Resonant Ultrasound Spectroscopy Research Articles

Using resonant ultrasound spectroscopy to characterize thermally conditioned high explosive materials

The ability to nondestructively quantify changes in mechanical properties of granular high explosive materials due to thermal conditioning is of importance for a myriad of civil and defense applications and could lead to better understanding of environmental aging-related effects for explosive material performance and safety. In this study, we report the first demonstration of using resonant ultrasound spectroscopy (RUS) to quantify the bulk elastic properties of granular high explosive materials at different bulk pressing densities and degree of thermal conditioning. Monitoring elastic property changes in granular explosive pressings has not yet been demonstrated using RUS, which is an appealing nondestructive characterization tool since it requires only dry point contact with the explosive material and can be applied to explosives with small form factors. Here, explosive material was studied in the form of binderized plastic bonded explosive pressings and unbinderized neat pressings, both of which are used commercially. Elastic stiffness coefficients calculated from the RUS measurements on the binderized and neat pressings 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 and different thermal exposure conditions. [This work was performed by LLNL under Contract No. DE-AC52-07NA27344 and document release number LLNL-ABS-858868.]

Resonant ultrasound spectroscopy for textured materials

Resonant ultrasound spectroscopy (RUS) is a method in which the least-squares fitting of a sample's measured resonance frequencies is used to determine the sample material's elastic constants. Difficulties arise when RUS is applied to textured materials, which are composed of crystallites that are neither completely aligned nor randomly oriented; such materials would have effective elastic tensors with 21 independent elastic constants, and this would overburden the conventional RUS analysis process. In any case, the elastic nature of some textured materials may be represented as the weighted average of the elastic tensors of the constituent crystalline material rotated in the directions of the individual crystallites. The collection of weights is the orientation distribution function (ODF). Now the least-squares fitting of a sample's measured resonance frequencies may be used to determine not the sample's elastic constants but instead its ODF. This is not trivial since the weights must be positive and sum to one, but it may be done with a simple modification of the conventional RUS software.

Enabling resonant ultrasound spectroscopy in extreme environments

Elastic moduli are fundamental thermodynamic susceptibilities that connect to thermodynamics, electronic structure, and mechanic properties. Thus, determining the changes of elastic moduli as a function of time or temperature is a powerful tool to study several thermodynamic and materials phenomena. Resonant Ultrasound Spectroscopy (RUS) determines 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 but lead to unstable positioning of the sample making it incompatible with extreme environments like high magnetic fields. In practice, even holding the sample produces contact forces that deviate from free-boundary conditions shifting resonant frequencies. In this talk, we show that, we can reduce the free-boundary conditions (by gluing/adhering the sample to the transducer), while still being able to obtain the full elastic tensor by a simple model of the sample-transducer interaction. This means elastic constants can be determined to within the uncertainty of conventional RUS, but with significant improvements in sample stability and control of sample orientation. We show the results of studying of several magnetic and structural phase-transitions using this new method.

Convergence properties of eigenfrequencies in RUS

An in-depth exploration of the asymptotic behavior of resonant frequencies in Resonant Ultrasound Spectroscopy (RUS), a non-destructive method for material property evaluation, is presented in this work. This work delves into the asymptotic analysis using Legendre polynomials for cuboid samples and examines the impact of increasing elements on eigenfrequencies. In this examination, we noted various elements concerning the computational boundaries and the influence of diagonal components on the asymptotes. The presence of a boundary for the asymptotes indicates limited information beyond a certain point. Additionally, how elastic constants influence these eigenfrequencies is discussed.

Laser-based resonant ultrasound spectroscopy for monitoring secondary phases in metastable Ti-alloys: From growth kinetics to high-throughput characterization

