Resonant Ultrasound Spectroscopy Research Articles

Characterization of temperature-dependent full-matrix constants of [001]c-poled Mn-doped 28PIN-43PMN-29PT single crystals using one sample

[001]c-poled Mn-doped xPb(In1/2Nb1/2)O3–(1–x–y)Pb(Mg1/3Nb2/3)O3–yPbTiO3 (PIN–PMN–PT:Mn) single crystals (SCs) in the rhombohedral phase possess not only excellent piezoelectric properties but also a high mechanical quality factor, which make them suitable for fabricating high-performance piezoelectric devices. Characterizing the temperature dependence (TD) of full-matrix constants is indispensable for their use in device design. However, there is a significant lack of relevant data. In this study, the TD of the clamped dielectric properties of [001]c-poled 28PIN-43PMN-29PT:Mn SCs was characterized using a dielectric temperature spectroscopy measurement system from 0 to 60 °C. Their elastic and piezoelectric constants were measured using resonant ultrasound spectroscopy in the same temperature range. With an increase in the temperature, all the elastic stiffness constants decreased, whereas all the clamped dielectric constants and the absolute values of all the piezoelectric stress constants increased. The characterization process required only a single sample, which ensured the consistency of the results. Furthermore, the electrical impedance spectra of the sample at 30 and 50 °C were measured and compared with those simulated using the finite-element method with the characterization results. The close agreement between them confirmed the reliability of the characterization results.

Profiling the thermal damage gradient in concrete using linear and non-linear ultrasonics

Processes such as carbonation and thermal damage result in a depth-dependent variation in concrete mechanical properties, which are typically characterized by invasive sampling and destructive testing. In this study, several ultrasonic testing methods are employed to nondestructively measure gradients in elastic properties within concrete and mortar slabs, induced by varying amount of exposure to elevated temperatures. The slabs are subjected to two distinct heat exposures, carefully chosen to create different gradients within the first few centimeters below the surface. The first exposure scenario following the ISO fire standard led to superficial damage. Deeper damage was achieved with radiant panels. We use linear and non-linear ultrasonic testing, with the aim of characterizing the resulting property gradients including refracted P-waves, analysis of surface wave dispersion and higher harmonic generation. Additionally, we employ NRUS (nonlinear resonant ultrasound spectroscopy) to test slices extracted from the different depths within the slabs. The ultrasonic test results are benchmarked and interpreted in relation to a suite of other multiphysical measurements (resistivity, capacity, temperature). This work represents a first crucial step towards the development of a new method for measuring gradients of nonlinear elastic properties within concrete through nondestructive ultrasonic testing.

Passive wall thickness monitoring using acoustic emission excitation

Erosion-corrosion is a problematic damage mechanism for the oil and gas industry. To manage the risk of erosion-corrosion networks of particle impact monitoring systems have been installed on pipelines in order to detect acoustic emission from abrasive sand particles impacting the inside surface of the pipe. It would be of value if the existing network of particle impact monitoring systems were not only capable of detecting particle impact, but also sizing the remaining wall thickness. Particle impact monitoring systems are passive and are not generally equipped for excitation. This paper explores the feasibility of using passive acoustic emission transducers for wall thickness measurement, utilizing the fact that active pulse-echo measurements can be approximated by autocorrelating diffuse acoustic waves, such as those generated by particle impact. Two measurement modalities are presented: a) time-of-flight measurements and b) resonant ultrasound spectroscopy measurements. The more usual time-of-flight based measurement is limited by the fact that acoustic emission transducers typically have sensitive bandwidths limited to <1 MHz. The relatively low frequency operation limits the use to thick wall components where the component thickness ≫ ultrasonic wavelength. In thinner walled components a resonant ultrasound spectroscopy approach is required. Experimental measurements are shown that are truly passive (with no purposeful excitation at all), and semi-passive, utilizing acoustic emission from sand impact or compressed air as the excitation source. Results show very good agreement with active measurements.

Domain wall dynamics in tungsten trioxide: Evidence for polar domain walls

Domain walls have distinct properties from the bulk, and tailoring them to suit the needs for device applications is critical. Tungsten trioxide, WO3, is of great interest for device applications that make use of domain wall properties; it exhibits a phenomenologically rich sequence of phase transitions, virtually all of which are ferroelastic in character, resulting in many sets of domain walls at low temperatures, each with their own unique properties. Domain wall motion and its contribution to the piezoelectric response have been investigated in WO3 from 300 to 180 K using resonant ultrasound spectroscopy (RUS) and resonant piezoelectric spectroscopy (RPS), which showed that the P21/n,P1¯, and P21/c phases give a piezoelectric response despite the bulk being nominally centrosymmetric. Second harmonic generation (SHG) confirmed that polarity was strongest within the domain walls, and additional weak signals were found in the domains. Domain wall mobility was investigated in the Pbcn,P21/n, and P21/c phases from 685 to 5 K. Domain walls in the P21/n and P1¯ were more mobile than those in the Pbcn and P21/c structures, and soon after the P1¯→P21/c transition the walls become pinned at ∼140K. Published by the American Physical Society 2024

