Acoustic Nonlinearity Parameter Research Articles

Comparative study of acoustic non-linearity parameter in binary mixtures of N,N-dimethylacetamide with Polyethylene Glycols at different temperatures

The present paper deals with the comparative evaluation of acoustic non-linearity parameter (B/A) for binary liquid mixtures of N, N-dimethylacetamide (DMA) with Polyethylene Glycol 200 (PEG 200) and Polyethylene Glycol 400 (PEG 400) using seven different approaches as Beyer, Hartmann, Ballou, H. Endo, Lu, Tong-Dong and Beyer-Tong Dong at temperatures 308.15, 318.15 and 328.15 K. The excess values of B/A have been computed using all seven approaches and substituted into the Redlich-Kister equation. The temperature and pressure derivatives of ultrasonic velocity using Beyer and Beyer- Tong Dong methods have been presented for both the mixtures. Molecular properties have also been calculated by Beyer-Tong Dong method using Sehgal’s relations. The aim of the present investigation is to check the validity and efficacy of different methods on the dimethylacetamide-Polyethylene Glycol mixtures and to get the better understanding about the nature and strength of the intermolecular interactions in the mixtures.

Nonlinear ultrasonic detection of partially closed cracks in metal plates using static component of lamb waves

This paper presents physical and experimental studies of the static component of Lamb waves (SCLWs) induced by partially closed cracks. The generation mechanism of SCLWs was investigated according to the nonlinear interaction between Lamb waves and partially closed cracks with various lengths, widths and orientation angles in finite element simulations. It was found that the SCLWs are more sensitive to the crack length, width and orientation angle as compared with the second harmonic Lamb waves. Fatigue crack evolution was further experimentally detected in aluminum alloy plates using SCLWs. Consistent with the simulation results, the acoustic nonlinearity parameter increases monotonically with increasing fatigue crack length. We show that the SCLWs are sensitive to partially closed cracks and can serve as a potential method to quantitatively evaluate the evolution of partially closed crack in metal plates. The findings of this study pave the way for the detection of partially closed crack using SCLWs in the field of nondestructive evaluation and structural health monitoring.

Experimental observation of static component generation by Lamb wave propagation in an elastic plate

The experimental observation of acoustic radiation induced static component (SC) generation by Lamb wave propagation in an elastic plate is first reported. An experimental approach to directly detect the generated SC of primary Lamb wave propagation in an elastic plate is proposed, where a low-frequency wedge transducer is used to detect the SC pulse generated by primary Lamb wave tone-burst that is excited by a high-frequency wedge transducer. The basic requirements are that the group velocity of primary Lamb wave needs to be equal to that of the s0 mode at zero frequency (i.e., the SC), and that the central frequency of the low-frequency wedge transducer needs to be near the center of the main lobe frequency range of the generated SC pulse. For this purpose, the S4 mode whose group velocity is equal to that of the generated SC is selected as the primary Lamb wave, and then the specific mode pair S4-s0 is focused and analyzed. Accompanying propagation of the S4 mode tone-burst, the generated SC pulse detected with the low-frequency wedge transducer is clearly observed. Through respectively measuring the amplitudes of the S4 mode and the generated SC for different spatial separation between the transmitting and receiving wedge transducers, the quantitative relationship of the relative nonlinear acoustic parameter with propagation distance is obtained. The experimental results show that the proposed approach can be used to directly detect the generated SC of Lamb wave propagation, and that the said SC does have a cumulative growth effect with propagation distance.

Measurement of third-order elastic constants using thermal modulation of ultrasonic waves

Third-order elastic constants (TOEC) play an important role in nonlinear material characterization, but measurements of TOEC are laborious with large error margins. This Letter presents the equations of wave velocity changes caused by homogeneous temperature variation and uniaxial stress in isotropic media and the expression of TOEC in terms of thermally induced velocity change and thermal strain. TOEC of an aluminum sample were experimentally determined by measuring ultrasonic wave velocity changes in the uniaxial loading test and the thermal modulation test. Experimental results showed good agreement between the two test methods. Owing to the simple test setup and high measurement sensitivity, the thermal modulation test is a potential experimental method to determine TOEC and absolute acoustic nonlinearity parameters.

