Nonlinear Ultrasonic Response Research Articles

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.

Long-term ultrasonic monitoring of concrete affected by alkali-silica reaction

This article presents continuous monitoring results of alkali-silica reaction (ASR) development in concrete specimens for over 400 days using ultrasonic testing and expansion measurements. Eight concrete specimens with nonreactive aggregate (Control), reactive coarse aggregate, and reactive fine aggregates were cast with two reinforced confinement conditions. The specimens were conditioned in an environmental chamber with high temperature and humidity (38°C and 90% relative humidity) to accelerate the ASR development. A multichannel ultrasonic monitoring system was developed to collect ultrasonic signals automatically, and the expansions in three directions were measured periodically. Results showed that the relative velocity change could detect the ASR initiation in all reactive specimens and show a correlation with expansion in the early stage. However, these correlations are inconsistent for different ASR specimens, and the velocity change becomes less sensitive to ASR damage in the late stage (after 300 days). Irrecoverable velocity drop was observed during every chamber shutdown period, especially in specimens with higher levels of ASR damage. This phenomenon suggests that the nonlinear ultrasonic response caused by the ambient temperature variation may indicate the ASR damage.

Data-driven time–frequency analysis of nonlinear Lamb waves for characterization of grain size distribution

Nondestructive characterization of grain size distribution is significant for revealing the mechanical properties of metal materials. Traditional linear ultrasonic methods have been applied to estimate mean grain size but are less sensitive to small grain size. Nonlinear ultrasonic technology shows high sensitivity to microstructures, while it unfortunately encounters underdetermined problem in the characterization of microstructures across multiple scales. Combining linear and nonlinear ultrasonic responses would be a quite attractive way to achieve comprehensive observation of microstructural evolution. This work presents a data-driven approach for characterizing grain size distribution using nonlinear Lamb waves. The short-time Fourier transform (STFT) of detected ultrasonic signals were input into a convolutional neural network (CNN) to comprehensively learn the implicit linear and nonlinear dynamics involved with grain size distribution. Multiple convolution kernels slide across the STFT images with multiscale receptive fields to collectively model hierarchical representations and capture local correlation of interesting from time-frequency domain. The trained model achieved 94.7% accuracy in predicting mean grain size, and also achieved 95.4% and 86.3% accuracy in predicting the expectation and standard deviation of the lognormal distribution of grain size, respectively. The visual activation maps demonstrate that local interesting features are successfully captured. In particular, the prediction accuracy was demonstrated to reduce greatly after removing the fundamental frequency and second harmonic from the STFT images, confirming that incorporating linear and nonlinear ultrasonic information is indispensable for accurate characterization of grain size distribution.

Deep learning-based solvability of underdetermined inverse problems in nonlinear ultrasonic characterization of micro damages

Detection and evaluation of micro-damages in the early stages of engineering failure are crucial for various industrial structures to ensure their safety and prevent further catastrophic accidents. The nonlinear ultrasonic technique (NUT) has gained increasing popularity and recognition for breaking through the detection sensitivity limit upon micro-damages that usually are invisible to conventional linear techniques. However, it remains an ongoing challenge to quantitatively characterize micro-damages using NUT due to great difficulties in fully modeling the complicated interaction mechanism between the nonlinear ultrasonic waves and micro-damages. This work presents a data-driven perspective for solving multiparameter underdetermined inverse problems that are at the core of NUT, while allowing by-passing the creation of high-fidelity physics-based models. Nonlinear Lamb wave measurements with group-velocity mismatching are conducted to introduce both size and localization information of damages to the assembled dataset. A nonlinearity-aware discrete wavelet transform-bidirectional long short-term memory network is proposed to directly process nonlinear ultrasonic responses to automatically model latent nonlinear dynamics, thus establishing the complex mapping between the nonlinear ultrasonic signals and the multi-dimensional damage features. In particular, an attempt is made to augment the physical explainability of the proposed deep learning approach through a frequency component importance analysis. The trained network enables accurate and explainable predictions of length and localization of closed cracks and robustness against varying degrees of noise. Our work paves a promising and practical way to promote the transformation of NUT from the qualitative analysis for accurate and efficient quantitative prediction.

