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The use of constrained global optimization appears to be a potential way to estimate single crystal elastic constants for low symmetry materials from diffraction measurements
Acoustoelasticity, a characteristic of material anharmonicity, gives rise to a link between wave propagation velocity and the stress state in materials. Ultrasonic techniques to monitor this coupling, particularly with high sensitivity and in a noncontact manner, can have widespread application both in the quantification of applied and residual stress and in the characterization of nonlinear material behavior through measurement of higher order elastic constants. Here, we use a laser ultrasonic technique to excite and detect zero group velocity (ZGV) Lamb wave resonances in aluminum plates under uniaxial loading. A laser line source is used to excite these resonances at different orientations with respect to the applied load, and the signals are detected using an interferometer. The effects of stress and source orientation on ZGV resonance frequencies are validated using the theory of acoustoelastic Lamb wave propagation. In addition, a model-based inversion technique is used to extract Murnaghan's third-order elastic constants from measurements of the stress dependence of the first two ZGV modes generated parallel and perpendicular to the applied load. Laser generation and detection of ZGV resonances is shown to be an effective and powerful approach for the noncontact and nondestructive acoustoelastic characterization of elastic waveguides.
The crystallographic orientations and residual stresses within recrystallizing grains in partially recrystallized beta titanium-Gum Metal-were examined non-destructively in 3D using synchrotron Differential Aperture X-ray Microscopy. Contrary to common assumptions, significant local stresses and stress variations are observed within the recrystallizing grains. The results reveal that the development of these local residual stresses depends on the plastic deformation mode and material's elastic constants, rather than grain properties such as size and orientation, or even the material's yield stress. This work provides insights valuable for the design of advanced materials with heterogeneous microstructures.
Previous studies showed that the thermally-induced ultrasonic bulk wave velocity change could be used to measure acoustoelastic coefficients and third-order elastic constants of elastic materials. This method is naturally immune from the ambient temperature effect and has improved sensitivity and a simpler test setup than the conventional acoustoelastic test. However, Rayleigh wave is preferred for thick components or structures with only one accessible surface. In this work, the thermo-hyperelastic constitutive equation, along with acoustoelastic theory, is used to derive the expression of the thermo-acoustoelastic coefficient (TAEC) of Rayleigh wave. The numerical relationship between the TAEC of Rayleigh wave and Murnaghan constants ( l, m and n ) are given for common metals. Further, the TAEC expressions for Rayleigh wave and shear wave are similar, and both are dominated by the constant m . The TAEC of Rayleigh wave was measured on an aluminum 6061 specimen using the thermal modulation experiment in a temperature range of 22 ~ 35°C. The measured TAEC shows good agreement with the theoretical calculation. Then the third-order elastic constants were calculated based on TAECs of bulk waves and Rayleigh wave.
Abstract Magnetic skyrmions are well-suited for encoding information because they are nano-sized, topologically stable, and only require ultra-low critical current densities j c to depin from the underlying atomic lattice. Above j c skyrmions exhibit well-controlled motion, making them prime candidates for race-track memories. In thin films thermally-activated creep motion of isolated skyrmions was observed below j c as predicted by theory. Uncontrolled skyrmion motion is detrimental for race-track memories and is not fully understood. Notably, the creep of skyrmion lattices in bulk materials remains to be explored. Here we show using resonant ultrasound spectroscopy—a probe highly sensitive to the coupling between skyrmion and atomic lattices—that in the prototypical skyrmion lattice material MnSi depinning occurs at $${j}_{c}^{* }$$ j c * that is only 4 percent of j c . Our experiments are in excellent agreement with Anderson-Kim theory for creep and allow us to reveal a new dynamic regime at ultra-low current densities characterized by thermally-activated skyrmion-lattice-creep with important consequences for applications.