Assessment of cortical bone fatigue using coded nonlinear ultrasound* *Project supported by the China Postdoctoral Science Foundation (Grant No. 2021M690709), the National Natural Science Foundation of China (Grant Nos. 11827808, 11874289, 11804056, and 12034005), the Program of Shanghai Academic Research Leader (Grant No. 19XD1400500), and the Project of Shanghai Science and Technology Innovation Plan (Grant No. 19441903400).

Bone fatigue accumulation is a factor leading to bone fracture, which is a progressive process of microdamage deteriorating under long-term and repeated stress. Since the microdamage of the early stage in bone is difficult to be investigated by linear ultrasound, the second harmonic generation method in nonlinear ultrasound technique is employed in this paper, which is proved to be more sensitive to microdamage. To solve the deficiency that the second harmonic component is easily submerged by noise in traditional nonlinear measurement, a weighted chirp coded sinusoidal signal was applied as the ultrasonic excitation, while pulse inversion is implemented at the receiving side. The effectiveness of this combination to improve the signal-to-noise ratio has been demonstrated by in vitro experiment. Progressive fatigue loading experiments were conducted on the cortical bone plate in vitro for microdamage generation. There was a significant increase in the slope of the acoustic nonlinearity parameter with the propagation distance (increased by 8% and 24% respectively) when the bone specimen was at a progressive level of microdamage. These results indicate that the coded nonlinear ultrasonic method might have the potential in diagnosing bone fatigue.

Transmission Phase Control of Annular Array Transducers for Efficient Second Harmonic Generation in the Presence of a Stress-Free Boundary

The through-transmission (TT) method is mainly used to measure the amplitude of the second harmonic from which the acoustic nonlinear parameter is determined for early damage detection of materials. The pulse echo (PE) method, however, has been excluded from nonlinear studies of solid materials because the stress-free boundary suppresses the generation of second harmonics. It is more demanding to develop the PE method for practical applications and this paper considers a novel phase shift technique of annular array transducers to improve second harmonic generation (SHG) at the stress-free boundary. The fundamental and second harmonic fields after phase-shifted radiation are calculated, and their received amplitudes are investigated. The phase difference between the two second harmonic components after reflection from the stress-free boundary is analyzed to explain the enhanced SHG. The PE method with optimal phase shift can generate an improved second harmonic amplitude as high as about 45% of the TT method. Four element array transducers are also found to be more efficient in improved SHG than two element transducers.

Compensation of a Second Harmonic Wave Included in an Incident Ultrasonic Wave for the Precise Measurement of the Acoustic Nonlinearity Parameter.

The incident second harmonic wave is a problematic issue for the precise measurement of the acoustic nonlinearity parameter. This paper proposes a compensation method to remove the effect of the incident second harmonic component in the measurement of the absolute acoustic nonlinearity parameter using the calibration method. For this, the second harmonic component detected by the receiving transducer is considered as the sum of the component due to material nonlinearity and the component included in the incident signal and a numerical calculation model is developed as a function of the propagation distance. In the model, the factors related to the material nonlinear parameter and the magnitude of the incident second harmonic component are unknown and these are determined by finding a value that best matches the experimental data according to the change in the propagation distance; compensation for the incident second harmonic component is then achieved. The case where the phase of the second harmonic wave due to material nonlinearity is opposite to that of the fundamental wave is also considered. To verify the validity of the proposed method, fused silica and aluminum alloy Al6061-T6 specimens with different thicknesses corresponding to the propagation distance are tested. The experimental results show that the nonlinear parameters changed significantly according to the propagation distance before compensation but were very stable after compensation. Additionally, the average values of the nonlinear parameter are 11.04 in the fused silica, which is within the literature value range (10.1 to 12.4), and that for the Al6061-T6 is 6.59, which is close to the literature value range (4.5 to 6.12).