A machine learning approach to nonlinear ultrasonics for classifying annealing conditions in austenitic stainless steel

This paper explores the feasibility of machine learning algorithms on nonlinear ultrasonics for classification of the austenitic stainless-steel material subjected to different annealing conditions. The material that is isothermally annealed at 1323 K for different soaking times showed a marginal variation in its nonlinearity parameter at larger mean grain sizes. The grain growth during annealing followed the Arrhenius type equation fairly well, which has been verified using a genetic algorithm approach. The machine learning algorithms are trained using features such as the ratio of the harmonic amplitudes, root-mean-square value, and the phase difference between the fundamental and second harmonic components derived from the nonlinear ultrasonic response. Upon evaluating the performance of decision tree and ensemble learning algorithms in the classification of annealed materials, it was observed that the LPBoost classifier has the highest accuracy of 97%. According to the results, it is concluded that a machine learning strategy based on a minimal number of features can effectively classify specimens that are otherwise indistinguishable in their nonlinear response. This research takes a step forward to the automation of non-destructive testing toward Industrial Revolution 4.0. The results also pointed out the necessity of parameter fusion in non-destructive decision making.

Autonomous characterization of grain size distribution using nonlinear Lamb waves based on deep learning.

Characterization of grain microstructures of metallic materials is crucial to materials science and engineering applications. Unfortunately, the universal electron microscopic methodologies can only capture two-dimensional local observations of the microstructures in a time-consuming destructive way. In this regard, the nonlinear ultrasonic technique shows the potential for efficient and nondestructive microstructure characterization due to its high sensitivity to microstructural features of materials, but is hindered by the ill-posed inverse problem for multiparameter estimation induced by the incomplete understanding of the complicated nonlinear mechanical interaction mechanism. We propose an explainable nonlinearity-aware multilevel wavelet decomposition-multichannel one-dimensional convolutional neural network to hierarchically extracts multilevel time-frequency features of the acoustic nonlinearity and automatically model latent nonlinear dynamics directly from the nonlinear ultrasonic responses. The results demonstrate that the proposed approach establishes the complex mapping between acoustic nonlinearity and microstructural features, thereby determining the lognormal distribution of grain size in metallic materials rather than only average grain size. In the meantime, the integration of the designed nonlinearity-aware network and the quantitative analysis of component importance provides an acceptable physical explainability of the deep learning approach for the nonlinear ultrasonic technique. Our study shows the promise of this technique for real-time in situ evaluation of microstructural evolution in various applications.

Investigation on characteristics of tensile damage and microstructure evolution of steel AISI 316L by nonlinear ultrasonic Lamb wave

In view of the high sensitivity to microstructure evolution of higher harmonics generated by the nonlinear ultrasonic method, the tensile damage in the stainless steel AISI 316L was evaluated by nonlinear ultrasonic Lamb wave. The effect of different degree of tensile deformation on nonlinear ultrasonic response in 316L was analyzed by considering the microstructure evolution and the test results. First, the power-law relation of nonlinear ultrasonic parameter and plastic strain is proposed. Meanwhile, martensitic transformation and the increasing of dislocation density can be observed in the micrographs of specimens with the increase of plastic deformation. Then, the same variation tendency of intergranularly averaged Kernel Average Misorientation (KAM), as well as the relative nonlinear ultrasonic parameter, demonstrated that the nonlinearity due to tensile damage is controlled by the evolution of microstructure that directly affects higher order elastic constant of stainless steel 316L. Furthermore, based on continuous damage mechanics, the method quantitatively characterizes the degradation of mechanical properties was proposed with a functional relation of damage variable and relative nonlinear parameter. The method proposed in this study provides a theoretical basis for online monitoring of the damage status of in-service equipment. It is of great significance for residual life assessment, structure integrity assessment, and service life extension of equipment.

