Resonant Ultrasound Spectroscopy Technique Research Articles

Elastic constants of equiatomic Fe–Ni Invar alloy single crystal

In a disordered fcc structure, the equiatomic Fe–Ni alloy is of great interest as a soft magnetic Invar alloy with a near zero or low thermal expansion coefficient. In the L10 ordered phase, it is of interest as a potential high-performance permanent magnet alloy. In this work, the first detailed measurements of the elastic constants in a [001]-oriented Fe-50 at. % Ni alloy single crystal under a no magnetic field condition were made using the resonant ultrasound spectroscopy technique. The elastic constants measured allow one to understand the nature of atomic bonding in a material and the mechanical response to applied stress. The single crystal sample having a rectangular parallelepiped shape was prepared from a single crystal grown using the vertical Bridgman technique. The elastic constants C11, C12, and C44 were obtained from the resonant frequencies observed over a frequency range of 100–900 kHz. Using these C11, C12, and C44 values, Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio were calculated to be 99.1 GPa, 73.4 GPa, 176.7 GPa, and 0.20, respectively. The large anisotropy factor of 3.29 highlights the strong directional dependence of the material’s mechanical behavior.

Resonant ultrasound spectroscopy measurement and modeling of additively manufactured octet truss lattice cubes

In this work, the elastic characteristics of additively manufactured Ti-5553 octet truss lattice cubes were examined using resonant ultrasound spectroscopy (RUS) techniques and correlated to X-ray computed tomography measurements of strut continuity. RUS models and measurements identified an outlier lattice possessing lower effective modulus despite larger effective density. Experimental measurements of density and effective Young's modulus were treated as input parameters in a homogenous anisotropic continuum model. The continuum model exhibited good agreement with experimental RUS measurements, thus confirming the potential for a simplified approximation of the octet truss lattice.

Determining the full elastic tensor using resonant ultrasound spectroscopy in extreme environments

Elastic moduli are fundamental thermodynamic susceptibilities that connect directly to thermodynamics, electronic structure and mechanic properties. Thus, determining the changes of elastic moduli as a function of time and temperature is a powerful tool to study a variety of phenomena. The Resonant Ultrasound Spectroscopy (RUS) technique is based on the measurement of mechanical resonance frequencies that can be made with extreme precision and used to compute the elastic moduli without corrections. In this talk, I will give show several examples of the use of RUS in different systems, ranging from magnetic phase transition, determining very small degrees of elastic anisotropy in metals as well as changes in time product of radioactive decay. I will discuss the latest advances made at Los Alamos on measuring and determination of elastic constants. This allow to track the resonance position with high precision, obtaining moduli with an absolute precision of 0.5% and relative changes smaller than part per 10 million.

Estimation of elastic properties of an additively manufactured lattice using resonant ultrasound spectroscopy.

Development of improved approaches in the characterization of additively manufactured structures continues to be a topic of interest for the advanced manufacturing community. This article will investigate an approach using resonant ultrasound spectroscopy (RUS) to determine the effective elastic constants of an orthotropic lattice structure. The evaluation is performed on a cube shaped 316 L stainless steel test specimen, constructed using selective laser melting techniques. The approach uses RUS techniques in conjunction with the assumption that in the frequency regime of interest, the wavelength of the diagnostic ultrasound is greater than the discrete structural features of the unit cell of the lattice; thus, the AM structure can be treated as an anisotropic continuum with effective material properties and symmetry inherited from the unit cell. The RUS analysis estimates the nine elastic coefficients associated with orthotropic sample symmetry, which, in turn, are used to determine the elastic moduli and Poisson ratios. Current results show good agreement between experiments and modeled data. Comparisons to published results are also in good agreement, indicating the potential applicability of this characterization technique for estimating the linear elastic properties of innovative additive manufactured metal lattice structures.