Measurement of Absolute Acoustic Nonlinearity Parameter Using Laser-Ultrasonic Detection

The absolute acoustic nonlinearity parameter β is defined by the displacement amplitudes of the fundamental and second-order harmonic frequency components of the ultrasonic wave propagating through the material. As β is a sensitive index for the micro-damage interior of industrial components at early stages, its measurement methods have been actively investigated. This study proposes a laser-ultrasonic detection method to measure β. This method provides (1) the β measurement in a noncontact and nondestructive manner, (2) inspection ability of different materials without complex calibration owing to direct ultrasonic displacement detection, and (3) applicability for the general milling machined surfaces of components owing to the use of a laser interferometer based on two-wave mixing in the photorefractive crystal. The performance of the proposed method is validated using copper and 6061 aluminum alloy specimens with sub-micrometer surface roughness. The experimental results demonstrated that the β values measured by the proposed method for the two specimens were consistent with those obtained by the conventional piezoelectric detection method and the range of previously published values.

Experimental investigation of the surface corrosion damage in plates based on nonlinear Lamb wave methods

This paper experimentally investigates the early stage damage caused by the surface corrosion in thin plates based on two nonlinear Lamb wave methods, which are the low-frequency S0 mode Lamb wave method and one-way S0-A0 Lamb mixing wave method. The experimental results show that the significant second/third harmonics and the resonant waves from these methods can be caused by the surface corrosion damage. Meanwhile, it is found that the normalized acoustic nonlinearity parameters in these methods increase monotonically with the number of corrosion times before the generation of the distinct cavities. Moreover, the position and the length of the surface corrosion region can be characterized by the resonant waves from one-way S0-A0 Lamb mixing wave method. This study reveals that the low-frequency S0 mode Lamb wave method and one-way S0-A0 Lamb mixing wave method are feasible to evaluate early stage damage caused by the surface corrosion.

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.

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.

Compressional Study of Mercury Through Thermodynamic and Thermoacoustical Parameters

Compressional study of Hg from 1 to 13 kbar pressures at three different temperatures (295.05 K, 313.65 K and 326.05 K) has been carried through thermodynamic properties (Pint, γ, Г) deduced theoretically from ρ and u data. Such study has also been presented using acoustical non-linearity parameter (B/A). Empirical correlations between ρ–u-thermodynamic properties were applied to Hg, for the first time and satisfactory results were obtained.

Experimental and Numerical Investigation of the Micro-Crack Damage in Elastic Solids by Two-Way Collinear Mixing Method.

This study experimentally and numerically investigated the nonlinear behavior of the resonant bulk waves generated by the two-way collinear mixing method in 5052 aluminum alloy with micro-crack damage. When the primary longitudinal and transverse waves mixed in the micro-crack damage region, numerical and experimental results both verified the generation of resonant waves if the resonant condition was satisfied. Meanwhile, we found that the acoustic nonlinearity parameter (ANP) increases monotonously with increases in micro-crack density, the size of the micro-crack region, the frequency of resonant waves and friction coefficient of micro-crack surfaces. Furthermore, the micro-crack damage in a specimen generated by low-temperature fatigue experiment was employed. It was found that the micro-crack damage region can be located by scanning the specimen based on the two-way collinear mixing method.

