Dynamic Acoustoelastic Testing Research Articles

Concrete cover characterisation using dynamic acousto-elastic testing and Rayleigh waves

This paper presents the application of surface Rayleigh waves in nonlinear dynamic acousto-elastic testing for the nondestructive evaluation of the concrete cover. Numerous physical phenomena, such as conditioning and slow dynamics, characterising the dynamic non-classical nonlinear elastic behaviour of many types of micro-heterogeneous solids, were observed in concrete. Rayleigh waves were used as probing waves to evaluate the effect of local property changes in a concrete cover. The proposed method was validated for two typical problems of concrete durability, in a case of thermal damage – distributed micro-damage – and in a case of carbonation – surface problem with determination of the carbonation depth. In both cases, the results showed that the relative variation as a function of material changes of the nonlinear parameters was much higher than that of the ultrasonic pulse velocity.

Dynamic acousto-elastic testing applied to a highly dispersive medium and evidence of shell buckling of lipid-coated gas microbubbles.

Dynamic acousto-elastic testing is applied to a mixture of lipid-coated microbubbles in water. A dynamic change of ambient pressure is produced by a 16 kHz pressure wave having a peak pressure amplitude of 28 kPa. The induced changes of phase velocity and attenuation are captured by a sequence of short ultrasound pulses with a center frequency of 4 MHz. As a consequence of the dispersion brought about by the resonance of microbubbles at a frequency close to 2 MHz, time-domain approaches like the cross-correlation method are shown to be unsuited to determine the variation in ultrasound wavespeed. A frequency-domain analysis shows that the acousto-elastic effect (first order pressure derivative of ultrasound phase velocity) depends on the ultrasound frequency. The acousto-elastic effect tends to that measured in water for an ultrasound frequency above the resonance frequency of microbubbles, while it is two orders of magnitude larger for an ultrasound frequency close to or below the resonance frequency of microbubbles. Besides the large magnitude of the acousto-elastic effect observed for an ultrasound frequency below the resonance frequency of microbubbles, the first order pressure derivative of ultrasound phase velocity is negative. This supports the occurrence of shell buckling of lipid-coated microbubbles induced by the 16 kHz pressure wave.

Investigation of the validity of Dynamic AcoustoElastic Testing for measuring nonlinear elasticity

Measurement of the dependence of the elastic moduli on the strain, i.e., the characterization of nonlinear elastic properties of solid media, poses intrinsic experimental difficulties. The Dynamic AcoustoElastic Technique has been recently developed as an efficient tool for the determination of the modulus in both compression and tension. The goal of the present paper is to discuss the limitations of the experimental implementation and the interpretation of the measured quantities in terms of nonlinear parameters. For this purpose, simulation results will be presented for both classical and nonclassical nonlinear elastic media.

Fast and slow dynamics in a nonlinear elastic bar excited by longitudinal vibrations

The dynamics of heterogeneous materials, like rocks and concrete, is complex. It includes such features as nonlinear elasticity, hysteresis, and long-time relaxation. This dynamics is very sensitive to microstructural changes and damage. The goal of this paper is to propose a physical model describing the longitudinal vibrations in heterogeneous material, and to develop a numerical strategy to solve the evolution equations. The theory relies on the coupling of two processes with radically different time scales: a fast process at the frequency of the excitation, governed by nonlinear elasticity and viscoelasticity, and a slow process, governed by the evolution of defects. The evolution equations are written as a nonlinear hyperbolic system with relaxation. A time-domain numerical scheme is developed, based on a splitting strategy. The features observed by numerical simulations show qualitative agreement with the features observed experimentally by Dynamic Acousto-Elastic Testing.

Modeling nonlinear viscoelasticity in dynamic acoustoelasticity

Dynamic Acoustoelastic Testing (DAET) has been developed to non-invasively assess the nonlinear viscoelastic properties of fluids and solids. We propose a phenomenologically motivated model for harmonic regime to identify nonlinear viscoelastic parameters from DAET experiments. The nonlinear elastic and viscous parameters are derived from the real and imaginary components of the Taylor series expansion of the complex longitudinal modulus. The model is applied to Newtonian fluids that exhibit classical elastic nonlinearities and glass beads saturated with water that exhibit nonclassical viscoelastic nonlinearities. Hysteresis, asymmetry, and DC offset are well accounted for in the model.

