Bulk Longitudinal Waves Research Articles

Theoretical analysis of the dimensionality of ultrasonic attenuation in polycrystalline materials with elongated grains

Abstract In the present work, the grain scattering-induced attenuation coefficient is obtained for longitudinal bulk waves in untextured cubic polycrystalline materials with elongated grains using proposed 2D and 3D theoretical models. These models are obtained based on previously developed 2D and 3D models for equiaxed grains. Comparison of the 2D and 3D models allows an analysis of the dimensionality of grain scattering-induced attenuation, which involves more complex mechanisms with elongated grains. In the higher stochastic scattering regime, both 3D and 2D longitudinal attenuations are found to be dependent on the grain size parallel to the wave propagation. In the Rayleigh scattering regime the 3D attenuation is volume dependent and in contrast, the 2D longitudinal attenuation is found to be cross-section dependent and is therefore helpful for identifying the 3D grain shape/rotation.

Measurement of thickness and ultrasonic velocities based on imaging method using laser-generated ultrasonic waves at thermoelastic regime

Abstract This study introduces a simple method for determining thickness and ultrasonic velocities, including skimming longitudinal waves, longitudinal waves, and shear waves, utilizing laser-induced ultrasonic waves at the thermoelastic regime and the time-position imaging technique. Laser scanning was performed on two aluminum samples with thicknesses of 6 mm and 10 mm, generating data on the arrival time of multiple wave modes according to the separated distances of two laser spots. Using the least squares technique, the data obtained from the experiment were employed to fit theoretical curves of various waves, enabling the simultaneous determination of several material parameters. The proposed method exhibits high accuracy in determining thickness, with a maximum relative error of 1% for thicknesses up to 10 mm. Additionally, comparisons with theoretical calculations reveal maximum errors of 1 % for shear wave velocity and 0.8 % for longitudinal wave velocity. The ratio between the velocity of skimming longitudinal wave and bulk longitudinal wave of 0.95 was established, providing a prospective method to calculate longitudinal wave velocity through guided waves along the surface.

Experimental and Theoretical Analysis of Rayleigh and Leaky-Sezawa Waves Propagating in ZnO/Fused Silica Substrates.

Piezoelectric c-axis oriented zinc oxide (ZnO) thin films, from 1.8 up to 6.6 µm thick, have been grown by the radio frequency magnetron sputtering technique onto fused silica substrates. A delay line consisting of two interdigital transducers (IDTs) with wavelength λ = 80 µm was photolithographically implemented onto the surface of the ZnO layers. Due to the IDTs' split-finger configuration and metallization ratio (0.5), the propagation of the fundamental, third, and ninth harmonic Rayleigh waves is excited; also, three leaky surface acoustic waves (SAWs) were detected travelling at a velocity close to that of the longitudinal bulk wave in SiO2. The acoustic waves' propagation in ZnO/fused silica was simulated by using the 2D finite-element method (FEM) technique to identify the nature of the experimentally detected waves. It turned out that, in addition to the fundamental and harmonic Rayleigh waves, high-frequency leaky surface waves are also excited by the harmonic wavelengths; such modes are identified as Sezawa waves under the cut-off, hereafter named leaky Sezawa (LS). The velocities of all the modes was found to be in good agreement with the theoretically calculated values. The existence of a low-loss region in the attenuation vs. layer thickness curve for the Sezawa wave below the cut-off was theoretically predicted and experimentally assessed.

Study on Thermodynamic Properties and Elastic Deformation of Full-Heusler Alloys Co2TaGa and Co2VGa by Statistical Moment Method

Heusler alloy is a ferromagnetic alloy based on the Heusler phase. It is an intermetallic alloy between metallic and non-metallic elements that can be non-ferromagnetic and has a BCC crystal structure. This paper presents the theory of thermodynamics and elastic deformation of full-Heusler A2BC alloy with BCC structure built on the basis of statistical moment method (SMM). The paper presents numerical results for the temperature and pressure dependence of the mean nearest neighbor distance between two atoms, the density, the volume, the thermal expansion coefficient, the isotherm and adiabatic compressibilities, the isothermal elastic modulus, the heat capacities at constant volume and pressure, Young’s modulus, the bulk modulus, longitudinal and transverse wave velocities of alloys Co2TaGa and Co2VGa when using the coordination sphere method and the Mie–Lennard-Jones pair interaction potential. Some SMM calculation results agree well with available ab initio calculation results.

