Resonant Ultrasound Spectroscopy Method Research Articles

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.

Classification of metal PBF-LB parts manufactured with different process parameters using resonant ultrasound spectroscopy

To face the challenges raised by the qualification of metallic additively manufactured (AM) complex shaped and rough finish parts, non-destructive testing (NDT) volumetric methods are required. X-ray computed tomography (XCT) is presently the favored technique; however, alternative methods are needed to overcome the requirement of technical skills and the high cost of the technique. XCT also has limitations regarding the size and density of parts. Here, we propose an easy to use, fast, and efficient global NDT volumetric method based on resonant ultrasound spectroscopy (RUS) which basic principle relies on the comparative analysis of natural resonant frequency spectra of similar parts from the same family, both of which vibrating as free as possible. The methods have already proven to have the ability to sort parts with defects from flawless parts. In the present study, we demonstrate that RUS can also segregate metallic parts manufactured with different AM system process parameters. Eleven sets of three parts were manufactured, using a metal laser-powder bed fusion process, with different wall thicknesses, laser powers, scanning speeds, and scanning strategies. These parts were tested by RUS and then analyzed using the Z-score statistical method. The AM process parameter changes clearly influenced the resonance responses of the parts, and thus, the method is able to classify the different groups of parts according to their process parameters. Hence, the RUS methods can provide industries convenient tools to not only identify defective parts but to also configure AM machine parameters according to the expected and desired material properties.

Assessment of material property variations with resonant ultrasound spectroscopy (RUS) when using additive manufacturing to print over existing parts

Additive manufacturing (AM) opens up many opportunities for repair and feature enhancement of existing components by 3D printing over already existing structures. However, much research, on the irregularities in the microstructure and lack of consistency in the material properties of the already existing portion and 3D printed additions is needed before such opportunities can be leveraged. In this paper, the potential discrepancy in the material properties of the already existing portion of the component and the 3D printed additions is investigated using a nondestructive testing (NDT) approach. Accordingly, in this study, AM is used for production of components forming the final part composition by adding new sections to the existing parts. Wire Arc Additive Manufacturing (WAAM) was used in this study as it has been the focus of many applications for printing over existing parts. The investigation is performed by considering a base structure for part composition, and inclusion of additional components fabricated with the WAAM method. Testing of the part integrity at different locations is done using Resonant Ultrasound Spectroscopy (RUS), and then comparing this with radiographic testing alternative. Results showed that the materials properties vary at different regions in existing and new deposition regions of the part, as well as in the transition area between the existing and new deposition region. These variations could be identified quickly and effectively using RUS method by examining frequency shifts or changes in spectrum amplitudes.

A new elastic characterization method for anisotropic bilayer specimens via Bayesian resonant ultrasound spectroscopy

A novel nondestructive method for complete elastic characterization of substrate-coating bilayer specimens with distinct anisotropic layers via resonant ultrasound spectroscopy (RUS) and Bayesian inversion is developed here. Bayesian formulations of the RUS inversion problem—of quantifying elastic properties given a measured list of resonance frequencies recorded from a single, typically small, precisely fabricated, macroscopically homogeneous, linear-elastic specimen—are a recent development. Here we report the first Bayesian formulation of the bilayer problem, and through a series of practical examples, demonstrate novel parameter estimation capabilities of our open-source CmdStan-RUS code. Finding specimen geometry and the number of resonance modes used for inversion strongly govern the ability to retrieve individual elastic moduli. The concept of “invertability” is explored for a range of relevant geometries using virtual specimens that resemble experimental bilayers of plasma sprayed ceramic coatings on single crystal metallic substrates. A range of Bayesian posterior evaluation methods are addressed, particularly considering the large computational cost of the bilayer forward model. Laplace approximation methods are thus developed and implemented for bilayer geometry design space modeling and expedient estimates of parameter uncertainties. Ideal specimen design, different noise models, the influence of prior distributions, dual-likelihood fits incorporating measurements of the bare substrate, and how Bayesian RUS methods differ from traditional RUS optimization are discussed.

