Anisotropic Elastic Constants Research Articles

Atomic bubbles in impurity-stabilized solid He4

The optical absorption and fluorescence spectra of alkali atoms isolated in liquid and solid He matrices depend on specific macroscopic matrix properties, such as their molar volume and (anisotropic) elasticity constants, and provide thus information about the quantum matrix. We apply optical spectroscopy to investigate the properties of a recently discovered impurity-stabilized doped He4 solid that exists in equilibrium with pressurized superfluid helium close to the solidification∕melting point of pure helium. The difference between the local He density around the implanted atoms obtained in the present experiment and the average density measured earlier suggests that the impurity-stabilized solid He is in fact a porous structure filled with liquid helium.

Comments on ‘Global anisotropic phase velocity maps for higher mode Love and Rayleigh waves’ by Visser, Trampert & Kennett

SUMMARY A recent paper by Visser et al. analyses large numbers of surface wave seismograms for velocity anisotropy by assuming the waves separate into two independent sets of modes with (implicitly) the Rayleigh- and Love-wave particle motion expected from propagation in isotropic substrates. Visser et al. claim they present ‘global anisotropic phase velocity maps for higher mode Rayleigh waves and Love waves’. I show that surface wave modes in an azimuthally varying anisotropic Earth are generalized modes with generalized elliptical particle-motion in three-dimensions that cannot be separated into independent sets of Rayleighand Love-modes with sagittal and transverse-horizontal particle motion. Inversion would lead to two independent sets of anisotropic elastic constants which would be inappropriate for modelling an anisotropic Earth.

Direct and ultrasonic measurements of macroscopic piezoelectricity in sintered hydroxyapatite

Macroscopic piezoelectricity in hydroxyapatite (HA) ceramic was measured by a direct quasistatic method and an ultrasonic interference technique. The effective symmetry of polycrystalline aggregate was established and a detailed theoretical analysis was carried out to determine by these two methods the shear piezoelectric coefficient, d14, of HA. Piezoelectric nature of HA was proved qualitatively although a specific quantitative value for the d14 coefficient could not be established. Ultrasound method was also employed to anisotropic elastic constants, which agreed well with those measured from the first principles.

Multiaxial Low Cycle Fatigue Life-Assessment of a Nickel Base Single Crystal Superalloy under Combined Tension-Torsion Loading

This paper studies on the tension-torsion multiaxial low cycle fatigue of YH61 nickel base single crystal superalloy at high temperature. Strain controlled tension-torsion low cycle fatigue tests were carried out at 1173K using YH61 hollow cylinder specimens of which specimen axis was crystallographic direction. Mises equivalent total strain range gave a large scatter in the correlation of multiaxial low cycle fatigue lives. On the other hand Mises equivalent plastic strain and Mises equivalent stress ranges correlated the multiaxial low cycle fatigue lives with a small scatter. The deformation behavior of the single crystal superalloy showed strong anisotropy under multiaxial loading due to the crystallographic texture, and the unsatisfactory life correlation with Mises total strain range resulted from the anisotropic deformation behavior of the specimen. A new strain parameter, taking account of the anisotropy of elastic constants into account was proposed, and the parameter estimated the multiaxial low cycle fatigue lives within a factor of 2 scatter band.

Elastic constants of metal/ceramic composites with lamellar microstructures: Finite element modelling and ultrasonic experiments

The elastic properties of single domains of lamellar AlSi12/Al 2O 3 composites produced by metal infiltration of freeze cast preforms have been examined. The anisotropic elastic constants determined from ultrasonic phase spectroscopy (UPS) experiments have been compared to microstructure based FE-models created with the program OOF2, micromechanical models (Mori–Tanaka and inverse Mori–Tanaka) and an analytical model for an ideal laminate. The influences of lamellae orientations and ceramic contents on the elastic constants have been investigated. Along the lamellae directions the microstructure based FE model and the inverse Mori–Tanaka model are in good agreement with experimental results. Perpendicular to the lamellae the experiment shows a stiffer than expected elastic behaviour.

Structural and elastic properties of LaAlO3 from first-principles calculations

Using the first-principles linearized augmented plane wave calculations within density functional theory, the stable structure, the phase transition, and elastic properties of the LaAlO3 are investigated. At low temperature, our calculation indicates that the rhombohedral R-3C phase is the most energetically stable structure among the three proposed structures: R-3C (No. 167), R-3M (No. 166), and R3C (No. 161). It is found that the LaAlO3 transforms from rhombohedral R-3C phase to cubic PM-3M phase with a volume change of 1% when the applied hydrostatic pressure is 15.4 GPa, which is consistent with the experimental value. The elastic constants, shear modulus, bulk modulus, and Poisson’s ratio of LaAlO3 are calculated and compared with corresponding experimental data. Our result shows that the rotation of the AlO6 octahedra in LaAlO3 has a large influence on the anisotropic elastic constants. From the calculated Debye temperature and elastic constants, the R-3C phase of LaAlO3 is predicted to be more thermostable and to exhibit higher fracture toughness than the high-pressured PM-3M phase.