Large Area Detection of Microstructural Defects with Multi-Mode Ultrasonic Signals

Cyclic loading or other stresses can lead to development of cracks and crack growth in mechanical structures, leading to eventual failure. While ultrasound imaging can be used for non-destructive testing of such structures, conventional ultrasound techniques are often limited by crack size, density, and areal coverage. An effective characterization of real-world, large-area structures is required at an early damage stage to prevent catastrophic failure and predict remaining life. In this study, a new nonlinear ultrasonic testing (NUT) method is proposed for large-area monitoring of practical structures with arbitrary complexity by using multiple-mode guided-wave ultrasonic signals. The proposed guided-wave NUT technique requires single-element transducers, simple electronics, and a mixed time-frequency domain signal processing. As a proof-of-concept demonstration, numerical simulations and experiments are performed on an A36 carbon steel beam assembly with previously formed microstructural defects that cause nonlinearities in ultrasonic response. The quadratic dependence of the nonlinear wave excitation on the input ultrasonic signal amplitude is shown by numerical simulations, and such a nonlinear ultrasonic response is experimentally observed in the zone with a high density of microstructural defects.

Ultrafast nonlinear ultrasonic measurement using femtosecond laser and modified lock-in detection

Ultrafast ultrasonic techniques using picosecond/femtosecond lasers show promise for the nondestructive evaluation at fine spatial resolutions because the induced ultrasonic waves have an extremely high frequency range, from GHz to THz. However, most existing applications are based on the linear feature variation of the measured ultrafast ultrasonic waves; this is limited by the linearity assumptions in lock-in detection schemes adopted for ultrafast ultrasonic measurement. This study proposes a technique to measure ultrafast nonlinear ultrasonic waves using a femtosecond laser and a modified lock-in detection scheme. The advantages of the proposed technique are as follows. (1) The developed technique can measure nonlinear ultrasonic waves induced by a femtosecond laser; (2) linear and nonlinear ultrasonic responses can be decomposed and measured using a modified lock-in detection scheme; and (3) the decomposed nonlinear ultrasonic waves can be used for effective micro defect detection and microstructure characterization at sub-micrometer scale. The proposed technique was used to successfully perform validation tests on micro crack detection in a silicon wafer and microstructure characterization of an additively manufactured Ti-6Al-4V sample.

Measuring friction at an interface using ultrasonic response.

Friction between sliding surfaces is a fundamental phenomenon prevalent in many aspects of engineering. There are many sliding contact tribometers that measure friction force in a laboratory environment. However, the transfer of laboratory data to real machine elements is unreliable. Results depend on the specimen configuration, surface condition and environment. In this work, a method has been developed that uses the nonlinear response of a high-power ultrasonic wave to deduce friction coefficient in situ at an interface. When the high-power shear wave strikes a frictional interface, relative slip can occur. It imposes a nonlinear response and causes generation of higher-order odd frequency components in received ultrasonic signals. The amplitude of the harmonics depends on contact stress and local friction coefficient. This nonlinear ultrasonic response has been investigated both numerically and experimentally. A simple one-dimensional model has been used to predict nonlinearity generation. This model has been compared with experiments conducted on aluminium rough surfaces pressed together under increasing loads. Two strategies have been used to estimate the friction coefficient by correlating experimental and numerical third-order nonlinearity. It has proved possible to determine the friction coefficient in situ at the interface; values in the range of 0.22 to 0.61 were measured for different surface configurations.

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.

Nonlinear ultrasonic response of voids and Cu precipitates in body-centered cubic Fe

Interpreting nonlinear ultrasonic signals detected in a nondestructive evaluation of radiation damage requires the knowledge of the correlation between defects and nonlinearity. In this work, molecular dynamics simulations are performed to study the effect of distributed vacancies, voids, Cu atoms, and Cu precipitates on the nonlinear ultrasonic response in body-centered cubic (bcc) Fe. The nonlinearity parameter calculated from the second harmonic amplitude in the perfect lattice is 2.73. Vacancies are found to increase the nonlinearity. However, clusters of vacancies in the form of spherical voids show an opposite effect. This finding can be used to conveniently distinguish vacancies from voids in the material. Unlike vacancies, individual Cu atoms decrease the nonlinearity. Clustering of Cu atoms into Cu precipitates further decreases the nonlinearity. Interestingly, precipitates with a diameter of 2 nm and larger exhibit a similar effect despite their different structure and coherency with the Fe matrix.