Elastic properties of additively manufactured alloys

With the advent of metal Additive Manufacturing (AM), or 3D printing, the focus on evaluating and fine-tuning the fabrication process has become crucial. High-resolution volumetric mapping of elastic properties throughout an AM built sample can be done, “biopsy” style, with the highly adaptable Resonant Ultrasound Spectroscopy (RUS) technique. We report results of elastic constants measurements on AM-fabricated Ti64 and CL 80CU bronze (i.e., Cu0.9Sn0.1) alloy with RUS. Despite an easily observable pore distribution, surprisingly sharp spectra and good RUS fits were obtained for both. The average E and G moduli obtained for AM Ti64 at room temperature are ≈104 and ≈39.4 GPa, respectively. The values are only a few percent lower than those of the traditionally manufactured alloy. Moreover, stress-strain measurements on dog-bone samples of Ti64 from the sample batch lead to a value of 101 GPa for E. Heat-treatment of as-manufactured Ti64 samples lead to a slight increase in both moduli. For the investigated bronze, an ≈10% variation of elastic properties within a cross section of a printed sample was observed. The average E and G moduli obtained for AMCL 80CU bronze at room temperature are ≈111 and ≈40.9 GPa, respectively.

Room and high temperature mechanical properties of Mg2Si, Mg2Sn and their solid solutions

Knowledge of the mechanical properties of thermoelectric materials at high temperature is required for the modelling and optimization of a thermoelectric generator under application conditions. We present room and high temperature characterization of Young’s modulus for Mg2Si, Mg2Sn and their solid solutions establishing a linear dependence, both on composition and on temperature.Through the comparison of Resonant Ultrasound Spectroscopy and free vibration techniques, we measure the elastic moduli with high precision. The comparison of our results (E = 110 GPa for Mg2Si and 78 GPa for Mg2Sn) to first principles calculations and experimentally reported data shows good agreement. Additionally, by estimating the Poisson ratio, we calculate the temperature-dependent shear modulus G and finally provide a simple bilinear function for Young’s and shear moduli as a function of temperature and composition.

Elastic moduli reduction in SiC-SiC tubular specimen after high heat flux neutron irradiation measured by resonant ultrasound spectroscopy

The initial results of a post-irradiation examination study conducted on a SiC-SiC tubular specimen irradiated under a high radial heat flux are presented herein. The elastic properties of the specimen were evaluated before and after the irradiation using the resonant ultrasound spectroscopy (RUS) technique. The composite tubular specimen was considered as an orthotropic elastic with nine elastic constants (Young's moduli, shear moduli and Poisson's ratios—three components of each) for representing its full elastic deformation behavior. All the elastic moduli decreased after irradiation; the reduction was as high as 35% in one of the moduli. The significant decrease in the moduli indicates the presence of microcracks. The results from a computational study show significant stress development in the specimen due to irradiation, primarily caused by differential swelling across the thickness of the specimen. The evaluated stresses exceed the proportional limit stress of the material, indicating the likelihood of matrix microcracking, and thus corroborating the results obtained from RUS. X-ray Computed Tomography (XCT) study confirmed the presence of cracks in the irradiated specimen. These cracks occurred at the inner region of the specimen and propagated in axial and hoop directions. These XCT results are in agreement with the RUS results and stress distribution results from the computational study.

High-temperature dependency of elastic mechanical behavior of two wrought magnesium alloys AZ31B and ZK60A studied by resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) was used to study the elastic mechanical properties and internal friction of two wrought magnesium alloys, AZ31B and ZK60A, from 25 °C to 450 °C. Samples in the rolled, transverse, and normal directions were characterized at 50 °C intervals to determine the temperature dependency of elastic moduli and stiffnesses for each direction. The temperature dependencies represented as, dE/dT, dG/dT, dB/dT, dC11/dT, dC12/dT, and dC44/dT are provided herein. To evaluate the RUS technique for these type of alloys, Young's modulus was also determined by conventional static tension testing and the results were compared. From the same RUS experiment, the internal friction variation with temperature was calculated for both alloys. The linear coefficients of thermal expansion for each direction over the temperature range considered were determined, as they were needed to estimate sample dimension at elevated temperature for the RUS measurements.This study shows that RUS can be a convenient and accurate technique to supply quantitative elastic mechanical data and fill the existing gaps on light metals characterization.

