A method of determining the shear modulus and Poisson's ratio of polymer materials

An experimental method is described which allows the shear modulus and Poisson's ratio of a polymer material to be determined as functions of temperature. Using commercial thermal mechanical analysis equipment, measurements are required of the thermal expansion coefficients of both unconstrained and constrained specimens, and of the Young's modulus. The constraint on a small disc-shaped polymer specimen is applied by a copper annulus. The basis of the method is that the apparent thermal expansion of the constrained specimen depends on the Poisson effect, and an analysis is given which enbles the Poisson's ratio to be determined. Some illustrative results are presented for a silicon rubber.     

纸浆模塑材料在不同加载条件下的力学特性

实验测量了纸浆模塑材料在不同加载条件下拉伸时的强度极限、弹性模量和泊松比等力学性能,同时给出了纸浆模塑材料的应力-应变曲线,为纸浆模塑缓冲包装结构的有限元分析和设计提供了基础数据.实验结果表明:当加载速率提高时,试件强度极限和弹性模量随之增加;当温度升高时,纸浆模塑材料的强度极限和弹性模量随之逐渐升高;当湿度升高时,纸浆模塑的强度极限和弹性模量随之降低.纸浆模塑材料单向拉伸时横向变形很小,且对温、湿度等环境因素影响敏感,泊松比的测量比较困难.数字图像相关测量方法具有灵敏度高、非接触、直接测量物体表面全场变形的特点,采用该测量方法解决了材料泊松比的测量问题.实验测得纸浆模塑材料泊松比为0.097.     

Feasibility of Estimation Methods for Measuring Young's Modulus of Wood by Three-Point Bending Test

We examined the feasibility of estimation methods for measuring Young's modulus of wood by the three-point bending test using spruce specimens (Picea sitchensis Carr.). By measuring the deflections at the midspan and at the midpoint between the loading and supporting points, Young's moduli were determined according to elementary and Timoshenko's beam theory. Additionally, longitudinal strain at the midspan was measured independently of measuring the deflections, and Young's modulus was also determined from the load-strain relation. The values of Young's modulus obtained by the different procedures were compared with each other, and the following results were obtained: (1) Measurement of two-point deflections was effective for obtaining Young's modulus while reducing the influence of shear deformation when the specimen had a small depth. (2) In the measurement of two-point deflections, the specimen configuration should be regarded as more important than the contact at the loading and supporting points. (3) The use of strain gauges should be taken into account as a standardized method for measuring Young's modulus by bending.     

The influence of hygrothermal conditions on the damage processes in quasi-isotropic carbon/epoxy laminates

The effects of hygrothermal conditions on damage development in quasi-isotropic carbon-fiber/epoxy laminates are described. First, monotonic and loading/unloading tensile tests were conducted on dry and wet specimens at ambient and high temperatures to compare the stress/strain response and damage development. The changes in the Young's modulus and Poisson's ratio were obtained experimentally from the monotonic tensile tests. The critical stresses for transverse cracking and delamination for the above three conditions are compared. The delamination area is measured by using scanning acoustic microscopy (SAM) at various loads to discuss the effects of delamination on the nonlinear stress/strain behavior. Next, the stress distributions under tensile load including hygrothermal residual stresses are computed by a finite-element code and their effects on damage initiation are discussed. Finally, a simple model for the prediction of the Young's modulus of a delaminated specimen is proposed. It is found that moisture increases the critical stresses for transverse cracking and delamination by reducing the residual stresses while high temperature decreases the critical stresses in spite of relaxation of the residual stresses. The results of the finite-element analysis provide some explanations for the onset of transverse cracking and delamination. The Young's modulus predicted by the present model agrees with experimental results better than that predicted by conventional models.     

Transverse tensile properties of an unbonded model composite

Models of unbonded composites have been made by drilling holes in aluminium alloy strip and plugging the holes with steel rods. These specimens, together with similar specimens left unplugged, have been tested in tension. Young's modulus, stress at the elastic limit and ultimate tensile stress have been measured. The results, particularly for the Young's modulus of the plugged strips, show a complex behaviour. The application of the results to real materials is discussed.     

