Acoustic Nonlinearity Parameter Research Articles

A Calibration Technique for Ultrasonic Immersion Transducers and Challenges in Moving Towards Immersion Based Harmonic Imaging

The present article describes the calibration of ultrasonic immersion transducers using reciprocity technique. A step-by-step procedure and instrumentation requirements for transducer calibration are presented. Challenges encountered during the calibration experiment such as diffraction and attenuation corrections, and mismatched electrical impedances were also explored. The calibrated transducer was used to measure the acoustic nonlinearity parameter (β) of distilled water using the finite amplitude method. The objective of the current study is to identify potential challenges while moving towards a nonlinear immersion scanning technique for immersed engineering solids. Challenges such as effect of additives (corrosion inhibitors, surfactants etc.), misalignment of transducers, and effect of longer propagation paths were explored. Additives to distilled water were found to decrease the β of the mixture, and for an axial transducer misalignment of 2 mm, β was observed to increase by a factor of 2. Finally, the effect of propagation distance and excitation amplitude is shown.

Analysis of acoustic nonlinearity parameter B/A in liquids containing ultrasound contrast agents.

The acoustic nonlinearity parameter B/A plays a significant role in the characterization of acoustic properties of various biomaterials and biological tissues. It has the potential to be a favorable imaging modality in contrast ultrasound imaging with coated microbubbles. However, the development of effective means for evaluating the nonlinearity parameter of suspensions of ultrasound contrast agents (UCAs, also known as bubbly liquids) remains open. The present paper formulates a new equation based on the thermodynamic method that correlates both attenuation and phase velocity of linear ultrasound. The simplicity of the present method makes the B/A estimation possible with a relatively rigorous mathematical derivation. The calculated nonlinearity parameter contains the contribution of dynamic effects of bubbles, and its low-frequency limit agrees with B/A estimated by the method of mixture law when the volume fraction is below 10-4. Furthermore, the maximum B/A in bubbly liquids can reach up to105, while the minimum can be as low as -105. The negative nonlinearity parameter indicates significantly different thermodynamic properties of bubbly liquids.

A data-driven approach to construct a quantitative relationship between microstructural features of fatigue cracks and contact acoustic nonlinearity

This study demonstrates the feasibility of a data-driven approach to construct a quantitative relationship between nonlinear acoustic parameters and microstructural features of contact interfaces. The near-surface nonlinearity is measured using dynamic acousto-elastic testing (DAET) with a surface wave probe, while the microstructural features are extracted from scanning electron microscopy (SEM) images of fatigue cracks. Four aluminum alloy samples, each having a fatigue crack are prepared. Six local nonlinearity parameters are measured at different locations along the crack propagation direction. A total of 40 local measurements are acquired. A principal component analysis (PCA) reveals that all six nonlinearity parameters are correlated and hence can be replaced by one principal component (PC). Fifteen crack micro-geometrical features at each measurement point were extracted from the SEM images. Regression analysis is used to relate the PC of the nonlinearity parameters to the microstructural features at the crack interface. We compare three regression models that take variable selection into account: stepwise multiple linear regression (MLR), stepwise principal component regression (PCR), and least absolute shrinkage and selection operator (LASSO). Despite having different principles, the three predictive models identify two features as the most significant in predicting the interface nonlinearity: the crack aperture (opening) distribution and the distance to the crack tip. The differences between the three models and the physical interpretation of the data-driven predictions are discussed.

Nonlinear Lamb wave for the evaluation of creep damage in modified 9Cr–1Mo steel

Higher harmonic generation using nonlinear ultrasonic is known to be very sensitive to microstructural degradation. This technique relies on nonlinear stress-strain relation i.e. nonlinear Hooke's law. The quantitative measurement to characterize the materials degradation is done by the nonlinear ultrasonic parameter, β. The objective of this work is to use nonlinear ultrasonic using Lamb wave to evaluate creep damage in modified 9Cr–1Mo steel. Relative change in β was seen to be dependent on the higher order elastic constants that evolve with microstructure as creep progresses as well as sub-structural changes. The extent of damage in the material due to creep exposure was evaluated by Kernel Average Misorientation (KAM) from EBSD and co-related with nonlinear acoustic parameter.