Elastic constants identification of irregular hard biological tissue materials using FEM-based resonant ultrasound spectroscopy

This paper aims to apply the resonant ultrasound spectroscopy technique (RUS) combined with micro computed tomography (μ-CT) and finite element method (FEM) to quantify the elastic constants of the irregular hard biological tissue material such as enamel. In this method, the resonant frequencies of an irregular shaped sample tested under stress-free boundary conditions are measured first. Then, micro-computed tomography (μ-CT) is used to acquire three-dimensional (3-D) geometry information of the sample, and the resonant frequencies are calculated with FEM. Thereby, an optimization procedure using the Levenberg-Marquardt algorithm updates the elastic constants in the FEM model until the output natural frequencies from the model fit the results from the RUS experiments. The proposed method has been tested first on a calibration material. To this purpose, titanium has been selected. The elastic constants of a rectangular parallelepiped shaped titanium sample obtained by the conventional RUS method and those of five irregular samples obtained by FEM-based RUS were in good agreement, displaying differences less than 2%. Once the method has been validated on titanium, it was applied to an enamel sample. The results show that the FEM-based RUS method can effectively identify the elastic constants of irregular titanium and enamel samples. This study expands the application range of RUS technology and provides a new method for the measurement of elastic properties of irregular hard biological tissue materials.

Accurate characterization of complete set constants of single domain 0.72Pb(Mg1/3Nb2/3)O3–0.28PbTiO3 single crystal by resonant ultrasound spectroscopy using only one sample

In order to find out the origin of the giant piezoelectric effects of relaxor-PbTiO3 single crystals when poled along nonpolar directions, it is necessary to obtain the complete physical property data of a single domain state. Conventional characterization methods using multiple samples of different geometries often produce inconsistent data set because the domain patterns produced during poling are strongly dependent on the sample geometry. Here, we used the resonant ultrasound spectroscopy (RUS) technique to determine the material constants of a single domain 0.72Pb(Mg1/3Nb2/3)O3–0.28PbTiO3 single crystal, which has a high mechanical quality factor (QM). Errors caused by sample-to-sample variation are avoided because all constants were measured from the same sample. The data set obtained is highly self-consistent, which provides a base for theoretical analysis as well as the input for simulation designs of piezoelectric devices. Comparison with data measured by other methods shows the advantage and higher accuracy of this characterization strategy.

Nonlinear acoustics evaluation of CO2 exposed sandstone

In an effort to better understand the hygro-thermo-mechanical behavior of geologic CO2 reservoir material, we investigate the non-linear behavior of elastic wave propagation in Berea sandstone samples, which are used as a standard for reservoir rock formations. Nonlinear characterization methods, including resonant ultrasound spectroscopy (RUS), dynamic acousto-elasticity (DAET), and single-impact nonlinear resonance techniques, are applied to pristine, damaged (distributed microfractures), and CO2 injected Berea samples; conventional linear vibrational and wave propagation measurements are also applied to the samples. The results of these sensitive test methods are compared to reveal the characteristics of geologic reservoir materials that are most affected by varying microstructural and environmental conditions. An analysis of the work also leads to potential bases for test methods that could be deployed in the field in the future to monitor the condition of reservoir formations and lead to better under...

Resonant ultrasound spectroscopy measurement of elastic properties of SnSe

Resonant Ultrasound Spectroscopy (RUS) is a precise experimental approach for investigating the elastic properties of solid materials at different temperatures and hydrostatic pressures. In RUS, the elastic stiffness tensor of crystalline solids with different crystal structures are determined from their vibrational resonance spectra. A study of the mechanical properties of thermoelectric materials can provide insights to their high efficiency and low thermal conductivity. SnSe is a thermoelectric material which exhibits a high efficiency and low thermal conductivity due to its anharmonicity and low symmetric crystal structure. SnSe exhibits a structural phase transition from Pnma to Cnma at ∼800 K, and the single layered orthorhombic crystal structure of SnSe results in nine independent elastic constants. In this study, RUS was used to determine the temperature dependent elastic properties of polycrystalline SnSe through its phase transition temperature. Use of RUS technique to better understand the temperature dependent elastic properties of low symmetry crystals will be discussed. The elastic constants of single crystal SnSe calculated by RUS at room temperature are in agreement of within ∼35% of theoretical reported values.

Investigation of natural frequencies of laser inertial confinement fusion capsules using resonant ultrasound spectroscopy

The natural frequency problem of laser inertial confinement fusion (ICF) capsules is one of the basic problems for determining non-destructively the elasticity modulus of each layer material using resonant ultrasound spectroscopy (RUS). In this paper, the frequency equation of isotropic one-layer hollow spheres was derived using three dimension (3D) elasticity theory and some simplified frequency equations were discussed under axisymmetric and spherical symmetry conditions. The corresponding equation of isotropic multi-layer hollow spheres was given employing transfer matrix method. To confirm the validity of the frequency equation and explore the feasibility of RUS for characterizing the ICF capsules, three representative capsules with a millimeter-sized diameter were determined by piezoelectric-based resonant ultrasound spectroscopy (PZT-RUS) and laser-based resonant ultrasound spectroscopy (LRUS) techniques. On the basis of both theoretical and experimental results, it is proved that the calculated and measured natural frequencies are accurate enough for determining the ICF capsules.