Nonlinear resonant bar of approximate Ramberg–Osgood type modulus defect

This study investigates the nonlinear vibration of a material bar with a modulus defect that causes observable hysteresis in the elastic regime. The Ramberg–Osgood equation is used to obtain an approximate model of the quasi-static stress–strain relationship for such a material, from which a phenomenological dynamic hysteresis function of arbitrary order is constructed. The nonlinear hysteresis is described with two parameters. Applying the hysteresis function leads to a nonlinear wave equation which is then solved for the longitudinal vibration of the bar using a perturbation method. The leading-order solution provides the strain-dependent resonance frequency and damping factor which are the two quantities measured in the nonlinear resonance ultrasound spectroscopy (NRUS). It is shown that the resonance frequency shift and damping increment hold, in general, a power-law dependence on the strain amplitude and the conventional linear dependence is a special case for the quadratic hysteresis. The derived formula is applied to existing data from bending and torsional NRUS-type experiments where the conventional linear fit appears to be clearly inadequate. Experimental resonance frequency shift data are fitted to determine the two hysteresis parameters, both of which vary with the changes in the material state. It is shown that the nonlinear damping ratio is a more general measure of the energy dissipation due to the increasing hysteresis and thus can be taken as a damage index. Consequently, this paper proposes a general procedure to analyze NRUS data for a wider range of materials. The present analysis is valid up to the yield strain which is sufficient to cover the strain amplitudes used in NRUS measurements.

Compliant Lattice Modulations Enable Anomalous Elasticity in Ni-Mn-Ga Martensite.

High mobility of twin boundaries in modulated martensites of Ni-Mn-Ga-based ferromagnetic shape memory alloys holds a promise for unique magnetomechanical applications. This feature has not been fully understood so far, and in particular, it has yet not been unveiled what makes the lattice mechanics of modulated Ni-Mn-Ga specifically different from other martensitic alloys. Here, results of dedicated laser-ultrasonic measurements on hierarchically twinned five-layer modulated (10M) crystals fill this gap. Using a combination of transient grating spectroscopy and laser-based resonant ultrasound spectroscopy, it is confirmed that there is a shear elastic instability in the lattice, being significantly stronger than in any other martensitic material and also than what the first-principles calculations for Ni-Mn-Ga predict. The experimental results reveal that the instability is directly related to the lattice modulations. A lattice-scale mechanism of dynamic faulting of the modulation sequence that explains this behavior is proposed; this mechanism can explain the extraordinary mobility of twin boundaries in 10M.

Effective Young’s modulus of highly porous 3D printed mono-material and coaxial structures

The dynamic elastic response of 3D macroporous scaffolds is crucial to determine their performance under operating conditions. In this work, the elastic behaviour of 3D printed bar-shaped scaffolds of γ-Al2O3 and γ-Al2O3/graphene nanoplatelets (GNP) composites (18 vol%), fabricated by Direct Ink Writing (DIW), is investigated. Dynamic Young’s modulus (E) is studied by the Impulse Excitation Technique (IET) and compared with theoretical results obtained by Finite Element Methods (FEM) and the multi-scale material simulator GeoDict®. In addition, Resonant Ultrasound Spectroscopy (RUS) is used to characterize E of single- and bi-material coaxial struts. While additions of GNP to γ-Al2O3 lead to an increase in E, it decreases in the coaxial struts due to the development of thermal residual stresses at the core/shell interface. The suitability of combining experimental and theoretical methods for the analysis of the elastic properties and the anisotropy associated with the lattice pattern is demonstrated.

Direct ink writing of woodpile-kind alumina phononic crystals for MHz regime

We report comprehensive work on the fabrication of alumina-based phononic crystals (PhCs) using direct ink writing (DIW), measurement of anisotropic properties, and identification of acoustic bandgaps. Woodpile-structure-kind PhCs of characteristic size 1.1 mm and 10 periods were fabricated from alumina and polyvinyl alcohol (PVA) solution, and processed by freezing under vacuum. Next, the anisotropic elastic constants of alumina were obtained from bulk specimens using resonant ultrasound spectroscopy. Band diagrams and transmission loss were computed using the finite-element method and good correlations were found between the bandgaps estimated by these methods. Multiple partial bandgaps and several local resonances were observed in many directions for frequencies below 2 MHz. This work is the first step toward developing ceramic PhC using additive manufacturing methods for high-temperature applications.

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.

