as the micro-crack becomes thicker. The amplitudes of sum and difference frequency are positively correlated with the length and width of the zero-thickness cohesive element in the composite laminates. Furthermore, amplitude ratio change is investigated and it can be used as an effective tool to detect inner defects in thin 3D plates.

Damage assessment in Q690 high strength structural steel using nonlinear Lamb waves

The nonlinear ultrasonic technique has been used to assess the plastic damage in High strength Q690 steel. The Q690 steel was stretched to different levels of plastic strain so as to obtain the specimen with different degrees of plastic damage. When strain was increased from 1% to 9%, the nonlinear parameter shows a general upward trend, and in the subsequent strain process, the nonlinear response drop off instead of going up. Meanwhile, metallographic examination indicates that, within the strain 9%, the growth of the void as well as the variation of dislocation structure and density are the main damage characteristic in Q690 steel. Many dislocation structures such as the dislocation cell and dislocation wall have formed in the tensile specimen, which is contribute to raise of the nonlinear effect. The results indicate that the nonlinear ultrasonic technique can be utilized to characterize the plastic damage in Q690 structural steel at the early stage.

SH wave generated Lamb wave in a plate with a localized region of material nonlinearity

AbstractHigher harmonics are sensitive to micro‐defects, which can be utilized in the development of nonlinear ultrasonic techniques (NLUTs). Thus, the higher harmonic generation by material nonlinearity has attracted considerable attention. However, few works have been done on the elastic wave propagation in a finite structure with a localized region of material nonlinearity. The propagation of the SH wave in a plate with a localized region of quadratic material nonlinearity is investigated in this paper. The nonlinear governing equations are reduced to a set of linear equations at different orders by using the perturbation method. The incident plane SH wave satisfies the zero‐order equations. The elastic waves generated by the nonlinear material region can be obtained by solving the first‐order equations, whose inhomogeneous terms can be regarded as the equivalent body forces and surface tractions. In the first‐order approximation, only the Lamb wave can be generated by the interaction of the SH wave with a region of quadratic material nonlinearity. In this paper, the analytical solution for the generated backward Lamb wave is obtained, whose amplitude varies with a material‐dependent constant linearly and with the length of the nonlinear region in the form of a sine function.

Numerical study of nonlinear elastic wave propagation in locally damaged engineering structures

AbstractIn this paper, the two‐dimensional (2‐D) ultrasonic wave propagation problem in an elastic half‐space with a localized damaged zone is numerically simulated by a mapped Chebyshev pseudo‐spectral collocation method [1]. The considered damaged zone, which is embedded in an undamaged host medium, is modelled by a nonlinear elastic and viscoelastic constitutive law. Classical nonlinear elastic and nonclassical hysteretic material behaviors are separately considered and evaluated. In particular, the classical nonlinear elasticity theory of Murnaghan [2] is implemented, while the hysteretic material behavior is modelled by the Duhem‐model. To transfer the constitutive relations from the one‐dimensional (1‐D) to the 2‐D case the Kelvin decomposition method is used. Furthermore, Convolutional Perfectly Matched Layers (CPML's) are used to simulate the semi‐infinite elastic half‐space. The computed time‐domain signals are transformed to the frequency‐domain and subsequently analyzed for different degrees of the wave attenuation and nonlinearity in the damage zone. The applications of the nonlinear ultrasonic technique are discussed based on the numerical results.

Applicability of nonlinear ultrasonic technique to evaluation of thermally aged CF8M cast stainless steel

Abstract Cast austenitic stainless steel (CASS) is used for fabricating different components of the primary reactor coolant system of pressurized water reactors. However, the thermal embrittlement of CASS resulting from long-term operation causes structural safety problems. Ultrasonic testing for flaw detection has been used to assess the thermal embrittlement of CASS; however, the high scattering and attenuation of the ultrasonic wave propagating through CASS make it difficult to accurately quantify the flaw size. In this paper, we present a different approach for evaluating the thermal embrittlement of CASS by assessing changes in the material properties of CASS using a nonlinear ultrasonic technique, which is a potential nondestructive method. For the evaluation, we prepared CF8M specimens that were thermally aged under four different heating conditions. Nonlinear ultrasonic measurements were performed using a contact piezoelectric method to obtain the relative ultrasonic nonlinearity parameter, and a mini-sized tensile test was performed to investigate the correlation of the parameter with material properties. Experimental results showed that the ultrasonic nonlinearity parameter had a correlation with tensile properties such as the tensile strength and elongation. Consequently, we could confirm the applicability of the nonlinear ultrasonic technique to the evaluation of the thermal embrittlement of CASS.

