Longitudinal critical angle singularities and their effect on V(Z)of the line-focus-beam acoustic microscope

In order to investigate a mechanism which causes a velocity difference between the longitudinal wave and leaky surface skimming compressional wave (LSSCW) observed in a line-focus-beam acoustic microscope, the analytic property of an acoustic reflection coefficient and its effect on a V(z) analysis were studied. A pole hidden in the unphysical Riemann sheet close to the longitudinal branch point is found to be responsible for the abrupt phase change at the longitudinal critical angle. This, together with an effect of a dominant Rayleigh wave pole, affects the V(z) measurement of the LSSCW. A method to estimate the longitudinal and shear wave velocities is discussed     

Acoustic microscopy measurement of elastic constants and massdensity

A method is presented to determine the elastic constants and the mass density of isotropic and anisotropic solids and anisotropic thin films. The velocity and attenuation of leaky surface acoustic waves (SAWs) have been obtained for specified propagation directions from V(z) curves measured by line-focus acoustic microscopy (LFAM). The experimentally obtained velocities have been compared to velocities obtained from a measurement model for the V(z) curve which simulates the experiment. Since the measured and simulated V(z) curves have the same systemic errors, the material constants are free of such errors. For an isotropic solid, Young's modulus E, the shear modulus G and the mass density ρ have been determined from the leaky Rayleigh wave velocity and attenuation, measured by LFAM, and a longitudinal wave velocity measured by a pulse-echo transit-time technique. For a cubic-crystalline solid, the ratios of the elastic constants to the mass density (c₁₁ /ρ, c₁₂/ρ, c₄₄/ρ) have been determined from the directional variation of measured SAW velocities, using a preliminary estimate of ρ. The mass density ρ has subsequently been determined by additionally using the attenuation of leaky SAWs in crystal symmetry directions. For a cubic-crystalline thin film deposited on a substrate, the elastic constants and the mass density (c₁₁, c₁₂, c₄₄, ρ) of the film have been determined from the directional variation of the measured SAW velocities, and a comparison of the corresponding attenuation coefficient with the measured attenuation coefficient has been used to verify the results     

Propagation properties of longitudinal leaky surface waves on lithium tetraborate

Theoretical and experimental results of longitudinal leaky surface waves with a higher phase velocity than that of ordinary leaky surface waves and a low propagation loss on lithium tetraborate (LBO) are investigated in detail. They propagate along the surface with a phase velocity close to that of longitudinal bulk wave, slightly radiating two kinds of shear bulk waves (or one shear bulk wave in the case that one of two shear wave terms is uncoupled) into the solid. Most surface components of the mode consist of a longitudinal wave term and an electromagnetic wave term. The detailed propagation properties of the longitudinal leaky surface waves on LBO with the Euler angles (phi, theta, 90 degrees ) are investigated theoretically and experimentally. The (011) cut of LBO was found to be desirable for higher frequency SAW devices. One of the reasons why that mode on LBO has a low propagation loss is also discussed.     

Influence of reflected waves from the back surface of thin solid-plate specimen on velocity measurements by line-focus-beam acoustic microscopy

We investigated the velocity measurements of leaky surface acoustic waves (LSAW) by line-focus-beam (LFB) acoustic microscopy of thin specimens for which the waves reflected from the back surface of the specimen (back reflection) must be included in the measurement model. The influence of back reflection resulted in a serious problem in measurement accuracy of the apparent changes of measured velocities. Using several samples of thin synthetic silica glasses, the determination of LSAW velocity affected by the reflected waves and the relationship between the specimen thickness and the apparent velocity change with a periodic frequency interval in the frequency dependence of measured LSAW velocities are discussed in detail. Three useful methods for eliminating that influence are proposed and demonstrated: first, separating the radio frequency (RF) pulsed wave signal from the specimen surface and the pulses reflected from the back surface by reducing the RF pulse width; second, scattering acoustic waves from the roughened back surface; and third, taking the moving average of measured frequency characteristics of LSAW velocities. It is shown that, among these methods, the moving average method is the most useful and effective as a general means to eliminate the influence and to determine intrinsic velocity values because this method needs no specimen process and no system change, and the same conventional V(z) curve measurement and analysis can be employed.     