Ultrasonic methods for the detection of near surface fatigue damage

Fatigue zones in a material can be identified using ultrasonic waves, as it has been shown that their propagation speed will reduce when travelling through such a zone. However, as fatigue damage is usually concentrated in a thin near-surface layer, through-thickness measurements result in very small changes of the average propagation speed across the full thickness, which are potentially difficult to reliably correlate to specific fatigue states. In this study, we have completed fatigue state assessments using Rayleigh waves, which travel on the surface of a material, to maximise those changes. We found that the use of Rayleigh waves amplifies the changes in speed, after propagation in the damaged region, by a factor of up to ten. The monotonic nature of the reduction in wave speed was verified against the theory using dislocation density measurements. Finally, a stiffness-reducing finite-element modelling technique, able to capture the effects of fatigue on the time of flight of longitudinal bulk and Rayleigh waves, was also derived and verified against the experimental measurements.

Simultaneous determination of Young's modulus and Poisson's ratio in metals from a single surface using laser-generated Rayleigh and leaky surface acoustic waves

Material elastic moduli are used to assess stiffness, elastic response, strength, and residual life. Ultrasound (US) measurements of propagation wave speeds (for longitudinal and shear waves) are now primary tools for non-destructive evaluation (NDE) of elastic moduli. Most US techniques measure the time-of-flight of through-transmission signals or reflected signals from the back wall. In both cases, an independently determined sample thickness is required. However, US methods are difficult for complex (non-flat) samples. When the local thickness is unknown, the propagation speed cannot be determined. On the other hand, the propagation speed of Rayleigh waves can be calculated without knowledge of sample thickness, but another independent measurement is still required to compute both Young's modulus and Poisson's ratio. We present a comprehensive theoretical background, numerical simulations, and experimental results that clearly show that when the material density is assumed known, both elastic constants of an isotropic metal sample can be determined with laser-ultrasound by tracking two types of surface propagating waves without any sample contact (both signal excitation and detection are performed optically). In addition to a conventional surface, or Rayleigh, acoustic wave, a leaky surface wave can also be launched with nanosecond laser pulses in the thermoelastic regime of excitation (i.e., without material ablation) close to the source that propagates along the sample surface with speed close to that of bulk longitudinal waves. Samples can be of arbitrary shape and their thickness need not be measured.

Methodology for Mapping the Residual Stress Field in Serviced Rails Using LCR Waves.

Non-destructive stress measurement by ultrasonic testing is based on calculating the acoustoelastic modulus obtained from the relationship between material stress and sound wave velocity. A critically refracted longitudinal (LCR) wave, which is a bulk longitudinal wave penetrating below and parallel to the surface below an effective depth, is most suitable for ultrasonic stress measurement tests because it exhibits a relatively large change in travel time in response to a change in stress. In particular, the residual stress distribution through the thickness of the subject can be calculated if transducers of different frequencies are applied because of the characteristic of propagation to different depths of penetration depending on the frequency. The main purpose of this study was to visualize the internal or residual stress distribution through the thickness of rails using LCR waves. To this end, LCR probes with different center frequencies were designed and manufactured, and the residual stress values ​​of an unused railroad rail and two used railroad rails operated under different conditions were calculated. This was done using the ultrasonic signals received from each probe, of which the distributions were mapped. Through these mapping results, different residual stress values could be calculated according to the depth. The differences in residual stress generation and distribution according to the conditions surrounding the contact between train wheels and rails, and their characteristics, were visualized and analyzed. As a result, it could be concluded that the non-destructive evaluation technique using LCR waves could detect differences in the residual stress of a rail, and thus can be used to measure the residual stress of the rail accurately.