Modeling dynamic acousto-elastic testing experiments: validation and perspectives.

Materials possessing micro-inhomogeneities often display a nonlinear response to mechanical solicitations, which is sensitive to the confining pressure acting on the sample. Dynamic acoustoelastic testing allows measurement of the instantaneous variations in the elastic modulus due to the change of the dynamic pressure induced by a low-frequency wave. This paper shows that a Preisach-Mayergoyz space based hysteretic multi-state elastic model provides an explanation for experimental observations in consolidated granular media and predicts memory and nonlinear effects comparable to those measured in rocks.

Characterizing the nonlinear interaction of S (shear) and P (longitudinal) waves in reservoir rocks

The nonlinear elastic response of rocks is known to be caused by internal microstructure, particularly cracks and fluids. In order to quantify this nonlinearity, this paper presents a method for characterizing the interaction of two nonresonant traveling waves: a low-amplitude P-wave probe and a high-amplitude lower frequency S-wave pump with their particle motions aligned. We measure changes in the arrival time of the P-wave probe as it passes through the perturbation created by a traveling S-wave pump in a sample of room-dry Berea sandstone (15 × 15 × 3 cm). The velocity measurements are made at times too short for the shear wave to reflect back from the bottom of the sample and interfere with the measurement. The S-wave pump induces strains of 0.3—2.2 × 10−6, and we observe changes in the P-wave probe arrival time of up to 100 ns, corresponding to a change in elastic properties of 0.2%. By changing the relative time delay between the probe and pump signals, we record the measured changes in travel time of the P-wave probe to recover the nonlinear parameters β~ −102 and δ ~−109 at room-temperature. This work significantly broadens the applicability of dynamic acousto-elastic testing by utilizing both S and P traveling waves.

In situ characterization of shallow elastic nonlinear parameters with Dynamic Acoustoelastic Testing

AbstractIn situ measurement of the elastic nonlinear site response is advantageous to provide optimal information for prediction of strong ground motion at a site. We report the first implementation of a technique known as Dynamic Acoustoelastic Testing (DAET) in situ with the ultimate goal of developing a new approach for site characterization. DAET has shown promising results at the laboratory scale for the study of nonlinear elasticity of Earth materials, detailing the full nonlinear elastic properties of the studied sample. We demonstrate the feasibility of DAET in situ and compare it to other methods (nonlinear resonance spectroscopy, wave amplitude dependence of propagation velocity, and wave distortion). Nonlinear elastic properties are characterized by DAET with the advantage of providing a local assessment compared to other methods, here at a depth of 4 m to 5 m. A vertical dynamic strain amplitude of 5 ×10−5 produces a relative change in compressional wave modulus of 6%. We measure an effective parameter of quadratic elastic nonlinearity of order −103, the same order of magnitude measured at the laboratory scale in rocks and in packs of unconsolidated glass beads. Hysteresis is observed in the variation in soil elasticity as a function of the instantaneous dynamic strain that evolves as the dynamic strain amplitude is increased from 9 ×10−7 to 5 ×10−5.

Ultrasound propagation in trabecular bone: A numerical study of the influence of microcracks

The accumulation of microdamage in trabecular bone tissue is suspected of being a predictive indicator of osteoporosis diagnosis. To quantify this microdamage, the Dynamic AcoustoElastic Testing (DAET) method measures the Time Of Flight (TOF) and amplitude variations of transmitted ultrasound (US) pulses, while the bone sample is submitted to a low frequency sinusoidal hydrostatic pressure (opening/closing of microcracks). However, DAET is both sensitive to viscoelastic properties changes and microcracks density. To verify the microcracks density contribution on DAET results, a numerical approach is proposed. Multliple configurations of microdamaged trabecular bone-tissue-like mesh have been simulated. A 2D pseudo-spectral time domain numerical model was then developed to simulate linear wave propagation in heterogeneous solids. The influence of the microcracks number and orientation on the US TOF was particularly investigated. Results are discussed and compared with experimental data obtained from DAET measurements in trabecular bone samples.