Ray representation of longitudinal lateral waves in acoustic microscopy

For object materials having a large enough Rayleigh velocity, the V(z) (where V is the output voltage and z is the defocus distance) variation is mainly due to interference between the fields of the geometrically reflected wave and the leaky Rayleigh wave. However, for materials, such as organic compounds, having a low Rayleigh velocity, the leaky Rayleigh wave is not excited. For this case, the lateral wave resulting from propagation along the surface of the longitudinal wave plays a significant role in determining the V(z) dependence. The effect of the lateral wave contribution on V(z) is studied. Ray optics is to derive an expression giving the influence of the longitudinal lateral wave. Good agreement is found between the theory and measurements for z not near zero. Because of the ease with which the longitudinal wave velocity can be obtained from V(z), one can conveniently determine the elastic constant c(11 ) of isotropic materials using the acoustic microscope.     

Leaky lamb waves of a piezoelectric plate subjected to conductive fluid loading: an experimental study

This paper proposes a novel experimental method for measuring the propagating characteristics of leaky Lamb waves in a piezoelectric plate surrounded by a fluid. It is a differential type of measurement and is very sensitive to the velocity change and wave attenuation of leaky Lamb waves induced by fluid-loading effects. Experimental measurements on an X-cut LiNbO3 plate immersed in a dielectric and conductive fluid have been carried out. The velocity change and wave attenuation of the leaky Lamb waves caused by dielectric and conductive loadings of the fluid have been experimentally determined. The measured data have been compared with the theoretical ones that are calculated from a partial wave analysis. For the wave velocity, very good agreements between the experimental and theoretical results are observed. For the wave attenuation, there are some discrepancies, but an important characteristic in the relationship between wave attenuation and fluid conductivity as predicted by the theory have been verified experimentally.     

Measurement uncertainty in the determination of total petroleum hydrocarbons (TPH) in soil by GC-FID

In this investigation two methods were used for estimating the measurement uncertainty due to sampling and analysis of petroleum hydrocarbon contaminated soil. Analysis of variance (ANOVA) was used for type A evaluation of the measurement uncertainty. The results showed that the statistical evaluation of measurement uncertainty can be complicated by the log-normality and heteroscedasticity of the data. Although mathematical transformation of raw data is widely suggested for overcoming the discrepancy between data and ANOVA assumptions, its use results in problems with the interpretation of the ANOVA results at the original scale.

The measurement uncertainty was also estimated from the calculated precision equations for sampling and analysis. Comparison of measurement uncertainty values with the equivalent values obtained with ANOVA revealed that ANOVA overestimates the expanded uncertainty at both low and high TPH concentrations. Consequently, correct selection of the statistical analysis method needs comprehensive knowledge of the assumptions and limitations of statistical methods and careful consideration of the special characteristics (distribution, constancy of measurement variance) of the raw data as these may affect the validity of the estimated uncertainty. The expanded uncertainty obtained in this study for the results of TPH determinations with linear measurement precision modelling was moderate, ranging from 21% at a TPH concentration of 895 mg/kg to 9% at a TPH concentration of 10 019 mg/kg. If a single sample taken in a survey is analyzed only once, then the analytical variance contributes the most to the measurement variance, ranging from 68– 80% at a TPH concentration of 100–10 000 mg/kg.     

An enhanced algorithm for evaluation of surface waves

A procedure based on the Stroh formalism is presented that yields the approximation for the planar harmonic Green's matrix function for piezoelectric half-space that is valid in the vicinity of the surface, or pseudosurface, wave number. This approximation can be directly exploited in the spectral-theoretical analysis of surface acoustic wave devices. Otherwise, the known characterization of the surface wave supporting substrate can be immediately inferred from it, like the wave velocity, piezoelectric coupling coefficient, the wave damping in the case of leaky pseudosurface waves, and the corresponding surface displacement velocities.     

Measuring the acoustic wave velocity and sample thickness using an ultrasonic transducer array

We suggest a new method for determining the longitudinal and transverse acoustic wave velocities and sample thicknesses, which is based on the measurement and analysis of pulsed echo signals by an array of ultrasonic transducers. Analytical expressions relating the delay of signals detected by the array and the values of parameters to be determined are obtained within the framework of a ray model of the measuring system. Measurements on a reference sample have been performed. The values of ultrasonic wave velocities and sample thickness obtained using the proposed technique agree with the results of measurements using independent methods.     

声学法测量复合绝缘子弹性常数

提出了一种实用的声学法测量复合材料弹性常数的方法.依据复合材料中声波速度与材料弹性常数之间的本构关系,测量不同传播方向的少数几个声速,就可以得到其弹性常数矩阵.以复合绝缘子为测量样品,为提高测量横波的精度,根据超声波在边界上的波型转换条件,使用常规纵波探头对由掠入射纵波产生的横波进行测量.     