Detection of local defect resonance intermodulation peaks using bicoherence analysis

The nonlinear ultrasonic technique is a popular and efficient way for the detection of small defects in any structural component. Local defect resonance (LDR) is one of the nonlinear ultrasonic techniques introduced recently for detection of damages in composites structures. LDR frequency is used to characterize small defects like delamination, cracks by generating high vibration amplitudes at the defect location. In this paper, an analytical study of the nonlinear intermodulation frequencies generated due to the interaction of two different exciting frequencies and their bicoherence analysis is presented in the case of aluminium plate having a flat bottom hole (FBH) and glass fiber reinforced polymer (GFRP) plates having multiple delaminations. The flexural wave propagation in asymmetric composite plate is shown by considering quadratic nonlinearity. The excitation frequency of the first transmitter is varying from LDR frequency to it's subharmonic and superharmonics while the other one is excited with a single periodic frequency (SPF). The analytical results are further verified by experimental investigations and good agreement is found. Local defect resonance intermodulation (LDRI) and single periodic frequency intermodulation (SPFI) are obtained in Fast Fourier transform (FFT) plots. In Bicoherence analysis, LDRI peaks are observed to possess higher bicoherence value and hence, their detection chance is higher during wideband excitation. Moreover, inclusion of subharmonic LDR frequencies will create lesser peaks and detection of all LDR frequencies is possible.

Preliminary Research on the Nonlinear Ultrasonic Detection of the Porosity of Porous Material Based on Dynamic Wavelet Fingerprint Technology.

Porosity is an important characteristic of porous material, which affects mechanical and material properties. In order to solve the problem that the large distribution range of pore size of porous materials leads to the large detection errors of porosity, the non-linear ultrasonic testing technique is applied. A graphite composite was used as the experimental object in the study. As the accuracy of porosity is directly related with feature extraction, the dynamic wavelet fingerprint (DWFP) technology was utilized to extract the feature parameter of the ultrasonic signals. The effects of the wavelet function, scale factor, and white slice ratio on the extraction of the nonlinear feature are discussed. The SEM photos were conducted using gray value to identify the aperture. The relationship between pore diameter and detection accuracy was studied. Its results show that the DWFP technology could identify the second harmonic component well, and the extracted nonlinear feature could be used for the quantitative trait of porosity. The larger the proportion of the small diameter holes and the smaller the aperture distribution range was, the smaller the error was. This preliminary research aimed to improve the nondestructive testing accuracy of porosity and it is beneficial to the application of porous material in the manufacturing field.

Application of an Optical Fiber Sensor for Nonlinear Ultrasonic Evaluation of Fatigue Crack

Nonlinear ultrasonic technique that evaluates the growth of the barely visible fatigue crack in metal is difficult to be achieved by conventional optical fiber sensor because of the critical requirements for sensor sensitivity and bandwidth. In this paper, a high-performance optical fiber sensor using phase-shifted fiber Bragg grating and balanced demodulation system was applied to detect the fundamental and second harmonic Lamb waves propagating in an aluminum plate. After the nonlinearity was calculated from the modes of the Lamb waveform detected by the optical fiber sensor, its change due to the second harmonic generation shows an exponential trend in a fatigue test, which can be used to evaluate the crack growth with sufficient reliability. The experimental results from the optical fiber sensor were validated by comparing with results from the PZT sensor. This paper facilitates the development of optics-based nonlinear ultrasonic structural health monitoring for fatigue crack evaluation.

