Showing papers on "Young's modulus published in 2007"

Mechanical properties of suspended graphene sheets

Abstract: Using an atomic force microscope, we measured effective spring constants of stacks of graphene sheets (less than 5) suspended over photolithographically defined trenches in silicon dioxide. Measurements were made on layered graphene sheets of thicknesses between 2 and 8nm, with measured spring constants scaling as expected with the dimensions of the suspended section, ranging from 1to5N∕m. When our data are fitted to a model for doubly clamped beams under tension, we extract a Young’s modulus of 0.5TPa, compared to 1TPa for bulk graphite along the basal plane, and tensions on the order of 10−7N.

Elastic membranes of close-packed nanoparticle arrays.

Abstract: Nanoparticle superlattices are hybrid materials composed of close-packed inorganic particles separated by short organic spacers. Most work so far has concentrated on the unique electronic, optical and magnetic behaviour of these systems. Here, we demonstrate that they also possess remarkable mechanical properties. We focus on two-dimensional arrays of close-packed nanoparticles and show that they can be stretched across micrometre-size holes. The resulting free-standing monolayer membranes extend over hundreds of particle diameters without crosslinking of the ligands or further embedding in polymer. To characterize the membranes we measured elastic properties with force microscopy and determined the array structure using transmission electron microscopy. For dodecanethiol-ligated 6-nm-diameter gold nanocrystal monolayers, we find a Young's modulus of the order of several GPa. This remarkable strength is coupled with high flexibility, enabling the membranes to bend easily while draping over edges. The arrays remain intact and able to withstand tensile stresses up to temperatures around 370 K. The purely elastic response of these ultrathin membranes, coupled with exceptional robustness and resilience at high temperatures should make them excellent candidates for a wide range of sensor applications.

Mechanical Properties of Steel Fiber-Reinforced Concrete

Abstract: This paper presents the results from an experimental program and an analytical assessment of the influence of addition of fibers on mechanical properties of concrete. Models derived based on the regression analysis of 60 test data for various mechanical properties of steel fiber-reinforced concrete have been presented. The various strength properties studied are cube and cylinder compres- sive strength, split tensile strength, modulus of rupture and postcracking performance, modulus of elasticity, Poisson's ratio, and strain corresponding to peak compressive stress. The variables considered are grade of concrete, namely, normal strength 35 MPa, moderately high strength 65 MPa, and high-strength concrete 85 MPa, and the volume fraction of the fiber Vf=0.0, 0.5, 1.0, and 1.5%. The strength of steel fiber-reinforced concrete predicted using the proposed models have been compared with the test data from the present study and with various other test data reported in the literature. The proposed model predicted the test data quite accurately. The study indicates that the fiber matrix interaction contributes significantly to enhancement of mechanical properties caused by the introduction of fibers, which is at variance with both existing models and formulations based on the law of mixtures. 85 MPa with various fiber dosages Vf=0, 0.5, 1.0, and 1.5%. An empirical relationship for various mechanical properties of SFRC has been proposed. The proposed model attempts to bring out the significance of fiber matrix interaction in all the strength properties. This study reports the experimental results of the strength properties of SFRC, namely, cube and cylinder compressive strength, split tensile strength, modulus of rupture, modulus of elasticity, Poisson's ratio, and strain corresponding to peak com- pressive stress. Empirical relationships were developed for vari- ous strength properties based on the regression analysis of the 60 test data. It is expected that these proposed models would be helpful in assessing the strength properties of fiber-reinforced concrete based on the matrix strength and fiber-RI.

