Ultrasonic Wave Speed Research Articles

T-matrix approach to shale acoustics

The T-matrix approach of quantum scattering theory is used here to place many long-wavelength equivalent-medium approximations for porous composites, polycrystals and cracked media on a common footing and to indicate their limitations, but also to derive some new results based on two-point statistics. In this way, we have obtained an insight into the difficult problem of elastic inclusions at finite concentrations, which is of foremost relevance when estimating the effective material parameters of porous/cracked shales, involving stacks of more or less horizontally aligned clay platelets, mixed together with more rounded silt minerals, and with fluid filling the spaces. A rather involved perturbative analysis of the effects of interactions between (or structural correlations among) the various inclusions (minerals and cavities) making up a real shale of hexagonal symmetry was performed in an attempt to obtain a better match between theoretical predictions (based on a combination of coherent and optical potential approximations) and experimental results (recovered from ultrasonic wave speeds) for the effective elastic stiffness tensor. For the particular data set considered in this study, the T-matrix approach was able to match the data better than the approach of Hornby et al., but the match was not completely satisfactory. Further progress in theoretical shale modelling may come from a better knowledge of the elastic properties of pure clay minerals, a more detailed knowledge of the microstructure of shales, the incorporation of constraints obtained from comparisons between theoretical predictions and experimental results, as well as a continuing development of the T-matrix approach. Numerical results (also for the effect of bedding parallel microcracks on the elasticity of such a real shale) have value in illustrating the importance of taking into account the effects of spatial distribution when trying to deal with non-dilute mixtures of highly contrasting material properties.

Experimental study of the seismic properties of the Eastern Alps (Italy) along the Aurina–Tures–Badia Valleys transect

In order to better constrain the interpretation and the nature of the seismic reflectors, experimental measurements at high confining pressure (up to 300 MPa) and room temperature of the compressional wave velocity (Vp) on 10 samples representative of the most common lithologies along the Aurina (Ahrntal), Tures (Tauferer Tal), and Badia (Abtei Tal) Valleys profile (Eastern Alps, Italy) have been performed. For each sample, the speed of ultrasonic waves was measured in three mutually perpendicular directions, parallel and normal to the rock foliation and lineation. The main results are: (a) Good agreement between the calculated vs. measured modal compositions of the considered rocks, indicating that they were presumably equilibrated at the estimated P– T conditions; therefore, the seismic properties are representative of the crustal level indicated by the thermobarometry. (b) Measured and calculated average Vp are in good agreement, and are typical of mid-crustal level (6.0–6.5 km/s). Only the amphibolites show Vp typical of the lower crust (7.2 km/s). (c) The seismic anisotropy of metapelites is very high (12–27%), both with orthorhombic and transverse isotropy symmetry; amphibolites are transversely isotropic with an anisotropy of 8%; orthogneisses and granitoids are isotropic or weakly anisotropic. (d) The contacts between amphibolites and all other rock types may generate good reflections, provided they are not steeply inclined. Although the metamorphic foliation remains steeply inclined, discordant buried sub-horizontal igneous contacts may be detected.

Ultrasonic wave speed measurement using the time-delay profile of rf-backscattered signals: simulation and experimental results.

Conventional methods determine the ultrasonic wave speed measuring the medium path length propagated by a pulsed wave and the corresponding time-of-flight. In this work, the wave speed is determined without the need of the path length. A transmit transducer sends a pulsed wave into the medium (wave speed constant along the beam axis) and the backscattered signal is collected by a hydrophone placed at two distinct positions near the transmitted beam. The time-delay profile, between gated windows of the two rf-signals received by the hydrophone, is determined using a cross-correlation method. Also, a theoretical time-delay profile is determined considering the wave speed as a parameter. The estimated wave speed is obtained upon minimization of the rms error between theoretical and experimental time-delay profiles. A PZT conically focused transmitting transducer with center frequency of 3.3 MHz, focal depth of 30 mm, and beam full width (-3 dB) of 2 mm at the focus was used together with a PZT hydrophone (0.8 mm of aperture). The method was applied to three phantoms (wave speed of 1220, 1540, and 1720 m/s) and, in vitro, to fresh bovine liver sample, immersed in a temperature-controlled water bath. The results present a relative speed error less than 3% when compared with the sound speed obtained by a conventional method.