Peri-ultrasound modeling for surface wave propagation

The interaction between surface wave and a surface breaking crack is studied using a novel fast modeling tool called peri-ultrasound that can model both linear and nonlinear ultrasonic response. This modeling approach is based on peridynamic theory. In this study, the surface wave is modeled by applying a triangular pulse excitation function on the surface of a large structure. The particle movements are simulated on both sides of the surface crack to investigate transmitted and reflected fields. This investigation shows that: (1) the computed amplitude spectra of the Rayleigh wave agrees with the experimental observation; and (2) the structure containing a surface breaking crack shows noticeable increase in its nonlinear behavior. The computed results have been also verified against the analytical solution for a half-plane problem made of homogenous, isotropic, linear elastic material (Lamb’s Problem).

Peri-Ultrasound Modeling of Dynamic Response of an Interface Crack Showing Wave Scattering and Crack Propagation

A cracked structure made of two different elastic materials having a Griffith crack at the interface is analyzed when it is subjected to pure shear loading and ultrasonic loading. The waves generated by the applied load and the crack propagation resulted from the shear loading are investigated. Peri-ultrasound modeling tool is used for this analysis. A comparison between experimental results and numerical predictions shows a very good matching between the two. Furthermore, the increase in nonlinear ultrasonic response in presence of the interface crack could also be modeled by this technique. The computed results show that when the interface crack propagates, then it breaks the interface at one end of the crack and breaks the material with lower elastic modulus at the other end. The unique feature of this peridynamics-based modeling tool is that it gives a complete picture of the structural response when it is loaded—it shows how elastic waves propagate in the structure and are scattered by the crack, how the crack surfaces open up, and then how crack starts to propagate. Different modeling tools are not needed to model these various phenomena.

Peri-ultrasound for modeling linear and nonlinear ultrasonic response

The objective of this paper is to introduce a novel fast modeling tool called peri-ultrasound for linear/nonlinear ultrasonic wave propagation modeling. This modeling approach is based on peridynamic theory. It does not require monitoring of the crack clapping phenomenon or artificially changing the stiffness of the element when two surfaces of the crack come in contact. Peri-ultrasound tool enables us to detect the material nonlinearity in very early stages of crack growth. Nonlinear ultrasonic behavior could be nicely modeled by the proposed peri-ultrasound tool. It is investigated how the material nonlinearity is affected by the presence of thin and thick cracks. From the normalized spectral plots the degree of material nonlinearity can be measured by extracting a feature called sideband peak count (SPC). Structures containing a thin crack show noticeable increase in their nonlinear behavior.

On the generation of nonlinear damage resonance intermodulation for elastic wave spectroscopy.

Recent nonlinear elastic wave spectroscopy experiments have shown that the nonlinear ultrasonic response of damaged composite materials can be enhanced by higher vibrations at the local damage resonance. In this paper, the mathematical formulation for the generation of nonlinear wave effects associated with continuous periodic excitation and the concept of local defect resonance is provided. Under the assumption of both quadratic and cubic approximation, the existence of higher harmonics of the excitation frequency, superharmonics of the damage resonance frequency and nonlinear wave effects, here named as nonlinear damage resonance intermodulation, which correspond to the nonlinear intermodulation between the driving and the damage resonance frequencies, is proved. All these nonlinear elastic effects are caused by the interaction of propagating ultrasonic waves with the local damage resonance and can be measured at locations different from the material defect one. The proposed analytical model is confirmed and validated through experimental transducer-based measurements of the steady-state nonlinear resonance response on a damaged composite sample. These results will provide opportunities for early detection and imaging of material flaws.

