Acoustoelastic Coefficient Research Articles

Temperature correction in acoustoelastic coefficient measurements

Acoustoelastic coefficients (AECs) of a material are used for determining third-order elastic constants (TOECs), measuring residual stress, and evaluating damage and deterioration by analyzing the change of wave velocity with stress. However, wave velocity measurements are highly sensitive to ambient or load-induced temperature changes. In this study, we proposed a temperature correction method that uses the measured temperature history and the temperature–velocity relationship of the test specimen. Acoustoelastic tests were performed in various ambient temperature conditions on three types of metals: 6063-T5 aluminum alloy (Al6063), 304 stainless steel (SS304), and 1018 low-carbon steel (S1018). Before temperature correction, the AEC measurements varied significantly, due to changes in the temperature of the specimen caused by both the ambient environment and mechanical loading. The results after the correction demonstrate that the proposed self-temperature correction method reduces temperature induced error, enabling highly accurate AEC measurements.

Assessment of residual stresses in railway rails using ultrasonic and Barkhausen noise techniques

Residual stress, a factor affecting the fatigue and fracture characteristics of rails, is formed during the processes of fabrication and heat treatment, and is also generated by shrinkage/tension due to the temperature differences and vertical loads on wheels due to the weight of vehicles. Moreover, damage to rails tends to accelerate due to residual stress caused by the continuous increase in the number of passes and the high speed of passing vehicles. Because this can have a direct effect on safety accidents on railroad rails, having a technique to evaluate and analyse the residual stresses in rails accurately is very important. In this paper, firstly, residual stresses applied in rails were evaluated using longitudinal critically refracted (LCR) wave. Non-destructive stress measurement using ultrasonic techniques is based on calculation of the acoustoelastic coefficient obtained from the relationship between material stress and LCR wave velocity. This is because LCR waves exhibit a relatively large change in flight time in relation to a change in stress compared to other ultrasonic modes. Barkhausen noise technique is also very suitable for measuring residual stresses on railway rails, which are ferromagnetic materials. Tensile and compression tests were performed with the specimens extracted from the inspection object, and the difference between the ultrasonic speed and the magnetization amplitude according to the applied stress was measured. Then, the feasibility of calculating the internal stresses in railway rails using the reference data obtained from the extracted specimens was determined, and the reliability of each method was verified. Furthermore, based on these results, the difference in the results for the loads asymmetrically applied according to the wheel shape was analysed by measuring for each part of new and used rails.

Nonlinear constitutive relation in acoustoelastic-orthotropic media and its wide azimuth seismic reflection coefficient characteristics for in-situ stress prediction

With the development of oil and gas exploration targets towards deep water and deep layer, change of subsurface rock physical properties caused by in-situ stress can no longer be ignored. Hence, it is of great significance to study the acoustoelasticity characteristics of rocks under complex subsurface stress environment. Based on acoustoelasticity theory and anisotropic analysis of rock under triaxial stress state, equivalent stiffness matrix of acoustoelastic-orthotropic media is established. According to the equivalent stiffness matrix, exact solution of reflection coefficient for stress-induced orthotropic media is derived. Through model experiments, reflection coefficient varies with incident and azimuth angle is analyzed. Based on the azimuthal characteristics of acoustoelastic medium reflection coefficient and in-situ stress prediction models, two in-situ stress characteristic parameters are proposed to describe in-situ stress distribution. Then, by numerical simulation, the law between azimuthal characteristics of acoustoelastic medium reflection coefficient and in-situ stress characteristic parameters is summarized. And an effective way to predict in-situ stress field that wide azimuth seismic data dependent is established. Finally, through actual wide azimuth seismic data in a field, the practicability of this in-situ stress prediction method rely on stress characteristic parameters is verified. The results illustrate that the prediction method of in-situ stress characteristic parameters can accurately describe the distribution of in-situ stress.