Holographic study of conventional and negative Poisson's ratio metallic foams: elasticity,yield and micro-deformation

An experimental study by holographic interferometry is reported of the following material properties of conventional and negative Poisson's ratio copper foams: Young's moduli, Poisson's ratios, yield strengths and characteristic lengths associated with inhomogeneous deformation. The Young's modulus and yield strength of the conventional copper foam were comparable to those predicted by microstructural modelling on the basis of cellular rib bending. The re-entrant copper foam exhibited a negative Poisson's ratio, as indicated by the elliptical contour fringes on the specimen surface in the bending tests. Inhomogeneous, non-affine deformation was observed holographically in both foam materials.     

Elastic properties measurement of glass layers fabricated onsilicon wafers for microelectronics and micromachines

Elastic properties such as the Young's modulus, the Poisson's ratio and the density of Si-B-O glass layers fabricated on (100) silicon substrates by the flame hydrolysis deposition method were measured. Thicknesses of the layers were about 20 μm. It was found that the Young's modulus decreased with the boron dopant concentration. The Poisson's ratio was about 0.26 regardless of the boron dopant concentration. The measured elastic properties will be used in the design of micromachines fabricated with silicon substrates and glass layers     

Measurement of Young's modulus and internal friction of an in situ Al-Al3Ni functionally gradient material

An in situ Al-Al₃Ni functionally gradient material (FGM) was produced by centrifugally casting an Al-20 mass% Ni alloy into a thick-walled tube. Four specimens, 90 mm long, with rectangular cross-sections (width × thickness) of 6 × 6, 6 × 5, 6 × 4 and 6 × 3 mm² were machined from the tube such that the thickness direction of the specimens was in the radial direction of the tube. The microstructure of the FGM tube consisted of granular morphology Al₃Ni as a second phase distributed within the aluminium matrix with an increasing volume fraction gradient from the inside to the outside of the tube. Thus, the thicker the specimen, the greater was the composition gradient and the thinner the specimen, the greater was the volume fraction of Al₃Ni. The dependence of the Young's modulus and internal friction on the composition gradient of the FGM was determined by a flexural forced-resonance technique from the resonant frequency and the resonance peak width, respectively, as a function of nominal specimen thickness. The Young's modulus of the Al₃Ni second phase was determined from a correlation plot of assumed Al₃Ni Young's modulus values against the calculated resonant frequency values corresponding to the associated FGM Young's modulus values. The latter were calculated using a rule of mixtures with a fixed matrix Young's modulus and a gradient volume fraction of Al₃Ni for each specimen thickness. By plotting the experimental FGM specimen resonant frequencies on this plot, the average Al₃Ni Young's modulus was found to be 140 GPa. The Young's modulus of the FGM was found to vary between 81.5 and 100.8 GPa across the 6 mm tube-wall thickness from the inner to outer surface, reflecting the 15.2 and 43.2 vol % Al₃Ni second phase, respectively. The measured internal friction increased with the volume fraction of Al₃Ni, and owing to the relatively large Al₃Ni particle size, was thereby dependent on the resultant increase in the second phase-matrix interface number density rather than the dislocation density.     

Elasto-optics in double-coated optical fibers induced by axial strain and hydrostatic pressure

Stresses, microbending loss, and refractive-index changes induced simultaneously by axial strain and hydrostatic pressure in double-coated optical fibers are analyzed. The lateral pressure and normal stresses in the optical fiber, primary coating, and secondary coating are derived. Also presented are the microbending loss and refractive-index changes in the glass fiber. The normal stresses are affected by axial strain, hydrostatic pressure, material properties, and thickness of the primary and secondary coatings. It is found that microbending loss decreases with increasing thickness, the Young's modulus, and the Poisson's ratio of the secondary coating but increases with the increasing Young's modulus and Poisson's ratio of the primary coating. Similarly, changes in refractive index in the glass fiber decrease with the increasing Young's modulus and Poisson's ratio of the secondary coating but increase with the increasing Young's modulus and Poisson's ratio of the primary coating. Therefore, to minimize microbending loss induced simultaneously by axial strain and hydrostatic pressure in the glass fiber, the polymeric coatings should be suitably selected. An optimal design procedure is also indicated.     