Contribution of dislocation pileups to acoustic nonlinearity parameter

This paper develops an analytical model to calculate the acoustic nonlinearity parameter induced by dislocation pileups in isotropic elastic solids. It shows that the pileup-induced acoustic nonlinearity parameter depends on the pileup length, number of dislocations in a pileup, Burgers vector, and dislocation density. Additionally, it is found that the formula for pileup-induced acoustic nonlinearity parameter has a similar mathematical form to those for other types of defects such as dislocation strings, dislocation dipoles, and extended dislocations. They are all scaled with a dimensionless parameter (Lch/b)n, where Lch is a characteristic length of the defect, b is the magnitude of the Burgers vector, and n is either 3 or 4.

The measurement of weld morphology and inclusions using ultrasonics

The morphology of welding pool (fusion zone and heat affected zone) includes a variety of microstructural constitutions (the formation of new boundaries, pores, and textures) that can affect the integrity of welded joint. Currently, microscopic observations are the common method to characterize the welding pool, which is a destructive post-welding procedure, and requires a complex preparation process. In this paper, linear and non-linear ultrasonic methods are investigated to measure the weld morphology and the presence of porosity nondestructively in welds manufactured with gas tungsten arc welding (GTAW). The weld morphology and the presence of porosity are quantified using microscopic investigations. The measurements show that the ultrasonic energy obtained by linear ultrasonics and the acoustic nonlinearity parameter obtained by nonlinear ultrasonics have good correlation with the weld morphology. The relationship between the ultrasonic energy and the weld morphology is validated further with numerical models. The linear UT at 1 MHz is not sensitive to the presence of porosity as the resolution is limited by ultrasonic wavelength. However, nonlinear ultrasonics has better sensitivity to the inclusions due to sub-wavelength resolution.

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.

Application of Fresnel Zone Plate Focused Beam to Optimized Sensor Design for Pulse-Echo Harmonic Generation Measurements.

In nonlinear acoustic measurements involving reflection from the stress-free boundary, the pulse-echo method could not be used because such a boundary is known to destructively change the second harmonic generation (SHG) process. The use of a focusing acoustic beam, however, can improve SHG after reflection from the specimen boundary, and nonlinear pulse-echo methods can be implemented as a practical means of measuring the acoustic nonlinear parameter (β) of solid specimens. This paper investigates the optimal sensor design for pulse-echo SHG and β measurements using Fresnel zone plate (FZP) focused beams. The conceptual design of a sensor configuration uses separate transmission and reception, where a broadband receiver is located at the center and a four-element FZP transmitter is positioned outside the receiver to create a focused beam at the specified position in a solid sample. Comprehensive simulations are performed for focused beam fields analysis and to determine the optimal sensor design using various combinations of focal length, receiver size and frequency. It is shown that the optimally designed sensors for 1 cm thick aluminum can produce the second harmonic amplitude and the uncorrected nonlinear parameter corresponding to the through-transmission method. The sensitivity of the optimal sensors to the changes in the designed sound velocity is analyzed and compared between the odd- and even-type FZPs.

Nondestructive evaluation of thermal aging of adhesive joints by using a nonlinear wave mixing technique

This paper describes the use of a wave mixing technique to monitor thermal aging of adhesive joints. This newly developed technique measures the acoustic nonlinearity parameter of the adhesive in the joint. One of the significant features of this technique is that it requires only one-side access to the adhesive joint being measured, which significantly increases the technique's utility in field applications. To demonstrate the effectiveness of the new technique, measurements are conducted on adhesively joined samples that are thermally aged under different heating conditions, i.e., different temperature profiles and aging times. The results show that the measured acoustic nonlinearity parameter of the adhesive is very sensitive to thermal aging. On the other hand, linear reflection from the adhesive layer remains almost a constant among all the aging conditions investigated in this study. It is therefore concluded that the acoustic nonlinearity parameter is a much more sensitive measure of thermal aging of adhesive joints.

Nonlinear ultrasonic damage evaluation system research and development and its application on S355J2W steel for high speed train

The nonlinear ultrasonic (NLU) technique has been proposed to monitor structure health. It is well known that damage of materials is generally accompanied by increase of the materials’ nonlinearity. However, after processing such as welding, the microstructure of the material will change, which might affect the behavior of materials’ nonlinearity after degradation, further, inducing inaccuracy in evaluation of the structure life. An NLU system is developed to characterize the damage due to plastic deformation in S355J2W weathering resistant steel specimens which underwent different heat treatment processes. The experimental results show that the NLU system is effective and accurate for the measurement of higher harmonic components, and acoustic nonlinear parameters (ANP) increase with the increase of tensile stress. The results also show that ANP response relates to the grain size.