Softening of Shear Elastic Coefficients in Shape Memory Alloys Near the Martensitic Transition: A Study by Laser-Based Resonant Ultrasound Spectroscopy

We discuss the suitability of laser-based resonant ultrasound spectroscopy (RUS) for the characterization of soft shearing modes in single crystals of shape memory alloys that are close to the transition temperatures. We show, using a numerical simulation, that the RUS method enables the accurate determination of the c′ shear elastic coefficient, even for very strong anisotropy, and without being sensitive to misorientations of the used single crystal. Subsequently, we apply the RUS method to single crystals of three typical examples of shape memory alloys (Cu-Al-Ni, Ni-Mn-Ga, and NiTi), and discuss the advantages of using the laser-based contactless RUS arrangement for temperature-resolved measurements of elastic constants.

Particle Swarm Optimization-Based Identification of the Elastic Properties in Resonant Ultrasound Spectroscopy.

Resonant ultrasound spectroscopy (RUS) is an experimental measurement method for obtaining elastic constants of an anisotropic material from the free resonant frequencies of a sample. One key step of the method is to adjust elastic constants to minimize the difference between calculated and experimental frequencies. The method has been widely used in the determination of elastic constants of solid materials with high Q value, such that the resonant frequencies can be easily extracted from the measured spectrum. However, for materials with high damping, the identification of the resonant modes becomes difficult due to the overlap of resonant peaks and the absence of some modes. Thus, the success of RUS depends largely on initial guessing of elastic constants. In this article, these limitations are addressed with a new RUS approach. First, the identification of resonant modes is transformed into a linear assignment problem solved by the Hungarian algorithm. Second, the inversion of the elastic tensor is achieved using the particle swarm optimization (PSO) algorithm. This method, having the ability of global optimization in the search space, is less sensitive to the initial guess of the elastic constants. The PSO algorithm was successfully applied for the first time to RUS data, providing estimates of elastic constants that were in good agreement with reference values. First, simulated data for a transversely isotropic sample of enamel of rectangular parallelepiped shape were used to validate the proposed RUS method. Second, the proposed RUS approach was validated using experimental data collected on a sample of transversally isotropic bone-mimicking material.

Elastic properties measurement of human enamel based on resonant ultrasound spectroscopy

ObjectivesTo investigate the elastic properties of human enamel using resonant ultrasound spectroscopy (RUS). MethodsSix rectangular parallelepiped specimens were prepared from six human third molars. For all specimens, the theoretical resonant frequencies were calculated using the Rayleigh-Ritz method, knowing the specimen mass density and dimensions, and using a priori stiffness constants. The experimental resonant frequencies were measured and extracted by RUS. Then, the optimal stiffness constants were retrieved by adjustment of the theoretical resonant frequencies to the measured ones based on the Levenberg-Marquardt method. The engineering elastic moduli, including Young’s moduli, shear moduli, and Poisson’s ratios, were also calculated based on the optimal stiffness constants. ResultsThe five independent stiffness constants C11, C12, C13, C33, and C44 were 90.2 ± 6.65 GPa, 34.7 ± 6.90 GPa, 29.5 ± 4.82 GPa, 83.5 ± 8.93 GPa, and 37.0 ± 10.9 GPa, respectively. Young’s moduli E11 and E33, shear moduli G13 and G12, and Poisson’s ratios υ12 and υ13 were 71.7 ± 7.34 GPa, 69.2 ± 7.32 GPa, 37.0 ± 10.9 GPa, 28.1 ± 4.35 GPa, 0.303 ± 0.098, and 0.248 ± 0.060, respectively. SignificanceElastic properties are critical for developing dental materials and designing dental prostheses. The RUS method may provide more precise measurement of elastic properties of dental materials.

On the complementarity between resistivity measurement and ultrasonic measurement for in-situ characterization of phase transitions in Ti-alloys

We present the results of in-situ characterization of the phase transitions in metastable β-Ti alloy Ti5553 by contactless laser-based resonant ultrasound spectroscopy method and electrical resistance measurement in a four probe configuration. Phase transformations were studied during continuous heating from the room temperature to 700 °C with various heating rates. We showed that both methods provide complementary results and can be successfully used for observation of phase transitions in metastable β-Ti alloys.