Studies of Size Effects on Carbon Nanotubes' Mechanical Properties by Using Different Potential Functions

We use molecular mechanics calculations to study size effects on mechanical properties of carbon nanotubes. Both single-walled nanotubes (SWNTs) and multi-walled nanotubes (MWNTs) are considered. The size-dependent Young's modulus decreases with the increasing tube diameter for a reactive empirical bond order (REBO) potential function. However, we observe a contrary trend if we use other potential functions such as the modified Morse potential function and the universal force field (UFF). Such confliction is only obtained for small tubes within cutoff diameters (3 nm for REBO and 1.5 nm for others). In light of these predictions, Young's moduli of large nanotubes concur with experimental results for all the potential functions. No matter which potential function is used, the Poisson's ratio decreases with the increasing tube diameter. We also study the chirality effects on mechanical properties of SWNTs. We find that the Young's moduli are insensitive to the chirality of nanotubes. The chirality effect on the Poisson's ratio is significant for the UFF but not the REBO or modified Morse potential functions.     

Effective creep Poisson's ratio for damaged concrete

First, creep data are presented for concrete under high sustained compressive stress which is, over the long-term strength of the concrete. Creep in both axial and lateral directions is reported. Creep Poisson's ratio has remarkable change before failure, and a sharp increase of creep Poisson's ratio can be observed in the region of failure.Secondly, a damage model is developed for the analysis of creep damage in both axial and lateral directions; effective Poisson's ratio of damaged material as a model parameter plays an important role for evaluating lateral damage, which is similar to the effective Young's modulus in evaluating axial damage.     

对弹体侵彻混凝土靶体阻力函数计算公式的探讨

基于动态球形空腔膨胀理论,探讨了混凝土材料的单轴抗压强度、弹性模量、泊松比、压力硬化系数对阻力函数的影响,并指出,混凝土靶体的弹性模量和单轴抗压强度对阻力函数影响较明显,而泊松比和压力硬化系数的影响可以忽略不计。在此基础上,该文忽略泊松比和压力硬化系数的影响,通过引入弹性模量与单轴抗压强度的关系式,分别建立了基于弹性-断裂-塑性和弹性-塑性两种靶体响应模型下,同时考虑单轴抗压强度和弹性模量影响的阻力函数理论公式,并建立了弹体侵彻靶体的加速度时程计算模型。通过与不同尺寸弹体侵彻实验数据对比,验证了该文提出阻力函数表达式的适用性及其在加速度时程以及较大尺寸弹体侵彻深度计算中的优 越性。     

声速法研究Cu_(58.1)Zr_(35.9)Al_6非晶合金的弹性性能

利用纵波掠入射法测量了超声波在Cu58.1Zr35.9Al6非晶合金中的传播速度。基于声波在各向同性、均匀固体介质中的传播规律,获得其弹性指标参数。结果表明:超声波在Cu58.1Zr35.9Al6非晶合金中传播的纵波速度为4820m/s,横波速度为2107m/s;由此得到的弹性指标以及热力学参数为:K=130GPa,G=33.6GPa,E=93.09GPa,泊松比σ=0.38,θD=283K。     

Investigation of the dynamic Young's modulus and vibration damping for cryomilled NiAl–AlN composites

Measurements were made of the dynamic Young's modulus (stiffness) and damping for NiAl specimens containing varying amounts of aluminium nitride and prepared by cryomilling. Five specimens of NiAl–AlN were measured at room temperature, each specimen having a different percentage of AlN in the range 1%–30%. Further measurements were made on the 1% and 30% AlN specimens for the temperature range 22–495°C. At room temperature, the Young's modulus of the NiAl–AlN specimens decreased linearly with increasing percentage of AlN. The temperature dependence of Young's modulus for the 1% and 30% AlN specimens was found to be linear. These results were compared with those of typical nickel-based superalloys for a similar temperature range. The damping for all of the NiAl–AlN specimens was of the order of that for other intermetallic compounds (10-3–10-4). The study opened up the possibility of NiAl–AlN being a less-expensive and more easily produced alternative to nickel-based superalloys for high-temperature, high-stiffness applications. © 1998 Kluwer Academic Publishers     

Determining elasticity characteristics for protective coatings

A method is proposed for determining the elastic modulus and Poisson's ratio for a protective coating in static uniaxial tension. The difference in Poisson's ratio between the substrate and the coating results in additional stresses, and the coating is in a planar state of stress. Formulas are derived for the coating's elasticity characteristics in terms of a single test on a coated specimen. That method has given the elastic modulus and Poisson's ratio for gas- plasma coatings.Translated from Problemy Prochnosti, No. 7, pp. 48–51, July, 1995.     