Processing and properties of carbon nanotubes reinforced aluminum composites

Abstract: Carbon nanotubes reinforced aluminum matrix composites were fabricated by isostatic pressing followed hot extrusion techniques. Differential scanning calorimetric, X-ray diffraction, field emission scanning electron microscopy, transmission electron microscopy has been carried out to examine the reaction condition of nanotubes and aluminum, and to analyze the composites structure. The effects of nanotubes content on mechanical properties of composites were investigated. Experimental results showed that nanotubes are homogeneously distributed in the composites. Some nanotubes act as bridges across cracks, others are pulled-out on fracture surfaces of composites. However, nanotubes react with aluminum and form Al4C3 phases when the temperature is above 656.3 °C. The nanotubes content affects significantly mechanical properties of composites. Meanwhile, the 1.0 wt.% nanotube/2024Al composite is found to exhibit the highest tensile strength and Young's modulus. The maximal increments of tensile strength and Young's modulus of the composite, compared with the 2024Al matrix, are 35.7% and 41.3%, respectively.

Compressive Behavior of Ultra-High-Performance Fiber-Reinforced Concrete

Abstract: An experimental program aimed at determining ultra-high performance fiber-reinforced concrete (UHPFRC) uniaxial compressive behaviors was conducted. Overall stress-strain behavior, strain capacity, modulus of elasticity, and strength of both steam-treated and untreated UHPFRC were determined by analyzing results of compression tested cylinders. Enhanced stiffness and exceptional compressive strength were exhibited by UHPFRC according to study results. The authors present modulus of elasticity as compression strength function and strength gain with time predictor equations. The authors present UHPFRC stress-strain response linearity and establish an ascending branch compressive stress-strain behavior equation.

Robust strategies for automated AFM force curve analysis--I. Non-adhesive indentation of soft, inhomogeneous materials.

Abstract: The atomic force microscope (AFM) has found wide applicability as a nanoindentation tool to measure local elastic properties of soft materials. An automated approach to the processing of AFM indentation data, namely, the extraction of Young's modulus, is essential to realizing the high-throughput potential of the instrument as an elasticity probe for typical soft materials that exhibit inhomogeneity at microscopic scales. This paper focuses on Hertzian analysis techniques, which are applicable to linear elastic indentation. We compiled a series of synergistic strategies into an algorithm that overcomes many of the complications that have previously impeded efforts to automate the fitting of contact mechanics models to indentation data. AFM raster data sets containing up to 1024 individual force-displacement curves and macroscopic compression data were obtained from testing polyvinyl alcohol gels of known composition. Local elastic properties of tissue-engineered cartilage were also measured by the AFM. All AFM data sets were processed using customized software based on the algorithm, and the extracted values of Young's modulus were compared to those obtained by macroscopic testing. Accuracy of the technique was verified by the good agreement between values of Young's modulus obtained by AFM and by direct compression of the synthetic gels. Validation of robustness was achieved by successfully fitting the vastly different types of force curves generated from the indentation of tissue-engineered cartilage. For AFM indentation data that are amenable to Hertzian analysis, the method presented here minimizes subjectivity in preprocessing and allows for improved consistency and minimized user intervention. Automated, large-scale analysis of indentation data holds tremendous potential in bioengineering applications, such as high-resolution elasticity mapping of natural and artificial tissues.

Strength properties of thermally modified softwoods and its relation to polymeric structural wood constituents

Abstract: Thermal modification at relatively high temperatures (ranging from 150 to 260 °C) is an effective method to improve the dimensional stability and resistance against fungal attack. This study was performed to investigate the impact of heat treatment on the mechanical properties of wood. An industrially-used two-stage heat treatment method under relative mild conditions (< 200 °C) was used to treat the boards. Heat treatment revealed a clear effect on the mechanical properties of softwood species. The tensile strength parallel to the grain showed a rather large decrease, whereas the compressive strength parallel to the fibre increased after heat treatment. The bending strength, which is a combination of the tensile stress, compressive stress and shear stress, was lower after heat treatment. This decrease was less than the decrease of only the tensile strength. The impact strength showed a rather large decrease after heat treatment. An increase of the modulus of elasticity during the bending test has been noticed after heat treatment. Changes and/or modifications of the main wood components appear to be involved in the effects of heat treatment on the mechanical properties. The possible effect of degradation and modification of hemicelluloses, degradation and/or crystallization of amorphous cellulose, and polycondensation reactions of lignin on the mechanical properties of heat treated wood have been discussed. The effect of natural defects, such as knots, resin pockets, abnormal slope of grain and reaction wood, on the strength properties of wood appeared to be affected by heat treatment. Nevertheless, heat treated timber shows potential for use in constructions, but it is important to carefully consider the stresses that occur in a construction and some practical consequences when heat treated timber is used.