Zero group velocity (ZGV) Lamb wave resonances are highly localized and sensitive to changes in material properties, making them a viable option for probing residual stresses and elastic nonlinearity through acoustoelastic effects. Temperature changes also influence ZGV modes and need to be accounted for, particularly when measuring the small frequency shifts associated with acoustoelastic effects. We use a laser-based ultrasonic system to measure the third-order elastic constants of several materials. A temperature compensation scheme is devised to remove the effects of temperature fluctuations from the measurements. Furthermore, the measured third-order elastic constants are used to predict the temperature dependence of the ZGV resonances using thermo-acoustoelasticity theory, and these predictions are compared to experimental measurements. We find that thermo-acoustoelasticity theory was unable to reliably predict the shift in ZGV resonances with temperature. These results could have important implications in understanding the limitations of thermo-acoustoelasticity theory and in developing precision ZGV resonance-based systems to detect and quantify residual stress in parts, a particularly relevant problem in additive manufacturing techniques including powder bed fusion and directed energy deposition.
In-situ measurement of surface acoustic wave (SAW) resonators were used to characterize piezoelectric materials behavior in a nuclear reactor environment. Lithium niobate and aluminum nitride devices were tested up to 500°C temperature and 450 kW reactor power (1.9x10 12 n/cm 2 s). The resonant frequency responds to step changes in temperature and power. Materials’ response are inferred from the observed resonant frequency changes, in particular the kinetic behavior is used to determine mechanisms responsible for observed changes. The observed response is attributed to two mechanisms: temperature increase from gamma heating and accumulation of radiation-induced defects. Both of these mechanisms alter the physical properties of the piezoelectric materials, particularly the elastic constants. The demonstrated repeatability and reliability of SAW devices are attractive for sensor applications in extreme environments.
Here, we report a comprehensive study on the elastic properties of a hexanary high-entropy alloy superconductor (ScZrNbTa) 0.685 [RhPd] 0.315 at room and cryogenic temperatures, by Resonant Ultrasound Spectroscopy experiments. The derived elastic constants are bulk modulus K=132.7 GPa, Young’s modulus E=121.0 GPa, shear modulus G=44.9 GPa, and Poisson’s ratio v= 0.348 for room temperature. The Young’s and shear moduli are ~ 10% larger than those in NbTi superconductor with similar T c , while the ductility is comparable. Moreover, the mechanical performance is further enhanced at cryogenic temperature. Our work confirms the advantageous mechanical properties of high-entropy alloy superconductors and suggests the application prospects.
Abstract Picosecond ultrasonics has seen wide application in the investigation of interfaces in semiconductors and 3D imaging in biological systems. Shear ultrasonic waves are important for elastic constant and grain orientation measurement in ceramic materials. In this study, we investigate the impact of grain orientation and material's elastic properties on the generation efficiency of shear waves by mode conversion at a transducer thin film/substrate interface. The solution of acoustic wave equations suggests that crystal grain orientation has a strong impact on the generated shear wave amplitude. This dependence is found to be closely related to the magnitude of longitudinal component of wave displacements. The applicability of analytical model is validated by the experimental results from time‐domain Brillouin scattering. Moreover, material properties determine acoustic wave amplitudes based on the acoustic mismatch model and, particularly, large elastic anisotropy defined by Zener ratio favors strong shear waves. In the light of this analysis, several recommendations on suitable grain orientations and film materials are made to facilitate shear wave detection.
Elastic properties are essential to the mechanical performance of materials, and therefore, can be tuned to design high-performance materials. In this study, the elastic constants of the equiatomic ternary refractory multi-principal-element alloys, NbTiV, and MoNbV, were investigated, using in-situ neutron diffraction and first-principles calculations. The experimentally measured and theoretically predicted elastic constants show a good agreement. The alloying effect of adding Ti and Mo into NbV base alloy on the elastic constants is studied. Particularly, adding Ti elements into the NbV alloy results in the increase of the Zener anisotropy ratio from 0.59 to 0.99, leading to the formation of the elastically isotropic NbTiV alloy, while the addition of Mo decreases the anisotropy ratio to 0.52. Pugh’s ratio (B/G), Cauchy pressure (C 12 -C 44 ), and Poisson’s ratio (ν) are used to predict the brittle/ductile nature of the studied alloys, which is consistent with the mechanical results. The present work provides valuable insights into the design of ductile and strong refractory high-entropy alloys by tuning the elastic properties.