Elastic Metagratings with Simultaneous Highly Efficient Control over Longitudinal and Transverse Waves for Multiple Functionalities

Elastic metagratings that can efficiently manipulate the propagation of bulk longitudinal and transverse waves are highly desired in various applications, such as geological exploration and nondestructive detection. Here, a class of elastic metagratings consisting of a one-dimensional array of elliptical hollow cylinders carved in a steel background is proposed and studied. With the help of elastic-wave-diffraction analysis and a genetic-algorithm-based optimization approach, these intelligently designed metagratings can reflect longitudinal and transverse waves in a highly efficient and spatially separated way. Various wave-front-manipulation functionalities, such as specular reflection for longitudinal waves and anomalous reflection for transverse waves, can be simultaneously achieved with an almost perfect efficiency. Interestingly, different functionalities over both longitudinal and transverse waves can be realized by using the same cylinders with different rotation angles. Due to the nonresonant characteristics, the exhibited functionality shows robustness over both working frequencies and unit-cell configurations, which are beneficial for practical applications.

Elastic Metagratings with Simultaneous Modulation of Reflected and Transmitted Waves

Elastic metagratings enabling independent and complete control of both reflection and transmission of bulk longitudinal and transverse waves are highly desired in application scenarios such as non-destructive assessment and structural health monitoring. In this work, we propose a kind of simply structured metagrating composed only of elliptical hollow cylinders carved periodically in a steel background. By utilizing the grating diffraction theory and genetic algorithm, we endow these metagratings with the attractive functionality of simultaneous and high-efficiency modulation of every reflection and transmission channel of both longitudinal and transverse waves. Interesting wave-front manipulation effects including pure mode conversion and anomalous deflection along the desired direction are clearly demonstrated through full-wave numerical simulations. Due to its subwavelength thickness and high manipulation efficiency, the proposed metagrating is expected to be useful in the design of multifunctional elastic planar devices.

Ultrasound characterization of bioinspired functionally graded soft-to-hard composites: Experiment and modeling.

Functional grading is a distinctive feature adopted by nature to improve the transition between tissues that present a strong mismatch in mechanical properties, a relevant example being the tendon-to-bone attachment. Recent progress in multi-material additive manufacturing now allows for the design and fabrication of bioinspired functionally graded soft-to-hard composites. Nevertheless, this emerging technology depends on several design variables, including both material and mechanistic ingredients, that are likely to affect the mechanical performance of such composites. In this paper, a model-based approach is developed to describe the interaction of ultrasound waves with homogeneous and heterogeneous additively manufactured samples, which respectively display a variation either of the material ingredients (e.g., ratio of the elementary constituents) or of their spatial arrangement (e.g., functional gradients, damage). Measurements are performed using longitudinal bulk waves, which are launched and detected using a linear transducer array. First, model is calibrated by exploiting the signals measured on the homogeneous samples, which allow identifying relationships between the model parameters and the material composition. Second, the model is validated by comparing the signals measured on the heterogeneous samples with those predicted numerically. Overall, the reported results pave the way for characterizing and optimizing multi-material systems that display complex bioinspired features.

Veering of Rayleigh–Lamb waves in orthorhombic materials

We analyse veering of Rayleigh–Lamb waves propagating in a plane of elastic symmetry for a thin orthotropic plate. We demonstrate that veering results from interference of partial waves in a similar manner as it occurs in systems composed of one-dimensional (1D) structures, such as beams or strings. Indeed, in the neighbourhood of a veering point, the system may be approximated by a pair of interacting tout strings, whose wave speed is the geometric average of the phase and group velocity of the relevant partial wave at the veering point. This complementary pair of partial waves provides the coupling terms in a form compatible with a action–reaction principle. We prove that veering of symmetric waves near the longitudinal bulk wave speed repeats itself indefinitely with the same structure. However, the dispersion behaviour of Rayleigh–Lamb waves are richer than that of 1D systems, and this reflects also on the veering pattern. In fact, the interacting tout string model fails whenever the dispersion branch is not guided by either partial wave. This often occurs when neighbouring veering points interact and partial waves no longer provide guiding curves.

Experimental Measurement of Residual Stress Distribution in Rail Specimens Using Ultrasonic LCR Waves

Longitudinal critically refracted (LCR) waves are considered bulk longitudinal waves and penetrate into an effective depth beneath the surface parallel to the material surface. Such LCR waves can be employed to measure residual stresses because the acoustoelastic effect is the basis for ultrasonic residual stress measurements. This effect is described by the relationship between change of wave travel time and stress applied when such waves propagate in a stressed medium. In this paper, stresses applied in a rail were evaluated by using a developed LCR probe. With this transducer, it was verified how the difference in the arrival times of the LCR waves showed a trend as the tensile stresses increased. The acoustoelastic coefficients were calculated using the relationship between the stresses and the travel times, and the residual stresses of the used rails were measured using these coefficients. In addition, the difference in residual stress distribution according to the characteristics of the wheel-rail contact surface was analyzed from the obtained residual stress value. It was concluded that this non-destructive evaluation technique using LCR waves could be employed for accurate stress measurement of rails because differences in stress applied to the rail can be detected.