Metamaterial improved nonlinear ultrasonics for fatigue damage detection

This article presents an improved nonlinear ultrasonic technique for fatigue damage detection utilizing a kind of carefully designed aluminum-lead composite metamaterial. It focuses on developing a bandgap metamaterial to improve the accuracy and identifiability of the superharmonic features from fatigue cracks by eliminating the inherent nonlinear components in the nonlinear ultrasonic technique. The study starts with the unit cell design through modal analysis by applying the Bloch–Floquet boundary condition to obtain the band structure. Based on the local resonance mechanism, by adjusting the height ratio between the aluminum and lead cylinders, the bandgaps covering the required frequency ranges can be opened up. Then, a chain of regularly arranged unit cells is modeled to analyze the spectral response and verify the bandgap effect through harmonic analysis. The targeted ultrasonic frequency component of guided waves within the bandgap can be mechanically filtered out. Subsequently, a finite element model of the pitch-catch active sensing procedure for fatigue crack detection is constructed via the coupled-field transient dynamic analysis. Nonlinear ultrasonic experiments with the designed metamaterial are carried out to verify the theoretical and numerical investigations. This paper demonstrates that the metamaterial, with its outstanding wave manipulation capability, shows great potential on structural health monitoring and nondestructive evaluation applications. The paper finishes with summary, concluding remarks, and suggestions for future work.

Simulation of crack induced nonlinear elasticity using the combined finite-discrete element method

Numerical simulation of nonlinear elastic wave propagation in solids with cracks is indispensable for decoding the complicated mechanisms associated with the nonlinear ultrasonic techniques in Non-Destructive Testing (NDT). Here, we introduce a two-dimensional implementation of the combined finite-discrete element method (FDEM), which merges the finite element method (FEM) and the discrete element method (DEM), to explicitly simulate the crack induced nonlinear elasticity in solids with both horizontal and inclined cracks. In the FDEM model, the solid is discretized into finite elements to capture the wave propagation in the bulk material, and the finite elements along the two sides of the crack also behave as discrete elements to track the normal and tangential interactions between crack surfaces. The simulation results show that for cracked models, nonlinear elasticity is generated only when the excitation amplitude is large enough to trigger the contact between crack surfaces, and the nonlinear behavior is very sensitive to the crack surface contact. The simulations reveal the influence of normal and tangential contact on the nonlinear elasticity generation. Moreover, the results demonstrate the capabilities of FDEM for decoding the causality of nonlinear elasticity in cracked solid and its potential to assist in Non-Destructive Testing (NDT).

Application of nonlinear ultrasonic technique to characterize the microresidual strain in metal

Abstract

Influence of Mesoscale and Macroscale Heterogeneities in Metals on Higher Harmonics Under Plastic Deformation

In nonlinear ultrasonic techniques, the material nonlinearity is observable in the ultrasonic signal through the generation of higher harmonics (HH). The HH generation, however, can be triggered by many sources. Any variation in the micro-, meso-, and macroscopic scales of the structure may collectively lead to HH generation. This paper presents a finite element approach with mesoscale heterogeneities explicitly modeled for the nonlinear wave propagation. The aim of this paper is to understand HH generation due to the non-mesoscale variation and non-uniform deformations introduced by the uniaxial tensile test. The study is divided into two parts: first, the effect of non-uniform plastic deformation resulted by geometrical variation of structures on HH is studied. The effect of non-uniformity due to mesoscale variations on HH is then analyzed. The numerical studies and predictions are crossly validated with nonlinear ultrasonic experiments and microscale imaging, including X-ray diffraction scanning. Numerical and experimental studies both indicate that non-uniform variations in different length scales affect the generation of both second- and third-harmonics and that both second- and third-harmonics acoustic nonlinearity parameters grow with the increase of plastic strain level. However, the third-harmonics acoustic nonlinearity coefficient is more sensitive when micro-, meso- and macrostructural variations exist.