Anisotropy of dynamic acoustoelasticity in limestone, influence of conditioning, and comparison with nonlinear resonance spectroscopy

Anisotropy of wave velocity and attenuation induced by a dynamic uniaxial strain is investigated by dynamic acoustoelastic testing in limestone. Nonlinear resonance spectroscopy is performed simultaneously for comparison. A compressional resonance of the sample at 6.8 kHz is excited to produce a dynamic strain with an amplitude varied from 10(-7) to 10(-5). A sequence of ultrasound pulses tracks variations in ultrasonic velocity and attenuation. Variations measured when the ultrasound pulses propagate in the direction of the uniaxial strain are 10 times larger than when the ultrasound propagation occurs perpendicularly. Variations consist of a "fast" variation at 6.8 kHz and an offset. Acoustically induced conditioning is found to reduce wave velocity and enhance attenuation (offset). It also modifies "fast" nonlinear elastodynamics, i.e., wave amplitude dependencies of ultrasonic velocity and attenuation. At the onset of conditioning and beyond, different excitation amplitudes bring the material to non-equilibrium states. After conversion of velocity-strain dynamic relations into elastic modulus-strain dynamic relations and integration with respect to strain, the dynamic stress-strain relation is obtained. Analysis of stress-strain hysteresis shows that hysteretic nonlinear elasticity is not a significant source of the amplitude-dependent dissipation measured by nonlinear resonance spectroscopy. Mechanisms causing conditioning are likely producing amplitude-dependent dissipation as well.

Measurement of nonlinear viscoelastic properties of fluids using Dynamic Acoustoelastic Testing

A nonlinear ultrasound-based method called Dynamic Acoustoelastic Testing (DAET) is used to assess nonlinear viscoelastic properties of fluids. This method is based on the interaction between two elastic waves: a low-frequency (LF) sinusoidal wave (4 kHz) to successively compress and expand the liquid as a bulk stress, and ultrasound (US) pulses (1 MHz) to simultaneously probe the sample at different states of the quasi-hydrostatic pressure. The DAET method provides estimations of the elastic nonlinearities issued from the Time Of Flight Modulations (TOFM) of the US pulses. The TOFM is plotted as a function of the LF acoustic pressure, allowing an estimation of the nonlinear elastic parameter B/A. In this study, we first present the results obtained in Newtonian fluids such as water and silicone oils. Simple viscoelastic gels (Carbomers and Xanthan gums) have also been tested exhibiting the same behavior: TOFM linearly related to LF pressure amplitude corresponding to classical quadratic nonlinearity. Finally, preliminary DAET measurements have been performed in biphasic systems composed of hard glass beads in a gel-based matrix and in gelatin during a gelation process.

Revealing highly complex elastic nonlinear (anelastic) behavior of Earth materials applying a new probe: Dynamic acoustoelastic testing

Recent work in medical nonlinear acoustics has led to the development of refined experimental method to measure material elastic nonlinear (anelastic) response. The technique, termed dynamic acoustoelastic testing, has significant implications for the development of a physics‐based theory because it provides information that existing methods cannot. It provides the means to dynamically study the velocity‐strain and attenuation‐strain relations through the full wave cycle in contrast to most methods that measure average response. The method relies on vibrating a sample at low frequency in order to cycle it through different levels of stress‐strain. Simultaneously, an ultrasonic source applies pulses and the change in wave speed and attenuation as a function of the low frequency strain is measured. We report preliminary results in eleven room‐dry rock samples. In crystalline rock, we expect that the elastic nonlinearity arises from the microcracks and dislocations contained within individual crystals. In contrast, sedimentary rocks may have other origins of elastic nonlinearity, currently under debate. A large quadratic elastic nonlinearity is observed in Berkeley blue granite, presumably due to microcracks and dislocation‐point defect interactions. In sedimentary rocks that include limestones and sandstones we observe behaviors that can differ markedly from the granite, potentially indicating different mechanical mechanisms. We further observe changes in measured nonlinear coefficients that are wave‐strain amplitude dependent. Ultimately we hope that the new approach will provide the means to quantitatively relate material nonlinear elastic behavior to the responsible features, that include soft bonds dislocations, microcracks, and the modulating influences of water content, temperature and pressure.

Ultrasound propagation in trabecular bone: a numerical study of the influence of micro-cracks

The accumulation of microdamage in trabecular bone tissue is suspected of being a predictive indicator of osteoporosis diagnosis. To quantify this microdamage, the Dynamic AcoustoElastic Testing (DAET) method measures the time of flight (TOF) and amplitude variations of transmitted ultrasound (US) pulses, while the bone sample is submitted to a low frequency pressure (opening/closing of microcracks). However, DAET is both sensitive to viscoelastic properties changes and microcracks density. To estimate the microcraks density contribution, a numerical approach is proposed, allowing simulations of different levels of microdamaged media. A 2D pseudo-spectral time domain numerical model was then developed to simulate linear wave propagation in heterogeneous solids including thermo-viscous attenuation. The influence of the microcracks number, size and orientation on the US TOF and amplitude was particularly investigated. Results are discussed and compared with experimental data extracted from DAET measurements in trabecular bone samples.

