Young's modulus surface and Poisson's ratio curve for cubic metals

The general expressions for the compliance , Young's modulus E(h k l) and Poisson's ratio υ(h k l, θ) along arbitrary loading direction [h k l] are given for cubic crystals. The representation surface for which the length of the radius vector in the [h k l] direction equals to E(h k l) and representation curve for which the length of the radius vector with angle θ deviated from the reference directions , and equals to υ(100, θ), υ(110, θ) and υ(111, θ) for example, are constructed for six FCC metals Ag, Al, Au, Cu, Ni, Pb and seven BCC metals Cr, Fe, Mo, Nb, Ta, V, W.     

Resonant ultrasound spectroscopy measurement of Young's modulus,shear modulus and Poisson's ratio as a function of porosity for alumina and hydroxyapatite

Modulus–porosity relationships are critical for engineered bone tissue scaffold materials such as hydroxyapatite (HA), where porosity is essential to biological function. Resonant ultrasound spectroscopy (RUS) measurements revealed that the Young's modulus, E, and shear modulus, G, of both alumina and HA decrease monotonically with increasing volume fraction porosity, P, for 0.06 < P < 0.39 (alumina) and 0.05 < P < 0.51 (HA). Although the elastic moduli of porous materials have been measured by a number of different ultrasonic resonance techniques (of which the RUS technique is one example) and over the last decade the elastic moduli of many solids have been measured by the RUS technique, this study is the first systematic RUS study of porous materials. Comparison of E versus P data for alumina (which has been studied extensively) with literature data from several measurement techniques indicates the RUS technique is effective for modulus–porosity measurements. Another key result is that although the HA specimens included in this study have a unimodal pore size distribution, the details of the decrease in E and G with increasing P agree well with literature data for HA with both unimodal and bimodal pore size distributions. In addition, Poisson's ratio exhibits a local minimum in the porosity range of 0.2 < P < 0.25 for both HA and alumina, which may be related to the pore morphology evolution during sintering.     

Determination of Young's modulus of epoxy coated polyethylene micro-cantilever using phase-shift shadow moiré method

Young′s moduli of various epoxy coated polyethylene terephthalate (PET) micro-cantilevers were determined from the deflection results obtained using the phase-shift shadow moiré (PSSM) method. The filler materials for epoxy coatings were aluminum and graphite powders that were mixed with epoxy at various percentages. Young′s moduli were calculated from theory based on the deflection results. The PET micro-cantilever coated with aluminum-epoxy coating showed increasing value of Young′s modulus when the ratios of the aluminum-epoxy were increased. The graphite-epoxy coating on the PET micro-cantilever also showed the same trend. The experimental results also show that Young′s modulus of the graphite-epoxy coating is higher than aluminum-epoxy coating in comparison at the same mixing ratio.     

Determination of silicone coating Young's modulus using atomic force microscopy

The polymerisation degree of thin polymer coatings was checked by following the variation of their local mechanical properties. Atomic force microscope (AFM) was used in an indentation mode to investigate the mechanical characteristics of silicone coatings on polycarbonate substrates. The evolution of Young's modulus of the silicone coatings was determined as a function of the polymer annealing time. We have used a relative method to measure Young's moduli, which involves a calibration step with a set of reference polymers. No variation was observed for the modulus of silicone coatings annealed during more than 40 min at 130 °C. This result indicates that over-heating does not modify the mechanical properties of the coating.     

Anisotropy of Young's modulus,shear modulus,and Poisson's ratio for the B2-phase of a Ti50Ni48Fe2 single crystal under hydrostatic compression conditions up to 0.6 GPa

We present calculations of Young's modulus, the shear modulus, and Poisson's ratio as a function of direction in the (100) and (110) planes of the B2 phase of a Ti₅₀Ni₄₈Fe₂ single crystal. The calculations were done on the basis of our measurements of the velocities of transverse and longitudinal ultrasonic waves propagating in the indicated alloy at atmospheric pressure and for a hydrostatic pressure of 0.6 GPa at a temperature of 298 K. We have shown that in contrast to the effect of temperature, as the pressure is reduced along the pathway to the martensitic transformation B2 R, application of pressure to the alloy found in the same pretransitional state increases the anisotropy of the crystal lattice.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 45–49, March, 1995.     