Thermoelastic properties of fiber composites with imperfect interface

Imperfect interface conditions are defined in terms of linear relations between interface tractions and displacement jumps. All of the thermoelastic properties of unidirectional fiber composites with such interface conditions are evaluated on the basis of the generalized self consistent scheme (GSCS) model. Results for elastic interphase are obtained as a special case by evaluation of interface parameters in terms of interphase characteristics. Numerical evaluation has shown that imperfect interface may have a significant effect on transverse thermal expansion coefficient, transverse shear and Young's moduli and axial shear modulus, a moderate effect on axial Poisson's ratio, small effect on axial thermal expansion coefficient and an insignificant effect on axial Young's modulus.     

Anelastic behaviour of materials under multiaxial strains

Data on Young's modulus and Poisson's ratio obtained in AISI-1080 steel, in the temperature region between about 300 and 600 K, are presented. The measurements have been performed in longitudinal excitation and several harmonics were used, to obtain Poisson's ratio from the measured resonant frequencies. The maximum observed in the temperature dependence of Young's modulus, for the fundamental resonant frequency, is attributed to a stress-induced disordering of carbon atoms in the octahedral interstices of the martensitic matrix. The increases of Young's modulus with temperature are described in terms of expressions deduced in the paper, which are based on Landau theory of second-order phase transitions. The critical temperature is related to theM _s temperature which characterizes the martensitic phase transition. Finally, the temperature dependence of Poisson's ratio is described in terms of a theory of anelastic behaviour under multiaxial strains, based on the standard anelastic solid model.     

Use of extensometers with spherically pointed pin ends for accurate determination of material qualities

Highly accurate FFA 10 mm inductive extensometers with spherical tips are used for materials testing. The pin ends are ground conical and spherically pointed ends of 16tm radius are then honed. The specimen is indented with a slightly greater cone angle and with the same nose radius by a similar conical-spherical taper shank. The extensometer is mounted in these indentations under a spring pressure that plasticises the spherical contact area and squeezes out unevennesses.
The shear modulus of steel was evaluated from four values of Young's modulus and four of Poisson's ratio in tension and compression, determined with such extensometers in 16 different tests under dead weights calibrated by the official standards institute. The four shear modulus values obtained have root mean square errors within ±0.5%.     

Experimental Evaluation of Dynamic Test Methodologies for Assessing the Elastic Constants of Granitic Rocks

Two dynamic test methodologies, the resonance method and the ultrasonic method, are used for assessing the elastic behaviour of granitic rocks. The experimental results obtained using two types of specimens: (i) rectangular beams (parallelepiped specimens); and (ii) cylindrical specimens (rod specimens); show that the resonance method used in this work is more adequate when both Young's modulus and Poisson's ratio are to be determined in these types of rocks. Moreover, it is demonstrated that test results obtained by resonance techniques are less dependent on specimen's geometry, size, and even surface roughness.     

Uniaxial tensile and shear deformation tests of gold-tin eutectic solder film

This paper describes a novel experimental technique for measuring mechanical properties of gold-tin (Au-Sn) eutectic solder film used for soldering package in microelectromechanical systems (MEMS). Dual-source DC magnetron sputtering was employed to deposit Au-20 weight % (wt%) Sn film. The tensile test with in situ X-ray diffraction (XRD) measurement evaluates the Young's modulus and Poisson's ratio at intermediate temperatures. The Young's modulus and Poisson's ratio at room temperature were found to be 51.3 GPa and 0.288, lower than bulk values. The Young's modulus decreased with increasing temperature, whereas the Poisson's ratio did not depend on temperature. The XRD tensile test also showed creep deformation behavior of Au-Sn film. We have developed a shear deformation test technique, which is performed by using Au-Sn film sandwiched by two single crystal silicon (Si) cantilever structures, to characterize the shear properties of the film. The shear moduli obtained from the shear deformation tests ranged from 11.5 to 13.3 GPa, about 38% lower than those from the XRD tensile tests. The measured shear strength from 12 to 17 MPa exhibited a temperature dependency. Information about the tensile and shear characteristics would likely to be of great use in designing Au-Sn soldering packages for MEMS.