Nonlinear Ultrasonic Testing Research Articles

Evaluation of Damage Process of a Coating by Using Nonlinear Ultrasonic Method

During the service or external loading of the surface coating, the damage accumulation may develop in the coating or at the interface between the substrate and the coating, but it is difficult to measure directly in the early stage, so the acoustic nonlinear parameters are used as the early damage index of the coating. In this paper, the nonlinear wave motion equation is solved by the perturbation method and the new relationship between the relative ratio of second-order parameter and third-order parameter was derived. The nonlinear ultrasonic testing system is used to detect received signals during tensile testing of for the specimen with Al2O3 coatings. It is found that when the stress is less than 260 MPa, the appearance of the coating has no obvious change, but the nonlinear coefficients measured by the experiment increase with the increase of the tensile stress. By comparing the curves of nonlinear coefficients and stress respectively, the fluctuation of curves the second-order nonlinear coefficient A2 and the relative nonlinear coefficient β′ to stress is relatively small, and close to the linear relationship with the tensile stress, which indicates that the two parameters of the specimen with Al2O3 coatings are more sensitive to the bonding conditions, and can be used as an evaluation method to track the coating damage.

Damage monitoring in rock specimens with pre-existing flaws by non-linear ultrasonic waves and digital image correlation

Pre-existing discontinuities act as the primary source of damage initiation processes in rock masses, and consequently govern their overall deformational behavior. As laboratory tests are critical for establishing constitutive behavior of rocks, in this study, the impact of a pre-existing flaw on rock damage behavior has been analyzed through laboratory-scale experiments. For this purpose, prismatic Barre granite specimens with an existing flaw were progressively damaged under uniaxial loading condition. A state-of-the-art non-linear ultrasonic testing (NLUT) method – the Scaling Subtraction Method (SSM) – was implemented in tandem with the two-dimensional (2D) digital image correlation (2D-DIC) technique for monitoring the impact of the flaw on the rock damage processes. NLUT-SSM allowed for experimental tracking of damage progression by analyzing the elasto-dynamic non-linear response of the rock volume originating at dynamic levels of strain. The non-linear response was characterized through the frequency-domain based evaluation of the non-linear indicator in the ultrasonic imaging areas (UIA). The 2D-DIC full-field strain profiles enabled a strain-based quantitative assessment of the magnitude of tensile and shear damage visible on the rock surface through the estimation of non-elastic apparent tensile and shear strains. The stress-induced changes in the magnitude of the non-linear indicator in the UIA regions showed that the NLUT-SSM technique is sensitive to capture the signatures of rock damage initiation and progression, with the pre-flawed region showing a higher degree of variation in the magnitude of the non-linear indicator. The results also quantitatively demonstrate that damage initially nucleates at the flaw tips, with the flaw tips having a relatively higher magnitude of tensile and shear damage in comparison to other areas of the specimen. The correlation between the non-linear indicator and damage showed that non-linear indicator has a near-linear direct correlation with tensile damage. In contrast, the magnitude of the non-linear indicator increased in an inconsistent non-linear manner with continued accumulation of shear damage. These findings are significant, in the sense that very few prior studies quantitatively analyzed the influence of a pre-existing flaw on rock damage behavior and examined the primary rock damage mechanism (tensile or shear) influencing changes in non-linear ultrasonic characteristics.

Fully noncontact inspection of closed surface crack with nonlinear laser ultrasonic testing method

Nonlinear ultrasonic testing method is one of few techniques that are effective for evaluating early material degradation and micro-crack initiation by analysing the nonlinear effects of ultrasonic waves. This study presents a noncontact nonlinear ultrasonic testing method based on lasers for closed surface crack inspection. A pulsed laser grating source by grating mask is applied to generate narrowband surface acoustic wave of a chosen frequency. A nonlinear numerical simulation based on Finite Element Method (FEM) is developed to simulate the generation of higher harmonics by closed surface crack. The simulation results show that the acoustic nonlinearity parameter increases with the micro closed crack length, while decreases with the micro closed crack buried depth. Moreover, the detection capability of this method is verified by an experiment. The experimental results show that the proposed laser-based nonlinear ultrasonic testing method can provide a fully noncontact and coupling-free measurement method for closed surface crack inspection.