Ultrasonic wave speed measurement using the time-delay profile of rf-backscattered signals

Conventional methods determine the ultrasonic wave speed by measuring the medium path length propagated by a pulsed wave and the corresponding time-of-flight. In this study, the wave speed is determined without the need of the path length. A transmitting transducer sends a pulsed wave into the medium (constant wave speed along the beam axis) and the backscattered signal is collected by a hydrophone placed at two distinct positions near the transmitted beam. The time-delay profile, between gated windows of the two rf-signals received by the hydrophone, is determined using a cross-correlation method. Also, a theoretical time-delay profile is determined considering the wave speed as a parameter. The measured wave speed is obtained upon minimization of the RMS error between theoretical and experimental time-delay profiles. A PZT conically focused transmitting transducer with center frequency of 3.3 MHz, focal depth of 20 mm and beam width (−6 dB) of 2 mm at the focus was used together with a PZT hydrophone, 0.8 mm in aperture. The method was applied to three phantoms (wave speed of 1220, 1501 and 1715 m/s) and, in vitro, to fresh bovine liver sample, immersed in a temperature-controlled water bath. The results vary within 3% of those obtained with a conventional method.

Application of orthogonal ultrasonic signals and binaural processing for imaging of the environment

Data acquisition rates in ultrasonic imaging systems are limited by the finite value of the speed of ultrasonic waves. In order to improve the imaging speed, it is proposed to perform simultaneous scanning of the environment in different directions. In order to avoid cross-talk between adjacent channels in different directions, different orthogonal signals are transmitted. Application of cross-correlation processing and non-linear iterative deconvolution enables the reliable separation of signals transmitted by different sources and reflected by multiple targets. The spatial positions of the targets are found using the data obtained after the non-linear deconvolution as the initial data for binaural or tri-aural processing. This approach has been exploited in ultrasonic sonar used for navigation of mobile robots.

Strongly correlated bistable sublattice and temperature hysteresis of elastic and thermal crystal properties

It is shown that in crystal lattices with a basis the cooperative behavior of a certain type of atoms performing optical long-wavelength vibrations in a double-well potential of the field of the matrix lattice may lead to the formation of a bistable sublattice. As a result of the interaction of the metastable states of such a sublattice with the vibrational states of the matrix lattice, the elastic and thermal properties of the crystal acquire anomalous, hysteresis-like, temperature curves. The concepts developed in the paper make it possible to obtain a qualitative interpretation, which agrees with the experimental data, of the hysteresis-like temperature dependence of the speed and absorption of ultrasonic waves, the specific heat, and the thermal conductivity in superconducting yttrium and bismuth cuprates.

Ultrasonics in an aluminum foam

Abstract Open celled foamed aluminum typically consists of an irregular frame of solid struts with typical lengths of the order of millimeters and thicknesses of a fraction of a millimeter. Total aluminum volume fractions are of the order of 10%. Quoted values of static modulus and mass density allow one to infer long wavelength (much greater than strut length) ultrasonic wave speeds. These predictions are compared with the velocities observed in 100 kHz transient signals. At higher frequencies, where wavelengths are comparable with strut lengths, ultrasound can be transported only diffusively. Wave speeds are unmeasurable and of little meaning anyway. We therefore also report on ultrasonic measurements appropriate for the high-frequency regime. These include diffusivity, absorption and modal density. Recent literature has reported measurements of diffusivities and absorption in other materials, particularly in metallic polycrystals. Measurements of modal densities are new.

Effective Moduli of Microcracked Rocks: Theories and Experiments

This paper compares and contrasts the predicted effective moduli by the self-consistent and noninteracting methods and examines the range of validity for both models; predictions by these two models are compared to experimental observations on natural rocks containing microcracks and artificial rocks containing inserted microcracks. Crack density (e) in real rocks is obtained by counting cracks under microscope and those in replicated rocks is, of course, predetermined; these crack densities are then compared to the crack densities interpreted from the changes in ultrasonic wave speeds, using either self-consistent model or noninteracting crack model. For natural rocks, the noninteracting prediction seems to agree better with experiments than the self-consistent method for E c 0.2, but both theoretical predictions deviate from experimental observation for e > 0.2. For replicated rocks, both theories give prediction comparable to experiments for E c 0.2, but underestimate the actual value for e > 0.2. Therefore, a better damage model is needed for solids with crack density larger than 0.2.

USING LABVIEW UNDER WINDOWS IN ADVANCED ULTRASONIC TESTING

Abstract Ultrasonic testing is used in a variety of applications. One application, the measurement of residual stress, utilizes acoustoelastic testing. In acoustoelastic testing, very small changes in ultrasonic wave speed are measured as a function of applied load. In this study, a testing setup has been implemented which utilizes National Instruments' LabVIEW software on a digital computer to control and analyze the acoustoelastic responses of various engineering materials. The high quality acoustoelastic results are indicative of the high resolution in ultrasonic wave speed measurements that is attained using this setup.

