On the use of hollow tube geometries for resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) can nondestructively obtain the elastic constants of compact specimens, however many materials have hollow cross-sections and frequency analysis of such geometries is required before inclusion in the RUS methodology. Resonant mode shapes of tubes with length equal to diameter and varying ratios of tube inner to outer diameter (Λ) as well as Poisson's ratio (ν) were identified by eigenvalue analysis using a commercial finite element code. Longitudinal and shear RUS experiments were conducted on tubes with Λ varying between 0 and 0.95 and compared to the numerical results. Simulations predict that the fundamental mode transitions from pure torsion to symmetric or antisymmetric ring bending at Λ = 0.3. The frequency of the first torsion mode is invariant to Λ and unequivocal identification of this mode is obscured by overlap of bending harmonics as Λ approaches 0.95. In the context of rapid calculation of isotropic elastic constants, shear moduli were calculated from the first torsional mode and Poisson's ratio was inferred from the Demarest maps of the mode structure's dependence upon Poisson's ratio. An average shear modulus of 27.5 + 1.5 ∕ -0.6 GPa, about 5% larger than literature values for 6061 aluminum, and ν of 0.33 were inferred. Errors are attributed to tube aspect ratios slightly greater than 1 and weak material anisotropy. Existing analytical solutions for ring bending modes derived from shell approximations and for infinitely long tubes under plane strain assumptions do not adequately describe the fundamental modes for short tubes. The shear modulus can be calculated for all Λ using the existing analytical solution.     

First-principles study on electronic structure and elastic properties of Ti2SC

We have performed first-principles study on electronic structure and elastic properties of Ti₂SC. The absence of band gap at the Fermi level and the finite value of the density of states at the Fermi energy reveal the metallic behavior of this compound. The five independent elastic constants were derived and the bulk modulus, Young's modulus, shear modulus, and Poisson's ratio were determined. The high bulk modulus and hardness was found to be originated from the strong Ti 3d-S 2p hybridization. Such strong MA bonding is unusual in the MAX phases studied so far. Ti₂SC is elastically stable and exhibits highly elastic isotropy.     

Combining Brillouin spectroscopy and laser-SAW technique for elastic property characterization of thick DLC films

Surface Brillouin spectroscopy (SBS) has been widely used for elastic property characterization of thin films. For films thicker than 500 nm, however, the wavelength of surface acoustic wave in the frequency range available for SBS is smaller than film thickness, and the SBS measures only the Rayleigh wave of the film. The laser-SAW technique, on the other hand, measures only the low-frequency portion of the surface acoustic wave dispersion and can estimate only one elastic modulus of the film (typically Young's modulus). In this work, we have combined the two methods to determine both Young's modulus and Poisson's ratio of a diamond-like carbon (DLC) film. It was found that reasonable estimates can be obtained for the longitudinal wave velocity, shear wave velocity, and Young's modulus of the film. The Poisson's ratio, however, still has a relatively large measurement error.     

二元Ni-Al合金极端条件下的弹性和热力学性能：全电子准谐波近似 cited: 1)

通过在原子尺度上建模来研究Al、NiAl和Ni₃Al合金在极端高温和高压下的点阵常数、弹性常数、弹性模量、泊松比和弹性各向异性因子等性质．计算得到的弹性常数均满足相应的力学稳定条件．由于NiAl和Ni₃Al具有较高的B=G值,在0～30 GPa内都属于延展性材料．通过包含电子热运动对体系吉布斯自由能贡献的全电子准谐近似方法,得到了高温高压下Al、NiAl和Ni₃Al合金的热膨胀系数、体积模量、热容和熵等．计算值与已有的实验值和理论值符合较好     

Elastic characterization of closed cell foams from impedance tube absorption tests

A method is presented to determine the bulk elastic properties of isotropic elastic closed-cell foams from impedance tube sound absorption tests. For such foams, a resonant sound absorption is generally observed, where acoustic energy is transformed into mechanical vibration, which in turn is dissipated into heat due to structural damping. This article shows how the bulk Young's modulus, Poisson's ratio, and damping loss factor can be deduced from the resonant absorption. Also, an optimal damping loss factor yielding 100% of absorption at the first resonance is defined from the developed theory. The method is introduced for a sliding edge condition which is an ideal condition. Then, the method is extended to a bonded edge condition which is more easily achievable and additionally enables the identification of the Poisson's ratio. The method is experimentally tested on expanding closed-cell foams to find their elastic properties in both cases. Using the found properties, sound absorption predictions using an equivalent solid model with and without surface absorption are compared to measurements. Good correlations are obtained when considering surface absorption.     