Study on Mechanical Properties of Basalt Fiber‐Reinforced Concrete with High Content of Stone Powder at High Temperatures

Concrete materials are an important part of global structure, and their fire resistance directly affects the safety of buildings and tunnels. In this study, basalt fiber was used to reinforce concrete with high content of stone powder in order to enhance its high‐temperature performance. The mechanical properties and ultrasonic characteristics at different temperatures were studied using the cube compressive strength test and nonlinear ultrasonic test. The results indicated that the addition of basalt fiber in specimens improved their compressive strength; however, this strength did not continuously increase with increases in the fiber length and fiber content, and the optimal values for fiber length and fiber content were determined to be 12 mm and 1 kg/m3 at 600°C, respectively. With increases in temperature, the unconfined compressive strength increased first and then decreased. When the temperature was 400°C, the unconfined compressive strength of the specimens reached their highest values and then decreased. When the temperature was 400°C and 600°C, the strength of the stone powder concrete with fiber was higher than that without fiber, which shows that fiber can improve the mechanical properties of concrete at high temperatures. Based on the Box‐Behnken design (BBD) method, the unconfined compressive strength response regression model of basalt fiber‐reinforced concrete with high content of stone powder, which follows parameters including fiber content, fiber length, and temperature at high‐temperature environments, was established, and it was found that the interaction of fiber content, fiber length, and the temperature was significant based on multifactor interaction analysis. The analysis of ultrasonic signals based on the S transform showed that, with increases in temperature, the amplitudes of the acoustic response signals, the corresponding frequency spectrum, and the time‐frequency spectrum were clearly reduced. At the same temperature, the amplitudes of the acoustic response signals of different concrete testing blocks did not change much and remained at the same level.

Optimal Design of Annular Phased Array Transducers for Material Nonlinearity Determination in Pulse–Echo Ultrasonic Testing

Nonlinear ultrasound has been proven to be a useful nondestructive testing tool for micro-damage inspection of materials and structures operating in harsh environment. When measuring the nonlinear second harmonic wave in a solid specimen in the pulse–echo (PE) testing mode, the stress-free boundary characteristics brings the received second harmonic component close to zero. Therefore, the PE method has never been employed to measure the so-called “nonlinear parameter (β)”, which is used to quantify the degree of micro-damage. When there are stress-free boundaries, a focused beam is known to improve the PE reception of the second harmonic wave, so phased-array (PA) transducers can be used to generate the focused beam. For the practical application of PE nonlinear ultrasonic testing, however, it is necessary to develop a new type of PA transducer that is completely different from conventional ones. In this paper, we propose a new annular PA transducer capable of measuring β with improved second harmonic reception in the PE mode. Basically, the annular PA transducer (APAT) consists of four external ring transmitters and an internal disk receiver at the center. The focused beam properties of the transducers are analyzed using a nonlinear sound beam model which incorporates the effects of beam diffraction, material attenuation, and boundary reflection. The optimal design of the APAT is performed in terms of the maximum second harmonic reception and the total correction close to one, and the results are presented in detail.

Fatigue Crack Detection in AISI 304 Austenitic Stainless Steel Using Nonlinear and Linear Ultrasonic Testing Methods

Fatigue cracks are often underestimated by traditional linear ultrasonic techniques due to the poor direction as well as narrow gaps within the cracks. The nonlinear ultrasonic testing technique is a promising method that may be used to solve this problem. In this study, the effects of traditional C scan imaging in measuring fatigue cracks are analyzed by comparing their results with that of metallography. Then, the finite amplitude method of nonlinear ultrasonic testing is used to detect micro-damages, and the influences of excitation voltage on the nonlinear coefficient are investigated. The results indicated that the accuracy in C scan imaging becomes worse when the crack’s surface is not perpendicular to the incident wave or if the crack’s gap is very small. In contrast, relative nonlinear coefficients under an optimum voltage increase according to the degree of micro-damage, which was found to not be affected by the status of macro-cracks but was particularly sensitive to the accumulation of micro-damage. This study suggests that nonlinear ultrasonic techniques be implemented to achieve beneficial effects in testing fatigue damage.

Characterization of Contact‐Type Defects in Mortar Using a Nonlinear Ultrasonic Method

Second harmonic generation (SHG) is one of the common techniques in the nonlinear ultrasonic test. The contact‐type defects play an important role in material damage, which are hard to be detected. The traditional nonlinear parameter β used to evaluate the micro damage in material is derived from the classical stress‐strain relation, which is more suitable for the anharmonicity of crystal rather than the contact‐type defects. Recently, the theoretical model based on the bilinear stiffness law was derived, and the validity and applicability need to be further studied. For this purpose, by the numerical method, the contact interface in mortar is characterized based on the damage indicator γ. The relation between the excitation voltage and γ is obtained. Moreover, the effects of the crack length and orientation on the damage indicator γ are also obtained. The experimental method is also used to characterize the contact interface in mortar. Combining with the existing work, the results obtained in this article are discussed, and further conclusions can be drawn. The conclusions in this article provide potential of quantitative detection of the contact interface and quality evaluation of bonding layers in materials.

