The Young's modulus and Poisson's ratio of arsenic,antimony and bismuth

The orientational dependences of the Young's modulus and Poisson's ratio of the A7 structure elements arsenic, antimony, and bismuth are investigated, using available experimental data of the six elastic compliance constants. The behaviour of these technical elastic constants in antimony and bismuth is shown to differ not only in degree but also in kind from that of arsenic, which exhibits the characteristics expected of a layer-like crystal; arsenic is elastically a very anisotropic material, its Young's modulus varies by a factor as large as 11.3: the largest anisotropy ratio reported for a metallic element.     

Effect of microstructure on internal friction and Young's modulus of aged Cu–Be alloy

This study is intended to determine the effect of microstructure on internal friction and Young's modulus as a function of stress in the elastic region of an aged Cu–Be alloy and to investigate the influence of transformed phases caused by precipitation hardening on both properties. Results show that internal friction and Young's modulus were influenced by different precipitates. Transformed phases and micromechanical mechanisms could be responsible for the changes in internal friction and Young's modulus. The microstructure of the alloy having Guinier–Preston zones appears to have low internal friction and dependence on stress after aging at 315 °C for 2 h. The Young's moduli of the long-term aged samples increased by approximately 2 GPa compared to that for the short-term aged samples and elastic instability up to a stress of 20% of the yield strength was observed.     

Internal stress relaxation based method for elastic stiffness characterization of very thin films

Accurate measurement of the Young's modulus of films with thickness smaller than a few hundreds of nanometers remains extremely challenging. The present method disclosed here is based on the combined measurements of the internal stress using the Stoney method and of the corresponding elastic strain obtained by releasing microstructures. Experimental validation is presented for silicon nitride films. The Young's moduli of the 100, 300, and 500 nm-thick films are equal to 193 ± 20 GPa, 226 ± 22 GPa, and 208 ± 18 GPa, respectively, in good agreement with nanoindentation test results. This very simple method can potentially be used for much thinner films and extended to materials involving no internal stress.     

Nonlinear elastic equation of state of solids subjected to uniaxial homogeneous loading

Applying the finite deformation theory to a solid, which possesses either cubic or isotropic symmetry at stress-free natural state and is subsequently loaded homogeneously in uniaxial direction, one obtains a stress (or strain) dependence of the Young's modulus, Poisson's ratio, and a volume (or density) change, together with a nonlinear elastic relation between stress and strain. These are all expressed in terms of the second and third order elastic constants of the solid material. These expressions are illustrated with examples of cubic silicon crystal, isotropic carbon steel, Pyrex glass, and polystyrene at the relaxed state.     

Chirality-dependent anisotropic elastic properties of a monolayer graphene nanosheet

An analytical approach is presented to predict the elastic properties of a monolayer graphene nanosheet based on interatomic potential energy and continuum mechanics. The elastic extension and torsional springs are utilized to simulate the stretching and angle variation of carbon-carbon bond, respectively. The constitutive equation of the graphene nanosheet is derived by using the strain energy density, and the analytical formulations for nonzero elastic constants are obtained. The in-plane elastic properties of the monolayer graphene nanosheet are proved to be anisotropic. In addition, Young's moduli, Poisson's ratios and shear modulus of the monolayer graphene nanosheet are calculated according to the force constants derived from Morse potential and AMBER force field, respectively, and they were proved to be chirality-dependent. The comparison with experimental results shows a very agreement.     

