Non-linear properties of metallic cellular materials with a negative Poisson's ratio

Negative Poisson's ratio copper foam was prepared and characterized experimentally. The transformation into re-entrant foam was accomplished by applying sequential permanent compressions above the yield point to achieve a triaxial compression. The Poisson's ratio of the re-entrant foam depended on strain and attained a relative minimum at strains near zero. Poisson's ratio as small as -0.8 was achieved. The strain dependence of properties occurred over a narrower range of strain than in the polymer foams studied earlier. Annealing of the foam resulted in a slightly greater magnitude of negative Poisson's ratio and greater toughness at the expense of a decrease in the Young's modulus.     

Fracture toughness of re-entrant foam materials with a negative Poisson's ratio: experiment and analysis

Fracture toughness of re-entrant foam materials with a negative Poisson's ratio is explored experimentally as a function of permanent volumetric compression ratio, a processing variable. J _IC values of toughness of negative Poisson's ratio open cell copper foams are enhanced by 80 percent, 130 percent, and 160 percent for permanent volumetric compression ratio values of 2.0, 2.5, and 3.0, respectively, compared to the J _IC value of the conventional foam (with a positive Poisson's ratio). Analytical study based on idealized polyhedral cell structures, approximating the shape of the conventional and re-entrant cells, disclose for re-entrant foam, toughness increasing as Poisson's ratio becomes more negative. The increase in toughness is accompanied by an increase in compliance, a combination not seen in conventional foam, and which may be useful in some applications such as sponges.     

Fabrication methods for auxetic foams

Auxetic materials have a negative Poisson's ratio, that is, they expand laterally when stretched longitudinally. Negative Poisson's ratio is an unusual property that affects many of the mechanical properties of the material, such as indentation resistance, compression, shear stiffness, and certain aspects of the dynamic performance. The unusual mechanical properties of auxetic foams are attributed to the deformation characteristics of re-entrant microstructures. One way of obtaining negative Poisson's ratio is by using a re-entrant cell structure. Auxetic foam was fabricated from a conventional polymeric foam. The fabrication method for making both small and large auxetic foam specimens is described. This revised version was published online in November 2006 with corrections to the Cover Date.     

Microstructural modelling of auxetic microporous polymers

A simple two-dimensional model for the deformation of auxetic microporous polymers (those with a negative Poisson's ratio) has been developed. This model network of rectangular nodules interconnected by fibrils has been further developed to include the possibilities of fibril hinging, flexure and stretching. Expressions for strain-dependent Poisson's ratio and Young's modulus have been derived and compared with experimental results on microporous PTFE and UHMWPE. A combination of the hinging mode followed by the stretching mode of deformation can be used to explain the general features of the experimental data for these auxetic polymers. The force coefficients governing the different modes of deformation are dependent on fibril dimensions and intrinsic material properties. By varying the geometry of the network, the model can be used to predict different combinations of Poisson's ratio with modulus, from large positive through to large negative values.     

环氧树脂复合泡沫材料的压缩力学性能

对空心玻璃微珠填充环氧树脂复合泡沫材料进行了准静态压缩实验, 研究了材料的宏观压缩力学性能, 并提出了弹性模量和屈服强度的预测公式。此外, 对压缩试件的断口进行了宏、细观观察, 研究了材料的压缩破坏机理。结果表明, 复合泡沫材料在压缩过程中, 具有普通泡沫材料的应力-应变曲线的典型特征, 在应变为2 %左右时材料发生屈服, 在应变大于30 %后发生破坏。此外, 材料的杨氏模量和强度均随密度的减小而下降, 预测公式给出的结果与实验值基本一致。压缩试件断口的宏、细观观察表明, 复合泡沫材料主要的破坏形式为剪切引起的弹塑性破坏。      

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.     

The effective modulus of super carbon nanotubes predicted by molecular structure mechanics

A super carbon nanotube (ST) is a kind of hierarchical structure constructed from carbon nanotubes (named as CNT arm tubes). With the detailed construction of a Y-junction considered, the effective mechanical properties of ST structures are studied by the molecular structure mechanics (MSM) method. The Young's modulus and shear modulus of STs are found to depend mainly on the aspect ratio of CNT arm tubes instead of the chirality of the ST. A scale law is adopted to express the relation between the effective modulus (Young's modulus or shear modulus) and the aspect ratio of the CNT arm tubes. The Poisson's ratio of the ST is affected by both the aspect ratio of the CNT arm tubes and the chirality of the ST. The deformation of the ST comes from both the bending and the stretching of the CNT arm tubes. The Y-junction acts as an reinforcement phase to make the bending and stretching couple together and induce large linearity in ST structures.     