Assessment of Material Dislocation Damage by Nonlinear Ultrasound

Under harsh environment or during service, the mechanical properties of materials or structure will deteriorate. Most of the simulations exhibit the phenomenon of nonlinearity by introducing the actual small defects, without considering dislocation. In this manuscript, subroutines are written to change the mechanical constitutive behaviour of materials. When the mechanical constitutive behaviour of the material is not linear any more, it is found that the propagation of ultrasonic wave in the material will show more obvious nonlinear phenomenon. Furthermore, the nonlinear detection coefficient is used to characterize the increase of harmonic components. This work provides a new idea for nonlinear ultrasonic testing.

Multi-Frequency Piezoelectric Micromachined Ultrasonic Transducers

In this paper multi-frequency piezoelectric MEMS ultrasonic transducers (pMUTs) are designed, characterized and tested for nondestructive evaluation (NDE) of solids. The transducers operate in flexural mode, and are tuned to three different frequencies namely 1 MHz, 1.5 MHz and 2 MHz. The microstructural layers consist of aluminum nitride (AlN) as an active sensing layer sandwiched between metal and doped silicon electrodes. pMUTs are designed with octagonal and circular membranes. The vibration of silicon membrane assists piezoelectric element to convert energies. The transducers are modeled numerically to obtain their dynamic characteristics. Piezoelectric Multi-User MEMS Processes (PiezoMUMPs) are utilized to manufacture pMUTs. The electromechanical characterization shows that the circular design has higher figure of merit as compared to the octagonal design due to more uniform stress distribution transferred between silicon and AlN layers. It is demonstrated that the piezeoelectric layer should be deposited up to the inflection point of diaphragm deformation. This avoids the signal cancellation due to opposite polarization. The performance of pMUTs as receiver is evaluated to detect the creep damage by implementing nonlinear ultrasonic testing (NLUT). NLUT is based on detecting higher harmonics in solids due to heterogeneity in materials. Significant amplification in the second harmonics is obtained due to highly narrowband and low damping characteristics of pMUTs that improves the resolution of NLUT to detect subwavelength damage. Higher harmonics can be detected using small footprint pMUT device, which is not possible with conventional piezoelectric transducers. This allows better spatial resolution of nonlinear measurement.

Research on High Temperature Aging Detection Method of Heat Resistant Steel Based on Nonlinear Ultrasound Detection Technology

Rapid detection of high temperature aging process and early damage is very important for TP347HFG austenitic heat resistant steel, which is brittle and has short stable expansion period. Nonlinear ultrasound technology is sensitive to micro-nano scale defects and has great potential in early damage detection. The relationship curve between thermal damage degree and ultrasonic nonlinearity coefficient is obtained by using non-linear ultrasound technology, and the microstructure evolution characteristics of materials are analyzed. The results show that the ultrasonic nonlinearity coefficient of TP347HFG steel increases with aging time. The maximum point appears at 500 h and then increases monotonously. This trend is related to the formation and loss of conformal strain state. The experimental results provide a theoretical basis for the non-linear ultrasonic testing of TP347HFG steel at high temperature.

A Study on Fatigue State Evaluation of Rail by the Use of Ultrasonic Nonlinearity.

Nonlinear ultrasonic testing has been accepted as a promising manner for evaluating material integrity in an early stage. Stress fatigue is the main threats to train safety, railways examinations for stress fatigue are more significant and necessary. A series of ultrasonic nonlinear wave experiments are conducted for rail specimens extracted from railhead with different degree of fatigue produced by three-point bent loading condition. The nonlinear parameter is the indicator of nonlinear waves for expressing the degree the fatigue. The experimental results show that the sensitivity of a third harmonic longitudinal wave is higher than second harmonic longitudinal wave testing. As the same time, collinear wave mixing shows strong relative with fatigue damages than a second longitudinal wave nondestructive testing (NDT) method and provides more reliable results than third harmonic longitudinal waves nonlinear testing method.

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.