Ab Initio Calculation of Elastic Constants of Ceramic Crystals

Abstract: An effective computational scheme to calculate the complete set of independent elastic constants as well as other structural parameters including bulk modulus, shear modulus, Young's modulus, and Poisson's ratio for crystals is reported. The scheme is based on the stress–strain analysis approach with the appropriate selection of strain governed by symmetry consideration. The first principles Vienna ab initio simulation package (VASP) is used in stress calculations. Comprehensive tests were performed for α-SiO2 and spinel MgAl2O4 with different exchange-correlation potentials, and different sets of computational parameters to investigate the relative accuracies of the calculations. A wide range of oxides, nitrides, and carbonate crystals with different crystal symmetries were chosen to test the scheme under both LDA and GGA approximations at zero temperature and pressure. Some of these calculations for large complex crystals are believed to be attempted for the first time. The calculated elastic constants show quite good agreement with the existing experimental data for almost all the examined systems with the exception of the relatively soft material such as α-SiO2 and the C14 parameter of some trigonal crystals expressed in the hexagonal form such as in α-Al2O3. Other structural properties derived from the elastic constants also show good agreements with the measured values.

Molecular dynamics study of the stress–strain behavior of carbon-nanotube reinforced Epon 862 composites

Abstract: Single-walled carbon nanotubes (CNTs) are used to reinforce epoxy Epon 862 matrix. Three periodic systems – a long CNT-reinforced Epon 862 composite, a short CNT-reinforced Epon 862 composite, and the Epon 862 matrix itself – are studied using the molecular dynamics. The stress–strain relations and the elastic Young's moduli along the longitudinal direction (parallel to CNT) are simulated with the results being also compared to those from the rule - of - mixture . Our results show that, with increasing strain in the longitudinal direction, the Young's modulus of CNT increases whilst that of the Epon 862 composite or matrix decreases. Furthermore, a long CNT can greatly improve the Young's modulus of the Epon 862 composite (about 10 times stiffer), which is also consistent with the prediction based on the rule - of - mixture at low strain level. Even a short CNT can also enhance the Young's modulus of the Epon 862 composite, with an increment of 20% being observed as compared to that of the Epon 862 matrix.

Hindered Crack Propagation in Materials with Periodically Varying Young's Modulus—Lessons from Biological Materials†