Metastable beta-Ti alloys undergo complex microstructural changes when annealed for extended times (hours, days, weeks) at temperatures below beta-transus. Contact-less RUS turns out to be a perfect tool for monitoring these processes, as well as for analyzing the properties of the alloys after the heat treatment. In the talk, we will illustrate this ability with three examples of recent advancements in this field. In particular, we will show that RUS is capable of analyzing (i) growth kinetics [1], from fast non-equilibrium phenomena to extremely slow processes; (ii) cubic symmetry conservation in single crystals with particles of various secondary phases [2]; and (iii) phase composition-elasticity relationships in series of oligocrystalline samples [3]. [1] Nejezchlebová et al. Elastic constants of β- Ti15Mo (2019) J Alloys Compounds, 792, pp. 960–967. [2] Olejňák et al. An ultrasound-based evaluation of cubic symmetry preservation and homogeneity in elastic behavior of β+ω and β+α Ti-alloys (2023) Materials and Design, 236, art. no. 112474. [3] Preisler et al., High-throughput characterization of elastic moduli of Ti-Nb-Zr-O biomedical alloys fabricated by field-assisted sintering technique (2023) J Alloys Compounds, 932, art. no. 167656.

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 etal. J. Acoust. Soc. Am. 90, 2154 (1991)JASMAN0001-496610.1121/1.401643]. 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. We apply this new approach to the recently discovered unconventional superconductor UTe_{2} and provide its elastic tensor at both 300 and 4 kelvin.

Statistical Analysis and Automation Through Machine Learning of Resonant Ultrasound Spectroscopy Data from Tests Performed on Complex Additively Manufactured Parts

Additive manufacturing brings inspection issues for quality assurance of final parts because non-destructive testing methods are faced with shape complexity, size, and high surface roughness. Thus, to drive additive manufacturing forward, advanced non-destructive testing methods are required. Methods based on resonant ultrasound spectroscopy (RUS) can take on all the challenges that come with additive manufacturing. Indeed, these full body inspection methods are adapted to shape complexity, to nearly any size, and to high degrees of surface roughness. Furthermore, they are easy to implement, fast and low cost. In this paper, we present the benefit of a resonant ultrasound spectroscopy method, combined with a statistical analysis through Z score implementation, to classify supposedly identical parts, from a batch comprised of several individual builds. We also demonstrate that the inspection can be further accelerated and automated, to make the analysis operator independent, whether the analysis of the resonant ultrasound spectroscopy data is performed supervised or unsupervised with machine learning algorithms.

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.

Resonant ultrasound spectroscopy of single crystalline KH2PO4

This study employs resonant ultrasound spectroscopy to investigate the elastic properties of single crystalline KH2PO4 (KDP) through the paraelectric to ferroelectric phase transition. Noteworthy anomalies are observed in selected resonance modes and their corresponding mechanical quality factors (Q-1) around the transition temperature. The thermal evolution of elastic constants (Cij) across the phase transition reveals a significant softening and stiffening behavior. The anomalous behavior of all elastic constants (Cij) across the phase transition suggests the involvement of higher-order coupling between the lattice and polarization in the KDP crystal. Furthermore, the bulk modulus (B) undergoes a sudden softening precisely at the transition, while the shear modulus (G) initially softens and subsequently stiffens across the transition.

Resonant ultrasound spectroscopy applications: Elastic moduli computation with x-ray computed tomography input for irregularly shaped objects.

Resonant ultrasound spectroscopy is a technique that uses a combination of experimentally measured resonant frequencies and physics-based computation of these frequencies to determine the entire set of single crystal elastic moduli of the material. Computation of the resonances is most often accomplished using the Rayleigh-Ritz energy minimization technique, and a basis function that requires sample with canonical geometry, such as a cylinder or a rectangular parallelepiped. Any deviation from canonical geometry can have a significant impact on the calculated resonance frequencies and the inverted elastic moduli. To overcome this limitation, this paper describes an approach that uses x-ray computed tomography data to generate accurate solid part model of components with complex geometry. The part model is then imported into an off-the-shelf finite element method (FEM) software to perform the forward problem. The FEM was combined with surrogate modeling for computation of resonance frequencies of both canonical and non-canonical samples, and ultimately, the inversion of elastic moduli.

Calculation of elastic constants of bulk metallic glasses from indentation tests

One of the challenges in the applications of instrumented indentation is to simultaneously measure elastic modulus and Poisson's ratio of homogeneous, isotropic materials. This work proposes empirical equations for simultaneous calculation of elastic modulus and Poisson's ratio of bulk metallic glasses (BMGs) from the ratio of the short diagonal length to the long diagonal length and the area of the Knoop imprint. The parameters presented in the empirical equations are determined first by Knoop microhardness tests of 24 BMGs, whose elastic moduli and Poisson's ratios are measured by resonant ultrasound spectroscopy. These empirical equations are further validated by the Knoop microhardness tests of other 3 BMGs, which yield elastic moduli and Poisson's ratios in good accordance with the corresponding ones available in the literature and with the results from nanoindentation tests. This work opens a new venue of Knoop microhardness test as an economical and efficient method to measure both elastic modulus and Poisson's ratio of BMGs.