Finite element simulation and experimental study of residual stress testing using nonlinear ultrasonic surface wave technique

Due to the influence of residual stress on material properties, residual stress measurement is particularly important for the optimization of structure designs and the condition monitoring of machines. In this paper, the influence of residual stress on materials nonlinearity was reported. Firstly, the propagation model of ultrasonic surface waves was established by the finite element method and the effect of frequency was studied to determine an appropriate frequency of acoustic nonlinearity parameters. Then, the different residual stresses were produced into specimen by adding internal stress in the material and the impact on acoustic nonlinearity parameter was studied. The results show that the nonlinearity of the material increases monotonously with the increase of residual stress. Experiments were done by using the nonlinear ultrasonic surface wave on three 7075Al alloy specimens under different residual stresses. Experimental data matched well with the simulation results. It has been shown that the nonlinear ultrasonic surface wave method has great potential in the residual stress detection and evaluation.

Microstructure-based model of nonlinear ultrasonic response in materials with distributed defects

Nonlinear ultrasonic technique is one of several promising nondestructive evaluation methods for monitoring the evolution of nanosized defects such as radiation-induced defects in nuclear materials. In this work, a microstructure-based phase-field model of dynamic deformation in elastically nonlinear materials has been developed for investigating the dynamic interaction between distributed defects and a propagating longitudinal sound wave. With the model, the effect of second phase precipitates’ size and properties on the nonlinearity parameter β that describes the magnitude of the 2nd harmonic wave was simulated. The results showed that (1) the nonlinearity parameter β increases as the elastic inhomogeneity increases regardless of whether the precipitates are softer or harder than the matrix; (2) β linearly increases with the increase of lattice mismatch strain; and (3) for a given volume fraction of second phase precipitates, β strongly depends on the precipitate size. The predicted precipitate size dependence of β agrees with the experimental data. These results demonstrate that the developed model enables one to predict the contributions of different nonlinear sources to β, to explain the signal physics behind the measured nonlinear ultrasonic response, and to guide the development of nonlinear ultrasound nondestructive detection of material defects in nuclear reactor materials.

Correction to: Evaluation of surface cracks of bending concrete using a fully non-contact air-coupled nonlinear ultrasonic technique

The article Evaluation of surface cracks of bending concrete using a fully non-contact air-coupled nonlinear ultrasonic technique, written by Jun Chen, Chenglong Yang and Quanquan Guo, was originally published online without open access.

Monitoring of Thermal Aging of Aluminum Alloy via Nonlinear Propagation of Acoustic Pulses Generated and Detected by Lasers

Nonlinear acoustic techniques are established tools for the characterization of micro-inhomogeneous materials with higher sensitivity, compared to linear ultrasonic techniques. In particular, the evaluation of material elastic quadratic nonlinearity via the detection of the second harmonic generation by acoustic waves is known to provide an assessment of the state variation of heat treated micro-structured materials. We report on the first application for non-destructive diagnostics of material thermal aging of finite-amplitude longitudinal acoustic pulses generated and detected by lasers. Finite-amplitude longitudinal pulses were launched in aluminum alloy samples by deposited liquid-suspended carbon particles layer irradiated by a nanosecond laser source. An out-of-plane displacement at the epicenter of the opposite sample surface was measured by an interferometer. This laser ultrasonic technique provided an opportunity to study the propagation in aluminum alloys of finite-amplitude acoustic pulses with a strain up to 5 × 10−3. The experiments revealed a signature of the hysteretic quadratic nonlinearity of micro-structured material manifested in an increase of the duration of detected acoustic pulses with an increase of their amplitude. The parameter of the hysteretic quadratic nonlinearity of the aluminum alloy (Al6061) was found to be of the order of 100 and to exhibit more than 50% variations in the process of the alloy thermal aging. By comparing the measured parameter of the hysteretic quadratic nonlinearity in aluminum alloys that were subjected to heat-treatment at 220 °C for different times (0 min, 20 min, 40 min, 1 h, 2 h, 10 h, 100 h, and 1000 h), with measurements of yield strength in same samples, it was established that the extrema in the dependence of the hysteretic nonlinearity and of the yield strength of this alloy on heat treatment time are correlated. This experimental observation provides the background for future research with the application goal of suggested nonlinear laser ultrasonic techniques for non-destructive evaluation of alloys’ strength and rigidity in the process of their heat treatment.