Ground-State Structure and Physical Properties of NB_2 Predicted from First Principles

Using the newly developed particle swarm optimization algorithm on crystal structural prediction,we predict a new class of boron nitride with stoichiometry of NB_2 at ambient pressure,which belongs to the tetragonal I4m2 space group.Then,its structure,elastic properties,electronic structure,and chemical bonding are investigated by first-principles calculations with the density functional theory.The phonon calculation and elastic constants confirm that the predicted NB_2 is dynamically and mechanically stable,respectively.The large bulk modulus,large shear modulus,large Young's modulus,and small Poisson's ratio show that the I4m2 NB_2 should be a new superhard material with a calculated theoretical Vickers hardness value of 66 GPa.Further analysis on density of states and eiectron localization function demonstrate that the strong B-B and B-N covalent bonds are the main reason for its high hardness in I4m2 NB_2.     

Determination of elastic modulus of a beam by using electronic speckle pattern interferometry

This paper proposes a sonic resonance test for an elastic modulus measurement which is based on the electronic speckle pattern interferometry. Previous measurement technique of elastic constant has the limitation of application for thin film or polymer material because contact to specimen affects the result. It has been developed as a non-contact optical measurement technique which can visualize resonance vibration mode shapes with whole field. The maximum vibration amplitude at each vibration mode shape is a clue to find the resonance frequencies. The dynamic elastic constant of test material can be easily determined from vibration of a beam equation using the measured resonance frequencies. The proposed technique is able to give high accurate elastic modulus of materials through a simple experimental set-up and analysis. The experimental result also compared to the theoretical result.     

Measurement of the elastic moduli of dense layers of oriented carbon nanotubes by a scanning force microscope

A technique is developed for measuring the modulus of elasticity of a material with a Nanoscan scanning force microscope on the basis of measuring the dependence of probe vibration frequency on the penetration depth of the needle into the specimen. This technique makes it possible to study materials with elastic moduli from 50 to 1000 GPa. The Young moduli of dense films of carbon nanotubes oriented at angles of 45° and 90° to the quartz substrate are measured. From their ratio, the Young modulus in the direction perpendicular to the tubes and the anisotropy of the elastic moduli are determined. A comparison of these values with the corresponding values obtained for a nanotube film deposited on a silicon substrate is carried out. On the basis of this comparison, a conclusion is made concerning the interaction between single-layer nanotubes and between nanotubes in a mixture of single-layer and multilayer ones.     

A Comprehensive Numerical Investigation on the Mechanical Properties of Hetero-Junction Carbon Nanotubes

A set of forty-three hetero-junction CNTs, made of forty-four homogeneous carbon nanotubes of different chiralities and configurations with all possible hetero-connection types, were numerically simulated, based on the finite element method in a commercial finite element software and their Young's and shear moduli, and critical buckling loads were obtained and evaluated under the tensile, torsional and buckling loads with an assumption of linear elastic deformation and also compared with each other. The comparison of the linear elastic behavior of hetero-junction CNTs and their corresponding fundamental tubes revealed that the size, type of the connection, and the bending angle in the structure of hetero-junction CNTs considerably influences the mechanical properties of these hetero-structures. It was also discovered that the Stone-Wales defect leads to lower elastic and torsional strength of hetero-junction CNTs when compared to homogeneous CNTs. However, the buckling strength of the hetero-junction CNTs was found to lie in the range of the buckling strength of their corresponding fundamental tubes. It was also determined that the shear modulus of hetero-junction carbon nanotubes generally tends to be closer to the shear modulus of their wider fundamental tubes while critical buckling loads of these heterostructures seem to be closer to critical buckling loads of their thinner fundamental tubes. The evaluation of the elastic properties of hetero-junction carbon nanotubes showed that among the hetero-junction models, those with armchair-armchair and zigzag-zigzag kinks have the highest elastic modulus while the models with armchair-zigzag connections show the lowest elastic stiffness. The results from torsion tests also revealed the fact that zigzag-zigzag and armchair-zigzag hetero-junction carbon nanotubes have the highest and the lowest shear modulus, respectively. Finally, it was observed that the highest critical buckling loads belong to armchair-armchair hetero-junction carbon nanotubes and the lowest buckling strength was found with the hetero-junction models with armchair-zigzag connection.     