Elastic constants of GaN grown by the oxide vapor phase epitaxy method

Oxide vapor phase epitaxy (OVPE) has attracted much attention as a highly efficient method for synthesizing high-quality bulk GaN crystals, but the mechanical properties of OVPE GaN have not been clarified. We measured the five independent elastic constants of the OVPE GaN by resonant ultrasound spectroscopy. The in-plane Young modulus E 1 and shear modulus C 66 of the OVPE GaN are smaller than those of the hydride vapor phase epitaxy GaN by 1.8% and 1.3%, respectively. These reductions agree with predictions by density functional theory calculations. We also calculated the Debye temperature, revealing that oxygen impurity decreases its magnitude.

Optimal measurement point selection for resonant ultrasound spectroscopy of complex-shaped specimens using principal component analysis

Traditional resonant ultrasound spectroscopy (RUS) uses the natural vibrations, or normal modes, of an object to determine the elastic properties of the object’s constituent material. When measuring the resonances of a sample, the measurement point is often selected based on user experience and intuition. This approach is often adequate when the sample has a simple geometry, but can be insufficient when testing complex-shaped samples. In such cases, multiple measurement points are used and the responses superimposed to obtain an overall resonance response. This approach can be effective but is time-intensive and can be still subject to error due to the possibility of missing modes. This paper introduces a method to automatically locate a minimal number of measurement points to extract sufficient modal information based on principal component analysis. The goal is to reduce the arbitrary nature of measurement point selection and measurement time while retaining the significant spectral information required for an accurate inversion. The efficacy of the method is demonstrated on a sample of relatively simple geometry as well as a part of greater complexity. The inversion results suggest that the modal information extracted from the few selected points is sufficient to yield accurate elastic constants.

An ultrasound-based evaluation of cubic symmetry preservation and homogeneity in elastic behavior of β + ω and β + α Ti-alloys

Elastic constants of dual-phase β-titanium alloys with different phase compositions and different volume fractions of individual phases were investigated using resonant ultrasound spectroscopy and transient grating spectroscopy. It was shown that even for high volume fractions of the secondary phases (ω and α), the crystals can retain cubic symmetry and homogeneity in their elastic behavior, both at the macro-scale and at the micro-scale, unless the secondary phases precipitate under external stress violating this symmetry. In contrast, a material heat-treated under uniaxial compression deviates from cubic symmetry in its macroscopic behavior, and its micro-scale elastic behavior is heterogeneous. The results also reveal that the ω and α particles have different impacts on the elastic constants of the β−matrix, the former affecting only the shear part of the elastic response, while the latter also the bulk modulus.

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.

Evaluation of elastic constants of particle accelerator cavity materials with Resonant Ultrasound Spectroscopy

European Spallation Source is a multi-nation, interdisciplinary research facility based on the world’s most powerful neutron source that will operate with high standards of availability and reliability minimizing downtime periods. In order to meet these goals, critical component’s performance and ageing need to be constantly monitored and assessed. Resonant Ultrasound Spectroscopy (RUS) is a highly versatile non-destructive technique for the definition of elasticity matrix of materials through the measurement of resonance frequencies. RUS could benefit the characterization of particle accelerator cavity materials exposed to challenging operational environments during project’s design and commissioning phases. This paper demonstrates the methodology and the first results on the implementation of this technique on Radio-Frequency Quadrupole (RFQ) structural copper. Rectangular parallelepiped samples of polycrystal, oxygen free, high purity Cu-OF copper were prepared and RUS measured on a designed experimental set-up. The obtained resonance frequencies were used as an input for the solution of the inverse eigenvalue problem using open-source objective function minimization software. The obtained results are compared with commercially available Finite Element Method (FEM) software defining a repeatable methodology for material property and defect characterization.