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.     

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。     

负泊松比材料和结构的研究进展

该文提出一种多弧段曲边内凹可调泊松比新型胞元。通过调整弧角,可以设计得到正泊松比、零泊松比和负泊松比的胞元结构。利用能量法求得结构的等效泊松比与等效弹性模量解析表达式,所得结果与有限元结果吻合较好。基于提出的新型胞元构建多胞蜂窝结构,利用数值方法讨论了低速和高速冲击作用下,正泊松比、零泊松比和负泊松比结构的冲击变形失效行为与单位质量能量吸收率。研究发现：低速冲击时,三种泊松比(正/零/负)结构的局部变形不同;高速冲击时,惯性效应使局部变形集中在冲击端,三种泊松比(正/零/负)结构的胞元变形模式不同。不论低速还是高速冲击,负泊松比结构都表现出优异的吸能效果。随着壁厚的增加,结构的吸能效果显著增强。     

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.     

Elastic properties of compacted metal powders

This paper describes a study of the unloading characteristics of compacts made from the uniaxial compression of metal powders in a cylindrical die. Spherical, irregular and dendritic copper powders and spherical stainless-steel powder were investigated to determine size, shape and material effects on the unloading response. This response was characterized in terms of Young's modulus and Poisson's ratio. Measures of these quantities were made at different relative densities by unloading from different peak axial stresses. With both parameters, there was a strong dependence on particle shape. The load response of lightly compressed material was found to be dominated by its particulate nature and interparticle forces. Unloading material in this condition gave values of Young's modulus that increased slightly and Poisson's ratio that decreased with increasing values of relative density. In contrast, the load response of heavily compressed material was found to be similar to that of a porous solid. Unloading material in this condition gave values of Young's modulusthat increased more steeply and Poisson's ratio that increased with increasing values for the starting relative density. Transition between these two types of behaviour depended on the particle shape, and also, to a lesser extent, the particle material. © 1998 Kluwer Academic Publishers     

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.     

Negative Poisson's ratio polyethylene foams

Various polyethylene foams were subjected to thermo-mechanical processing with the aim of transforming them into re-entrant materials exhibiting negative Poisson's ratio. Following transformation, large cell foams (cell sizes of 1 and 2 mm) exhibited re-entrant cell structure and negative Poisson's ratio over a range of processing times and temperatures. Poisson's ratio vs. strain for these foams was similar to prior results for reticulated polyurethane foams. Following processing, microcellular polyethylene foam was densified but cells remained convex; it did not exhibit a substantial negative Poisson's ratio. This foam had a different transition temperature as determined via DSC than the large cell foams.     

Application of homogenization FEM analysis to regular and re-entrant honeycomb structures

Honeycomb structures are widely used in structural applications because of their high strength per density. Re-entrant honeycomb structures with negative Poisson's ratios may be envisaged to have many potential applications. In this study, an homogenization finite element method (FEM) technique developed for the analysis of spatially periodic materials is applied for the analysis of linear elastic responses of the regular and re-entrant honeycomb structures. Young's modulus of the regular honeycomb increased with volume fraction. Poisson's ratio of the regular honeycomb structure decreased from unity as volume fraction increased. The re-entrant honeycomb structure had a negative Poisson's ratio, its value dependent upon the inverted angle of cell ribs. Young's modulus of the re-entrant honeycomb structure decreased as the inverted angle of cell ribs increased. The results are in good agreement with previous analytical results. This homogenization theory is also applicable to three-dimensional foam materials — conventional and re-entrant.Nomenclature b _i Body force - E, E _ijkl Young's modulus, elasticity tensor - E _e Effective Young's modulus - E _ijkl ^H Homogenized elasticity tensor - t _i Traction - u _i , u Displacement - v _i , v Virtual displacement - x _i , x Macroscale coordinate - y _i , y microscale coordinate - Microscopic/macroscopic ratio - Volume fraction - v Poisson's ratio - v_e Effective Poisson's ratio - _ij Stress - _P ^KL Microscale parameter of separation of variables     