Field-deployable measurement technique for absolute acoustic nonlinearity parameter values

Over the past two decades, several researchers have demonstrated that changes in the acoustic nonlinearity parameter β can be related to changes in material properties due to mechanical and/or thermal degradation processes. Generally, a piezoelectric sensor-based detection method is used to measure changes in β values because it is operationally simpler than the complex capacitive detection method. However, this method is limited to measuring only relative changes in β values; whereas, the absolute β values of components in service often need to be measured in the field to quantify the degradation level. Accordingly, a novel field-deployable method for measuring absolute β values was developed in this study. Nonlinear ultrasonic experiments were conducted using capacitive detection, conventional piezoelectric sensor-based detection, and proposed detection methods, and the results were compared. The β values of a copper single-crystal sample measured using the new and the capacitive detection methods were 2.49 and 2.1, respectively, and those obtained using the conventional piezoelectric sensor-based detection method ranged between 90 and 130. The test results confirm that the proposed field-deployable measurement method produces more consistent absolute β values without involving the complexity of the capacitive detection method.

Characterization of inner layer thickness change of a composite circular tube using nonlinear circumferential guided wave: A feasibility study* *Project supported by the National Natural Science Foundation of China (Grant Nos. 12074050, 11834008, and 11704410).

The feasibility of using the nonlinear effect of primary circumferential guided wave (CGW) propagation for characterizing the change of inner layer thickness of a composite circular tube (CCT) has been investigated. An appropriate mode pair of the fundamental and double-frequency CGWs (DFCGWs) has been selected to enable the second harmonics of primary wave mode in the given CCT to accumulate along the circumferential direction. When changes in the inner layer thickness (described as the equivalent inner layer thickness) take place, the corresponding nonlinear CGW measurements are conducted. It is found that there is a direct correlation between change of equivalent inner layer thickness of the CCT and the relative acoustic nonlinearity parameter (Δβ) measured with CGWs propagating through one full circumference, and that the effect of second-harmonic generation (SHG) is very sensitive to change in the inner layer thickness. The experimental result obtained demonstrates the feasibility for quantitatively assessing the change of equivalent inner layer thickness in CCTs using the effect of SHG by primary CGW propagation.

ОБ АКУСТИЧЕСКИХ ПАРАМЕТРАХ МЕТАЛЛА КОНСТРУКЦИИ ПРИ НАКОПЛЕНИИ ПОВРЕЖДЕНИЙ

In the work with the use of nondestructive control methods, the issues of determining acceptable durability or safe resource are considered. It is shown that the design monitoring procedure can be presented as follows: determines the original state zero zone, where the material of the product was subjected to low operational loads; further, with the use of nondestructive control methods, the acoustic parameter is measured (without disassembling the product)., such as the speed of elastic acoustic waves, nonlinear acoustic parameter, difference of velocities with twofrequency sensing, etc.; acoustic scanning of the product's metal is performed, in areas where there have been significant loads, signoff voltages, leading to an intensive accumulation of damage (the destruction of metal leading to cracks); defined zone “N” where the metal state parameter, for which the value is taken, characterizing the difference of the acoustic parameter (the speed of elastic waves, nonlinear acoustic parameter, the difference in velocity in twofrequency sensing) relative to the same parameter in the zone of zero exceeds the established level. The regularities established in the work linking the presence of plastic deformation with the difference in the delays (velocity) of elastic Rayleigh waves at different sounding frequencies at a fixed base between the emitter and the receiver of elastic waves, as well as the behavior of a nonlinear acoustic parameter during the safe resource time, suggest the possibility of using the observd fact as a principle for controlling the limiting state of the material due to plastic deformations on industrial structures. Based on the proposed approach, an engineering methodology for determining the technical condition of the material of the structures of production facilities is proposed, which allows to establish three stages of operation: the reliable operation mode; the controlled operation mode and the critical operation mode.

Evaluation and Comparative Study of Acoustic Non-Linearity Parameter of Liquid Metals and Alloys using Sound Speed and Density Data

The non-linearity acoustic parameter (B/A) has been computed for six pure liquid metal alloys (Na, K, Rb, Cs, Pb and Sn), four liquid metal alloys (K-Rb, Na-Cs, Pb-Sn and Na-K) and other several liquid metals at different temperatures. This parameter has been calculated by using three different approaches viz. Hartmann method, Ballou rule and Johnson et al. method. The input data required density, sound speed and thermal expansivity were taken from literature. A comparative study has been carried out and quite satisfactory results are obtained.