Ab initio calculation of elastic properties of rock-salt and zinc-blend MgS under pressure

The elastic properties of zinc-blend (ZB) and rock-salt (RS) MgS are calculated by ab initio method. The calculation shows that the enthalpy for RS structure and for ZB structure essentially is the same at ambient pressure. The ZB structure becomes unstable above 5 GPa. For these two structures, the pressure dependences of typical elastic properties, i.e. the bulk modulus, the shear modulus, the Young's modulus, the Poisson's ratio, and the anisotropy factor, are presented. The Debye temperature and sound velocity under high pressure have also been calculated. Debye approximation is used to estimate the zero-point vibrational energy.     

Structural,Elastic, and Electronic Properties of a New Phase of Carbon

Based on density function theory with the ultrasoft pseudopotential scheme in the frame of the local density approximation and the generalized gradient approximation, the structural, elastic, and electronic properties of carbon with P222₁ phase have been systematically studied in this paper. The calculated results show that the P222₁ phase of carbon is mechanically stable and dynamically stable at ambient pressure. The anisotropy studies of Young's modulus, Poisson's ratio, shear anisotropic factor, the percentage of elastic anisotropy for bulk modulus, the percentage of elastic anisotropy for shear modulus and the universal anisotropic index show that P222₁ phase of carbon exhibits anisotropy. In addition, P222₁ phase is an indirect semiconductor with bandgap of 3.423 eV. But, the band gap of P222₁ phase for carbon increase with increasing pressure.     

Theoretics-directed effect of copper or aluminum content on the ductility characteristics of Al-based(Al_3Ti,AlTi,AlCu,AlTiCu_2)intermetallic compounds

First-principle simulations have been applied to investigate the effect of copper(Cu) or aluminum(Al) content on the ductility of Al_3Ti,AlTi,AlCu,and AlTiCu_2 alloys.The mechanical stable and elastic properties of Al-based intermetallic compounds are researched by density functional theory with the generalized gradient approximation(DFT-GGA).The calculated lattice constants are in conformity with the previous experimental and theoretical data.The deduced elastic constants show that the investigated Al_3Ti,AlTi,AlCu,and AlTiCu_2 structures are mechanically stable.Shear modulus,Young's modulus,Poisson's ratio,and the ratio B/G have also been figured out by using reckoned elastic constants.A further analysis of Young's modulus and Poisson's ratio reveals that the third added element copper content has significant effects on the Al-Ti-based ICs ductile character.     

Elastic properties and electronic structures of lanthanide hexaborides

The structural, elastic, and electronic properties of a series of lanthanide hexaborides(Ln B6) have been investigated by performing ab initio calculations based on the density functional theory using the Vienna ab initio simulation package.The calculated lattice and elastic constants of Ln B6 are in good agreement with the available experimental data and other theoretical results. The polycrystalline Young's modulus, shear modulus, the ratio of bulk to shear modulus B/G, Poisson's ratios, Zener anisotropy factors, as well as the Debye temperature are calculated, and all of the properties display some regularity with increasing atomic number of lanthanide atoms, whereas anomalies are observed for Eu B6 and Yb B6. In addition, detailed electronic structure calculations are carried out to shed light on the peculiar elastic properties of Ln B6.The total density of states demonstrates the existence of a pseudogap and indicates lower structure stability of Eu B6 and Yb B6 compared with others.     

Dynamic torsion of a two-layer viscoelastic beam

The complex dynamic shear modulus of soft polymeric materials may be determined in principle at low and audio frequencies from torsion pendulum and torsional resonance experiments on metal strips coated with the polymer. In order to determine the polymer shear properties from such experiments, it is necessary to know the torsional rigidity of the two-layer compound beam. This is calculated in the paper by using classical elasticity theory, for the particular case when the metal shear modulus is much greater than that of the soft coating. The theory of dynamic torsion tests is then briefly reviewed and experiments are suggested for determining the polymer dynamic shear properties. A discussion is also given of the effectiveness of polymer coatings as a damping treatment for torsional vibrations.     

