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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

RUScal : Software for the analysis of resonant ultrasound spectroscopy measurements

Resonant ultrasound spectroscopy is used to nondestructively measure the elastic resonances of small solids to elucidate the material's elastic properties or other qualities like size, shape, or composition. In this work, we introduce the software RUScal for the purpose of determining elastic properties by analyzing the eigenfrequencies of solid specimens with common shapes, such as rectangular parallelepipeds, cylinders (solid and hollow tube), ellipsoids, and octahedrons, as well as irregularly shaped ellipsoids that can be described analytically. All symmetry classes are supported, from isotropic to triclinic, along with the option to add or remove up to three orthogonal mirror planes as well as the ability to reorient the crystal axes with respect the sample edges via Euler angles. Additional features include tools to help find initial sets of elastic constants, including grid exploration and Monte Carlo methods, a tool to analyze frequencies as a function of sample length or crystal orientation, an error analysis tool to assess fit quality, and formatting of the input and output files for batch fitting, e.g., as a function of temperature. This software was validated with published resonant ultrasound spectroscopy data for various materials, shapes, and symmetries with noted improvements in calculation time compared to finite element methods.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Enabling resonant ultrasound spectroscopy in high magnetic fields

Resonant ultrasound spectroscopy (RUS) is a powerful method to determine elastic constants with high accuracy and precision from a single measurement of the mechanical resonances of a sample. Conventionally, the quantitative extraction of elastic moduli with RUS assumes free boundary conditions which can often lead to the adoption of unstable sample positioning between ultrasonic transducers that is incompatible with extreme environments like high magnetic fields. We show that, under specific conditions, introducing a small amount of adhesive between a RUS sample and ultrasonic transducers introduces a perturbation to the free resonance condition which can be accounted for by a simple model. This means elastic constants can be determined to within the uncertainty of conventional RUS, but with significant improvements including sample stability and control of sample orientation. We demonstrate the efficacy of this approach with measurements on a range of materials including room temperature measurements on polycrystalline metals, temperature-dependent measurements of the structural phase transition in strontium titanate single crystals, and magnetic field-dependent measurements of magnetic phase transitions in gadolinium polycrystals up to 14 T.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Resonant ultrasound spectroscopy for crystalline samples containing initial strain

Resonant ultrasound spectroscopy (RUS) is a mature and robust technique for the nondestructive characterization of the elastic properties of solids capable of providing the elastic constants of anisotropic crystalline solids. The traditional method is based on assuming that the solid is linear elastic and, therefore, obeys a linearized Hookean constitutive relationship (Hooke’s law). In this work, an alternative constitutive law is provided that allows for an initial strain or prestrain to be present stemming from residual stress. Then, the constitutive relationship is integrated into the RUS framework. The model is demonstrated using a realistic prestrain field obtained by simulating shot-peening processing of a polycrystalline Cu sample. The sensitivity of the resonances to the developed prestrain is established and discussed. This work allows researchers to consider the influence of initial strain or residual stress in their samples and the potential influence on accurate elastic constant estimates. The model also supports the potential of RUS for the nondestructive characterization of prestrain in materials.

42 ENGINEERING↗
DOE OSTI2021

Resonant ultrasound spectroscopy probe for in-situ neutron scattering measurements

Resonant ultrasound spectroscopy (RUS) is an efficient, nondestructive technique to study the elastic properties of solids. A low-temperature (2-300 K) probe has been assembled and tested at the NOMAD beamline at the Spallation Neutron Source at Oak Ridge National Laboratory to assess the probe's neutronic properties, data acquisition system, and compatibility with existing sample environment. A case study on a bulk metallic glass, La 65 Cu 20 Al 10 Co 5, served to benchmark both hardware and software developments. The elastic constants of the metallic glass were determined as a function of temperature between 4 and 300 K and were used to guide neutron diffraction measurements at NOMAD. Tracking of a specific RUS peak center frequency and width enabled live monitoring of the sample temperature evolution that lagged thermometry by upwards of 40 K near room temperature. Assembly of a high-temperature (300-875 K) probe is underway and both probes are scheduled to be available to users by late-2021. Our aim is to provide users with live monitoring of an intrinsic variable at the neutron scattering beamlines, in addition to existing controls, to monitor the state of their samples and its elastic moduli and make informed decisions in real time.