Determination of Poisson's ratio of solid circular rods by impact-echo method

A new and quick approach is proposed to evaluate Poisson's ratio of materials with only the measured longitudinal and cross-sectional resonance frequencies from the impact-echo test on a solid circular rod of known dimension. Both the longitudinal and guided wave propagation theories are used to derive the required equations through regression analysis. Procedure to verify the adequate length of solid rod specimen to obtain a valid Poisson's ratio is described. Experimental data of four materials, concrete, steel, stainless steel and brass, illustrated with the proposed approach show satisfactory results.     

单层石墨烯杨氏模量的理论模型

石墨烯力学性能的研究对其在半导体技术中的应用是十分重要的,本文基于半连续体模型并结合石墨烯纳米结构特性,通过对原子的描述构建了石墨烯形变分量和位移分量的新关系,从而给出了单层石墨烯结构形变能,并计算了不同尺寸单层石墨烯的杨氏模量值.通过对不同方向杨氏模量的分析,讨论了单层石墨烯的手性行为.结果表明:随着尺寸的增加,单层石墨烯两个方向的杨氏模量分别趋于0.746 TPa和0.743 TPa,当尺寸相同时,两方向杨氏模量的最大差值不超过0.003 TPa,此结果与文献报道结果相符.在小应变情况下,单层石墨烯薄膜呈各向同性,且薄膜尺寸变化对该特性影响不大.该计算结果对研究石墨烯的其它力学特性提供一定的参考价值.     

杨氏弹性模量测量仪的改进

测定杨氏弹性模量的实验是大学物理实验课的重要实验之一,通过反复多次的实验探索,对杨氏弹性模量测量仪的关键性组件——光杠杆进行了有效改进从而彻底消除了光杠杆易翻落摔坏的隐患,使更换镜片方便,反射像十分易于寻找,实验效果非常明显.     

Size dependence of Young's modulus in ZnO nanowires

We report a size dependence of Young's modulus in [0001] oriented ZnO nanowires (NWs) with diameters ranging from 17 to 550 nm for the first time. The measured modulus for NWs with diameters smaller than about 120 nm is increasing dramatically with the decreasing diameters, and is significantly higher than that of the larger ones whose modulus tends to that of bulk ZnO. A core-shell composite NW model in terms of the surface stiffening effect correlated with significant bond length contractions occurred near the {1010} free surfaces (which extend several layers deep into the bulk and fade off slowly) is proposed to explore the origin of the size dependence, and present experimental result is well explained. Furthermore, it is possible to estimate the size-related elastic properties of GaN nanotubes and relative nanostructures by using this model.     

Optical measurement of Young's modulus of a micro-beam

This paper presents an optical method based on the interference of light beams of equal path difference for the measurement of the Young's modulus of a micro-beam. An optical wedge which consists of an optical plate and a micro-beam which forms part of a micro-accelerometer is illuminated by a collimated monochromatic sodium light beam. Loading on the micro-beam is accomplished by a loading-pin mounted on a three-axis translation stage and the resulting interference fringe pattern is observed using a CCD camera connected to a computer. Loadings are recorded using a high-sensitive load cell which measures loads of up to 200 g with a resolution of 0.01 g. Test results conducted on micro-beams of different sizes show good repeatability and comparison of the experimental results with theory shows good agreement.     

Magneto-phonon contribution into the Young's modulus of gadolinium

Theoretical and experimental investigation has been made of the magnetic contribution to the Young's modulus of rare earth ferromagnet gadolinium. Experimental study includes measurements of the Young's modulus as a function of temperature, magnetic field and magnetization of gadolinium. Theoretical analysis is based on the account of phonon anharmonicity which gives rise to the dependence of Debye temperature on magnetization. Spontaneous magnetic contribution to the Young's modulus of Gd is found to be proportional to the squared magnetization of the metal. The magnetic contribution is also induced by magnetizing magnet due to the paraprocess. Received: 9 April 1996 / Revised: 26 January 1998 / Accepted: 26 February 1998     

Thermal stability and Young's modulus of mechanically exfoliated flexible mica

In recent years, mica has been successfully used as a substrate for the growth of flexible epitaxial ferroelectric oxide thin films. Here, we systematically investigated the flexibility of mica in terms of its thickness, repeated bending/unbending, extremely hot/cold conditions, and successive thermal cycling. A 20-μm-thick sheet of mica is flexible even up to the bending radius of 5 mm, and it is durable for 20,000 cycles of up- and down-bending. In addition, the mica shows flexibility at 10 and 773 K, and thermal cycling stability for the temperature variation of ca. 400 K. Compared with the widely used flexible polyimide, mica has a significantly higher Young's modulus (ca. 5.4 GPa) and negligible hysteresis in the force-displacement curve. These results show that mica should be a suitable substrate for piezoelectric energy-harvesting applications of ferroelectric oxide thin films at extremely low and high temperatures.     