Ultrasonic and FEM residual stress measurement in dissimilar St37–St52 welding

Numerous industries, like the military, the oil and gas industry, etc., rely heavily on dissimilar welding. The welding process leaves the structure with a variety of defects, such as residual stress, that degrade its performance and static and fatigue properties. Consequently, weld residual stress must be accurately measured. In this study, ultrasonic and finite element techniques are developed to assess the residual stress in dissimilar St37/St52 welding. In addition, hole-drilling technique is employed to confirm FEM and ultrasonic data. Probe fixture is designed and built for ultrasonic stress measurement, and the acoustoelastic coefficient is measured in St37 and St52. In welding finite element analysis, the Goldak model is used as the heat source, the Brekstad model is employed as the heat loss, and the Dflux subroutine is developed to apply the heat source to the weld line using the sedimentary method. The FEM and ultrasonic data are in good correlation with the hole drilling results (maximum error of 9%). The findings indicate that there is a high degree of concordance between the data gathered by FEM and ultrasonic technique (with error less than 1.75% at the weld zone).

Reliability verification of stress data from extracted specimens using LCR wave stress data from full-section rail specimens

Non-destructive stress measurement using ultrasonic techniques is based on calculation of the acoustoelastic coefficient obtained from the relationship between material stress and sound wave velocity. Longitudinal critically refracted (LCR) waves are the most suitable for ultrasonic stress measurement testing. This is because these waves exhibit a relatively large change in flight time in relation to a change in stress. In general, to calculate the acoustoelastic coefficient, tensile tests are performed with specimens extracted from the test objects to be inspected, and the difference in the speed of ultrasonic waves is measured in relation to the stress applied. However, train rails are usually subjected to compressive loads and no research has been conducted to confirm whether the results obtained using this method match the coefficients obtained from test objects in full cross-section. Therefore, results from compression tests on full cross-section specimens are needed as reference data to determine the reliability of the results obtained using extracted specimens. In this study, experiments were conducted to compare the result from applying compressive loads to full cross-section specimens to the experimental result obtained from specimens extracted from each rail section. For this purpose, ultrasonic probes capable of generating LCR waves were designed and manufactured to apply the technique to measure the applied stress. Based on the results obtained using this probe, the acoustoelastic coefficient values obtained from each specimen were compared. Then, the feasibility of calculating the internal stresses in railway rails using the acoustoelastic constants obtained from the extracted specimens was determined, and the reliability of the method was verified. It was concluded that there was no significant difference in the acoustoelastic coefficients calculated using the data from extracted specimens and those using full cross-section specimens.

Effect of ultrasonic impact treatment on surface stress evaluation of laser cladding coating by using critically refracted longitudinal wave

Based on the Lcr wave acoustoelastic effect, surface stress of laser cladding Fe314 alloy coating after ultrasonic impact treat (UIT) was measured, and relation between Lcr wave acoustoelastic coefficient and repetition rate of UIT was discussed in this paper. The laser cladding Fe314 alloy coating was prepared on surface of carbon steel and impacted with different repetition rates of UIT by using UIT-300 system. After that, the experimental system of stress measurement with Lcr wave, consisting of a ultrasonic wave generator, a digital oscilloscope and two Lcr wave transducers (including one transmitting transducer and one receiving transducer) with 2.5MHz frequency, was used to collect Lcr waves of coating with calibration test, and then the difference in time of flight between Lcr waves was calculated with the cross correlation theory. To explain experimental results, the microstructure and three dimensional surface topography of coating were observed by using SEM and LSCM. Results show that as repetition rate of UIT increases, the Lcr wave acoustoelastic coefficient increases, when it reaches 300%, the Lcr wave acoustoelastic coefficient also reaches the maximum, after that the Lcr wave acoustoelastic coefficient decreases irregularly as repetition rates of UIT increases further. Compared with the Lcr wave acoustoelastic theory, when stress is in the range of turning point stress, there is a deviation on experimental result, and that deviation becomes more obvious as stress and repetition rate of UIT increase. It is analyzed that the change of microstructure, deformation state and initial stress of coating caused by UIT and different repetition rate are main reasons.