Torres, James↗
DOE OSTI2024

Resonant Ultrasound Spectroscopy for Irregularly Shaped Samples and Its Application to Uranium Ditelluride

Resonant ultrasound spectroscopy (RUS) is a powerful technique for measuring the full elastic tensor of a given material in a single experiment. Previously, this technique was practically limited to regularly shaped samples such as rectangular parallelepipeds, spheres, and cylinders [W. M. Visscher et al. J. Acoust. Soc. Am. 90, 2154 (1991)]. We demonstrate a new method for determining the elastic moduli of irregularly shaped samples, extending the applicability of RUS to a much larger set of materials. Here, we apply this new approach to the recently discovered unconventional superconductor UTe 2 and provide its elastic tensor at both 300 and 4 kelvin.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Demonstrating resonant ultrasound spectroscopy as a viable technique to characterize thermally conditioned high explosive materials

We present results of resonant ultrasound spectroscopy (RUS) measurements applied to granular high explosive materials at different bulk pressing densities and degree of thermal conditioning. The material chosen in this study is a ubiquitously used explosive material known as pentaerythritol tetranitrate (PETN), which is used commercially in civil and defense applications both as a binderized plastic bonded explosive material and an unbinderized neat material. However, changes in granular PETN bulk elastic properties due to thermal conditioning, which could have implications for better understanding environmental aging-related effects, have not been well studied even though it is believed that elasticity may play an important role in explosive material initiation mechanisms. Furthermore, monitoring elastic property changes in granular explosive pressings has not yet been demonstrated using RUS, which is an appealing non-destructive characterization tool that requires only dry point contact with the explosive material. To this end, we report the first study using RUS to quantify the elastic properties of binderized and neat PETN pressings as well as to quantify changes in elastic properties as a function of both thermal conditioning and bulk pressing density. Elastic stiffness coefficients, sometimes more commonly referred to as elastic constants, calculated from the RUS measurements on the different PETN-based materials show a significant increase for the post-conditioned samples compared to the pre-conditioned samples. This trend of increasing elastic properties with thermal conditioning was consistent for different density pressings, different thermal exposure conditions, and even different neat PETN pressings of differing average crystal sizes and/or specific surface areas.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Determining elastic anisotropy of textured polycrystals using resonant ultrasound spectroscopy

Abstract Polycrystalline materials can have complex anisotropic properties depending on their crystallographic texture and crystal structure. In this study, we use resonant ultrasound spectroscopy (RUS) to nondestructively quantify the elastic anisotropy in extruded aluminum alloy 1100-O, an inherently low-anisotropy material. Further, we show that RUS can be used to indirectly provide a description of the material’s texture, which in the present case is found to be transversely isotropic. By determining the entire elastic tensor, we can identify the level and orientation of the anisotropy originated during extrusion. The relative anisotropy of the compressive (c 11 /c 33 ) and shear (c 44 /c 66 ) elastic constants is 1.5% ± 0.5% and 5.7% ± 0.5%, respectively, where the elastic constants (five independent elastic constants for transversely isotropic) are those associated with the extrusion axis that defines the symmetry of the texture. These results indicate that the texture is expected to have transversely isotropic symmetry. This finding is confirmed by two additional approaches. First, we confirm elastic constants and the degree of elastic anisotropy by direct sound velocity measurements using ultrasonic pulse echo. Second, neutron diffraction (ND) data confirm the symmetry of the bulk texture consistent with extrusion-induced anisotropy, and polycrystal elasticity simulations using the elastic self-consistent model with input from ND textures and aluminum single-crystal elastic constants render similar levels of polycrystal elastic anisotropy to those measured by RUS. We demonstrate the ability of RUS to detect texture-induced anisotropy in inherently low-anisotropy materials. Therefore, as many other common materials have intrinsically higher elastic anisotropy, this technique should be applicable for similar levels of texture, providing an efficient general diagnostic and characterization tool.