The resonant ultrasound spectroscopy method for determining the Poisson׳s ratio of spheres over the full range

The method for determining the Poisson׳s ratio of isotropic spheres was studied via resonant ultrasound spectroscopy (RUS). To that end, The mode structure maps for freely vibrating isotropic spheres were obtained via finite element method over the full range of Poisson׳s ratio (−1 to+0.5). RUS measurements for spherical samples (indium, steel, SiO2, 13.5wt% In–Sn, and copper foam) were compared with the numerical results and the Poisson׳s ratios were determined as +0.4, +0.3, +0.2, −0.08, and −0.3, respectively. The effects of slight shape imperfection upon the first 12 modes were analyzed for various Poisson׳s ratios, and were found to be negligible in interpretation of the experimental results.

Ultrasonic detection of ductile-to-brittle transitions in free-cutting aluminum alloys

Resonant ultrasound spectroscopy (RUS) is applied to detect the ductile-to-brittle and brittle-to-ductile transitions in an AA6262 free-cutting aluminum alloy during thermal cycling. It is shown that the RUS method is sensitive enough to detect reliably the melting and solidification temperatures of micro-sized Mg3Bi2–Bi eutectic particles responsible for these transitions, although the volume fraction of the particles is very small (~1%) and is even decreasing with the cycling. The proposed RUS approach is compared with differential scanning calorimetry (DSC); the latter method is shown to be unable to detect the transition temperatures especially when transition intervals are broad. The results reveal that the phase transitions of the eutectic particles exhibit a significant hysteresis and pronounced asymmetry between melting and solidification.

Using resonant ultrasound spectroscopy on samples with and without conducting coatings to measure piezoelectric constants

Piezoelectrics are often used at low temperatures, but among the large number of piezoelectric materials, only one (quartz) has had its properties measured at low temperatures. Because measuring piezoelectric constants with the traditional electrical impedance method has shortcomings, particularly at liquid helium temperatures, it would be advantageous to make measurements with resonant ultrasound spectroscopy (RUS). EerNisse and Holland (1967) established a theoretical basis and Ogi et al. (2002) demonstrated an experimental RUS method. A problem with RUS for piezoelectrics is that resonance frequencies are much more sensitive to elastic behavior than to piezoelectric behavior, so that extraordinary precision is required. However, one may make a RUS measurement on a sample twice, once with an electrically conducting coating on sample faces and once without, and analyze the differences in the frequency spectra. Because the effect of the conducting coating depends more on the piezoelectric behavior than on the elastic behavior, analyzing the frequency differences suppresses the dependence on the elastic constants and enhances the measurement of the piezoelectric constants. This paper will present theoretical and experimental results for this RUS method.

Development and validation of resonant ultrasound spectroscopy for the measurement of cortical bone elasticity on small cylindrical samples

Documentation of cortical bone elastic properties is important for orthopedic applications and fracture risk prediction. Cortical bone is heterogeneous and anisotropic. Ideally, measurements should be performed on cylindrical samples of characteristic size of a few millimeters, which are adapted to the native geometry and size of bones. Our objective was to measure bone with resonant ultrasound spectroscopy (RUS), which is a powerful method to determine the elastic constants of a sample from a set of its resonant frequencies. Application of RUS to bone is difficult due to viscoelasticity, which causes resonance peaks to overlap. Some of the resonances in the investigated frequency band cannot be observed. The formulation of the inverse problem, which requires pairing measured and predicted frequencies, must be adapted in the case of bone. We developed dedicated signal processing methods to retrieve resonant frequencies from overlapping peaks. A probabilistic approach was used, which allows an automated pairing based on a Bayesian criterion. The method was validated on isotropic (PMMA) and anisotropic (bone phantom) calibrated materials. The adapted RUS method allows the automated assessment of bone elasticity with a precision of a few percents, which is a significant improvement over traditional methods based on velocity measurements.