Processing dependence of Young's modulus of Ti-base nanostructured alloys

The cooling rate and heat treatment dependence of Young's modulus for Ti-base multicomponent nanostructure-dendrite composites exhibits a very different response compared with the monolithic nanostructured or normal grain-sized Ti alloys. With increasing cooling rate, the decrease in the volume fraction of the micrometer-sized β-phase dendrites induces a significant increase in Young's modulus for most of these composites. This increase can cover the decrease in Young's modulus induced by the reduction of grain size of the nanostructured matrix. Heat treatment induces a significant increase in Young's modulus due to the precipitation of intermetallics and/or α-phase in the nanostructured matrix.     

Measurement of Poisson's ratio using Newton's rings

A simple optical method of measuring Poisson's ratio is reported. It is most applicable to polymer spheres in circumstances where conventional nondestructive testing is not possible. The method relies on the use of microscopic investigations of Newton's rings to measure the radius of the Hertzian contact between the test sample and a flat glass plate. Measurement over a range of loads gives an estimate of Poisson's ratio provided that Young's modulus is known for the sample.     

Ductile titanium alloy with low Poisson's ratio

We report a ductile beta-type titanium alloy with body-centered cubic (bcc) crystal structure having a low Poisson's ratio of 0.14. The almost identical ultralow bulk and shear moduli of approximately 24 GPa combined with an ultrahigh strength of approximately 0.9 GPa contribute to easy crystal distortion due to much-weakened chemical bonding of atoms in the crystal, leading to significant elastic softening in tension and elastic hardening in compression. The peculiar elastic and plastic deformation behaviors of the alloy are interpreted as a result of approaching the elastic limit of the bcc crystal under applied stress.     

Negative Poisson's ratio materials via isotropic interactions

We show that under tension a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintuitively, have a negative Poisson's ratio, or auxetic behavior. We derive the conditions under which the triangular lattice in two dimensions and lattices with cubic symmetry in three dimensions exhibit a negative Poisson's ratio. In the former case, the simple Lennard-Jones potential can give rise to auxetic behavior. In the latter case, a negative Poisson's ratio can be exhibited even when the material is constrained to be elastically isotropic.     

On Poisson's ratio of glass and liquid vitrification characteristics

The apparent activation energy for viscous flow of a glass-forming liquid, E_a , and its ratio to temperature T_f , m_f (=?E_a /2.3T_f ), are seen as a measure of the viscosity's departure from the Arrhenius equation. As the viscosity, η, increases on cooling, E_a and m_f increase. On slow cooling, a liquid vitrifies at a lower T, higher η and higher m_f , and on rapid cooling it vitrifies at a higher T, lower η and lower m_f . It is argued that Poisson's ratio, υ _Poisson , and the instantaneous bulk modulus to shear modulus ratio, K _∞/G _∞, of a liquid (and glass) would decrease as it departs from Arrhenius behaviour or m_f increases. Available data on structural relaxation of metal alloy glasses confirm it. Therefore, as a glass spontaneously becomes denser with time, m_f increases and its state becomes dilationally stiffer. This finding is opposite to the correlation that, amongst glass-forming liquids of different chemical compositions, υ _Poisson and K _∞/G _∞ increase when departing from Arrhenius behaviour at T_g or m increases (V.N. Novikov and A.P. Sokolov, Nature 431 961 (2004)). Further analysis shows that a liquid's structure has a predominant effect on its elastic constants.     

驻波法测杨氏模量及误差分析

驻波法运用驻波原理,采用人为控制金属丝形变,测出金属丝驻波基频,得出其张力,从而求出金属丝杨氏模量.相对传统方法,驻波法避免了金属丝直径和形变的测量,其不确定度基本上仅由千分尺精度决定,故而具有操作简单,测量准确度高的特点.