Use of Non-Linear Ultrasonic Techniques to Detect Cracks Due to Steel Corrosion in Reinforced Concrete Structures.

In this work, non-linear ultrasonic wave techniques have been used to detect the onset of micro-cracking due to steel corrosion in model reinforced concrete elements. The specimens were of prismatic shape with a single steel rebar. The corrosion was forced by admixing an appropriate amount of sodium chloride at the moment of preparing the concrete mix, and by the application of an electric field, using a constant current density power source, and making the steel rebar work as the anode, and an external counter-electrode as the cathode. The preliminary results indicate that the onset of cracking seems to be accompanied by the appearance of higher-harmonic generation at the output signal (harmonic distortion), when the system is excited by the means of an ultrasound wave with a burst central frequency. Other phenomena related to the micro-cracks induced by corrosion, such is the parametric generation with respect to the fundamental amplitude, have not been observed until now.

Characterization of Microstructural Evolution by Ultrasonic Nonlinear Parameters Adjusted by Attenuation Factor

The use of an acoustic nonlinear response has been accepted as a promising alternative for the assessment of micro-structural damage in metallic solids. However, the full mechanism of the acoustic nonlinear response caused by the material micro-damages is quite complex and not yet well understood. In this paper, the effect of material microstructural evolution on acoustic nonlinear response of ultrasonic waves is investigated in rolled copper and brass. Microstructural evolution in the specimens is artificially controlled by cold rolling and annealing treatments. The correlations of acoustic nonlinear responses of ultrasonic waves in the specimens corresponding to the microstructural changes are obtained experimentally. To eliminate the influence of attenuation, which was induced by microstructural changes in specimens, experimentally-measured nonlinear parameters are corrected by an attenuation correction term. An obvious decrease of nonlinearity with the increase of grain size is found in the study. In addition, the influences of material micro-damages introduced by cold rolling on the acoustic nonlinear response in specimens are compared with the ones of grain boundaries controlled by heat treatment in specimens. The experimental results show that the degradation of material mechanical properties is not always accompanied by the increase of acoustic nonlinearity generated. It suggested that the nonlinear ultrasonic technique can be used to effectively characterize the material degradations, under the condition that the variations of grain sizes in the specimens under different damage states are negligible.

A Pulse Inversion-Based Nonlinear Ultrasonic Technique using a Single-Cycle Longitudinal Wave for Evaluating Localized Material Degradation in Plates

General nonlinear ultrasonic techniques (NUTs) use tone-burst ultrasonic waves with a narrow bandwidth so that the fundamental frequency component and the second-order harmonic component can be clearly separated in the frequency domain. Meanwhile, when using a longitudinal wave propagating in the thickness direction, the number of cycles of tone-burst signals can be limited by the object thickness. In some cases, only a pulsed signal or a single-cycle signal, which has broad bandwidth, may be applicable to avoid superposition of the first transmitted wave and the multi-reflected waves. Such cases complicate the use of general NUTs, and it is necessary to apply a method to precisely extract the second-order harmonic component even in broadband signals to the NUT. In this study, the pulse inversion (PI) method, which can extract only even harmonics or odd harmonics by superposing or subtracting two wave signals obtained from 180° out-of-phase inputs, is applied to an NUT using broadband ultrasound. The performance of the PI-based NUT with respect to material degradation is verified using a series of heat-treated aluminum alloy specimens with various levels of precipitates. The experimental results show that the nonlinearity parameters measured with single-cycle signals agree well with the previous well-validated experimental results obtained using narrowband signals. Next, the PI-based NUT is used to assess the localized material degradation of a stainless steel plate subjected to high-cycle fatigue. The experimental results show that the profile of the measured nonlinearity parameters as a function of scan position is consistent with the intended distribution of localized fatigue damage, which demonstrates the potential feasibility of the proposed technique for evaluation of localized material degradation in plates.