We determine the strength of laser shock-compressed polycrystalline diamond at stresses above the Hugoniot elastic limit using a technique combining x-ray diffraction from the Linac Coherent Light Source with velocity interferometry. X-ray diffraction is used to measure lattice strains, and velocity interferometry is used to infer shock and particle velocities. These measurements, combined with density-dependent elastic constants calculated using density functional theory, enable determination of material strength above the Hugoniot elastic limit. Furthermore, our results indicate that diamond retains approximately 20 GPa of strength at longitudinal stresses of 150–300 GPa under shock compression.
The third-order elastic (TOE) model has been used to describe the widely observed nonlinear mechanical behaviors of earth materials. In addition to linear elastic constants ( λ , μ ), three nonlinear elastic moduli ( A , B , C ) are required for isotropic rocks. Contrary to previous research on dynamic TOE moduli, this study followed the protocol to measure strain and stress under uniaxial and hydrostatic compressive tests statically, which were later used to invert for the full set of TOE moduli for four standard rock types with differing pore structures of a porous oolitic limestone, quartz-rich sandstones, and a dense crystalline basalt. The applicability of the TOE model to characterize nonlinearity depends on the fulfillment of path-independence and small-strain assumptions. Using the measured static TOE moduli, the finite element model demonstrates that the stress in the vicinity of the wellbore is more amplified than the stress in the linear elastic case, which leads to a wider zone of rock failure around the wellbore. Due to the long-standing discrepancy between static and dynamic moduli, the rarely reported full set of static TOE moduli is necessary and will benefit future research in understanding the effect of rock nonlinearity on geophysical and geomechanical applications, such as long-term safe storage of CO 2 and generating process of geohazards.
Complete tensors of the second- and third-order elastic constants of the organic molecular crystals acetaminophen, pentaerythritol tetranitrate (PETN), cyclotrimethylene trinitramine (RDX), cyclotetramethylene tetranitramine (HMX), 1,1-diamino-2,2-dinitroethylene (FOX-7), hexanitrohexaazaisowurtzitane (CL-20), and erythritol tetranitrate (ETN) have been calculated using dispersion-corrected density functional theory. The sets of second- and third-order elastic constants are expected to provide a more accurate and reliable description of the behavior of these materials under nonhydrostatic loads than pressure- and volume-dependent second-order elastic constants. The tensors of second-order constants have been compared with experimental data and/or other calculations when possible, and with the exception of results for CL-20 from Brillouin scattering experiments, we find good agreement. The calculated third-order elastic constants of PETN are in very good agreement with the subset of third-order constants derived from experimental wave speed measurements. The elastic anisotropies of the crystals have been estimated using the universal elastic anisotropy index, which shows that the crystals fall into three groups with low anisotropy (PETN, RDX, and CL-20), moderate anisotropy (acetaminophen, HMX, and ETN), and high elastic anisotropy (FOX-7).
In situ synchrotron X-ray and neutron diffraction experiments provide a powerful approach to measure lattice strains in bulk polycrystalline materials. They are being increasingly used for quantitative characterization of microscale deformation within and between grains and phases. Here we use a self-consistent micromechanics model to obtain a general analytic solution of the grain-level lattice strains and diffraction elastic constants for a broad class of elastically isotropic polycrystals with cubic crystal symmetry. This analytic solution reveals a direct linear relationship between the reciprocal of the elastic diffraction constant and the orientation index parameter along the direction of any diffraction vector, including tensile loading and transverse directions. The straightforward numerical implementation of this solution provides diffraction elastic constants for 26 representative cubic polycrystals. Finally, analytic solutions of this kind can serve to benchmark in situ diffraction measurements of lattice strains and also facilitate high-throughput studies of microscale stresses and diffraction elastic constants in polycrystalline materials.