Контроль натяга колец подшипников поверхностными волнами с использованием эффекта акустоупругости

In this paper, experimental and computational studies of the method of controlling the tension of bearing rings using the acoustoelasticity effect, based on measuring the characteristics of surface elastic waves propagating in a stressed medium, are carried out. Tuning samples of bearing rings tension on the axle neck of a freight car wheelset with an error of no more than 7 microns were developed and manufactured. Certification of a hydraulic stand for loading bearing rings, simulating their press fit on the axle, was performed. For surface waves, the acoustoelastic coefficient was measured by a Rayleigh wave pulse that repeatedly circled the ring. The correlation method for determining the delay time of a wave in a loaded ring relative to the unloaded one is optimized according to the condition of error minimization. The main reasons for the appearance of errors and uncertainties in the absolute time of propagation of a surface wave through the ring are considered: the influence of waves reflected from the boundaries, the curvature of the surface, and attenuation. The bearing ring tension was measured using the acoustoelasticity effect and the uncertainty of the stress measurement was estimated.

Inline Measurement of Acoustoelastic Coefficient in Conductive Sheet Material With Electromagnetic Loading System

In ultrasonic non-destructive testing technology, the method to detect the stress of metal plates using longitudinal critically refracted waves (LCR) is increasingly developing, in which the calculation of acoustoelastic coefficient of the metal plate is indispensable. However, due to the influence of the metallic material's in-service environment on acoustoelastic coefficient, the existing calculation method of the acoustoelastic coefficient cannot meet the engineering requirements. Therefore, an inline measurement method based on electromagnetic loading is proposed in this paper. The calculation formula for the inline measurement of acoustoelastic coefficient is derived. An electromagnetic loading experimental platform is designed, including an electromagnetic loading module, an ultrasonic detecting module, and a delay control module. The loading test of a 1060 aluminum plate is carried out using the designed platform. The flight time of LCR waves is measured experimentally and used in the calculation formula of acoustoelastic coefficient. The experimental results of acoustoelastic coefficient meet the accuracy requirement of less than 5%, which can be used for stress measurement. So, the inline measurement method of acoustoelastic coefficient proposed in this paper is feasible.

Subsurface Stress Measurement in GIS Epoxy Composite by Using LCR Waves

Internal stress in basin insulators of gas-insulated metal-enclosed switchgear (GIS) can lead to cracks, which affects the safe operation of these apparatuses. In this research, we proposed a subsurface internal stress measurement method for GIS epoxy composites. This method is based on an ultrasonic longitudinal critically refracted (LCR) wave technique. In this study, some epoxy composite specimens were synthesized with similar materials and manufacturing processes to those of 252 kV GIS basin insulators. An ultrasonic stress measurement system that utilized the LCR wave technique was set-up to investigate the relationship between stress and LCR wave propagation time, as well as to measure the compressive stress of the epoxy specimen within 0–50 MPa. The results show that LCR wave propagation time linearly decreased when stress increased in the subsurface zone and the acoustoelastic coefficient was −4.95. We found the relative errors of stress measurements to be less than 13%.

Burial Depth Effect of Crack on the Lcr Wave Acoustoelastic Coefficient for Stress Measurement of Laser Cladding Coating.

In this paper, the influence of burial depth of crack on stress measurement of laser cladding coating with the critical refracted longitudinal wave (Lcr wave) was discussed based on the Lcr wave acoustoelastic effect. The regular rectangular slots with different depths that were used to simulate the burial crack in coating was based on the equivalent theory. The experimental system including an ultrasonic wave generator, digital oscilloscope (2.5 GHz sampling rate), and two Lcr wave transducers (2.5 MHz center frequency) was used to collect the Lcr wave under different tensile loads, and the Lcr wave was denoised by using wavelet analysis technology, then the fracture morphology was observed using SEM. The results show that after the denoising by wavelet analysis technology, the signal-to-noise ratio of Lcr wave becomes bigger and the mean square deviation of Lcr wave becomes smaller. When the tensile load is within the turning point load, the difference in time of flight between Lcr wave increases linearly as the tensile load increases, and the deviation of the experimental results becomes obvious as the tensile load increases. When the tensile load is the same, as the burial depth of the slot increases, the nominal Lcr wave acoustoelastic coefficient decreases and tends to be stable gradually. At last, the experimental results are discussed based on the Lcr wave acoustoelastic effect and deformation theory, and it is analyzed that the uneven deformation caused by the interface in coating, anisotropic microstructure, and the burial crack is considered as the main reason.