高阶剪切变形板理论下FG-GRC板的屈曲和弯曲分析

基于三阶剪切变形板理论(TSDPT)和正弦剪切变形板理论(SSDPT),研究了功能梯度石墨烯增强复合材料(FG-GRC)板的屈曲和弯曲行为,并通过与一阶剪切变形板理论(FSDPT)计算结果的比较,分析了TSDPT、SSDPT与FSDPT在FG-GRC板屈曲和弯曲力学行为研究过程中的差异。材料的有效杨氏模量通过修正的Halpin-Tsai微观力学模型估算,有效泊松比通过混合律确定。利用最小势能原理推导出了包含五个未知量的控制方程,并获得了简支FG-GRC矩形板弯曲挠度和临界屈曲载荷Navier形式的解析解。数值结果表明：与TSDPT和SSDPT相比,FSDPT明显高估了FG-X型FG-GRC板的临界屈曲载荷而明显低估了其弯曲挠度,且略微低估了FG-O型FG-GRC板的临界屈曲载荷而略微高估了其弯曲挠度,而UD型和FG-A型FG-GRC板在三种理论下的计算结果几乎完全一致;TSDPT和SSDPT在计算FG-GRC板的弯曲挠度和临界屈曲载荷时结果十分相近;当板的总层数NL小于10层～15层时,弯曲载荷比率和临界屈曲载荷比率的变化非常显著,当总层数NL超过10层～15层时,弯曲载荷比率和临界屈...     

发泡聚乙烯醇缓冲机理研究

通过对不同密度的发泡聚乙烯醇进行静态压缩试验以及用扫描电镜观察不同压缩阶段泡孔结构的变化,分析了发泡聚乙烯醇的力学性能及缓冲机理。结果表明:材料静态压缩应力-应变曲线呈现线弹性、塑性屈服及密实化3个阶段;发泡聚乙烯醇不同方向力学性能的差异表明了其结构各向异性;材料的弹性模量及屈服强度与其泡孔结构有关,均会随着密度的增加而增大,材料的能量吸收效率在应变为0.55左右的区域达到最大值,具有最佳的吸能效果。最后分析了发泡聚乙烯醇压缩变形机理,其主要以孔壁弯曲变形为主,孔径很大时孔隙中流动气体对其压缩性能的影响可忽略不计。为开发不同泡孔结构发泡聚乙烯醇材料应用于各种产品的缓冲包装设计提供参考。     

Non-linear properties of polymer cellular materials with a negative Poisson's ratio

Negative Poisson's ratio polymeric cellular solids (re-entrant foams) were studied to ascertain the optimal processing procedures which give rise to the smallest value of Poisson's ratio. The non-linear stress-strain relationship was determined for both conventional and re-entrant foams; it depended upon the permanent volumetric compression achieved during the processing procedure. Poisson's ratio of re-entrant foam measured as a function of strain was found to have a relative minimum at small strains. The toughness of re-entrant foam increased with permanent volumetric compression, and hence with density.     

Review on auxetic materials

Although a negative Poisson's ratio (that is, a lateral extension in response to stretching) is not forbidden by thermodynamics, for almost all common materials the Poisson's ratio is positive. In 1987, Lakes first discovered negative Poisson's ratio effect in polyurethane (PU) foam with re-entrant structures, which was named anti-rubber, auxetic, and dilatational by later researchers. In this paper, the term 'auxetic' will be used. Since then, investigation on the auxetic materials has held major interest, focusing on finding more materials with negative Poisson's ratio, and on examining the mechanisms, properties and applications. Therefore, more materials were found to have the counter-intuitive effect of auxeticity due to different structural or microstructrual mechanisms. The present article reviews the latest advances in auxetic materials, their structural mechanisms, performance and applications.     

Deformation mechanisms in negative Poisson's ratio materials: structural aspects

Poisson's ratio in materials is governed by the following aspects of the microstructure: the presence of rotational degrees of freedom, non-affine deformation kinematics, or anisotropic structure. Several structural models are examined. The non-affine kinematics are seen to be essential for the production of negative Poisson's ratios for isotropic materials containing central force linkages of positive stiffness. Non-central forces combined with pre-load can also give rise to a negative Poisson's ratio in isotropic materials. A chiral microstructure with noncentral force interaction or non-affine deformation can also exhibit a negative Poisson's ratio. Toughness and damage resistance in these materials may be affected by the Poisson's ratio itself, as well as by generalized continuum aspects associated with the microstructure.