An integrated in-situ neutron diffraction and elastic plastic self-consistent crystal plasticity (EPSC-CP) modeling scheme is performed on a binary Al–12Ce alloy and a ternary Al–12Ce–0.4Mg alloys. Using this scheme, the constitutive parameters, i.e. elastic constants and slip system parameters of individual phases can be calibrated which can be used in microstructure-based CP models to predict materials performance. From this study, it is shown that the elastic constants of Al 11 Ce 3 intermetallics calculated from density function theory calculation in the literature are rather accurate. When applied to the EPSC-CP model, the lattice strains of both the binary and ternary alloys are correctly predicted as compared with experiments, and large lattice strain differences between Al (100) plane and Al 11 Ce 3 (010) plane are demonstrated. The slip system parameters calibrated by the scheme shows that the addition of 0.4 wt% Mg in the alloy has little influence on the critical resolved shear stress of initial dislocation glide in the Al matrix which caused plastic yield in the material. This can be explained by the very dilute Mg solute content in the Al solid solution, causing large spacing of Al–Mg lattice misfit sites and little impact on resistance of dislocation glide at initial yield. The 0.4 wt% Mg addition, on the other hand, has a large influence on the hardening term in the slip system parameters, indicating those Al–Mg misfit sites do help dislocation accumulation during the deformation. The impact of dilute Mg addition on the Al slip system parameters is also reflected in the flow behavior of the ternary alloy: little impact on the yield stress, but a large impact on working hardening and tensile strength of the materials which is consistent with the literature.
In-situ measurement of LiNbO 3 based surface acoustic wave (SAW) crystal resonator device under irradiation was demonstrated and used to characterize the impact of radiation on physical properties of this material. The resonant frequency of the SAW device was monitored as the output power of the reactor was varied. Upon step increase of the reactor power, a gradual shift in the device’s resonant frequency was observed. This frequency shift initially exhibits a linear growth and eventually reaches an equilibrium value proportional to the reactor power. The observed behavior can be attributed to two competing processes: increase of temperature due to gamma heating or accumulation of irradiation induced defects. In both cases, the response is attributed to changes in the physical properties of LiNbO 3 , particularly the elastic constants. This demonstrated ability to measure materials properties under irradiation is attractive for development of sensors and performing materials science under irradiation.
Tristructural isotropic (TRISO) particles show great promise as a candidate fuel for use in several next-generation high-temperature nuclear reactor designs due to their structural integrity and fuel performance at high temperatures and burnups. Computational codes exist that can simulate TRISO fuel performance characteristics and failure probabilities under extreme conditions which require knowledge of the TRISO coatings’ thermophysical properties. The thermophysical descriptions of the TRISO particle's layers (i.e., buffer, pyrolytic carbon, and silicon carbide) currently used in fuel performance codes, however, assume that many of these properties are constant with respect to temperature or texture. In this paper, we obtain the full elastic stiffness tensors of the carbon and silicon carbide layers, which have transversely isotropic symmetry. Additionally, the calculated elastic properties of each of the coating layers are in remarkable agreement with the current models at room temperature and correct orientations. Additionally, the textured 3C-SiC layer was found to exhibit novel auxetic behavior above 1500 °C. The anisotropic temperature-dependent thermal conductivities of the carbon layers were calculated using acoustical Grüneisen-Debye theory which are in excellent agreement with current models at room temperature and correct orientations. These texture- and temperature-dependent relationships can be incorporated into the thermophysical description of TRISO particles in order to more accurately model fuel performance and failure probabilities under extreme conditions in forthcoming high-fidelity computational simulations.
This project evaluates the ability to derive elastic material properties for novel additively manufactured carbon-polymer matrix materials. Initially stress-strain equilibrium equations were thought to be sufficient to characterize the elastic region of material performance. However, initial test data shows the cured material behaves nonlinearly in the elastic region. To properly determine the elastic performance, additional strain data must be collected in future testing. This paper discusses the initial test data, methods and models used to describe nonlinear elasticity, and the determination of mean elastic material properties, such as Lame’s constants, using the stress-strain equilibrium equations.