36 MATERIALS SCIENCE↗
DOE OSTI2023

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. Here, 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.

42 ENGINEERING↗
DOE OSTI2020

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.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Demonstration of acoustic monitoring for structural health of microreactors: Through use of neural networks and resonant ultrasound spectroscopy

Nuclear microreactors prioritize modularity and portability and are intended to be a cost-effective technology for non-conventional nuclear markets. As such, the development of microreactors into a safe and feasible solution for energy security applications will necessitate the development of non-destructive technologies to monitor the integrity of inaccessible reactors components during operation. This demonstration applies linear and nonlinear acoustic techniques, in combination with machine learning, to detect and classify mechanical changes (stress and damage) in a test article which are broadly representative of potential operating challenges within a functioning microreactor. All necessary data has been collected for this demonstration, with minor experimental issues identified that can be addressed in follow-on work. Motivated by the expected conditions within a functioning microreactor, we have demonstrated our monitoring techniques on a core-block-like test article using an unstructured excitation source that approximates the noisy acoustic environment expected during reactor operation. At all stress states mechanically applied to the test article, a machine learning model using an artificial neural network was able to classify with 100% accuracy whether a 3D laser vibrometry point measurement was made on an intact or artificially defective test article. Further, model predictions about whether the defect interface was rough or smooth were 95% accurate, indicating the ability of acoustic techniques to recover defect characteristics. Resonant ultrasound spectroscopy (RUS) was also applied to the dataset to provide further quantitative insights about material properties. RUS analysis was ultimately hampered by several minor experimental and data issues, limiting results to certain cases for this demonstration. Last, analysis using nonlinear RUS exhibited sensitivity to changing levels of applied stresses for each intact and defective state. As presented in this demonstration, acoustic monitoring exhibits sensitivity to stress changes, which are of concern due to high thermal gradients expected during startup and operation. Further, our techniques distinguish between measurements made on intact and damaged test articles.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

One-component order parameter in URu 2 Si 2 uncovered by resonant ultrasound spectroscopy and machine learning

The unusual correlated state that emerges in URu 2 Si 2 below T HO = 17.5 K is known as “hidden order” because even basic characteristics of the order parameter, such as its dimensionality (whether it has one component or two), are “hidden.” We use resonant ultrasound spectroscopy to measure the symmetry-resolved elastic anomalies across T HO . We observe no anomalies in the shear elastic moduli, providing strong thermodynamic evidence for a one-component order parameter. We develop a machine learning framework that reaches this conclusion directly from the raw data, even in a crystal that is too small for traditional resonant ultrasound. Our result rules out a broad class of theories of hidden order based on two-component order parameters, and constrains the nature of the fluctuations from which unconventional superconductivity emerges at lower temperature. Our machine learning framework is a powerful new tool for classifying the ubiquitous competing orders in correlated electron systems.

42 ENGINEERING↗
DOE OSTI2022

Enhanced resonant ultrasound spectroscopy for measurement of the elastic properties of multi-material systems

Understanding the elastic properties of materials is critical for their safe incorporation and predictable performance. Current methods of bulk elastic characterization often have notable limitations for in situ structural applications, with usage restricted to simple geometries and material distributions. To address these existing issues, this study sought to expand the capabilities of resonant ultrasound spectroscopy (RUS), an established nondestructive evaluation method, to include the characterization of isotropic multi-material samples. In this work, finite-element-based RUS analysis consisted of numerical simulations and experimental testing of composite samples comprised of material pairs with varying elasticity and density contrasts. Utilizing genetic algorithm inversion and mode matching, our results demonstrate that elastic properties of multi-material samples can be reliably identified within several percent of known or nominal values using a minimum number of identified resonance modes, given sample mass is held consistent. The accurate recovery of material properties for composite samples of varying material similarity and geometry expands the pool of viable samples for RUS and advances the method towards in situ inspection and evaluation.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Determination of single crystal elastic moduli of KTb3F10 by resonant ultrasound spectroscopy