Analytical model of Dynamic AcoustoElastic Testing measurements in trabecular bone tissue: a rheological approach

A dynamic acoustoelastic testing (DAET) method based on the interaction of two acoustical waves was developed to measure viscoelastic properties of trabecular bone tissue. While a sinusoidal low-frequency (LF) acoustic wave successively compresses and expands the medium, ultrasonic (US) pulses are generated to probe the uniformly stressed medium (quasi-static pressure, pLF). The US pulses velocity and amplitude (c, A) vary with respect to the medium stress level. These modulations (c(pLF)-c(0); A(pLF)-A(0)) are plotted as a function of the instantaneous LF pressure. From these rheograms, nonlinear elastic and viscous (dissipative) parameters, β' and β” respectively, are extracted. Since the US velocity is directly related to the medium viscoelastic modulus (M*), considering either the celerity variations or the modulus variations as a function of LF pressure is equivalent. In this perspective, we developed an analytical model of the variations of M*, derived from the Kelvin-Voigt approach (M* as a functio...

Nonlinear elastodynamics in micro-inhomogeneous solids observed by head-wave based dynamic acoustoelastic testing

Dynamic acoustoelastic testing provides a more complete insight into the acoustic nonlinearity exhibited by micro-inhomogeneous media like granular and cracked materials. This method consists of measuring time of flight and energy modulations of pulsed ultrasonic waves induced by a low-frequency standing wave. Here pulsed ultrasonic head waves were employed to assess elastic and dissipative nonlinearities in a region near the surface of a solid. Synchronization of the ultrasound pulse sequence with the low-frequency excitation provided instantaneous variations in the elastic modulus and the attenuation as functions of the instantaneous low-frequency strain. Weak quadratic elastic nonlinearity and no dissipative nonlinearity were detected in duralumin. In limestone, distinction between tensile and compressive behaviors revealed an asymmetry in the acoustic nonlinearity and hysteresis in both the elastic modulus and the attenuation variations. Measured nonlinear acoustical parameters are in good agreement with values obtained by different techniques. Reversible acoustically induced conditioning modified the acoustic nonlinearity both quantitatively and qualitatively. It reduced tension-compression asymmetry, suggesting a nonequilibrium modification of the sources of acoustic nonlinearity. Additionally to the metrology of the acoustic nonlinearity, head wave based dynamic acoustoelastic testing may be a useful tool to monitor changes in the microstructure or the accumulation of damage in solids.

Détection du micro-endommagement dans le tissu osseux trabéculaire par une méthode d’acousto-élasticité dynamique

Osteoporosis affects the whole skeleton strength leading to an actual fracture risk. Associated to a high level of morbidity, it is a critical public health issue. During the last decades, several X-rays and ultrasound devices have been developed to help the clinicians in their diagnosis. They are essentially related to bone mass while several factors are responsible for this pathology. Among them, microdamage has an interesting place. Nonlinear acoustic methods have already shown their ability to detect microcracks in different geophysical and industrial materials. We present a dynamic acousto-elastic testing (interaction of a very low frequency tone burst and high frequency pulses) to measure viscoelastic and dissipative nonlinearities. Applied to trabecular bone samples (human defatted calcanei), this method has shown a high level of nonlinearity in very dense regions of the calcanei. However, native microdamage is often at the limit of the method sensibility. To better evaluate this parameter, we have performed acousto-elastic measurements before and after inducing microdamage thanks to a compression fatigue test. We observed higher nonlinearity after induced damage. Moreover, the level of acoustic nonlinearity has been correlated to actual damage accumulation thanks to confocal microscopy analysis. However, acousto-elasticity measurements repeatability is weak. Correct reproducibility is observed for low level of nonlinearity (low level of microcracks). For high level of nonlinearity, quite different nonlinear behaviors are usually observed from one measurement to the next one.

