Acoustic Nonlinearity Parameter Research Articles

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.

Nonlinear Rayleigh surface waves to characterize microscale damage due to alkali-silica reaction (ASR) in full-scale, nuclear concrete specimens

Nonlinear Rayleigh surface waves are used to monitor the damage state due to alkali-silica reaction (ASR) in full-scale reinforced concrete block specimens created as part of a full-scale testing program for concrete nuclear containment structures. The measurement technique uses a wedge/transducer source to generate and a non-contact, air-coupled receiver to detect nonlinear Rayleigh surface waves to obtain the acoustic nonlinearity parameters for three different reinforced block concrete specimens – a confined and an unconfined ASR specimen, plus a control specimen – at three different time intervals. These results further validate the utility of nonlinear Rayleigh waves to quantify the progress of microscale damage due to ASR in full-scale, concrete structures.

Nonlinear effects of micro-cracks on acoustic surface and wedge waves

Micro-cracks give rise to non-analytic behavior of the stress-strain relation. For the case of a homogeneous spatial distribution of aligned flat micro-cracks, the influence of this property of the stress-strain relation on harmonic generation is analyzed for Rayleigh waves and for acoustic wedge waves with the help of a simple micromechanical model adopted from the literature. For the efficiencies of harmonic generation of these guided waves, explicit expressions are derived in terms of the corresponding linear wave fields. The initial growth rates of the second harmonic, i.e., the acoustic nonlinearity parameter, has been evaluated numerically for steel as matrix material. The growth rate of the second harmonic of Rayleigh waves has also been determined for microcrack distributions with random orientation, using a model expression for the strain energy in terms of strain invariants known in a geophysical context.

Detection and Characterization of Randomly Distributed Micro-cracks in Elastic Solids by One-Way Collinear Mixing Method

Numerical simulations on the propagation of bulk waves in elastic solids with randomly distributed micro-cracks by the one-way collinear mixing method are performed to investigate the behavior of the resonant wave. The results show that the resonant wave can be generated due to the effect of micro-cracks, and the position and the size of micro-crack zone can be detected by the time signal of the resonant wave. Based on statistical analysis from numerous results of random micro-crack models, we find that the acoustic nonlinear parameter increases linearly with the micro-crack density and the size of micro-crack zone, which is also related to the frequency of resonant wave and friction coefficient of micro-crack surfaces. This study numerically reveals that the one way mixing method can be employed to quantitatively identify and characterize micro-cracks in elastic solids.

Characterization of microstructural changes due to prolonged thermal exposure of directionally solidified Ni-base super alloy CM 247LC using ultrasonic

The high temperature strength of directionally solidified Ni-base super alloy CM 247LC strongly depends on the morphology, volume fraction, size and size distribution of γ′ precipitate (Ni3Al) in the FCC γ matrix. The microstructure of the alloy is engineered to achieve the right combination of these parameters that provides the required high temperature strength and creep resistance. The alloy contains high volume fraction of coherent γ′ precipitates having near cubic shape. High temperature exposure of gas turbine components made out of the alloy leads to coarsening of the γ′ precipitates and broadening of the γ matrix channel. This in turn, adversely affects the high temperature mechanical properties of the alloy. The present study endeavours to non-destructively characterize such detrimental changes in the microstructure that controls the mechanical properties and limits the life of components. The microstructural changes of the fully heat treated alloy exposed at 980 °C for different hours (100–1200) of thermal exposure have been characterized using ultrasonic methods. Changes in microstructural parameters due to different hours of thermal exposure have been correlated with changes in ultrasonic velocity, ultrasonic attenuation coefficient and second order acoustic nonlinearity parameter. It is observed that the change in attenuation is predominantly by absorption of the ultrasonic wave due to dislocation damping in the γ channels. Nonlinear ultrasonic parameter changes with thermal exposure predominantly due to the alteration of dislocation precipitate interaction. A dislocation precipitation interaction model for ultrasonic wave distortion has been used to explain the observed variation in nonlinear parameter. A microstructural parameter has been identified that varies in a similar way as ultrasonic attenuation and second order ultrasonic parameter. It is shown that variations in the acoustic non-linearity parameter follow the trend more closely with the identified microstructural parameter.

Generation Mechanism of Nonlinear Rayleigh Surface Waves for Randomly Distributed Surface Micro-Cracks.

This paper investigates the propagation of Rayleigh surface waves in structures with randomly distributed surface micro-cracks using numerical simulations. The results revealed a significant ultrasonic nonlinear effect caused by the surface micro-cracks, which is mainly represented by a second harmonic with even more distinct third/quadruple harmonics. Based on statistical analysis from the numerous results of random micro-crack models, it is clearly found that the acoustic nonlinear parameter increases linearly with micro-crack density, the proportion of surface cracks, the size of micro-crack zone, and the excitation frequency. This study theoretically reveals that nonlinear Rayleigh surface waves are feasible for use in quantitatively identifying the physical characteristics of surface micro-cracks in structures.

Noncontact nonlinear resonance ultrasound spectroscopy (NRUS) for small metallic specimens

The objective of this research is to use nonlinear resonance ultrasound spectroscopy (NRUS) to evaluate the sensitivity of the nonclassical hysteretic nonlinearity parameter, α to microscopic material damage in metallic specimens. The proposed NRUS procedure uses both a noncontact source and receiver – an air-coupled piezoelectric transducer source and a laser vibrometer receiver – to excite and detect the axial motion of a slender rod. This fully noncontact configuration avoids mechanical contact which can adversely influence the measurements. This NRUS procedure measures αf and αQ by calculating the amount of the shift of the resonance frequency and the change of quality factor (Q) as a function of increasing excitation amplitudes. The sensitivity of this NRUS measured α parameters to small changes in microstructure is demonstrated on a series of thermally aged 17-4 PH stainless steel samples. These hysteretic nonlinearity (αf and αQ) results are then compared to (quadratic) acoustic nonlinearity parameter (β) values previously measured on these same 17-4 PH samples to demonstrate the sensitivity of the hysteretic nonlinearity parameters to changes in microstructure due to precipitate formation.