Elastic and anelastic behavior associated with magnetic ordering in the skyrmion host Cu2OSeO3

Magnetic ordering in Cu2OSeO3 occurs without any detectable changes in the lattice symmetry but involves significant coupling with strain. The strain coupling effects in Cu2OSeO3 have been investigated with a focus on the skyrmion lattice by examining elastic and anelastic properties. Resonant ultrasound spectroscopy has been used to measure these properties of a Cu2OSeO3 single crystal as a function of temperature and magnetic field. On heating, the skyrmion phase has been characterized by slightly softer elasticity compared to the helical phase. However, there were no obvious anomalies in elastic and anelastic properties associated with the boundary of the stability field of the skyrmion lattice. Evolution of elastic properties with magnetic field, passing through the stability field of the skyrmion lattice, showed a characteristic pattern of a glassy state, where an equilibrium state is never reached. These imply that coupling of the skyrmions with strain is extremely weak in Cu2OSeO3, leading to glassy or liquidlike behavior of skyrmions. Three Debye-like loss peaks were observed near ∼40, ∼50, and ∼60K. The relaxation mechanism for the 40 K loss peak has been found to have a single relaxation time. Overlapping acoustic loss peaks in the temperature interval ∼50–62K suggest that the magnetic transitions with variable temperature in this temperature range involve freezing of some dynamic aspect(s) of the magnetic structure with an activation energy of ∼0.1–0.15 eV. Published by the American Physical Society 2024

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

Modeling resonant ultrasound of synthetic polycrystalline microstructures produced by Dream3D

Resonant ultrasound spectroscopy (RUS) is established for determining elastic constants of homogeneous solids. Often applied to polycrystalline materials like metals, RUS presumes homogeneity based on the microstructure's scale. This presumption is challenged with large grain sizes and higher-order modes, complicating homogeneity testing in real samples due to the need for 3D metallurgical analysis. An alternative is RUS modeling on digitized synthetic microstructures. This presentation investigates the RUS variational model with Rayleigh-Ritz solutions on microstructures created using Dream3D. It starts with a proof for solutions that minimize the Lagrangian in heterogeneous solids. Subsequently, Rayleigh-Ritz volume integrals are numerically evaluated for synthetic polycrystalline microstructures, as spatial heterogeneity precludes analytical solutions. No homogeneity assumption is made. The 3D integrals, requiring advanced GPU processing for a detailed mesh, lead to forward model results. These will be compared against common homogenization schemes, highlighting new insights when using RUS for material characterization of polycrystalline materials.

Characterization of effective elastic constants and anisotropy directions for Wire Arc Additive Manufactured steel samples using RUS

In recent years, Resonant Ultrasound Spectroscopy (RUS) has been extensively applied to objects produced by additive manufacturing to characterize elastic material properties, detect defects or geometrical deviations. In this talk, we analyze samples that were produced using the wire-arc additive manufacturing (WAAM) process using different grades of steel wires. Resonance spectra were obtained and allowed to classify samples as either elastically isotropic or anisotropic. Detailed investigation on anisotropic samples (produced with 316L wire) under an orthotropy hypothesis showed that the samples were markedly softer along the layer deposition direction. Subsequent investigation using EBSD confirmed the results obtained with RUS. They also allowed to quantitatively model the elastic constants using the Voigt-Reuss-Hill averaging theory, which were in good agreement with the ones obtained using the RUS inverse problem.

Inverse problems in resonant ultrasound spectroscopy based on spectra perturbation

In RUS, the fit between the experimental resonant spectrum and the result of the inversion procedure is usually worse than the inaccuracy of the experimental measurement of the resonant frequencies. Thus, it can be problematic to extract any valuable information from slight perturbation of experimental spectra, where the experimental frequency shift falls well below the accuracy of this fit. However, the inverse procedure can be reformulated and instead of fitting the resonant frequencies itself, it can be based on the direct fitting of the frequency perturbations. In this contribution, we show two examples of the use of this approach (i) quantitative RUS evaluation of the elasticity of micrometric and submicrometric surface layers from frequency differences measured before and after layer deposition [1] and (ii) in situ characterization of the thermal degradation of the bonding layer in a bimetallic system [2]. [1] Thomasová M. et al. Young's moduli of sputter-deposited NiTi films determined by resonant ultrasound spectroscopy: Austenite, R-phase, and martensite (2015) Scripta Materialia, 101, pp. 24–27. [2] Janovská M. et al Characterization of bonding quality of a cold-sprayed deposit by laser resonant ultrasound spectroscopy (2020) Ultrasonics, 106, art. no. 106140.

Resonant ultrasound spectroscopy experimental design and optimization

Resonant Ultrasound Spectroscopy (RUS) is a nondestructive material characterization technique that utilizes solid body resonances to estimate elastic moduli. This method is advantageous over traditional mechanical testing due to the significantly lower number of required samples to estimate the same number of moduli. The goal of this project is to develop a high-throughput RUS system capable of measuring experimental resonances and mode shapes in a fraction of the time of traditional RUS measurements. A new system was designed which leverages data/image analysis algorithms to aid in sample alignment and data collection. A standardized sample geometry was also analyzed by performing a geometric sensitivity study and optimizing the aspect ratio of lengths of a parallelepiped. The results show that the optimized sample geometry is consistent between materials with varying elastic properties. In order to validate the design of the new RUS system a comparative study to an existing system was conducted. The results show that the newly designed system produces comparable resonant frequency and mode shape measurements.