Elastic and magnetoelastic properties of TbMnO3 single crystal by nanosecond time resolved acoustics and first-principles calculations

Time resolved pump and probe acoustics and first-principles calculations were employed to assess elastic properties of the TbMnO3 perovskite manganite having orthorhombic symmetry. Measuring sound velocities of bulk longitudinal and shear acoustic waves propagating along at least two different directions in the high symmetry planes (100), (010) and (001), provided a powerful mean to selectively determine the six diagonal elastic constants C 11 = 227 GPa, C 22 = 349 GPa, C 33 = 274 GPa, C 44 = 71 GPa, C 55 = 57 GPa, C 66 = 62 GPa. Among the three remaining off-diagonal ones, C 23 = 103 GPa was determined with a bissectrice direction. Density functional theory calculations with colinear spin-polarized provided complementary insights on their optical, elastic and magnetoelastic properties.

Study of the ultrasonic creeping wave propagation over a concave metal surface

Creeping ultrasonic waves are used in echo flaw detection of near-surface and near-bottom zones of metal products of plane-parallel or cylindrical shape. The creeping (lateral) waves are also used in testing products by the time-of-flight diffraction method as the earliest (reference) signal, followed by the useful signals of waves diffracted on metal discontinuities. The purpose of this study is to evaluate the ability of the creeping wave to propagate over a concave metal surface. We have studied experimentally the attenuation of the amplitude of a creeping wave with the distance upon wave propagation over concave metal surfaces of different radii. The velocity of propagation of the creeping wave does not depend on the radius of curvature and equals to the velocity of the bulk longitudinal wave. The results obtained provide the possibility of using the time-of-flight diffraction method in control of the objects with concave surfaces, in particular, for in-tube testing.

Evaluating the elastic properties of Al2O3–Al FGMs by longitudinal and transverse ultrasonic bulk waves velocity features

The present study aimed to investigate the elastic properties of functionally graded materials using ultrasonic bulk wave velocity features. To this end, three Al2O3–Al FGM samples were fabricated by spark plasma sintering method at three different temperatures (1050 °C, 1400 °C, and 1450 °C). In addition, two homogenous aluminum and alumina samples were fabricated to evaluate the properties of the initial materials using the initial powders. Ultrasonic pulse-echo technique was applied on fabricated samples in order to measure the longitudinal and transverse wave velocities. The elastic properties of the graded samples were obtained by wave velocity features and Archimedes density. The alumina and aluminum elastic modulus were measured as 394 and 70 GPa, respectively. The results indicated that increasing the sintering temperature from 1050 °C to 1400 °C and 1450 °C leads to considerable improvement in the average elastic modulus. The average elastic modulus of the graded bundle sintered at 1450 °C (308 GPa) was about 8.5% higher than that of the one sintered at 1400 °C (284 GPa). The microstructure analogies of samples illustrated micro-voids and phases agglomeration in all samples. The highest wave attenuation was observed in the graded sample with the lowest sintering temperature, i.e., the largest number of micro-voids caused the highest energy absorption in the graded bundle sintered at 1050 °C.

Characterization of Concrete by Using Bulk Longitudinal Ultrasonic Waves at Low Frequencies- Correlation with Compressive Strength Testing

Concrete is a complex porous material. This porosity comes from the air trapped during mixing and also from the free water that did not react with the cement. In this work, we varied the porosity rate in concrete specimens, in order to evaluate its effect on the acoustic and mechanical properties of the material during its maturation age. These test pieces were made according to EN 196-1: 2016 of different dimensions and with three mass ratios Water/Cement (W/C=0.45, W/C=0.50 and W/C=0.65). The ultrasonic measurements were done in the direct transmission mode, using 54 kHz nominal frequency transducers, transmitting in the longitudinal mode. The results showed an increase in the propagation velocity with the age of maturation for all W/C ratios and an overall decrease in its value with this ratio. On the other hand, the attenuation coefficient increased slightly with the frequency in a quasi-linear manner, while its overall value decreased with the age of maturity of the concrete. For comparison, a destructive method was used. This consisted of crushing tests to determine the compressive strength. This latter increased with the age of maturation of the concrete for all W/C ratios, but decreased when these ratios increased. These results showed the same trend as those obtained for the ultrasonic group velocity. This allowed us to deduce a correlation law between the acoustical and mechanical parameters for all ratios with a high determination coefficient. These investigations confirm the effectiveness of ultrasonic methods in evaluating the quality of concrete.