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy

During the operation of high power electromechanical devices, a temperature rise is unavoidable due to mechanical and electrical losses, causing the degradation of device performance. In order to evaluate such degradations using computer simulations, full matrix material properties at elevated temperatures are needed as inputs. It is extremely difficult to measure such data for ferroelectric materials due to their strong anisotropic nature and property variation among samples of different geometries. Because the degree of depolarization is boundary condition dependent, data obtained by the IEEE (Institute of Electrical and Electronics Engineers) impedance resonance technique, which requires several samples with drastically different geometries, usually lack self-consistency. The resonant ultrasound spectroscopy (RUS) technique allows the full set material constants to be measured using only one sample, which can eliminate errors caused by sample to sample variation. A detailed RUS procedure is demonstrated here using a lead zirconate titanate (PZT-4) piezoceramic sample. In the example, the complete set of material constants was measured from room temperature to 120 °C. Measured free dielectric constants and were compared with calculated ones based on the measured full set data, and piezoelectric constants d15 and d33 were also calculated using different formulas. Excellent agreement was found in the entire range of temperatures, which confirmed the self-consistency of the data set obtained by the RUS.

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy.

During the operation of high power electromechanical devices, a temperature rise is unavoidable due to mechanical and electrical losses, causing the degradation of device performance. In order to evaluate such degradations using computer simulations, full matrix material properties at elevated temperatures are needed as inputs. It is extremely difficult to measure such data for ferroelectric materials due to their strong anisotropic nature and property variation among samples of different geometries. Because the degree of depolarization is boundary condition dependent, data obtained by the IEEE (Institute of Electrical and Electronics Engineers) impedance resonance technique, which requires several samples with drastically different geometries, usually lack self-consistency. The resonant ultrasound spectroscopy (RUS) technique allows the full set material constants to be measured using only one sample, which can eliminate errors caused by sample to sample variation. A detailed RUS procedure is demonstrated here using a lead zirconate titanate (PZT-4) piezoceramic sample. In the example, the complete set of material constants was measured from room temperature to 120 °C. Measured free dielectric constants and were compared with calculated ones based on the measured full set data, and piezoelectric constants d15 and d33 were also calculated using different formulas. Excellent agreement was found in the entire range of temperatures, which confirmed the self-consistency of the data set obtained by the RUS.

High temperature resonant ultrasound spectroscopy study on Lead Magnesium Niobate—Lead Titanate (PMN-PT) relaxor ferro-electric material

Lead magnesium niobate-lead titanate [(1-x)PbMg1/3Nb2/3O3-xPbTiO3] is a perovskite relaxor ferroelectric material exhibiting superior electromechanical coupling compared to the conventional piezoelectric materials. In this work, non-poled single crystal PMN-PT material with the composition near morphotropic phase boundary (MPB) was investigated in the temperature range of 400 K—800 K where the material is reported to be in the cubic phase. High temperature resonant ultrasound spectroscopy (HT-RUS) technique was used to probe temperature dependency of elastic constants derived from the measured resonant modes. Non-monotonic resonant frequency trends in the temperature regime indicate stiffening of the material, followed by gradual softening typically observed in heated materials. Elastic constants confirmed this stiffening in the temperature range of 400 K—673 K, where the stiffness constants C11 and C44 increased approximately by 40% and 33% respectively. Acoustic attenuation, derived from the quality factor (Q), exhibits a minimum around the temperature where the stiffness is maximum and, significantly higher attenuation observed at temperatures below 400 K. The temperature range 395 K—405 K was identified as a transition temperature range, where the material showed an abrupt change in the resonant spectrum and, the material emerges from the MPB characterized by this very high acoustic attenuation. This transition temperature compares favorably with dielectric constant measurements reported in the literature.

In-situ Young's moduli of the constitutive layers in a solid oxide fuel cell

In-situ Young's moduli of thin constituent layers of a solid oxide fuel cell (SOFC) are needed to estimate the mechanical reliability of the fuel cell unit. Because a robust technique to measure the same is not available, an improved methodology is proposed to determine the in-situ Young's moduli of thin ceramic layers of a substrate-supported SOFC. The measured Young's moduli of the constituent layers were found to be close to those of corresponding bulk materials using the resonant ultrasound spectroscopy (RUS) technique but were different from the values obtained using nanoindentation.