KTb3F10 (KTF) has been developed in recent years as a candidate Faraday rotator material because of its cubic symmetry, high figures of merit, and low absorption coefficient. While considerable efforts have focused on crystal growth and optical properties, investigations of fundamental thermodynamic behavior of KTF have been limited. Here, we report elastic moduli C11, C12, and C44 of single crystalline KTF measured by resonant ultrasound spectroscopy from 280 K up to 300 K and the obtained temperature derivatives of each modulus. We additionally report the single crystal elastic moduli of the rare-earth garnet Y3Al5O12 (YAG), yielding results that agree well with the prior literature. We found C11=135.62 GPa, C12=58.11 GPa, and C44=44.81 GPa for KTF and C11=332.43 GPa, C12=109.58 GPa, and C44=114.81 GPa for YAG at room temperature. The present results have been compared with previous experimental and theoretical results and with common oxide and fluoride optical materials, revealing the relative softness of KTF. The low elastic moduli of KTF are, in turn, responsible for its low thermal conductivity and low Debye frequency compared to other laser host materials.

Balodhi, Ashiwini (ORCID:0000000290496382)↗
DOE OSTI2022

Determination of single-crystal elastic moduli of Li RE F 4 ( RE =Y, Gd, and Tb) by resonant ultrasound spectroscopy

The tetragonal fluoro-scheelite Li RE F 4 compounds (RE = rare earth) have been shown to exhibit a variety of useful optical and magnetic properties. While LiYF 4 has been widely studied, many of the fundamental thermodynamic properties of other members of this family remain unknown. Here, we report the complete elastic tensors (C ij ) of single-crystalline LiYF 4 , LiTbF 4 , and LiGdF 4 using resonant ultrasound spectroscopy and density functional theory (DFT). Here we compare the results for LiYF 4 with prior experimental results using time-of-flight ultrasound methods. This is the first report, however, of the experimental elastic tensors of LiTbF 4 and LiGdF 4 . The present results point to a softening of the elastic moduli of the Li RE F 4 system when Y is replaced by the larger ionic radius of Tb or Gd. Furthermore, we find that just 0.3% doping with Nd on the Y site also leads to a slight softening of the moduli. The variation of the elastic moduli as a function of temperature up to 216°C was also measured. A nearly linear softening of all seven independent elastic moduli was observed with increasing temperature. Phonon dispersions and phonon density of states obtained by DFT support the experimental finding of a significantly higher sound velocity due to lighter Y atoms in LiYF 4 , as compared to heavier LiTbF 4 and LiGdF 4 .

36 MATERIALS SCIENCE↗
DOE OSTI2025

The role of fast and slow dynamics in nonlinear resonant ultrasound spectroscopy of consolidated granular materials

Abstract Elastic nonlinearity observed in consolidated granular media can be attributed to the combination of slow and fast effects, which give rise to hysteresis and relaxation of both modulus and damping after the sample is perturbed. A consequence is a high level of complexity in the measurements of the sample linear and nonlinear elastic parameters. The results of experiments are dependent on the experimental protocol that is adopted to measure the relevant quantities and it is hard to quantify parameters with accuracy and repeatability. Here we focus on examining Nonlinear Resonant Ultrasound Spectroscopy, showing experimentally the role of slow dynamics in the process and quantifying/discussing its influence on the quantification of nonlinearity. We also propose a model to describe the process, which shows that different contributions to nonlinearity (e.g., classical and hysteretic) could be due to physical features (defects) relaxing with different relaxation times.

Science & Technology - Other Topics↗