Acoustic nonlinearity parameter measurements in a pulse-echo setup with the stress-free reflection boundary.

This paper describes the acoustic nonlinearity parameter (β) determination for fluids using a pulse-echo method with the stress-free boundary. A newly derived β formula requires the measurement of the fundamental and second harmonic displacements with appropriate corrections for attenuation, diffraction, and boundary reflection. Measurements are composed of two steps: receiver calibration and harmonic generation. The β values calculated for water at several distances between the planar transducer and the water-air interface are in good agreement with literature, providing a validation for the method.

In situ nonlinear ultrasonic technique for monitoring microcracking in concrete subjected to creep and cyclic loading

This research conducts in situ nonlinear ultrasonic (NLU) measurements for real time monitoring of load-induced damage in concrete. For the in situ measurements on a cylindrical specimen under sustained load, a previously developed second harmonic generation (SHG) technique with non-contact detection is adapted to a cylindrical specimen geometry. This new setup is validated by demonstrating that the measured nonlinear Rayleigh wave signals are equivalent to those in a flat half space, and thus the acoustic nonlinearity parameter, β can be defined and interpreted in the same way. Both the acoustic nonlinearity parameter and strain are measured to quantitatively assess the early-age damage in a set of concrete specimens subjected to either 25 days of creep, or 11 cycles of cyclic loading at room temperature. The experimental results show that the acoustic nonlinearity parameter is sensitive to early-stage microcrack formation under both loading conditions – the measured β can be directly linked to the accumulated microscale damage. This paper demonstrates the potential of NLU for the in situ monitoring of mechanical load-induced microscale damage in concrete components.

Symmetry properties of second harmonics generated by antisymmetric Lamb waves

Symmetry properties of second harmonics generated by antisymmetric primary Lamb waves are systematically studied in this work. In theory, the acoustic field of second harmonic Lamb waves is obtained by using the perturbation approximation and normal modal method, and the energy flux transfer from the primary Lamb waves to second harmonics is mainly explored. Symmetry analyses indicate that either the symmetric or antisymmetric Lamb waves can merely generate the symmetric second harmonics. Finite element simulations are performed on the nonlinear Lamb wave propagation of the antisymmetric A0 mode in the low frequency region. The signals of the second harmonics and the symmetric second harmonic s0 mode are found to be exactly equivalent in the time domain. The relative acoustic nonlinearity parameter A2/A12 oscillates with the propagation distance, and the oscillation amplitude and spatial period are well consistent with the theoretical prediction of the A0-s0 mode pair, which means that only the second harmonic s0 mode is generated by the antisymmetric primary A0 mode. Experiments are further conducted to examine the cumulative generation of symmetric second harmonics for the antisymmetric-symmetric mode pair A3-s6. Results show that A2/A12 increases linearly with the propagation distance, which means that the symmetric second harmonic s6 mode is generated cumulatively by the antisymmetric primary A3 mode. The present investigation systematically corroborates the proposed theory that only symmetric second harmonics can be generated accompanying the propagation of antisymmetric primary Lamb waves in a plate.

Acoustical Nonlinearity, Sound Absorption, and Scattering in Bubble-Saturated Seawater

A correlation between acoustical nonlinearity, sound absorption, and scattering in a subsurface bubble-saturated layer is established. A model of effective parameters of a bubbly liquid is developed that allows one to obtain results coinciding with experimental field studies. It is shown that “bubbly clouds” under the sea surface increase substantially the sound scattering and the nonlinear acoustic parameter of the seawater.

공기 접촉식 초음파 수신을 통한 알루미늄 소재의 상대 비선형 측정

비선형 초음파는 재료의 손상 상태나 특성을 평가하기 위해 사용되고 있으며, 정량적인 측정 지표로서 절대비선형 파라미터(β)가 자주 사용되고 있다. 비선형 파라미터 측정값에 영향을 미치는 여러 가지 인자가운데서 수신탐촉자와 시편 사이에 접촉 압력을 일정하게 유지하는 일은 검사의 신뢰성과 반복성을 위해 중요하다. 기존의 접촉식 초음파 수신 과정을 개선하기 위한 방법으로서 공기접촉식 탐촉자의 사용이 대안이 될 수 있다. 본 연구에서는 먼저 회절 및 감쇠 보정을 적용한 상대비선형 파라미터(β′)를 정의하고, 참조시편에 대한 목표시편의 상대비선형 파라미터 비(β′/β′SUBref/SUB)는 절대비선형 파라미터 비(β′/β′SUBref/SUB)와 동일함을 입증하였다. 이렇게 함으로써 참조시편의 종류와 두께에 대한 제한이 완전히 없어지며, βref를 아는 경우 상대비선형 측정으로부터 목표시편의 β 측정이 가능하다. 시편과 공기로 이루어진 이중매질의 회절 및 감쇠 보정 식을 유도하고, 재료의 비선형 특성이 잘 알려진 세 가지 종류의 알루미늄 시편에 대하여 공기접촉식 탐촉자를 이용하여 β′을 각각 측정하였다. 임의의 참조시편을 사용하여 각 알루미늄 종류에 대해 측정한 β′/β′SUBref/SUB는 β/βSUBref/SUB와 7% 이내로 잘 일치하였다.