Anatomic variation in the elastic anisotropy of cortical bone tissue in the human femur

Experimental investigations for anatomic variation in the magnitude and anisotropy of elastic constants in human femoral cortical bone tissue have typically focused on a limited number of convenient sites near the mid-diaphysis. However, the proximal and distal ends of the diaphysis are more clinically relevant to common orthopaedic procedures and interesting mechanobiology. Therefore, the objective of this study was to measure anatomic variation in the elastic anisotropy and inhomogeneity of human cortical bone tissue along the entire length (15%–85% of the total femur length), and around the periphery (anterior, medial, posterior and lateral quadrants) of the femoral diaphysis, using ultrasonic wave propagation in the three orthogonal specimen axes. The elastic symmetry of tissue in the distal and extreme proximal portions of the diaphysis (15%–45% and 75%–85% of the total femur length, respectively) was, at most, orthotropic. In contrast, the elastic symmetry of tissue near the mid- and proximal mid-diaphysis (50%–70% of the total femur length) was reasonably approximated as transversely isotropic. The magnitudes of elastic constants generally reached maxima near the mid- and proximal mid-diaphysis in the lateral and medial quadrants, and decreased toward the epiphyses, as well as the posterior and anterior quadrants. The elastic anisotropy ratio in the longitudinal and radial anatomic axes showed the opposite trends. These variations were significantly correlated with the apparent tissue density, as expected. In summary, the human femur exhibited statistically significant anatomic variation in elastic anisotropy, which may have important implications for whole bone numerical models and mechanobiology.

In Vivo μMRI-Based Finite Element and Morphological Analyses of Tibial Trabecular Bone in Eugonadal and Hypogonadal Men Before and After Testosterone Treatment

Osteoporosis is a major public health problem in men. Hypogonadal men have decreased BMD and deteriorated trabecular bone architecture compared with eugonadal men. Testosterone treatment improves their BMD and trabecular structure. We tested the hypothesis that testosterone replacement in hypogonadal men would also improve their bone's mechanical properties. Ten untreated severely hypogonadal and 10 eugonadal men were selected. The hypogonadal men were treated with a testosterone gel for 24 mo to maintain their serum testosterone concentrations within the normal range. Each subject was assessed before and after 6, 12, and 24 mo of testosterone treatment by microMRI of the distal tibia. A subvolume of each microMR image was converted to a microfinite element (microFE) model, and six analyses were performed, representing three compression and three shear tests. The anisotropic stiffness tensor was calculated, from which the orthotropic elastic material constants were derived. Changes in microarchitecture were also quantified using newly developed individual trabeculae segmentation (ITS)-based and standard morphological analyses. The accuracy of these techniques was examined with simulated microMR images. Significant differences in four estimated anisotropic elastic material constants and most morphological parameters were detected between the eugonadal and hypogonadal men. No significant change in estimated elastic moduli and morphological parameters was detected in the eugonadal group over 24 mo. After 24 mo of treatment, significant increases in estimated elastic moduli E(22) (9.0%), E(33) (5.1%), G(23) (7.2%), and G(12) (9.4%) of hypogonadal men were detected. These increases were accompanied by significant increases in trabecular plate thickness. These results suggest that 24 mo of testosterone treatment of hypogonadal men improves estimated elastic moduli of tibial trabecular bone by increased trabecular plate thickness.

Ultrasound and the biomechanical competence of bone

Ultrasound is a mechanical wave and consequently has a unique potential to characterize the mechanical properties of bone. In some applications, such as determination of the anisotropic elastic constants of cortical bone specimens, this potential has been realized. In other applications, including the hugely important field of clinical measurements, current ultrasonic techniques struggle to provide information directly relating to mechanical properties. This article reviews the successes and shortcomings of ultrasound as a tool for determination of bone mechanical properties and highlights those new developments likely to bring progress in the future.

Elastic Constants of Co/Pt Superlattice Studied by Acoustic Measurements and Ab initio Calculations

The anisotropic elastic constants of Co/Pt superlattice thin films were measured by resonant ultrasound spectroscopy and picosecond laser ultrasound. The experimental results were compared with the ab initio calculations for perfect superlattices. The calculated out-of-plane elastic constant C33 is consistent with the measured value within 4%. However, the measured in-plane elastic constant C11 is smaller than the calculated value by 15–20%.