Nonlinearity in the propagation of acoustic waves: Simulation and experimental validation in a creep damaged material

Abstract A 3-Dimensional mathematical model has been developed to understand the nonlinear characteristics of an acoustic wave propagating in a creep-damaged medium. Nonlinearities were assumed to be originated from the material due to creep damage in terms of change in precipitate size, nucleation, and growth of micro voids. For carrying out mathematical simulation in this research, a nonlinear material model has been used and the dynamic value of second order elastic constants as well as density measured for the specimen after each creep interruption were incorporated into it. For studying acoustic wave propagation inside the model of Inconel 600 alloy, a common excitation and acquiring point (pulse-echo mode) has been selected via the acoustoelastic effect. The signal received has been used for calculating the acoustic nonlinearity parameter (β) which is the indicative parameter for expressing progression of damage in the material. This parameter β can be calculated as the ratio of the amplitude of the transmitted signal to the square of the amplitude of the second harmonic and is dependent on the elastic constants of the material. The simulation results obtained through the model were validated experimentally. A drastic increase in β was observed at the transition region from secondary to tertiary stage of creep in the studied material, which is due to the increase in the volume fraction of precipitates as well as micro void initiation and are the dominating cause of material failure. So, this technique can be used for assessment of localized deformation in any material much prior to failure.

Nonlinear ultrasonic technique for the characterization of microstructure in additive materials.

This study employs nonlinear ultrasonic techniques to track microstructural changes in additively manufactured metals. The second harmonic generation technique based on the transmission of Rayleigh surface waves is used to measure the acoustic nonlinearity parameter, β. Stainless steel specimens are made through three procedures: traditional wrought manufacturing, laser-powder bed fusion, and laser engineered net shaping. The β parameter is measured through successive steps of an annealing heat treatment intended to decrease dislocation density. Dislocation density is known to be sensitive to manufacturing variables. In agreement with fundamental material models for the dislocation-acoustic nonlinearity relationship in the second harmonic generation, β drops in each specimen throughout the heat treatment before recrystallization. Geometrically necessary dislocations (GNDs) are measured from electron back-scatter diffraction as a quantitative indicator of dislocations; average GND density and β are found to have a statistical correlation coefficient of 0.852 showing the sensitivity of β to dislocations in additively manufactured metals. Moreover, β shows an excellent correlation with hardness, which is a measure of the macroscopic effect of dislocations.

Impact Damage Detection in Patch-Repaired CFRP Laminates Using Nonlinear Lamb Waves.

Carbon fiber-reinforced polymer (CFRP) laminates, a key composite material, are widely used in aircraft structures and are susceptible to low-velocity impact (LVI) damage from bird strikes, lightning strikes, hail impacts and other situations. Therefore, finding a method that repairs the damaged structure and detects the effect of these repairs under LVI is a very important goal. In this work, the repair effect of LVI damage in CFRP laminates repaired with patches of various sizes is investigated via experimental and numerical nonlinear Lamb wave analyses. An integrated numerical procedure that combines LVI with nonlinear Lamb wave detection is developed to predict the nonlinear Lamb wave behavior in LVI-damaged patch-repaired CFRP laminates. The CFRP laminate damage in the nonlinear Lamb wave simulation is evaluated based on relative acoustic nonlinearity parameters (RANPs). As a result, the integrated numerical procedure is validated with drop-weight impact tests and RAM-5000 SNAP nonlinear ultrasonic detection system. An optimal patch design is established via interpolation to optimize the absorbed energy, delamination surface area, second RANP and third RANP with different patch repair sizes. These parameters exhibit consistent curve fitting trends, indicating that they can be used as important indicators of impact damage. The optimal circular patch design with a radius of 2.5 r has better impact resistance behavior and repair performance.