Effects of Cyclic and Monotonic Deformations on Nonlinear Ultrasonic Response of Austenitic Stainless Steel: A Comparative Study

The effect of plastic deformations on the nonlinear ultrasonic response in austenite stainless steel was investigated under the tensile, asymmetric cyclic, and symmetric cyclic loadings. Nonlinear ultrasonic wave measurement was performed on the interrupted specimens. Results show that cyclic and monotonic plastic deformations lead to the significantly different acoustic nonlinear response. The increase of dislocation density and martensite transformation causes the increase of acoustic nonlinearity. By contrast, the well-developed cell structures decrease the acoustic nonlinear response. Under the asymmetric cyclic loading condition, the lightly decrease of acoustic nonlinearity is caused by the development of cell structures, while the slight increase of acoustic nonlinearity should be attributed to the increase of martensite transformation. Comparatively, the severe increase of acoustic nonlinearity during the first stage under symmetric cyclic loading is ascribed to the fast generation of dislocation structures and martensite transformation.

Experimental and numerical studies of nonlinear ultrasonic responses on plastic deformation in weld joints**Project supported by the National Natural Science Foundation of China (Grant Nos. 51325504, 11474093, and 11474361) and the Shanghai Rising-Star Program, China (Grant No. 14QA1401200).

The experimental measurements and numerical simulations are performed to study ultrasonic nonlinear responses from the plastic deformation in weld joints. The ultrasonic nonlinear signals are measured in the plastic deformed 30Cr2Ni4MoV specimens, and the results show that the nonlinear parameter monotonically increases with the plastic strain, and that the variation of nonlinear parameter in the weld region is maximal compared with those in the heat-affected zone and base regions. Microscopic images relating to the microstructure evolution of the weld region are studied to reveal that the change of nonlinear parameter is mainly attributed to dislocation evolutions in the process of plastic deformation loading. Meanwhile, the finite element model is developed to investigate nonlinear behaviors of ultrasonic waves propagating in a plastic deformed material based on the nonlinear stress–strain constitutive relationship in a medium. Moreover, a pinned string model is adopted to simulate dislocation evolution during plastic damages. The simulation and experimental results show that they are in good consistency with each other, and reveal a rising acoustic nonlinearity due to the variations of dislocation length and density and the resulting stress concentration.

Резонансные дефекты: новый подход к повышению чувствительности методов НК с использованием ультразвуковой стимуляции дефектов

The presence of a defect leads to a local decrease in rigidity for a certain mass of the material and therefore manifests in a particular characteristic frequency of the defect. A frequency match between the driving ultrasonic wave and this characteristic frequency provides a Local Defect Resonance (LDR) and results in efficient energy delivery from the wave into the defect. In this paper, such a selective ultrasonic activation of resonant defects is suggested to enhance nonlinear ultrasonic, optical and thermal defect responses. Multiple case studies demonstrate that the resonant excitation of a defect results in a high local vibration and enhancement of sensitivity in ultrasonic NDT and imaging of defects via laser vibrometry, thermosonics, nonlinearity and shearography readily measurable even for a few mW of ultrasonic power. The LDR-based NDT methods require much lower ultrasonic power to activate the defects that makes it possible to avoid high- power ultrasonic instrumentation.

Nondestructive evaluation of notched cracks in mortars by nonlinear ultrasonic technique

In this paper, a nonlinear ultrasonic technique is used to nondestructively characterise concentrated defects in cement-based materials. Cracks are artificially notched in mortar samples and five different crack widths are used to simulate increased damage of samples. The relative ratio of second harmonic amplitude to the square of fundamental ultrasonic signal amplitude is defined as the damage indicator of the nonlinear ultrasonic technique, which is measured for mortar samples in conjunction with a typical linear nondestructive evaluation parameter – ultrasonic pulse velocity. It is found that both linear and nonlinear damage parameters have a good correlation with the change of crack width, while the nonlinearity parameter shows a better sensitivity to the width increase. In addition, the nonlinearity parameter presents an exponential increase with the crack growth, indicating an accelerating nonlinear ultrasonic response of materials to increased internal damage in the late phase. The results demonstrate that the nonlinear ultrasonic technique based on the second harmonic principle keeps the high sensitivity to the isolated cracks in cement-based materials, similarly to the case of distributed cracks in previous studies. The developed technique could thus be a useful experimental tool for the assessment of concentrated damage of concrete structures.