Dynamic acoustoelastic testing of weakly pre-loaded unconsolidated water-saturated glass beads

Dynamic acoustoelastic testing is applied to weakly pre-loaded unconsolidated water-saturated glass beads. The gravitational acceleration produces, on the probed beads, a static stress of order 130 Pa, thus the granular medium is close to the jamming transition. A low-frequency (LF) acoustic wave gently disturbs the medium, inducing successively slight expansion and compaction of the granular packing expected to modulate the number of contacts between beads. Ultrasound (US) pulses are emitted simultaneously to dynamically detect the induced modification of the granular skeleton. US propagation velocity and attenuation both increase when the LF pressure increases. The quadratic nonlinear elastic parameter β, related to the pressure dependence of US propagation velocity, was measured in the range 60-530 if water-saturated glass beads are considered as an effective medium. A dynamic modification of US scattering induced by beads is proposed to modulate US attenuation. Complex hysteretic behaviors and tension-compression asymmetry are also observed and analyzed by time-domain and spectral analyses. Furthermore acoustic nonlinearities are measured in cases of quasi-static and dynamic variations of the LF wave amplitude, providing quantitatively similar acoustic nonlinearities but qualitatively different.

Dynamic acoustoelastic testing for noninvasive detection of microdamage in cortical tissue of long bones.

First developed for trabecular bone, dynamic acoustoelastic testing (DAT) is based on the measurement of ultrasound (US) pulses time of flight and energy modulations (TOFM and EMs) induced by a low-frequency (LF) acoustic wave, synchronously injected in the probed medium. The technique needs the LF wave to be quasi-uniform in the investigated region and quasi-static in time (compared with the US TOF). US TOFM and EM are related to elastic and dissipative nonlinearities, respectively. Here is presented the application of the technique to cortical tissue of long bones. A LF vibration is generated along the axis of the sample whose frequency corresponds to the first compressional resonance mode. Simultaneously, US pulses are emitted and received by a dedicated probe, after propagation along the axis of the sample. The emitter-receiver distance is chosen and the position of the US probe is adjusted so that the head wave arrives first in time. US TOFM and EM are thus computed using the head wave. After validation in an aluminum cylinder where no dissipative nonlinearity but weak quadratic elastic nonlinearity is observed, in vitro results are presented for bone. DAT is performed on diaphyseal bone sections before and after mechanical damage was induced.

Monitoring trabecular bone microdamage using a dynamic acousto-elastic testing method

Dynamic acousto-elastic testing (DAET) is based on the coupling of a low-frequency (LF) acoustic wave and high-frequency ultrasound (US) pulses (probing wave). It was developed to measure US viscoelastic and dissipative non-linearity in trabecular bone. It is well known that this complex biphasic medium contains microdamage, even when tissues are healthy. The purpose of the present study was to assess the sensitivity of DAET to monitor microdamage in human calcanei. Three protocols were therefore performed to investigate the regional heterogeneity of the calcaneus, the correlation between DAET measurements and microdamage revealed by histology, and DAET sensitivity to mechanically induced fatigue microdamage. The non-linear elastic parameter beta was computed for all these protocols. The study demonstrated the presence of high viscoelastic and dissipative non-linearity only in the region of the calcaneus close to the anterior talocalcaneal articulation (region of high bone density). Protocols 1 and 2 also showed that most unsorted calcanei did not naturally exhibit high non-linearity, which is correlated with a low level of microcracks. Nevertheless, when microdamage was actually present, high levels of US non-linearity were always found, with characteristic non-linear signatures such as hysteresis and tension/compression asymmetry. Finally, protocol 3 demonstrated the high sensitivity of DAET measurement to fatigue-induced microdamage.

Remote dynamic acoustoelastic testing: Elastic and dissipative acoustic nonlinearities measured under hydrostatic tension and compression

Remote dynamic acoustoelastic testing is proposed to provide a noninvasive and regional measurement of elastic and dissipative acoustic nonlinearities in fluids and solids. The probed medium is dynamically stressed by a low-frequency sinusoidal variation in the hydrostatic pressure in the surrounding fluid. Simultaneously, ultrasound pulses propagate undergoing time of flight and energy modulations, associated with elastic and dissipative nonlinearities, respectively. Acoustic nonlinearities in tension phases can be distinguished from those measured in compression phases. Instantaneous modulations of ultrasound time of flight and energy are analyzed as functions of the instantaneous low-frequency acoustic pressure, similar to a quasistatic acoustoelastic testing.