Phase stability and elastic properties of Cr–V alloys

V is the only element in the periodic table that forms a complete solid solution with Cr and thus is particularly important in alloying strategy to ductilize Cr. This study combines first-principles density functional theory calculations and experiments to investigate the phase stability and elastic properties of Cr–V binary alloys. The cluster expansion study reveals the formation of various ordered compounds at low temperatures that were not previously known. These compounds become unstable due to the configurational entropy of bcc solid solution as the temperature is increased. The elastic constants of ordered and disordered compounds are calculated at both T = 0 K and finite temperatures. The overall trends in elastic properties are in agreement with measurements using the resonant ultrasound spectroscopy method. The calculations predict that addition of V to Cr decreases both the bulk modulus and the shear modulus, and enhances the Poisson’s ratio, in agreement with experiments. Decrease in the bulk modulus is correlated to decrease in the valence electron density and increase in the lattice constant. An enhanced Poisson’s ratio for bcc Cr–V alloys (compared to pure Cr) is associated with an increased density of states at the Fermi level. Furthermore, the difference charge density in the bonding region in the (110) slip plane is highest for pure Cr and decreases gradually as V is added. The present calculation also predicts a negative Cauchy pressure for pure Cr, and it becomes positive upon alloying with V. The intrinsic ductilizing effect from V may contribute, at least partially, to the experimentally observed ductilizing phenomenon in the literature.

Anisotropic elasticity of DyScO3 substrates

The full elastic tensor of orthorhombic dysprosium scandate (DyScO3) at room temperature was determined by resonant ultrasound spectroscopy (RUS). Measurements were performed on three 500 μm thick substrates with orientations (110), (100) and (001) in the Pbnm (a < b < c) setting. For this purpose, a modification of the RUS method was developed, enabling simultaneous processing of the resonant spectra of several platelet-shaped samples with different crystallographic orientations. The obtained results are compared with ab initio calculations and with elastic constants of other rare-earth scandates, and are used for discussion of the in-plane elasticity of the (110)-oriented substrate.

Evaluation of elastic properties of DLC layers using resonant ultrasound spectroscopy and AFM nanoindentation

Elastic properties of diamond-like carbon (DLC) layers with gradient carbon–silicon interlayer were studied by resonant ultrasound spectroscopy (RUS) and standard nano-indentation technique. The DLC layers were prepared by pulsed laser deposition on SiC/Si substrates. The RUS method is based on modal analysis of the specimen vibration. The resonant frequency shifts caused by the layer are for the evaluation of the dynamic in-plane elastic properties of the deposited DLC. The results were compared with the quasi-statical quantities — Young's modulus and hardness, obtained by nanoindentation using the AFM tip.

K0.46Na0.54NbO3 ferroelectric ceramics: chemical synthesis, electro-mechanical characteristics, local crystal chemistry and elastic anomalies

K(0.46)Na(0.54)NbO(3) ceramics have been fabricated via a chemical synthesis route. It was found that 500 °C heat treatment is sufficient to crystallize the niobate powder and the ceramic sintered at 1080 °C in air shows good ferroelectric and piezoelectric properties (P(r) ~ 15 μC cm(-2), d(33) ~ 120 pC N(-1)). Electron diffraction patterns not only determine the space group symmetry of Pcm2(1) for the first time, but also reveal structural disorder in K(0.46)Na(0.54)NbO(3), and 1-D correlated strings of Nb-O atomic displacements are suggested to account for the polar behaviour. Elastic constants such as the bulk and shear moduli as well as their evolution with temperature were also measured using the resonant ultrasound spectroscopy method.

Experimental measurement of the elastic tensor of single crystal rare earth scandates utilizing resonant ultrasound spectroscopy.