Characterization of Tempering Behaviour of Modified 9Cr-1Mo Steel by Ultrasonic Lamb wave Mixing

This work demonstrates the use of mixing of ultrasonic Lamb waves to characterize the tempering behaviour in metallic plate. Lamb wave mixing has been used to measure the generated second harmonic during tempering of mod.9Cr-1Mo steel plate. As-received material is normalized at 1080°C and then tempered in the temperature range of 600 - 850°C with a step size of 50°C for 1.5hrs and followed by furnace cooling. Lamb wave mixing technique has been used to assess the tempering behaviour of this material. Nonlinear ultrasonic parameter β which is the ratio of 2nd harmonic amplitude to the multiplication of the fundamental amplitudes is determined from the mixing wave at each temperature and correlated with microstructural characteristics. It is seen that this nonlinear acoustic parameter (β) is sensitive towards coherency strain generated between precipitate and matrix during tempering.

Coding of Probe Signals in the Tomography of Acoustic Nonlinear Parameters

Different ways of coding radiated signals that probe a tomographized object such as a liquid medium are compared in order to reconstruct the spatial distribution of acoustic nonlinear parameters using a small number of transducers. The results from reconstructing model nonlinear scatterers are discussed. The region of spatial frequencies available for reconstruction is analyzed.

Changes in linear and nonlinear elastic properties of aluminium alloy under static deformation

Mechanical tests and ultrasonic measurements of an aluminium alloy sample were carried out. As a result, the dependencies of velocities of shear and longitudinal waves as well as acoustoelastic coefficients for waves’ propagation times on the sample elongation were received. The linear and nonlinear elastic constants were calculated. It is shown that the effective elastic properties significantly change under plastic deformation. In addition, it presents the results of the determination of the acoustic nonlinearity parameter and acoustoelastic coefficients for different values of the sample deformation.

Experimental and Numerical Study of Nonlinear Lamb Waves of a Low-Frequency S₀ Mode in Plates with Quadratic Nonlinearity.

This paper investigates the propagation of low-frequency S0 mode Lamb waves in plates with quadratic nonlinearity through numerical simulations and experimental measurements. Both numerical and experimental results manifest distinct ultrasonic nonlinear behavior which is mainly presented by the second harmonics. Meanwhile, we find that both the acoustic nonlinearity parameter and dispersion distance show the exponential decay trend with the increase of frequency-thickness. Moreover, the results reveal that the frequency is key to affect the acoustic nonlinearity parameter and dispersion distance with the same frequency-thickness. This study theoretically and experimentally reveals that nonlinear Lamb waves of the low-frequency S0 mode are feasible to quantitatively identify material weak nonlinearity in plates.

Combination of Phase Matching and Phase-Reversal Approaches for Thermal Damage Assessment by Second Harmonic Lamb Waves.

It is known that measurement and extraction of the tiny amplitude of second harmonic Lamb waves are the main difficulties for practical applications of the nonlinear Lamb wave technique. In this study, phase-reversal approaches and phase matching technique are combined to build up the second-harmonic generation (SHG) of Lamb waves. A specific Lamb wave mode pair, which satisfied phase matching conditions, is selected to ensure the generation of cumulative second harmonic waves. Lamb wave signals with the same frequency but in reverse phase, propagating in the given specimen, are added together to counteract the fundamental waves, and simultaneously to enhance the signals of the second harmonic generated. The obtained results show that the phase-reversal approach can enhance the signals of second harmonic Lamb waves, and effectively counteract that of the fundamental waves. The approach is applied to assess the thermal-induced material degradation in the stainless steel plates. Distinctions of the acoustic nonlinearity parameters under different degraded levels are clearly shown in an improved repeatable and reliable manner, while those of linear wave velocity in the specimens are neglectable. The experimental investigations performed indicate that the proposed approach can be taken as a promising alternative for assessment of material degradation in its early stages.

Fatigue Damage Evaluation Using Nonlinear Lamb Waves with Quasi Phase-Velocity Matching at Low Frequency

Due to the dispersive and multimode natures, only nonlinear Lamb waves with exact phase-velocity matching were generally used in previous studies to evaluate the evenly distributed microstructural evolution in the incipient stage of material degradation, because of the cumulative generation of second harmonics, which was also found within a significant propagation distance for mode pair S0-s0 with quasi phase-velocity matching at low frequency. To explore the feasibility of fatigue damage evaluation by using this mode pair and fully utilize its unique merits, the cumulative second harmonic analysis was performed on aluminum alloy specimens with various material damage produced by the continuous low cycle fatigue tests. Similar to mode pair S1-s2 with exact phase-velocity matching, a mountain shape curve between the normalized acoustic nonlinearity parameter and the fatigue life was also achieved with the peak point at about 0.65 fatigue life for mode pair S0-s0, even though a relatively higher sensitivity to fatigue damage was observed for mode pair S1-s2. The excited frequency selection was further analyzed in a certain frequency range, where the quasi phase-velocity matching condition was satisfied for mode pair S0-s0 owing to the less dispersive property. Results show that the fatigue damage can be effectively detected using the mode pair S0-s0, and a relatively lower excited frequency was preferred due to its higher sensitivity to microstructural evolution.