기가헤르츠 대역의 체적 종파를 이용한 세라믹 박막의 탄성 계수 측정

Picosecond ultrasonic evaluation on the Young’s modulus of a ceramic thin-film was performed in the present study. A 100nm thick silicon nitride thin-film was deposited on a silicon wafer using the plasma enhanced chemical vapor deposition technique and gigahertz-frequency longitudinal bulk waves were excited in the film using a femtosecond laser setup. A thermoelastic equation was numerically solved using the finite difference method and compared to the experimental data to estimate the elastic property of the film. Results show that the present measurement technique can effectively evaluate the film’s Young’s modulus and it is recognized that the modulus is 60-70% lower than that of its bulk status. This study is expected to provide a way to characterize nanoscale ceramics with very high spatial and temporal resolutions for the design and analysis of microelectromechanical systems and thin-film based devices.

Nonlocal Damage Mechanics for Quantification of Health for Piezoelectric Sensor

In this paper, a novel method to quantify the incubation of damage on piezoelectric crystal is presented. An intrinsic length scale parameter obtained from nonlocal field theory is used as a novel measure for quantification of damage precursor. Features such as amplitude decay, attenuation, frequency shifts and higher harmonics of guided waves are commonly-used damage features. Quantification of the precursors to damage by considering the mentioned features in a single framework is a difficult proposition. Therefore, a nonlocal field theory is formulated and a nonlocal damage index is proposed. The underlying idea of the paper is that inception of the damage at the micro scale manifests the evolution of damage at the macro scale. In this paper, we proposed a nonlocal field theory, which can efficiently quantify the inception of damage on piezoelectric crystals. The strength of the method is demonstrated by employing the surface acoustic waves (SAWs) and longitudinal bulk waves in Lithium Niobate (LiNbO3) single crystal. A control damage was introduced and its manifestation was expressed using the intrinsic dominant length scale. The SAWs were excited and detected using interdigital transducers (IDT) for healthy and damage state. The acoustic imaging of microscale damage in piezoelectric crystal was conducted using scanning acoustic microscopy (SAM). The intrinsic damage state was then quantified by overlaying changes in time of flight (TOF) and frequency shift on the angular dispersion relationship.

Studying the Effect of Microscopic Medium Inhomogeneity on the Propagation of Surface Waves

Based on the analysis of literature data, it has been shown that a system of microcracks rapidly nucleates and develops in a surface layer of several grain sizes under fatigue loading. This brings about changes in the elastic modulus and density of the material. These can be described in the form of material’s effective characteristics. The problem of the propagation of a surface wave has been solved for a microscopically inhomogeneous medium with dispersion and insignificant surface-layer variations. Using the example of testing 08Kh18N10T steel samples for low-cycle fatigue, it has been shown that the propagation speed of surface waves changes at a higher rate than that of bulk (longitudinal and shear) waves; this can be used in the tasks of testing materials at early stages of fatigue failure.

Selective modal excitation for optimization of waveguide based bulk ultrasonic transducers

The use of waveguides for ultrasonic transduction is advantageous in numerous applications such as measurement of flow, temperature and material properties under harsh environments. However, typically waveguide transducers do not use any mode control. This paper describes aspects of mode selection for waveguide based transduction of bulk longitudinal ultrasonic waves in a target metallic specimen. It is proposed that specific waveguide modes with suitable modal structure and matched acoustical impedance can significantly enhance the transduction of bulk ultrasonic waves in the specimen sample. Using circular cylindrical waveguides excited by magnetostriction, experimental results guided by finite element simulations and analysis are presented, demonstrating the feasibility of the approach. An example application in the form of a bulk longitudinal wave ultrasonic transducer is also provided illustrating the improvement in the signal quality using the proposed concept.