Abstract: Many biological materials, such as bone, nacre or biosilica, are known to be both stiff and tough. Their structure is hierarchical and appears to be optimized at all levels of hierarchy to combine the properties of its primary components, which are a tough protein and stiff mineral. Bone, for example, is a nanocomposite and the deformation pattern is clearly hierarchical. In lamellar cortical bone, fibrillar units aggregate into laminate sheets, in analogy to plywood. This lamellar structure has a dramatic effect on fracture toughness. Nacre and biosilica are also layered structures where thin organic layers separate sheets of aragonite mineral and biosilica, respectively. The high toughness of such layered biological structures is intriguing and may serve as a model for artificial layered composites. A possible origin for the toughness in layered structures is the deflection of racks at weak interfaces. However, we know from theoretical fracture mechanics that a variation of the material properties alone (even without inherently weak interfaces) may result in a shielding or anti-shielding effect to the crack tip, which leads to a change of the crack driving force and the energy consumed by the fracture process. In the current work, we therefore analyse the driving force onto cracks propagating inside a material where the Young’s modulus varies in a periodic way in a given direction (perpendicular to the lamellae). We derive a simple design criterion to obtain laminate structures without driving force for crack propagation perpendicular to the lamellae. We consider a crack in a plane configuration of unit thickness with the crack tip located at the point P, see Figure 1. Globally, the material is assumed to be elastic with a constant Young’s modulus Efar and a Poisson’s ratio m far away from the crack tip P. Inside a circular region with the radius R, however, the Young’s modulus E varies in space. We assume that this variation is periodic in x-direction with an average value E0. The specimen is loaded by a stress ∑ in y-direction on the upper and lower parts of the boundary Cfar (indicated as “o” and “u” in Fig. 1). The crack flanks are assumed to be stressfree. The stress field r near the crack tip T is described by the classical “near-tip field” expressed in polar coordinates r,h and the stress intensity factor KI, for details see the fracture mechanics literature, e.g., Gross et al., Ch. 4.2. The specific elastic strain energy density r e 2 can be calculated analytically for constant E and plane stress or strain conditions as

Electronic structure, chemical bonding and elastic properties of the first thorium‐containing nitride perovskite TaThN3

Abstract: The full-potential linearized augmented plane wave method with the generalized gradient approximation for the exchange and correlation potential (LAPW-GGA) is used to understand the electronic and elastic properties of the first thorium-containing nitride perovskite TaThN3. Total and partial density of states, charge distributions as well as the elastic constants, bulk modulus, compressibility, shear modulus, Young modulus and Poisson ratio are obtained for the first time and analyzed in comparison with cubic ThN. The chemical bonding in TaThN3 is a combination of ionic Th–N and of mixed covalent–ionic Ta–N bonds. The cubic TaThN3 is semiconducting with the direct gap at about 0.65 eV. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Mechanical properties and fine structure of drawn polymers

Abstract: Complex moduli of oriented specimens of polyethylene (PE), polypropylene (PP), polyoxymethylene, polyethylene oxide), and polytetrahydrofuran were measured in sheet form as a function of direction. The dynamic tensile modulus (E′) along the stretched direction (0° direction) was found to be lower than that perpendicular to the stretched direction (90° direction) above the temperature of primary dispersion (αa) for all polymers cited above. Below the temperature of an dispersion the E′ value of 0° direction is higher than that of 90° direction as expected from the anisotropy of modulus of the crystal. This fact leads us to the model that the crystalline region (C) and this amorphous region (A) are arranged mainly in series along the stretched direction and at the same time the C region should be more or less continuous along the 90° direction. The actual drawn sample is composed of many microfibrils as proved l y the x-ray small-angle scattering. Those conditions imposed on the model should be satisfied even when many microfibrils are bound together into a fiber. This picture agrees with the structural model of hot-drawn PE presented by Hosemann after its slight modification. Effects of cold drawing on the anisotropy of modulus were also surveyed.

Size dependence of effective Young’s modulus of nanoporous gold

Abstract: Nanoporous gold (NPG) is a brittle, three-dimensional, random structure of Au with nanometer scale open porosity that is made by dealloying Au∕Ag alloys in acid. In this work, Young’s modulus of NPG with controlled porosity variation between 3 and 40nm is determined by mechanical testing of ∼100nm thick, free standing, large-grained, stress-free films of NPG using a buckling-based method [C. Stafford et al., Nat. Mater. 3, 545 (2005)]. Results showing a dramatic rise in the effective Young’s modulus of NPG with decreasing ligament size, especially below 10nm are presented, and possible reasons for this behavior are discussed.