Acoustic microscopy measurement of elastic constants and massdensity

A method is presented to determine the elastic constants and the mass density of isotropic and anisotropic solids and anisotropic thin films. The velocity and attenuation of leaky surface acoustic waves (SAWs) have been obtained for specified propagation directions from V(z) curves measured by line-focus acoustic microscopy (LFAM). The experimentally obtained velocities have been compared to velocities obtained from a measurement model for the V(z) curve which simulates the experiment. Since the measured and simulated V(z) curves have the same systemic errors, the material constants are free of such errors. For an isotropic solid, Young's modulus E, the shear modulus G and the mass density ρ have been determined from the leaky Rayleigh wave velocity and attenuation, measured by LFAM, and a longitudinal wave velocity measured by a pulse-echo transit-time technique. For a cubic-crystalline solid, the ratios of the elastic constants to the mass density (c₁₁ /ρ, c₁₂/ρ, c₄₄/ρ) have been determined from the directional variation of measured SAW velocities, using a preliminary estimate of ρ. The mass density ρ has subsequently been determined by additionally using the attenuation of leaky SAWs in crystal symmetry directions. For a cubic-crystalline thin film deposited on a substrate, the elastic constants and the mass density (c₁₁, c₁₂, c₄₄, ρ) of the film have been determined from the directional variation of the measured SAW velocities, and a comparison of the corresponding attenuation coefficient with the measured attenuation coefficient has been used to verify the results     

Effect of on-axis tensile loading on shear properties of an orthogonal 3D woven SiC/SiC composite

The present study examines in-plane and out-of-plane shear properties of an orthogonal 3D woven SiC fiber/SiC matrix composite. A composite beam with rectangular cross-section was subjected to a small torsional moment, and the torsional rigidities were measured using an optical lever. Based on the Lekhnitskii’s equation (Saint–Venant torsion theory) for a orthotropic material, the in-plane and out-of-plane shear moduli were simultaneously calculated. The estimated in-plane shear modulus agreed with the modulus measured from ±45° off-axis tensile testing. The effect of on-axis (0°/90°) tensile stress on the shear stiffness properties was also investigated by the repeated torsional tests after step-wise tensile loading. Both in-plane and out-of-plane shear moduli decreased by about 50% with increasing the on-axis tensile stress, and it is mainly due to the transverse crack propagation in 90° fiber bundles and matrix cracking in 0° fiber bundles. It was demonstrated that the torsional test is an effective method to estimate out-of-plane shear modulus of ceramic matrix composites, because a thick specimen is not required.     

Statistical analysis of ice fracture characteristics

This paper addresses the fracture toughness and strength characteristics of ice taken from Notoro Lagoon in the Okhotsk Sea close to Hokkaido. Experimental values of tensile and bending strengths, and fracture toughness of sea ice conformed to Weibull statistical distribution. The proposed model predicts variation in fracture toughness as a function of the statistical distribution of ice grain sizes, effective surface energy, and elastic constants of ice. A very good agreement between experimental cumulative probability of fracture toughness and predicted distribution of fracture toughness of sea ice has been found. Computing the Weibull stress of sea ice, the dependence of fracture probability on stress intensity factor has been established. This result is in very good agreement with the presented method for the prediction of fracture toughness of sea ice.     

Temperature-dependent Young's modulus of an SiCw/Al2O3 composite

Using a computer-controlled resonant-bar apparatus at frequencies near 5 kHz, we determined the temperature-dependent (86–732 K) Young's modulus of a ceramic-ceramic composite with a 0.30 volume fraction of SiC whiskers in an Al₂O₃ matrix. Using a megahertz-frequency pulse-echo method, it was verified that the composite shows little anisotropy (variation of the elastic properties with direction). Using a scattered-plane-wave ensemble-average method, we modelled the ambient-temperature elastic constants and found good model-observation agreement. To model the behaviour of the Young's modulus with temperature, Varshni's three-parameter relationship for Einstein-oscillator monocrystals was used. Again, good model-observation agreement was found. The mechanical-loss spectrum showed no remarkable features, indicating good whisker-matrix interface properties up to 732 K.     