Instrumentação para espectroscopia de ressonância de ultrassom

A técnica de espectroscopia de ressonância de ultrassom possibilita a determinação simultânea de todos os componentes do tensor de elasticidade do material que constitui a amostra. Neste trabalho é descrita a montagem de um dispositivo de espectroscopia de ressonância de ultrassom automatizado, que possibilita a análise de pequenas amostras na forma de paralelepípedos, cilindros ou esferas. A aplicação deste dispositivo é exemplificada com a determinação das constantes elásticas de amostras policristalinas de alumina e níquel. Os resultados obtidos diferem dos valores esperados em, no máximo, 2,6% e 0,91% para a alumina e níquel, respectivamente, e ilustram a aplicação deste dispositivo na determinação das constantes elásticas de pequenas amostras.

Non Destructive Characterization of Cortical Bone Micro-Damage by Nonlinear Resonant Ultrasound Spectroscopy

The objective of the study was to evaluate the ability of a nonlinear ultrasound technique, the so-called nonlinear resonant ultrasound spectroscopy (NRUS) technique, for detecting early microdamage accumulation in cortical bone induced by four-point bending fatigue. Small parallelepiped beam-shaped human cortical bone specimens were subjected to cyclic four-point bending fatigue in several steps. The specimens were prepared to control damage localization during four-point bending fatigue cycling and to unambiguously identify resonant modes for NRUS measurements. NRUS measurements were achieved to follow the evolution of the nonlinear hysteretic elastic behavior during fatigue-induced damage. After each fatigue step, a small number of specimens was removed from the protocol and set apart to quantitatively assess the microcrack number density and length using synchrotron radiation micro-computed tomography (SR-µCT). The results showed a significant effect of damage steps on the nonlinear hysteretic elastic behavior. No significant change in the overall length of microcracks was observed in damaged regions compared to the load-free control regions. Only an increased number of shortest microcracks, those in the lowest quartile, was noticed. This was suggestive of newly formed microcracks during the early phases of damage accumulation. The variation of nonlinear hysteretic elastic behavior was significantly correlated to the variation of the density of short microcracks. Our results suggest that the nonlinear hysteretic elastic behavior is sensitive to early bone microdamage. Therefore NRUS technique can be used to monitor fatigue microdamage progression in in vitro experiments.

비선형 초음파공명 특성을 이용한 미세균열 탐지

기존 비파괴평가 기술의 결함 탐지 한계를 극복하기 위하여 비선형 초음파공명 특성을 이용한 미세 균열 진단 기술을 개발하였다. 가진 전압에 따른 초음파공명 주파수의 천이현상과 정규화 공명 진폭 감소 현상을 비선형 초음파공명 특성 파라미터로 제안하였으며 이를 실험적으로 확인하였다. CT 시편에 피로시험을 통하여 미세한 자연 균열을 생성하였으며 피로 사이클 단계마다 초음파공명주파수와 정규화 공명진폭의 변화를 측정하였다. 무결함 또는 10 <TEX>${\mu}m$</TEX> 정도의 매우 미세한 균열이 존재하는 시편에서는 초음파공명 주파수 천이현상이나 정규화 공명 진폭의 변화가 나타나지 않는 반면에 30 <TEX>${\mu}m$</TEX>급 이상의 미세 균열 시편에서는 균열 크기가 증가함에 따라 초음파공명주파수의 천이 현상이나 정규화 공명 진폭의 감소량이 증가함을 확인하였다. In order to overcome the detection limit by the current nondestructive evaluation technology, a nonlinear resonant ultrasound spectroscopy(NRUS) technique was applied for detection of micro-scale cracks in a material. A down-shift of the resonance frequency and a variation of normalized amplitude of the resonance pattern were suggested as the nonlinear parameter for detection of micro-scale cracks in a materials. A natural-like crack were produced in a standard compact tension(CT) specimen by a low cycle fatigue test and the resonance patterns were acquired in each fatigue step. As the exciting voltage increases, a down-shift of resonance frequency were increases as well as the normalized amplitude decrease. This nonlinear effects were significant and even greater in the cracked specimen, but not observed in a intact specimen.