SAW velocity measurement of crystals and thin films by the phasevelocity scanning of interference fringes

We present principle and application of a novel noncontact velocity measurement of surface acoustic waves (SAW) on crystals and thin films using laser interference fringes scanned at the phase velocity of SAW. The scanning interference fringes (SIF) are produced by intersecting two laser beams with a frequency difference. The SAW velocity within the laser beam spot is measured as the ratio of observed SAW frequency and predetermined wave number of the SIF. The frequency measurement can be quite precise because of a large number of generated SAW carriers and amplitude enhancement effect. The SAW velocity measurement is free from the water loading effect accompanying the leaky SAW measurements. This principle was successfully applied to evaluate Si ₃N₄ and SiO₂ films deposited on Si (001) surface     

Measurement of ultrasonic wave velocity in a solid under gas pressures up to 0·4 GPa

A set-up is described for the measurement of longitudinal and transverse wave velocities in a solid under gas pressures up to 0·4 GPa. To check the performance of the set-up, the elastic constants of Se and As₂Se₃ glasses and their pressure derivatives were obtained from the wave velocity data and compared with the data available in the literature.     

Effect of periodic surface roughness on V(z) curves for the line-focus acoustic microscope

A specimen with a periodic surface profile is considered to estimate the effect of surface roughness on the V(z) curve for the line-focus acoustic microscope. The Fourier optics approach is used to obtain the response of the lens and the Rayleigh-Fourier method is used to obtain the reflection coefficients for plane wave incidence from the fluid side on the periodic surface. An integral expression is obtained to calculate V(z) curves for periodic surface profiles. The V(z) curves are used to calculate the leaky Rayleigh wave velocities by applying the fast Fourier technique. Numerical results are presented to display the effect of sinusoidal surface roughness on the V(z) curves and the corresponding leaky Rayleigh wave velocities.     

Characterization of the alumina–zirconia ceramic system by ultrasonic velocity measurements

In this work an alumina–zirconia ceramic composites have been prepared with α-Al₂O₃ contents from 10 to 95 wt.%. The alumina–zirconia ceramic system was characterized by means of precise ultrasonic velocity measurements. In order to find out the factors affecting the variation in wave velocity, the ceramic composite have been examined by X-ray diffraction (XRD) and (SEM) scanning electron microscopy. It was found that the ultrasonic velocity measurements changed considerably with respect to the ceramic composite composition. In particular, we studied the behavior of the physical material property hardness, an important parameter of the ceramic composite mechanical properties, with respect to the variation in the longitudinal and shear wave velocities. Shear wave velocities exhibited a stronger interaction with microstructural and sub-structural features as compared to that of longitudinal waves. In particular, this phenomena was observed for the highest α-Al₂O₃ content composite. Interestingly, an excellent correlation between ultrasonic velocity measurements and ceramic composite hardness was observed.     

A new point contact surface acoustic wave transducer for measurement of acoustoelastic effect of polymethylmethacrylate

A new acoustic transducer and measurement method have been developed for precise measurement of surface wave velocity. This measurement method is used to investigate the acoustoelastic effects for waves propagating on the surface of a polymethylmethacrylate (PMMA) sample. The transducer uses two miniature conical PZT elements for acoustic wave transmitter and receiver on the sample surface; hence, it can be viewed as a point- source/point-receiver transducer. Acoustic waves are excited and detected with the PZT elements, and the wave velocity can be accurately determined with a cross-correlation waveform comparison method. The transducer and its measurement method are particularly sensitive and accurate in determining small changes in wave velocity; therefore, they are applied to the measurement of acoustoelastic effects in PMMA materials. Both the surface skimming longitudinal wave and Rayleigh surface wave can be simultaneously excited and measured. With a uniaxial-loaded PMMA sample, both acoustoelastic effects for surface skimming longitudinal wave and Rayleigh waves of PMMA are measured. The acoustoelastic coefficients for both types of surface wave motions are simultaneously determined. The transducer and its measurement method provide a practical way for measuring surface stresses nondestructively.     