A multi-parameter ultrasonic evaluation of mean grain size using optimization

An evaluation model based on multiple ultrasonic parameters was developed to control mean absolute error between an actual measured value and a model calculation value. Superalloy GH4169 was used to validate the presented model. A multi-dimensional ultrasonic parameter set was built for each sample by ultrasonic and nonlinear ultrasonic test and parameter calculation. The feature scale of different parameters was restricted to the same range using normalization. The dimensionality of the parameter set was descended by a correlation metric with grain size. A new one-dimensional ultrasonic characteristic parameter was comprised of the select normalized set of ultrasonic parameters by quadratic polynomial, exponential, Gauss kernel and linear mapping functions with undetermined coefficients. The relationship between the new ultrasonic multiple eigenvalues mapping parameter and estimated grain size was expressed using a linear fitting function. An optimization problem aimed at minimizing the mean absolute error between the estimated and quantitative measured grain size was solved using evolutionary algorithms to obtain coefficients for the mapping and fitting functions. These calculations were used to generate four full multi-parameter ultrasonic evaluation models, which were benchmarked against three single parameter evaluation models (i.e. velocity, attenuation coefficient, and backscattering). The performance analysis and verification using leave-one-out cross-validation demonstrate the utility of the MUE model through its high precision, good stabilization, super anti-interference and practicality.

Thermal modulation of nonlinear ultrasonic wave for concrete damage evaluation.

A nonlinear ultrasonic test is proposed for material damage evaluation using thermal modulation. Temperature change excites and modulates nonlinear behavior of ultrasonic waves in concrete. Coda wave interferometry was used to analyze the relative velocity change of ultrasonic wave with temperature variations. On concrete samples with different levels of thermal damage, experimental results indicate that the samples with a higher damage level demonstrated higher sensitivity to temperature variations. In addition, a slow dynamics nonlinear behavior was observed. When the temperature changed and then remained constant, the wave velocity gradually approached to its equilibrium value.

Nonlinear ultrasonic test of concrete cubes with induced crack

Second and third harmonic ratios method to evaluate initial damage in concrete have been extensively studied. However, some regularities of this technique still not clear in current stage. In order to better understand the regularity of nonlinear parameters β and γ on micro and macro damage in concrete, the cracks with different damage scales are induced in concrete specimens. Three levels of test voltage are applied to intact concrete specimens, with the purpose to demonstrate the excitation voltage has an unneglectable effect on nonlinear parameters. The regularity of nonlinear parameters on crack orientation is also obtained in this study. The results of the experiment have considerable importance with respect to the method of higher harmonic ratios for concrete and other inhomogeneous materials.

Non-linear ultrasonic monitoring of damage progression in disparate rocks

This paper focusses on non-destructive characterization of stress-induced damage progression in three types of rocks by experimentally capturing the elasto-dynamic non-linear response of the rocks, with the hypothesis that non-linear approaches have increased sensitivity relative to linear ultrasonic testing approaches. For this task, a non-linear ultrasonic testing procedure known as the Scaling Subtraction Method (SSM) has been implemented on uniaxially loaded rock specimens. The SSM procedure is based on exciting the damaged medium with two acoustic signals at different amplitudes consecutively. The linearly rescaled acoustic response at low excitation is subtracted from the response at large amplitude excitation for quantification of the elastic non-linearity of the medium by a non-linear indicator θ. At first, aluminum, Lyons sandstone, granodiorite and Gosford sandstone specimens were characterized using SSM and their inherent non-linearity was quantified. After this, the rock specimens were loaded under uniaxial compressive step-loading and ultrasonic measurements were performed simultaneously at each loading step. The non-linear indicator θ was calculated as the specimens were progressively damaged, and the changes in the non-linear response were linked to the different physical processes accompanying damage progression in rocks. The study concluded that the non-linear SSM technique is capable of sensitively recording signatures of the different stages of damage evolution in rocks.

Application of Wavelet and EEMD Joint Denoising in Nonlinear Ultrasonic Testing of Concrete

The health state of concrete is deteriorating during its service. Nonlinear ultrasonic detection based on the amplitude of the fundamental and the second harmonic is considered to be a powerful tool for the discovery of the microcrack in concrete. However, the research on processing the nonlinear ultrasonic signal is still insufficient. In order to highlight the real frequency domain components in the nonlinear ultrasonic signal, wavelet and ensemble empirical mode decomposition (EEMD) were joined to denoise the numerical and measured signal. The optimal wavelet base and the decomposition level were determined by the signal‐to‐noise ratios (SNRs). Then, the wavelet threshold denoising signal was decomposed by EEMD, omitting the high‐frequency components and ultimately achieving the desired denoising effect. The denoising result of the test signals demonstrates that this method is effective in denoising the details of the ultrasonic signal and improving the reliability and adaptability of the nonlinear ultrasonic testing. In this experiment, the concrete with the microcrack was tested by linear and nonlinear ultrasonic methods. Based on the variation regularity of the nonlinear ultrasonic coefficient β and velocity v, we can conclude that the nonlinear ultrasonic parameter β is more sensitive to the microcrack in concrete than the traditional wave velocity v. The nonlinear ultrasonic testing can be an important supplement to the current nondestructive testing technique of the concrete.