An Ultrasonic Longitudinal Through-Transmission Method to Measure the Compressive Internal Stress in Epoxy Composite Specimens of Gas-Insulated Metal-Enclosed Switchgear

Situations of internal stress in basin insulators inside gas-insulated metal-enclosed switchgear (GIS) can lead to cracks, which can influence the safety and stability of apparatus. However, there is currently no research on internal stress measurements for composites of GIS basin insulators, and only measurements for surface stress. In this paper, an internal stress measurement method for GIS epoxy composite is proposed using an ultrasonic longitudinal through-transmission technique based on the acoustoelastic effect. An internal stress measurement system is developed to investigate the relationship between the uniaxial compressive internal stress and the velocity of the ultrasonic wave vertical to the stress in epoxy composite within a range of 0–70 MPa, and to calculate the acoustoelastic coefficient of epoxy composite. The effects of system delay are eliminated in measuring the propagation time. Some epoxy composite cuboid specimens with similar materials and using a manufacturing process similar to those of 252 kV GIS basin insulators are synthesized, and the uniformity of the internal stress in cuboid specimens is verified by finite element simulation. The results reveal a linear increase of the ultrasonic longitudinal wave velocity with increasing stress. It has been shown that the average acoustoelastic coefficient of GIS epoxy composites, using the longitudinal waves vertical to the stress, is 4.556 × 10−5/MPa. Additionally, the absolute errors of the internal stress measurements are less than 12.397 MPa. This research shows that the ultrasonic method based on the acoustoelastic effect for measuring the internal stress in GIS epoxy composites is feasible.

Feasibility of Evaluating Acoustoelastic Coefficient of Concrete under Tensile Stress with One-Sided Ultrasonic Method

In this paper, an experimental study on the feasibility of evaluating acoustoelastic coefficient of concrete with one-sided ultrasonic pulse method under tensile stress is conducted. Tensile load cycles are imposed on prismatic concrete specimens and ultrasonic wave velocities are measured simultaneously. Acoustoelastic coefficients are obtained by linear fit of the test results and compared to correlate results in literature. The feasibility of evaluating acoustoelastic coefficient of concrete with one-sided ultrasonic method under tensile stress is discussed.

Correction for Microstructure Effect on Residual Stress Measurement of SR-FSW Joint with Lcr Wave

Correction method for microstructure effect on residual stress of self-reacting friction stir weld joint measured with longitudinal critically refracted wave was discussed in this study. Two longitudinal critically refracted wave transducers, the spacing between which was fixed, were used, then the acoustoelastic formula was optimized, and difference in time of flight between longitudinal critically refracted wave, which replaced propagation velocity as characteristic parameter for residual stress measurement, was determined by the cross correlation theory, at last the influence of microstructure on residual stress of self-reacting friction stir weld joint was solved. Results show that as stress increases, the deviation in difference in time of flight becomes obvious, and when stress reaches stress turning point, experimental result is not agreed with the acoustoelastic theory as stress increases further. Step length is an important factor for difference in time of flight, and one cycle is seen as optimal step length. For acoustoelastic coefficient, the value of nugget zone is biggest, and the value of (heat affected zone + thermal mechanical affected zone) is smallest, in addition, the value of advancing side is slightly bigger than that of retreating side. Finally, residual stress of self-reacting friction stir weld joint was corrected with longitudinal critically refracted wave, and the result is verified by hole-drilling.