Residual Stress in α-Brass during Annealing

The evolution of residual stress and crystallographic texture during thermal treatment was studied using X-ray diffraction. Polycrystalline α-brass samples were examined after cold rolling and afterwards after annealing at different temperatures in the range of 50 0C - 450 0C. Additionally, the width of the diffraction peak was measured in order to estimate the variation of the dislocation density. The interpretation of experimental data was based on a fitting procedure for which the anisotropic diffraction elastic constants calculated by a self-consistent approach were used. As the result of analysis, the values of the first order and second order stresses were determined in each sample.

Microscale Characterization of Mechanical Properties

Lilliputian techniques for measuring the mechanical response of microscale specimens are being developed to characterize the performance and reliability of microelectromechanical systems (MEMS) and other small-scale entities. The challenges associated with the preparation, handling, and testing of small volumes of material have spawned a variety of techniques; this review focuses on uniaxial testing. Results from these experiments provide valuable insight into size-scale effects on the elastic, brittle, and ductile behavior of micron-sized structures. Fundamental elastic interactions show no size effect; in-plane moduli can be predicted from anisotropic elastic constants if crystallographic texture is properly considered. Intrinsic fracture toughness is also size independent, although the fracture strength of brittle MEMS materials is extremely dependent on flaw size and distribution. By contrast, size effects on the strength of ductile materials suggest that the operation of intrinsic dislocation processes in greatly reduced or confined volumes alters their generation, multiplication, interaction, and motion.

Phase Field Study for Self-Assemble of the Second Phase Particles in Coherent Phase Transition

We present a phase field model for coherent phase transition and its application to the self-assembled arrangement of second phase particles in coherent phase transition. The model developed here is free from the interface instability due to the contribution of chemical free energy and correctly describes elastically inhomogeneous system. It is observed that coherent misfit strain and anisotropy of elastic constants induce the interface instability that brings about the particle splitting and the self-assembled alignment of second phase particles. Their arrangement to the elastically soft direction occurs only in the system where the elastic contant of the precipitates is larger than that of the matrix phase.

Interpretation of Acoustic Parameters Obtained by EMAR Measurement for Non-destructive Hydrogen Concentration Measurement in Zr Alloy

An obvious quantitative relation between hydrogen concentrations in zirconium alloy and acoustic anisotropy parameters obtained by the electromagnetic acoustic resonance (EMAR) method was reported. To elucidate the mechanism, the acoustic parameters were calculated based on the elastic theory and the equation of motion. The acoustic parameters obtained by the EMAR method were interpreted quantitatively using the anisotropic elastic constants of the specimen, and values calculated from texture data for non-hydrogen charged specimens showed good agreement with those obtained by the EMAR method. Calculated temperature dependence of the acoustic anisotropy for the non-hydrogen charged specimen also agreed well with that by the EMAR method. The consistencies demonstrated that the absolute values of the acoustic parameters for non-hydrogen charged specimens can be calculated from both the texture data of (0002) pole figure and the elastic constants of the specimen. Hydrogen addition up to approximately 650 ppm was found not to change the original (0002) pole figure and, correspondingly, no hydrogen concentration dependence of the acoustic parameters was obtained from the calculation. These results implied that the zirconium hydride itself played an important role for the change in the acoustic parameters of the hydrogen charged specimens, and the importance of obtaining the information on the elastic constants of the zirconium hydride was pointed out.

Preferred orientation and elastic anisotropy of illite-rich shale

Shales display significant seismic anisotropy that is attributed in part to preferred orientation of constituent minerals. This orientation pattern has been difficult to quantify because of the poor crystallinity and small grain size of clay minerals. A new method is introduced that uses high-energy synchrotron X-rays to obtain diffraction images in transmission geometry and applies it to an illite-rich shale. The images are analyzed with the crystallographic Rietveld method to obtain quantitative information about phase proportions, crystal structure, grain size, and preferred orientation (texture) that is the focus of the study. Textures for illite are extremely strong, with a maximum of 10 multiples of a random distribution for (001) pole figures. From the three-dimensional orientation distribution of crystallites, and single-crystal elastic properties, the intrinsic anisotropic elastic constants of the illite aggregate (excluding contribution from aligned micropores) can be calculated by appropriate medium averaging. The illitic shale displays roughly transverse isotropy with [Formula: see text] close to [Formula: see text] and more than twice as strong as [Formula: see text]. This method will lend itself to investigate complex polymineralic shales and quantify the contribution of preferred orientation to macroscopic anisotropy.