Moisture effects on isobutylene‐isoprene copolymer‐based composite barrier. I: Moisture diffusion and detection

AbstractExperiments have assessed how moisture and heat influence the functional and structural integrity of butyl rubber matrix composites used as protective barriers. This paper, which is first of a series, reports the findings on the subjects of moisture diffusion and its effect on ultrasonic wave propagation of composite barriers. On exposure to high humidity at elevated temperatures, carbon black‐reinforced butyl rubber composite barriers were found to absorb substantial moisture, with the hygroscopic reinforcement phase making a more significant contribution than the matrix. The moisture diffusion coefficients for both composite and unreinforced vulcanizate were close to each other at each exposure temperature, and had the same temperature dependence. The calculated activation energies of moisture diffusion indicate that the moisture absorption rate of the carbon black phase is governed by the moisture diffusion rate of the matrix. Ultrasonic wave speed appeared to be a viable means of monitoring the moisture absorption of composite barriers. On exposure to moist heat, relative ultrasonic wave speeds for both composite and unreinforced vulcanizate decreased continuously.

Ultrasonic Characterization of Rolling and Recrystallization Textures in Aluminum

Crystallographic texture, which plays an important role in many forming operations, is developed during sheet metal processing. Improved product quality could be achieved if the texture could be measured, quickly and inexpensively, during different stages of the processing. One potential scheme, involving measurement of the angular dependence of the speed of ultrasonic waves propagating in the plane of the sheet is described, as applied to aluminum. While this technique has been successfully used in steel sheets, application to aluminum is more difficult because of the smaller elastic anisotropy of the crystallites. This paper presents the results of a detailed study of the strengths and weaknesses of the approach. Included are discussions of signal processing factors, the accuracy of the ultrasonically determined , and a comparison between measured by ultrasonics and by diffraction techniques (both X‐ray and neutron). It is found that relative velocity measurements are very good for determining and . These measurements can easily distinguish between rolling and recrystallization textures, and can also detect more subtle variations in recrystallization textures. A systematic offset in the prediction of is also reported, which is believed to be a consequence of unknown alloy dependence of the single crystal elastic constants and texture free velocities, quantities which play a key role in inferring this quantity from absolute measurements.

Ultrasonic detection of microstructure changes in cast iron

Ultrasonic waves are monitored to detect the microstructure changes in cast iron. Specimens are made from nonalloyed spheroidal graphite cast iron (before and after heat treatment), eutectoid carbon steel (0.8% C), and ingot iron. The ultrasonic longitudinal wave speed increased with increase in the graphite shape factor, pearlite volume fraction, specific length of grain boundaries and cementite-ferrite interface boundaries. Decrease in the wave speed corresponds to increase in the graphite volume fraction, graphite precipitates and austenitizing temperature and time.

An Experimental Investigation of Damage Evolution in a Ceramic Matrix Composite

The mechanical behavior of a glass-ceramic matrix composite, SiC/CAS (calcium aluminosilicate reinforced with unidirectional SiC fibers), is studied. Results based on uniaxial tension experiments are presented for specimens with fibers aligned in the loading direction. Axial and transverse strain gages on all four gage section surfaces and in situ acoustic emission and ultrasonic wave speed measurements were used to monitor the evolution of damage. All measurements were made with high-resolution, continuous data acquisition. Post-test optical and scanning electron microscopy was also used to identify the various micromechanisms of damage. The experimental results demonstrate the existence of “zones of deformation” which are associated with the onset of different damage mechanisms. It is shown that the observed stress-strain behavior can be explained in terms of the material properties of the matrix and the fiber, the material processing, and the postulated zones of deformation.

Evaluation of tortuosity in acoustic porous materials saturated by air

Tortuosity is an important parameter for the prediction of the acoustical properties of porous sound absorbing materials. The evaluation of tortuosity by resistivity measurements is now used in several laboratories, although this method presents several drawbacks. In particular, the complete saturation by a conducting fluid of a porous foam having a high flow resistivity is difficult to obtain without partially damaging the structure of the cells. A simple technique based on ultrasonic wavespeed measurements in a material saturated by air is described. This method has been used previously only for water or superfluid helium saturated materials.