Metallurgical Characterization of a Low Carbon Steel Microstructure Using Linear and Nonlinear Ultrasonics

In this study, linear and nonlinear ultrasonic (UT) methods are utilized to evaluate the microstructures of A572 low carbon steel samples that were intercritically heat-treated at three temperatures and quenched to room temperature. The microstructures were also qualitatively and quantitatively assessed using standard metallography. ImageJ software was used to measure the amount of the phases. Correlations between ferrite content and linear velocity and the acoustoelastic coefficient are established. The experiments show that the UT linear and nonlinear velocities are affected by varying the amounts of ferrite and martensite. The acoustoelastic coefficient is found to be more sensitive to small changes in ferrite volume fraction.

Study of the Acoustoelastic Effect in an Anisotropic Plastically Deformed Material

The paper discusses the dependence of shear elastic waves birefringence on applied mechanical stress and preliminary plastic deformation of a material. A technique involving precision acoustic pulse echo measurements and software processing of the received time scan of signals from a piezoelectric transducer is described, which makes it possible to determine the propagation time of elastic waves with an accuracy of at least 0.5 ns. The dependences of the intrinsic acoustic birefringence and the acoustoelastic coefficient on plastic deformation in a carbon steel sample are investigated. After 12% plastic deformation of the sample, the average value of the acoustoelastic coefficient changes by 30%; the average value of the intrinsic acoustic birefringence changes by 60%. A correlation is observed between the intrinsic acoustic birefringence and the acoustoelastic coefficient. Using the theory of elastic wave propagation in a solid, the obtained experimental data are explained by manifestation of the acoustoelastic effect and the influence of the structural state on the effective elastic properties. The effect of plastic deformation on the accuracy of determining stress is qualitatively assessed. The error in determining stress during 1% plastic deformation is about 40 MPa, i.e., 13% of the yield strength for this material in the initial state.

Investigation of the Effect of Aluminum Alloy Position on Residual Stresses in Dissimilar fsw Weld by Using the Ultrasonic Method

The main goal of this study is to show the effect of the advancing side (AD) and the retreating side (RT) position on the Residual stresses and local mechanical behaviour of dissimilar friction stir welds of aluminum alloys AA2024-T3 and AA7075-T6. Different samples were produced by varying the rotational speed of the tool (1200 and 1400 rpm) and the alloy position regarding the advancing side of the tool. Ultrasonic Method has been used to evaluate Residual Stresses. This method is based on the acoustoelastic effect, which measures the velocity variation of the elastic waves according to the stress state of the material. This can be achieved through a calibration test, which permits the determination of the acoustoelastic coefficient (K). The results show a tensile stress in the Nugget (N), the heat affected zone (HAZ) and a compression stress in the base metal (BM). Increasing the rotational speed reduces the amplitude of the longitudinal residual stresses with a high reduction in the case where AA7075 - T6 is in the advancing side whit 1400 rpm. This has been directly associated to the increase in the heat input and the reduction of the thermal mismatch between different areas of the weld. The microstructure effect of aluminum alloy position acts on the acoustoelastic constant K. The choice of t0 corrects the overestimated residual stresses in the (HAZ) and (N).

Investigations of the Structural and Strain-Stress State of the Rails of Current Production by the Acoustic Elasticity Method

Представлены результаты экспериментальных измерений остаточных напряжений в элементах рельса, измеренных электромагнитно-акустическим структуроскопом СЭМА с использованием метода акустоупругости. Оценка внутренних напряжений произведена также в отдельных элементах рельса. Настройка чувствительности структуроскопа СЭМА и определение коэффициента акустоупругой связи выполнены в лабораторных условиях путем создания в отрезке рельса напряженного состояния одноосного сжатия в направлении продольной оси на испытательной машине Instron 300DX. Отмечена высокая чувствительность и достоверность измерений с погрешностью определения механических напряжений до 2 МПа и соответствие зарегистрированных структуроскопом механических напряжений нагрузке рельса, реализуемой на стенде. Остаточные напряжения, определяемые акустоупругим методом по измеряемой разнице времени пробега двух ортогонально поляризованных сдвиговых волн на участке от головки до подошвы и обратно, являются усредненными по сечению рельса и несут информацию о величине продольных напряжений в рельсе. Диапазон разброса измеренных в лаборатории остаточных напряжений в отрезках рельсов составил 49…67 МПа. С ростом сжимающей нагрузки происходит уменьшение скорости головной волны на всех измеряемых участках рельса. Для относительной оценки остаточных напряжений в отдельных элементах рельса выполнены измерения скорости распространения акустических волн по головке, шейке и подошве, показавшие, что остаточные напряжения в продольном направлении рельса, как правило, носят сжимающий характер для головки и растягивающий - для шейки.