Microstructures and properties of biomedical TiNbZrFe β-titanium alloy under aging conditions

A metastable β-titanium alloy Ti–28Nb–13Zr–0.5Fe (TNZF alloy for short) was designed for implant biomedical application. The forged specimens were solute-treated at 850 °C followed by water quenching and then aged at 350 °C, 450 °C, and 550 °C for 2–6 h in order to evaluate the effect of phase transformation during ageing on the biomechanical compatibility of the alloy. The quenched microstructure consists of lath α″ martensite and β phase. A large quantities of shuttle-like ω phase precipitate at 350 °C, leading to the drastic increase of strength and elastic modulus and the decrease of plasticity. Ageing at 450 °C for 4 h, small amount of elliptic ω phase and dot α phase precipitate from β matrix. With increasing ageing time α precipitations begin to coarsen and precipitation free zones (PFZs) form around prior β grain boundaries. Needle-like α phase precipitates on grain boundaries and intra-grains when aged at 550 °C. Both PFZs and grain boundary α precipitates are prone to bring about the intergranular fracture and thus have adverse effects on the tensile strength and fracture plasticity. The quenched microstructure has good combination properties of high strength, high plasticity and low elastic modulus.     

Electronic structure and mechanical properties of layered compound YB_2C_2:A promising precursor for making two dimensional(2D) B_2C_2 nets

Layered compounds play pivotal roles as precursors for producing 2D materials through mechanical exfoliation(micro-mechanical cleavage) or chemical approaches. Therefore, searching for layered compounds with sharp anisotropic chemical bonding and properties becomes emergent. In this work, the stability, electronic structure, elastic properties, and lattice dynamics of YB_2C_2 were investigated. Strong anisotropy in elastic properties is revealed, i.e., high Young's modulus in a-b plane but low Young's modulus in c direction. The maximum to minimum Young's modulus ratio is 2.41 and 2.45 for YB_2C_2 with P42/mmc and P4/mbm symmetry, respectively. The most likely systems for shear sliding or microdelaminating are(001)[100] and(001)[010]. The anisotropic elastic properties are underpinned by the anisotropic chemical bonding, i.e., strong bonding within the B_2C_2 nets and weak bonding between Y atom layers and B_2C_2 nets. YB_2C_2 is electrically conductive and the contributions to the electrical conductivity are from delocalized Y 4de_g as well as B _2p_z and _ pzelectrons. The layered crystal structure, sharp anisotropic mechanical properties, and metallic conductivity endorse YB_2C_2 promising as a precursor for new 2D B_2C_2 nets.     

Stress in Thin Films;Diffraction Elastic Constants and Grain Interaction

Untextured bulk polycrystals usually possess macroscopically isotropic elastic properties whereas for most thin films transvers isotropy is expected,owing to the limited dimenionlity .The usually applied models for the calculation of elstic constants of polycrystals from single crystal elastic contants(so-called grain interaction models)erroneously predict macroscopic isotropy for an(untextured) thin film.This paper presents a summary of recent work where it has been demonstrated for the first time by X-ray diffraction analysis of stresses in thin films that elastic grain interaction can lead to macroscopically anisotropic behaviour (shown by non-linear sin^2φ plots).A new grain interaction model,predictin the macroscopically anisotropic behaviour of thin films,is proposed.     

Influence of sintering temperatures on hardness and Young''s modulus of tricalcium phosphate bioceramic by nanoindentation technique

Nanoindentation experiments on tricalcium phosphate (TCP) bioceramic sintered at different temperatures were performed with a Berkovich indenter for determining hardness and elastic modulus from load and displacement data. The hardness and Young's modulus increased with the increase of sintering temperature up to 1300 °C, but the Young's modulus decreased with the further increase of sintering temperatures at 1400 and 1500 °C. X-ray diffraction (XRD) results showed that the transformation β→-TCP happened when the sintering temperature reached around 1400 °C, which contributed to the decreases of modulus at 1400 and 1500 °C. Scanning electron microscopy (SEM) results showed that the sintering effect was improved with the increase in sintering temperature.     

Low-temperature manganese contributions to the elastic constants of face-centred-cubic Fe-Cr-Ni stainless steel

By ultrasonic methods, we determined the elastic constants between 295 and 4 K of nominally Fe-18Cr-8Ni alloys (in wt%) containing up to 6% manganese. We report five elastic constants:C ₁ = longitudinal modulus,B = bulk modulus,E = Young modulus,G = shear modulus, and v = Poisson ratio. At all temperatures, manganese lowers all these elastic constants. With the exception of v, larger reductions occur at 4 K than at 295 K. At 4 K, the bulk modulus decreases more than the shear modulus: approximately 0.54 and 0.30% per per cent manganese, respectively. Manganese raises the magnetic-transition temperature, which occurs between 40 and 90 K, by approximately 9 K per per cent manganese. A simple model predicts the volume increase accompanying Mn alloying. However, a simple model fails to predict the elastic-constant reductions; this suggests magnetic interatomic interactions.     