Using resonant ultrasound spectroscopy (RUS) in combination with ab initio calculations, the complete elastic tensor of four rare earth scandates, SmScO3, TbScO3, NdScO3, and EuScO3, was determined. These recently developed materials are useful for a variety of novel applications including strain‐induced thin film growth of superlattices used in sonic lasers. In these applications, the dynamic lattice properties are of importance and are directly related to the elastic constants. The RUS method for determining the elastic constants is accomplished by iteratively comparing the experimentally determined resonant frequencies of a sample with a set of calculated frequencies. These calculated frequencies are generated from an assumed set of elastic constants. In order for the RUS method to reproduce the elastic tensor of the sample, reasonable initial elastic constants are required. For these newly developed materials, the initial elastic constants were obtained using ab initio calculations. Utilizing RUS, the...

Mode identified resonant ultrasound spectroscopy.

Resonant ultrasound spectroscopy (RUS) is a powerful tool for determining all independent elastic constants (Cij) of solids. Successful inverse calculation for Cij requires mode identification for measured resonance frequencies. In this lecture, two mode‐identified RUS methods developed by the author are presented. One is the electromagnetic acoustic resonance (EMAR) [Ogi et al., J. Acoust. Soc. Am. 106, 660 (1999)]. Using a solenoid coil and static magnetic field, vibrations of a specimen are measured through the electromagnetic‐force mechanisms. Detectable vibrational modes are controlled by changing the magnetic‐field direction. Because of the noncontacting measurement, it is applied to measurements at high temperatures easily. The second method incorporates the laser‐Doppler interferometry into RUS (RUS‐LDI method) [Ogi et al., J. Acoust. Soc. Am. 112, 2553 (2002)]. The specimen is set on the needle piezoelectric tripod in vacuum, and its displacement distributions at resonances are measured by laser interferometry for mode identification. It was applied to determine the piezoelectric coefficients and internal‐friction tensors as well as Cij of various piezoelectric materials, and also to thin‐film Cij. Because the contributions of the piezoelectric coefficients and thin‐film Cij to resonance frequencies are very small, correct mode identification becomes significantly important in their determination.

Electric field effects in RUS measurements

Much of the power of the Resonant Ultrasound Spectroscopy (RUS) technique is the ability to make mechanical resonance measurements while the environment of the sample is changed. Temperature and magnetic field are important examples. Due to the common use of piezoelectric transducers near the sample, applied electric fields introduce complications, but many materials have technologically interesting responses to applied static and RF electric fields. Non-contact optical, buffered, or shielded transducers permit the application of charge and externally applied electric fields while making RUS measurements. For conducting samples, in vacuum, charging produces a small negative pressure in the volume of the material – a state rarely explored. At very high charges we influence the electron density near the surface so the propagation of surface waves and their resonances may give us a handle on the relationship of electron density to bond strength and elasticity. Our preliminary results indicate a charge sign dependent effect, but we are studying a number of possible other effects induced by charging. In dielectric materials, external electric fields influence the strain response, particularly in ferroelectrics. Experiments to study this connection at phase transformations are planned. The fact that many geological samples contain single crystal quartz suggests a possible use of the piezoelectric response to drive vibrations using applied RF fields. In polycrystals, averaging of strains in randomly oriented crystals implies using the “statistical residual” strain as the drive. The ability to excite vibrations in quartzite polycrystals and arenites is explored. We present results of experimental and theoretical approaches to electric field effects using RUS methods.

Using structural acoustics methods to study new materials.

In structural acoustics it is usually necessary to know the vibration properties of the structure under study, and this requires knowing the elastic constants of the materials involved. A relatively recent and powerful method for measuring elastic constants is resonant ultrasound spectroscopy (RUS). Very new and exotic materials for structures often require RUS; the reason is that new materials, when first fabricated, are often available only in very small samples (a few hundred micrometers) or as thin films on substrates, and RUS is the best method for handling such samples. On some occasions samples are fragile or chemically reactive so that they cannot be polished into the shapes required by conventional RUS. Thus, it has been necessary to develop a RUS analysis for arbitrarily shaped samples. This has been accomplished by borrowing a method from structural acoustics: the finite element method (FEM). The discussion of the application of FEM to RUS for arbitrarily shaped samples will include bridging the gap between theory (involving matrices as boldfaced symbols without indices in textbooks on FEM) and actual lines of computer code. Applications of the RUS method for materials will also be discussed.