Structural and elastic properties of antiperovskites XNBa3 (X=As, Sb) under pressure effect

First-principle calculations of structural, elastic and high pressure properties of antiperovskites XNBa₃ (X=As, Sb) are performed, using the full-potential linear muffin-tin orbital (FP-LMTO) method. The local density approximation (LDA) is used for the exchange-correlation (XC) potential. Results are given for lattice constant, bulk modulus and its pressure derivatives. We have determined the elastic constants C₁₁, C₁₂ and C₄₄ and their pressure dependence. We derived shear moduli, Young's modulus, Poisson's ratio and Lamé's constants for ideal polycrystalline XNBa₃ aggregates. By analyzing the ratio of the bulk to shear moduli, we conclude that XNBa₃ compounds are brittle in nature. We estimated the Debye temperature of XNBa₃ from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of AsNBa₃ and SbNBa₃ compounds, and it still awaits experimental confirmation.     

Resonance method of measuring shear viscoelastic properties of liquid media based on excitation of torsional oscillations in tubes

Possibilities of using torsional oscillations for measuring viscoelastic properties of liquids are discussed. The theory of torsional oscillations of an elastic tube filled with the media to be investigated possessing viscosity and shear elasticity is developed. It is shown that to determine a complex shear modulus it is sufficient to determine the resonance frequency and Q-factor of torsional oscillations. An experimental installation and the results of measurements of viscoelastic modulus of glycerin and oil of one oilfield within the temperature range from −10° to 60°C are given. The experimental installation allows measuring a viscoelastic modulus within the range of acoustic logging frequencies (10–20 kHz). The obtained results are compared with the results of rheometric measurements.     

Phase transition, elastic, thermodynamic properties of zinc-blend BeSe from first-principles

The structural phase transition, elastic, thermodynamics properties of BeSe in zinc-blende were investigated by performing first-principles calculations within generalized gradient approximation. The phase transition pressure P_t between the B3 phase and the B8 phase of BeSe was determined. The pressure dependencies of elastic constants, shear modulus, Young's modulus, and Poisson's ratio of BeSe are calculated. The thermodynamic properties of the zinc-blende structure BeSe are calculated by using the quasi-harmonic Debye model. The pressure and temperature dependencies of the heat capacity and the thermal expansion coefficient, as well as the Grüneisen parameter are investigated systematically in the ranges of 0–50 GPa and 0–1200 K.     

L12型铝合金的结构、弹性和电子性质的第一性原理研究

运用第一性原理方法研究了L12型铝合金相Al3Sc和Al3Zr的晶体结构、电子结构和弹性.结合能和形成能的计算表明,两种合金具有较强的合金化能力,且Al3Zr较Al3Sc具有更强的结构稳定性.电子结构分析表明,费米能级以下较多的价电子数决定了Al3Zr具有较强的结构稳定性.计算并分析比较了两种合金相的单晶弹性常数(C11,C12和C44)以及多晶弹性模量(体弹性模量B、剪切模量G、杨氏模量Y、泊松比ν和各向异性因子A).通过对比实验和其他理论计算结果,进一步分析和解释了两种合金相的力学性质.     

Pressure-driven "molecular metal" to "atomic metal" transition in crystalline Ga

We present the ultrasonic study of gallium (Ga I) under high pressure up to 1.7 GPa, including the measurements of the density and elastic properties during phase transitions to Ga II and to a liquid state. The observed large drop of both bulk and shear moduli (by 30% and 55%, correspondingly) during the phase transition to Ga II, as well as the increase of the Poisson's ratio from typically "covalent" ( approximately 0.22) to "metallic" ( approximately 0.32) values, experimentally testifies to the coexistence of a molecular and metallic behavior in Ga I and to the disappearance of the "covalency" during the transition to Ga II. A high value of the pressure derivative of the bulk modulus for Ga I and the increase in the Poisson's ratio can be associated with the weakening of the covalency in compressed Ga I and considered as a precursor of the transition to normal metal.