Influence of acoustoelastic coefficient on wave time of flight in stress measurement in piezoelectric self-excited system

This paper presents the Self-excited Acoustical System (SAS) in elastic construction stress change measurement. The system is based on the acoustical autoresonance phenomena and enables an indirect measurement of the construction effort level. The essence of the SAS system is to use a piezoelectric vibration emitter and a piezoelectric vibration receiver placed at a distance, which are coupled with a proper power amplifier, and which are operating in a closed loop with a positive feedback. This causes the excitation of the system. The change of the velocity of wave propagation, which is associated with the change of the resonance frequency in the system is caused by the stress change in the examined material. A variable, which determines the change of the acoustic wave velocity, is called an acoustoelastic coefficient β. Such a coefficient allows to determine the absolute stress value in the tested material.

Investigation of influences of mixing parameters on acoustoelastic coefficient of concrete using coda wave interferometry

The stress dependence of ultrasonic wave velocity is known as the acoustoelastic effect. This effect is useful for stress monitoring if the acoustoelastic coefficient of a subject medium is known. The acoustoelastic coefficients of metallic materials such as steel have been studied widely. However, the acoustoelastic coefficient of concrete has not been well understood yet. Basic constituents of concrete are water, cement, and aggregates. The mix proportion of those constituents greatly affects many mechanical and physical properties of concrete and so does the acoustoelastic coefficient of concrete. In this study, influence of the water-cement ratio (w/c ratio) and the fine-coarse aggregates ratio (fa/ta ratio) on the acoustoelastic coefficient of concrete was investigated. The w/c and the fa/ta ratios are important parameters in mix design and affect wave behaviors in concrete. Load-controlled uni-axial compression tests were performed on concrete specimens. Ultrasonic wave measurements were also performed during the compression tests. The stretching coda wave interferometry method was used to obtain the relative velocity change of ultrasonic waves with respect to the stress level of the specimens. From the experimental results, it was found that the w/c ratio greatly affects the acoustoelastic coefficient while the fa/ta ratio does not. The acoustoelastic coefficient increased from <TEX>$0.003073MPa^{-1}$</TEX> to <TEX>$0.005553MPa^{-1}$</TEX> when the w/c ratio was increased from 0.4 to 0.5. On the other hand, the acoustoelastic coefficient changed in small from <TEX>$0.003606MPa^{-1}$</TEX> to <TEX>$0.003801MPa^{-1}$</TEX> when the fa/ta ratio was increased from 0.3 to 0.5. Finally, it was also found that the relative velocity change has a linear relationship with the stress level of concrete.

Imaging textural variation in the acoustoelastic coefficient of aluminum using surface acoustic waves.

Much interest has arisen in nonlinear acoustic techniques because of their reported sensitivity to variations in residual stress, fatigue life, and creep damage when compared to traditional linear ultrasonic techniques. However, there is also evidence that the nonlinear acoustic properties are also sensitive to material microstructure. As many industrially relevant materials have a polycrystalline structure, this could potentially complicate the monitoring of material processes when using nonlinear acoustics. Variations in the nonlinear acoustoelastic coefficient on the same length scale as the microstructure of a polycrystalline sample of aluminum are investigated in this paper. This is achieved by the development of a measurement protocol that allows imaging of the acoustoelastic response of a material across a samples surface at the same time as imaging the microstructure. The development, validation, and limitations of this technique are discussed. The nonlinear acoustic response is found to vary spatially by a large factor (>20) between different grains. A relationship is observed when the spatial variation of the acoustoelastic coefficient is compared to the variation in material microstructure.