The integration of superlattices and immersion nonlinear ultrasonics to enhance damage detection threshold

We demonstrate the enhancement of immersion nonlinear ultrasonic testing (NLUT) by exploiting superlattices (SLs). NLUT can detect sub-wavelength micro-structural changes in solids by measuring the fundamental and second harmonic frequencies. The amplitude of second harmonic frequency increases with the presence of defects or other heterogeneities. The immersion NLUT is beneficial as water provides a consistent coupling condition; however, water generates high non-linearity that can mask the weak non-linearity originated from the micro-structural features in solids. In this research, SLs are proposed to remove the non-linearity arisen from water and experimental instruments. The SLs made of a periodic arrangement of composite layers can provide a band gap to restrict the propagation of a specific range of frequencies between transmitter and receiver. The periodic arrangement of solid-fluid layers is numerically designed and experimentally adapted to the immersion NLUT. Our results imply that the periodic array of 100 μm thick glass and 100 μm thick water layers provides a band gap that blocks 4.5 MHz (the second harmonic frequency), while this periodic structure passes 2.25 MHz (the first harmonic frequency). The improvement in the sensitivity of the NLUT is demonstrated through detecting the micro-structural changes associated with plastic deformation in aluminum 1100 specimens. It is revealed that the proposed methodology enhances the damage detection sensitivity of immersion NLUT by an order of magnitude as compared to the current practice.

Numerical study on sub-harmonic generation due to interior and surface breaking cracks with contact boundary conditions using time-domain boundary element method

Recently, the ultrasonic testing (UT) based on the contact acoustic nonlinearity (CAN) has attracted notice as a new technique for detection of closed cracks which cannot be detected by using the linear UT (LUT). In the nonlinear UT (NLUT), detection and size measurement of flaws are conducted via the frequency spectrum analysis of nonlinear ultrasonic waves which consist of higher- and sub-harmonic waves. Although the mechanism of higher-harmonic generation due to CAN has been understood mostly from theoretical and experimental points of view, that of sub-harmonic generation has not been revealed yet. In addition, there are few numerical and theoretical studies on the phenomenon of sub-harmonic generation due to the CAN. In this paper, the boundary integral equation for two-dimensional (2-D) elastic wave scattering by cracks is formulated and numerically solved to investigate the behavior of the sub-harmonic waves. The clapping motion and dynamic friction on crack faces are modeled by considering contact boundary conditions, and their interaction with the characteristic of frequency response in the corresponding linear system is investigated. In this study, time-domain numerical simulations are implemented for both an interior crack in an unbounded elastic solid and a surface breaking crack in an elastic half-space. Some frequency response analyses for a linear system corresponding to the time-domain nonlinear simulations are also performed by using the frequency-domain boundary element method. From obtained numerical results, the causes of sub-harmonic generation are discussed.

Dynamic acousto-elastic testing of concrete with a coda-wave probe: comparison with standard linear and nonlinear ultrasonic techniques

The use of nonlinear acoustic techniques in solids consists in measuring wave distortion arising from compliant features such as cracks, soft intergrain bonds and dislocations. As such, they provide very powerful nondestructive tools to monitor the onset of damage within materials. In particular, a recent technique called dynamic acousto-elasticity testing (DAET) gives unprecedented details on the nonlinear elastic response of materials (classical and non-classical nonlinear features including hysteresis, transient elastic softening and slow relaxation). Here, we provide a comprehensive set of linear and nonlinear acoustic responses on two prismatic concrete specimens; one intact and one pre-compressed to about 70% of its ultimate strength. The two linear techniques used are Ultrasonic Pulse Velocity (UPV) and Resonance Ultrasound Spectroscopy (RUS), while the nonlinear ones include DAET (fast and slow dynamics) as well as Nonlinear Resonance Ultrasound Spectroscopy (NRUS). In addition, the DAET results correspond to a configuration where the (incoherent) coda portion of the ultrasonic record is used to probe the samples, as opposed to a (coherent) first arrival wave in standard DAET tests. We find that the two visually identical specimens are indistinguishable based on parameters measured by linear techniques (UPV and RUS). On the contrary, the extracted nonlinear parameters from NRUS and DAET are consistent and orders of magnitude greater for the damaged specimen than those for the intact one. This compiled set of linear and nonlinear ultrasonic testing data including the most advanced technique (DAET) provides a benchmark comparison for their use in the field of material characterization.