Determination of sound velocity by resonant ultrasound spectroscopy and complementary inelastic scattering

In this talk, I am going to highlight the complementarity of resonant ultrasound spectroscopy and (nuclear) inelastic scattering of synchrotron radiation for determining the sound velocity in condensed matter systems. Following a very brief introduction, characteristic examples of condensed matter systems relevant to material science in which the sound velocity is extracted using both experimental methods at ambient pressure and low temperature will be shown. The strengths of (nuclear) inelastic scattering of synchrotron radiation for obtaining the sound velocity at extreme pressure (up to ca. 200 GPa) and temperature (up to ca. 2000 K) relevant to geosciences will be discussed and relevant examples will be presented.

Resonant ultrasound spectroscopy of hybrid metal additive manufacturing

Additive manufacturing has been targeted as the next high-impact fabrication technique for parts and components. Hybrid metal additive manufacturing (AM) refers to the 3-D printed fabrication process involving secondary manufacturing processes or energy sources and multifunctional printing. Specific layers are altered within the build using additional processes (i.e., milling or peening) that are synergistic with the additive process. This combination alters the sample microstructure and can refine grains, increase dislocation density, or induce residual stresses. The effect of these hybrid layers is typically not confined within the layer alone but has a compounding effect on preceding layers. The goal is to control the changes in print parameters throughout the build to enhance component performance, but unique challenges remain for nondestructive validation of such samples. Traditional ultrasonic methods on hybrid-AM components have successfully mapped material variations with sufficient spatial resolution. However, the use of resonance ultrasound spectroscopy (RUS) for hybrid-AM is less developed. In this presentation, the use of RUS is described relative to the characterization of hybrid AM 316L stainless steel samples. The spatial organization of the hybrid samples affects the resonances relative to their mode shape. Computational models are used to quantify the impact of the hybrid processes.

An improved inversion method for shale elastic parameters measurement based on ultrasonic resonance spectroscopy

The accurate measurement of elastic parameters of shale cores has important guidance for the exploration and development of shale oil and gas. The traditional shale acoustic experiment requires multiple samples from different angles and its preparation process is complex. Resonant Ultrasound Spectroscopy has the advantages of repeatable measurement, high accuracy, and the ability to obtain all elastic parameters from a single small sample. However, the influence of clamping force and measuring angle needs comprehensive analysis to ensure that formant can be measured as many and accurately as possible. This research first conducts sensitivity analysis on the elastic parameters of different shale to guide the experiment. In addition, due to the more complex inversion objective function of the anisotropic shale compared to isotropic samples, the traditional Levenberg–Marquardt method has a strong dependence on the initial value and is prone to falling into local optimal solution. The L-BFGS (limited memory BFGS) method is introduced into the inversion of anisotropic elastic parameters of shale, which can significantly improve the inversion efficiency. Finally, the robustness and reliability of the inversion method are validated through theoretical and experimental measurement results. [Work supported by the National Natural Science Foundation of China (42004117 and 42127807).]

Nonlinear resonant ultrasound spectroscopy using white-noise excitation

Nonlinear resonant ultrasound spectroscopy (NRUS) is a technique for non-destructive sample evaluation by which a strain-dependent nonlinear parameter is quantified that exhibits heightened sensitivity to defects as compared to monitoring of linear resonance attributes. As NRUS measurements have traditionally used a controlled sweep of sinusoidal inputs, applications of the method have been largely limited to laboratory experiments. Here we present NRUS results which utilized a white noise signal as input, in order to better approximate ambient excitation and facilitate efficient validation using time-domain models. Studied samples were chosen to reflect a range of nonlinear responses and underlying mechanisms (acrylic, sandstone, fractured steel). We excited the studied samples using bonded piezoelectric transducers which delivered white-noise inputs at increasing amplitudes, with the nonlinear response measured with a laser doppler vibrometer. By comparing results against those obtained from traditional NRUS, we find comparable trends in the nonlinear parameter under white-noise excitation, including similar relative differences in magnitude across the samples and consistent values across similar mode shapes. While we note that white-noise strain estimation is complicated by simultaneous excitation of multiple resonant modes, NRUS results from white-noise excitation demonstrate promising viability of the technique for (1) in-situ inspection, and (2) a more-tractable approach to model the physics of various NRUS signals.