Acoustic nonlinearity parameter induced by extended dislocations

Excess acoustic nonlinearity is a signature of microstructural defects on a propagating ultrasound. By measuring the excess acoustic nonlinearity parameter, defect characteristics can be inferred nondestructively through ultrasonic techniques. To this end, proper models are needed to relate the excess acoustic nonlinearity parameter with defect characteristics. In this study, an analytical model for extended dislocations is developed that relates the excess acoustic nonlinearity parameter with characteristics of the extended dislocation including dislocation density, stacking fault energy, and equilibrium distance between the two partial dislocations that form the extended dislocation. According to this model, the excess acoustic nonlinearity parameter induced by extended dislocations consists of a stress-independent term and a stress-dependent term. Both terms are scaled with (Lchar/b)n, where Lchar is the equilibrium distance between the two partials, b is the magnitude of Burgers vector, and n is 3 and 4 for the stress-independent and stress-dependent terms, respectively. The model will be useful for interpreting results from ultrasonic nondestructive evaluation of material defects.

Acoustic Nonlinearity Parameters Due to Microstructural Defects

This study presents a general approach to derive the acoustic nonlinearity parameters induced by various types of dislocation configurations including dislocation strings (monopoles), dislocation dipoles, dislocation pileups and extended dislocations. It is found that expressions of the acoustic nonlinearity parameter induced by such a variety of dislocation configurations share a common mathematical form. They are all scaled with $$\left( {L_{\mathrm{ch}} /b} \right) ^{n}$$ , where $$L_{\mathrm{ch}} $$ is a characteristic length of the dislocation configuration, b is the magnitude of the Burgers vector, and n is either 3 or 4. Semiquantitative analysis is presented to compare the magnitudes of the acoustic nonlinearity parameters among different types of dislocation configurations.

Investigation of molecular interactions in binary mixture of dimethyl carbonate + N-methylformamide at T = (303.15, 308.15, 313.15 and 318.15) K

Density (ρ) and speed of sound (u) of binary liquid mixtures of dimethyl carbonate and N-methylformamide have been determined at T = (303.15, 308.15, 313.15 and 318.15) K over the entire composition range. Experimental data are used to evaluate excess values of molar volume ( $$V_{\text{m}}^{\text{E}}$$ ), isentropic compressibility ( $$k_{\text{s}}^{\text{E}}$$ ), isothermal compressibility ( $$k_{\text{T}}^{\text{E}}$$ ), intermolecular free length ( $$L_{\text{f}}^{\text{E}}$$ ), acoustic impedance ( $$Z^{\text{E}}$$ ) and ultrasonic speed ( $$u^{\text{E}}$$ ). The VE data in the present investigation were analysed by using Prigogine–Flory–Patterson (PFP) theory. Partial and excess partial molar volumes ( $$\bar{V}_{{{\text{m}},1}}$$ , $$\bar{V}_{{{\text{m}},2}}$$ ), ( $$\bar{V}_{{{\text{m}},1}}^{\text{E}}$$ , $$\bar{V}_{{{\text{m}},2}}^{\text{E}}$$ ) and partial and excess partial molar volume of the components at infinite dilution ( $$\overline{V}_{{{\text{m}},1}}^{\infty }$$ , $$\overline{V}_{{{\text{m}},2}}^{\infty }$$ ), ( $$\overline{V}_{{{\text{m}},1}}^{{{\text{E}},\infty }}$$ , $$\overline{V}_{{{\text{m}},2}}^{{{\text{E}},\infty }}$$ ) at T = (303.15, 308.15, 313.15, 318.15) K have been calculated. The excess/deviation properties were fitted to Redlich–Kister equation to obtain their coefficients and standard deviations. The present investigation also comprises the acoustic nonlinearity parameter (B/A) in the mixtures and calculation of cohesive energy $$\Delta A$$ , Van der Wall’s constants (a, b) and distance of closest approach (d). Moreover, various semi-empirical relations of ultrasonic speed have been used to correlate the theoretical velocities. FT-IR spectra of pure components and their binaries have been measured at T = 298.15 K.