Near point-source longitudinal and transverse mode ultrasonic arrays for material characterization

Specially constructed near point-source ultrasonic transducers (0.75 MHz) were designed to preferentially stimulate and receive the one longitudinal (P) and two transverse (S) propagation modes. Arrays of these transducers were placed on a rectangular prism of common soda-lime glass, which served as an ideal homogeneous, isotropic medium, to evaluate the uncertainty of a newly developed phase velocity measurement method. Through the use of the Radon transform, the data were transformed from the offset-time (x-t) domain to the intercept time-horizontal slowness (τ-P) domain. From the shape of the curves in the τ-p domain, the phase velocity of the propagating waves may be determined for a range of directions. The phase velocities determined using this method were accurate for incidence angles up to 76°, 64° and 77° for the P, SV, and SH wave modes, respectively. Phase velocities of 5724±64, 3411±30, and 3467±15 m/s were determined for the P-wave, SV-wave, and SH-wave modes, respectively. This agrees with the direct transmission P-wave and S-wave velocities of 5690±60 and 3440±26 m/s, respectively, to better than 1%     

Elastic property measurement using Rayleigh-Lamb waves

A nondestructive technique is described for the measurement of elastic constants of isotropic plates using ultrasonic Rayleigh-Lamb waves. The experimental method employs continuous harmonic waves and a pair of variable-angle contact transducers in pitch-catch mode. The phase velocity of the R-L waves at a particular frequency is determined from the phase shift over a measured path length. This simple experimental technique can measure phase velocity over the range 1–10 mm/µs with an error of less than 0.5% over a frequency range of 50 kHz-2 MHz. Individual symmetric and antisymmetric modes can be generated through the selection of transducer angle and frequency. Young's modulus and Poisson's ratio for the material are calculated from measurements of frequency and phase velocity by a nonlinear least squares solution to the dispersion equations. The sensitivity of the nonlinear least squares function to the measurement region of the dispersion curve is investigated. It was found that estimations of material properties are more accurate and less sensitive to small experimental errors when only selected frequencies and R-L modes are used in the least squares calculation. This technique is demonstrated with several isotropic materials and with both thick (6 mm) and thin (0.8 mm) plates. Values for elastic constants determined by the contact transducer Lamb wave technique compare favorably with values measured using the pulse-echo-overlap method. The uncertainty in measurements of Young's modulus and Poisson's ratio was less than 1% and 2%, respectively. The technique has advantages over more traditional methods for measuring elastic properties when it is desirable to use wavelengths greater than the plate thickness, when properties may vary with frequency, or when it is necessary to measure in-plane elastic properties of thin plate structures.     

Elastic Property Measurement Using Rayleigh-Lamb Waves

Abstract

A nondestructive technique is described for the measurement of elastic constants of isotropic plates using ultrasonic Rayleigh-Lamb waves. The experimental method employs continuous harmonic waves and a pair of variable-angle contact transducers in pitch-catch mode. The phase velocity of the R-L waves at a particular frequency is determined from the phase shift over a measured path length. This simple experimental technique can measure phase velocity over the range 1–10 mm/μs with an error of less than 0.5% over a frequency range of 50 kHz-2 MHz. Individual symmetric and antisymmetric modes can be generated through the selection of transducer angle and frequency. Young's modulus and Poisson's ratio for the material are calculated from measurements of frequency and phase velocity by a nonlinear least squares solution to the dispersion equations. The sensitivity of the nonlinear least squares function to the measurement region of the dispersion curve is investigated. It was found that estimations of material properties are more accurate and less sensitive to small experimental errors when only selected frequencies and R-L modes are used in the least squares calculation. This technique is demonstrated with several isotropic materials and with both thick (6 mm) and thin (0.8 mm) plates. Values for elastic constants determined by the contact transducer Lamb wave technique compare favorably with values measured using the pulse-echo-overlap method. The uncertainty in measurements of Young's modulus and Poisson's ratio was less than 1% and 2%, respectively. The technique has advantages over more traditional methods for measuring elastic properties when it is desirable to use wavelengths greater than the plate thickness, when properties may vary with frequency, or when it is necessary to measure in-plane elastic properties of thin plate structures.     

Guided acoustic wave propagation for porcelain coatingcharacterization

In this paper a measurement technique to obtain dispersion curves for guided acoustic modes in porcelain-coated steel is described. The measurement is performed with two angled ultrasonic longitudinal transducers in a pitch catch configuration by employing an immersion technique. Phase velocities for the guided modes are selected through the variation of the angle formed by the transmitter beam with the surface normal vector. The excitation signal of the transmitting transducer is a narrow band pulse. For each phase velocity, the guided mode frequencies are recovered by evaluating the frequency minima of the reflection coefficient