Incremental recrystallization/grain growth driven by elastic strain energy release in a thermomechanically fatigued lead-free solder joint

A single shear lap solder joint specimen with lead-free eutectic Sn–Ag solder on copper substrates was exposed to 1500 thermomechanical fatigue (TMF) cycles between −15° (3.5 h) and 150 °C (20 min) to generate intrinsic thermal strains. The 0.15-mm-thick solder joint had a cross-sectional area of 1 mm 2. Orientation imaging microscopy was used to examine changes in the tin microstructure as a function of the number of TMF cycles. The tin phase consisted of embedded minority orientations within an initial dominant orientation, which varied by about 25° from one end of the joint to the other, by means of lattice curvature and low angle boundaries. Between about 150 and 750 cycles, an incremental recrystallization/grain growth process occurred where a minority solidification twin orientation grew and consumed the dominant initial orientation. An elastic FEM analysis incorporating anisotropic thermal expansion and elastic constants indicated that the final orientation had an internal stress state that was 20–100% smaller than the initial orientation, when subjected to a temperature change. The release of elastic strain energy provided the thermodynamic driving force for recrystallization/grain growth.

Interpretation of Acoustic Parameters Obtained by EMAR Measurement for Non-destructive Hydrogen Concentration Measurement in Zr Alloy

An obvious quantitative relation between hydrogen concentrations in zirconium alloy and acoustic anisotropy parameters obtained by the electromagnetic acoustic resonance (EMAR) method was reported. To elucidate the mechanism, the acoustic parameters were calculated based on the elastic theory and the equation of motion. The acoustic parameters obtained by the EMAR method were interpreted quantitatively using the anisotropic elastic constants of the specimen, and values calculated from texture data for non-hydrogen charged specimens showed good agreement with those obtained by the EMAR method. Calculated temperature dependence of the acoustic anisotropy for the non-hydrogen charged specimen also agreed well with that by the EMAR method. The consistencies demonstrated that the absolute values of the acoustic parameters for non-hydrogen charged specimens can be calculated from both the texture data of (0002) pole figure and the elastic constants of the specimen. Hydrogen addition up to approximately 650 ppm was found not to change the original (0002) pole figure and, correspondingly, no hydrogen concentration dependence of the acoustic parameters was obtained from the calculation. These results implied that the zirconium hydride itself played an important role for the change in the acoustic parameters of the hydrogen charged specimens, and the importance of obtaining the information on the elastic constants of the zirconium hydride was pointed out.

Influences of grain structure on thermally induced stresses in 3D IC inter-wafer vias

We discuss the development of a grain-continuum model to examine the effects of thermally induced stress in 3D IC inter-wafer vias. We demonstrate the approach using stress-driven grain boundary migration in polycrystalline copper films, assuming that migration is due to vacancy migration. The anisotropic elastic constants of single crystal Cu are used for each grain, after aligning them with each grain’s orientation. Stresses are thermally induced in a series of films, including one with a dominant texture surrounding a single grain. Grain boundary velocities are calculated from the fluxes of vacancies to grain boundaries. The computed velocities are then used to update the level sets that represent the grain boundaries using the PLENTE software.

Plastic strain-induced rafting of γ′ precipitates in Ni superalloys: Elasticity analysis

Rafting in Ni-based superalloys is investigated by examining the dependence of elastic energy on the shape and orientation of γ′ particles. The precipitation misfit strain and the plastic strain occurring in the matrix are taken into account. The elastic energies associated with spherical or disc-shaped particles with different orientations are evaluated for some combinations of transformation strain and matrix plastic strain. The anisotropy in elastic constants as well as the difference in elastic constant between the particles and matrix are taken into account. It is found that the elastic energy becomes minimum when γ′ particles adopt a certain shape and direction with respect to the elongation axis 〈0 0 1〉. These results are in agreement with the rafted morphologies observed in crept superalloys. The onset of the shearing of rafted γ′ particles, leading to accelerated creep of the alloy, is also discussed by examining the stress state of rafted γ′ particles.

Atomic composition profile change of SiGe islands during Si capping

The 6% Ge isocomposition profile change of individual SiGe islands during Si capping at 640°C is investigated by atomic force microscopy combined with a selective etching procedure. The island shape transforms from a dome to a {103}-faceted pyramid at a Si capping thickness of 0.32nm, followed by the decreasing of pyramid facet inclination with increasing Si capping layer thickness. The 6% Ge isocomposition profiles show that the island with more highly Si enriched at its one base corner before Si capping becomes to be more highly Si intermixed along pyramid base diagonals during Si capping. This Si enrichment evolution inside an island during Si capping can be attributed to the exchange of capped Si atoms that aggregated to the island by surface diffusion with Ge atoms from inside the island by both atomic surface segregation and interdiffusion rather than to the atomic interdiffusion at the interface between the island and the Si substrate. In addition, the observed Si enrichment along the island base diagonals is attempted to be explained on the basis of the elastic constant anisotropy of the Si and Ge materials in (001) plane.