Determining protein concentration in milk mixtures by measuring speed of ultrasonic waves travelling through milk and comparing with ultrasonic wave speed in distilled water : Belo Agric. Mech. Inst. SU-1723520; 30 March 1993

Determining protein concentration in milk mixtures by measuring speed of ultrasonic waves travelling through milk and comparing with ultrasonic wave speed in distilled water : Belo Agric. Mech. Inst. SU-1723520; 30 March 1993

Determining protein and fat content in milk by measuring speed of ultrasonic waves in analysed milk at two specified temperatures : Belo Agric. Mech. Inst. SU-1723521; 30 March 1992

Determining protein and fat content in milk by measuring speed of ultrasonic waves in analysed milk at two specified temperatures : Belo Agric. Mech. Inst. SU-1723521; 30 March 1992

Phase and group velocity considerations for dynamic modulus measurement in anisotropic media

In anisotropic media, the direction of energy propagation does not necessarily coincide with the wave normal, i.e. the energy flux vector does not coincide with the wave normal. Since, experimentally, one measures group velocity not phase velocity, one must therefore be careful in interpreting ultrasonic wave speed measurements in anisotropic media. This is of particular importance in elastic property reconstruction where acoustic velocity measurements are used as the basis for determining anisotropic material properties. In this work, the consequences of energy flux deviation from the wave normal are considered for typical experimental geometries. Particular attention is devoted to developing appropriate relationships between the phase velocity and ultrasonic transit time measurements, as these relations are most useful for elastic property reconstruction. In all the cases considered, it is shown that the phase velocity can be directly calculated from appropriate time delay measurements.

Determination of the elastic constants of anisotropic materials using laser-generated ultrasonic signals

This paper presents the solution of the materials characterization problem in which the elastic constants of an anisotropic material are determined from ultrasonic wavespeed measurements made in nonprincipal directions of a specimen. The ultrasonic waves were generated via the point-source/point-receiver technique using a pulsed laser as a source and a miniature, point-like transducer as a receiver. Data were acquired during a scan of the source along one of the principal acoustic axes of symmetry of the material. In each waveform the arrivals of the quasi-longitudinal and the two quasi-shear bulk modes were measured and the elastic constants of the material were then recovered using an optimization algorithm. Experimental results are presented for a transversely isotropic, unidirectional fiberglass/polyester and a single crystal specimen of silicon. It was found that the nonlinear fit between the measured and the recovered longitudinal slowness values is excellent. Some discrepancies are observed in the data for the two shear modes. These are shown to be related to the complexity of the detected signals.

Determination of the elastic constants of anisotropic composite materials via laser photoacoustics

This paper presents the solution of the inverse anisotropic medium problem in which the elastic constants of an anisotropic composite material are determined from ultrasonic wave speed measurements made in nonprincipal directions of a specimen. The ultrasonic waves were generated via the point-source/point-receiver technique using a 2-ns pulsed Nd:Yag laser as a source and a 2.5-mm-diam capacitive or a 1.3-mm piezoelectric transducer as a receiver. Data were acquired during an isoangular scan of the source relative to one of the principal acoustic axes of symmetry. In each waveform, the arrivals of the quasilongitudinal and the two quasishear bulk modes were measured. The elastic constants of the material were then recovered using an optimization algorithm. Experimental results are presented for a transversely isotropic composite material. It was found that the nonlinear fit between the experimental and the recovered slowness values is excellent. Some discrepancies are observed for the two shear modes. These are shown to be related to the complexity of the detected signals.

Nondestructive measurement of texture and nine elastic constants of rolled metal sheets by EMAT

All the lowest-order independent coefficients W400, W420, and W440 for the crystallographic orientation distribution function were obtained nondestructively for thin rolled steel sheets by measuring ultrasonic wave speeds and making use of the known values of the single-crystal elastic constants. All the ultrasonic wave speeds were measured by EMAT so that no acoustic coupling medium was necessary, and the measurements were done quickly and with very good reproducibility. Pole figures were calculated using the obtained coefficients W400, W420, and W440 and the results were quite similar to the pole figures obtained by the x-ray diffraction method. It is well known that a rolled steel sheet can be modeled as an orthorhombic continuum having nine different elastic constants. It is also known that only six of the nine constants are independent when the sheet is a polycrystal of cubic crystallites and assuming that the macroscopic properties can be predicted by an averaging scheme. All these nine constants were calculated using the obtained W400, W420, W440, and the known single-crystal elastic constants. Young's moduli in the plane of the rolled steel sheet were also calculated and compared with the measured plastic strain ratio. Good relations were obtained between the average Young's modulus E and the average plastic strain ratio r.