Resonant Ultrasound Spectroscopy Research Articles

Determination of elastic constants in complex-shaped materials through vibration-mode-pattern-matching-assisted resonant ultrasound spectroscopy

Determination of elastic constants in complex-shaped materials through vibration-mode-pattern-matching-assisted resonant ultrasound spectroscopy

Temperature-dependent characterization of full tensor properties of [111]c poled Mn-doped 28PIN-43PMN-29PT single crystals

The temperature-dependent characterization of full tensor properties of single-domain relaxor-based single crystals (SCs) is important for understanding the influence of temperature on the properties of their multidomain SCs. However, no relevant results have been published because characterization is difficult to achieve using the traditional electric resonance method. In this Letter, the temperature-dependent elastic and piezoelectric properties of single-domain [111]c poled Mn-doped 28Pb(In1/2Nb1/2)O3-43Pb(Mg1/3Nb2/3)O3-29PbTiO3 SCs were investigated in the range of 20–80 °C by resonant ultrasound spectroscopy (RUS) using a rectangular parallelepiped sample. The temperature-dependent dielectric constants were calculated from the measured capacitances of the sample. The results are self-consistent because they were obtained from the same sample. The elastic constants obtained using the ultrasonic pulse-echo method agree closely with those obtained using RUS. Moreover, the experimental results of electric impedance spectrum agree closely with those simulated using the material constants characterized herein, indicating that the characterization is reliable.

Impact of relative humidity variations on Carrara marble mechanical properties investigated by nonlinear resonant ultrasound spectroscopy

Like many other stones, marble mechanical properties can be significantly changed in presence of water. Water most often induces a weakening which can lead to marble degradation when coupled to temperature variations. Yet, marble artefacts are more frequently subjected to relative humidity (RH) variations than episodes of water imbibition and/or drastic temperature variations. Thus, one could wonder how do variations of RH alone impact marble mechanical state. In this study, Carrara Gioia marble samples are subjected to adsorption-desorption cycles. They were previously thermally-damaged between 40 and 105 °C, and their microstructure was characterized for each heating temperature. The evolution of their mechanical properties is monitored non-destructively with two parameters measured by Nonlinear Resonant Ultrasound Spectroscopy. The resonant frequency decreases weakly with increasing RH, indicating a diminution in sample stiffness due to low moisture-induced softening. The nonlinear parameter increases strongly, probably due to higher capillary pressure associated to a capillary condensation increase with RH. However, these phenomena are reversible: during adsorption-desorption cycling both parameters remain quite constant for a given RH. Therefore, while a RH increase impacts the mechanical properties of Carrara marble, adsorption-desorption cycling shows a reversible behavior which does not induce any permanent change in mechanical properties.

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.

Tensile and micro-compression behaviour of AISI 316L austenitic stainless steel single crystals at 20 °C and 300 °C: Experiments, modelling and simulations

The mechanical behaviour of 316L stainless steel single crystal is characterised at room temperature and 300°C. Elasticity moduli at room temperature are obtained with resonant ultrasound spectroscopy. Their dependence on temperature is calibrated with molecular dynamics simulations. The plastic behaviour is characterised by tensile tests on millimetre-sized single crystal specimens and compression tests on micrometre-sized single crystal specimens. A constitutive model of crystal plasticity based on dislocation density hardening at finite strains is developed and implemented in an open-source material subroutine compatible with several finite element (FE) and fast Fourier transform (FFT) solvers. Tensile curves at room temperature and 300°C are used to calibrate the interaction coefficients for self and coplanar dislocation interactions. The dislocation mean free path for obstacle dislocations and the annihilation distance are also calibrated. The calibrated model predicts tensile curves in excellent agreement with experimental data. In addition, the predicted plastic strain fields are in good agreement with the experimental fields obtained by digital image correlation. Semi-quantitative agreement between simulation and experimental data is obtained for micro-compression tests without further calibration of the model. Finally, an extension to polycrystals with grain size effects is finally proposed. The predicted strain hardening behaviour is compared with experimental data on stainless steel polycrystals.

Elastic, Anelastic, and Thermal Properties of P91 Steel with Microstructural Variability

Grade 91 steel has been used in nuclear and fossil power plants since the 1970s. Manufacturing variabilities resulting from manufacturing, repair, and management activities have been attributed to lowered creep and fatigue life. This paper characterizes the elastic, thermal, and anelastic properties of P91 steel with different microstructures. Eight different microstructural conditions were identified as acceptable, gross, and gradual degradations. Ultrasonic testing was used to measure velocities, and resonant ultrasound spectroscopy was used to measure internal friction. The thermal diffusivity was measured along with Vicker’s hardness and grain size. A model for internal friction was used to combine the measured elastic and thermal properties. The results suggest that the current understanding of internal friction and its sources may be incomplete for complex microstructures like grade 91. From an nondestructive evaluation perspective, the results suggest that the internal friction has the highest sensitivity to microstructure changes, compared to elastic and thermal properties.

Elastic constant estimation for low-Q materials using convolutional neural network based resonant ultrasound spectroscopy

Elastic constant estimation for low-Q materials using convolutional neural network based resonant ultrasound spectroscopy

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.