Measurement and analysis of elastic and anelastic properties of alumina and silicon carbide

Measurements of dynamic Young's modulus, E, and damping as a function of temperature, T, were made for alumina and silicon carbide. The Young's modulus data were compared with some from the literature, and analysed in terms of a theoretical framework relating the Debye temperature, θD, with the elastic constants. For both materials this analysis yielded a ratio T₀/θ_D which was near 0.4, where T₀ is an empirical fitting constant for the plot of (E(0)−E)/T versus 1/T (E(0) is the value of E at 0 K). The analysis of the damping data in terms of an Arrhenius type dependence led to effective activation energies near kT, where k is Boltzmann's constant. This revised version was published online in November 2006 with corrections to the Cover Date.     

The technical constants of some cubic and non-cubic materials

The elastic constants (technical constants) for some polycrystalline materials of cubic and non-cubic (hexagonal, tetragonal, trigonal and orthorhombic) symmetry have been computed by a new averaging scheme involving the squared reciprocal sound velocities. The computed values are compared with those from the averaging scheme of Hill. An examination of the data reveals that the predictions for the shear modulus and Young's modulus of cubic materials agree with those of Hill within 0.01% and 0.5%, respectively, while the new scheme overestimates the values of the bulk modulus for cubic materials by 3.8% on average. For the non-cubic materials, the predicted values of shear modulus, Young's modulus and bulk modulus are within 2.7%, 0.3% and 13.5%, respectively, of Hill's values.     

具有球形胞体结构的泡沫塑料弹性常数的确定

通过微分法导出了泡沫塑料剪切模量和体积模量所满足的微分方程组，并利用泡沫塑料各向同性弹性常数间满足的关系求解；得到了泡沫塑料剪切模量与体积模量的关系，确定了剪切模量与材料孔隙比的关系；并且将本文结果同其他已有模型了对比。     

Elastic properties of lanthanum gallogermanate glasses

Room temperature ultrasonic velocities of eight lanthanum gallogermanate glasses were determined by pulse-echo technique. The results indicate that both longitudinal and transverse velocities of these glasses are composition dependent. The density and index of refraction of the samples were also studied. The experimental results were used to obtain elastic constants. The measured values of Young's modulus and bulk modulus for our glasses show good agreement with the theoretically calculated results based on the model of Makishima and Mackenzie.     

Saint-Venant's principle for two-dimensional anisotropic elasticity

Summary A self-equilibrated system of forces acting in a small region of an elastic solid results in a strain energy density that decreases rapidly as the distance from the loaded region increases. If the set of forces is in astatic equilibrium, the strain energy density decreases more rapidly than if the forces are merely self-equilibrated. For an anisotropic solid, there is a small rate-of-decrease of strain energy density in the direction where Young's modulus is the largest. The effect of anisotropy on the distribution of radial displacements is much more exagerated in the direction where the modulus is large than is the case for stress or strain energy density. These results are pertinent to applications of Saint-Venant's principle in the case of anisotropic solids; e.g. structures made from a unidirectional fibrous composite.     

等离子喷涂热障涂层材料弹性模量与硬度的压痕测试分析

采用纳米压痕法,研究了经高温热循环处理后的等离子喷涂热障涂层材料弹性模量和硬度的抛物线式演变规律,并采用 Weibull统计分析方法对纳米压痕测试数据进行了处理和分析,提高了实验数据的可靠性.结果表明,经过高温热循环处理之后,不同位置处的热障涂层弹性模量和硬度都呈现出明显的各向异性分布.随着热循环次数的增加,涂层表面和...