A molecular mechanics approach for analyzing tensile nonlinear deformation behavior of single-walled carbon nanotubes

Abstract: In this paper, by capturing the atomic informa- tion and reflecting the behaviour governed by the nonlin- ear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single- walled carbon nanotubes (SWCNT's) is established to describe the nonlinear stress-strain curve of SWCNT's and to predict both the elastic properties and breaking strain of SWCNT's during tensile deformation. An analysis based on the virtual internal bond (VIB) model proposed by P. Zhang et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an acceptable analytical method for analyzing the mechanical behavior of SWCNT's. of CNT's. The Young's modulus of CNT's was found to be about 1 TPa (2-5). Many theories of mechanics have also been proposed to study the mechanical properties of CNT's. Zhang et al. (6) developed a continuum mechanics approach to model elastic properties of single-walled carbon nanotubes (SWCNT's), and the Young's modulus of SWCNT's was pre- dicted to be 0.705 TPa. Li and Chou (7) presented a structural mechanics approach to model the deformation of CNT's, and calculated the Young's moduli for CNT's with different radii. A similar approach was presented by Chang and Gao (8), and the chirality- and size-dependent elastic properties such as Young's modulus, Poisson's ratio and shear modulus were predicted (9,10). Moreover, the nonlinear effect of SWCNT's was taken into account (11) recently. In view of the unrealistic demand of computational power to study materials of practical size, atomistic simulations are deemed unsuitable for the study of large scaled nanometer materials in large time spans. Therefore, various attempts have been made by researchers to introduce atomic character- istics into the mechanical theory. For example, the molecular mechanics originally developed by chemical scientists (12) can be considered one of the successful attempts. According to the definition of Burkert and Allinger (12), the total potential energy, U , is constitutive of several individual energy terms corresponding to bond stretching, angle bend- ing, torsion, and van der Waals interactions, respectively: U = � Ustretch + � Ubend

Cellular solids with tunable positive or negative thermal expansion of unbounded magnitude

Abstract: Material microstructures are presented with a coefficient of thermal expansion larger in magnitude than that of either constituent. Thermal expansion can be large positive, zero, or large negative. Three-dimensional lattices with void space exceed two-phase bounds but obey three-phase bounds; lattices and normal materials have a trend of expansion decreasing with modulus. Two-phase composites with a negative stiffness phase exceed bounds that assume positive strain energy density. The author determined Young’s modulus and its relation to thermal expansion. Behavior of these composites is compared with that of homogeneous solids in expansion-modulus maps.

Elastic constants and internal friction of martensitic steel, ferritic-pearlitic steel, and α-iron

Abstract: The elastic constants and internal friction of induction hardened and unhardened SAE 1050 plain-carbon steel at ambient temperatures were determined by resonant ultrasonic spectroscopy. The hardened specimen contained only martensite and the unhardened specimen was ferrite-pearlite. Using an inverse Ritz algorithm with assumed orthorhombic symmetry, all nine independent elastic-stiffness coefficients were determined, and, from the resonance peak widths, all nine components of the internal-friction tensor were determined. Similar measurements and analysis on monocrystalline α-iron were performed. The steel has slight elastic anisotropy, and the isotropically approximated elastic moduli were lower in the martensite than in ferrite-pearlite: shear modulus by 3.6%, bulk modulus by 1.2%, Young modulus by 3.2%, and Poisson ratio by 1.5%. Isotropically approximated elastic moduli of α-iron were 0.6–1.3% higher than ferrite-pearlite. All components of the internal-friction in martensite were higher than those of ferrite-pearlite, but lower than those of α-iron.

Discrete element method for modelling solid and particulate materials

Abstract: The discrete element method (DEM) is developed in this study as a general and robust technique for unified two-dimensional modelling of the mechanical behaviour of solid and particulate materials, including the transition from solid phase to particulate phase Inter-element parameters (contact stiffnesses and failure criteria) are theoretically established as functions of element size and commonly accepted material parameters including Young's modulus, Poisson's ratio, ultimate tensile strength, and fracture toughness A main feature of such an approach is that it promises to provide convergence with refinement of a DEM discretization Regarding contact failure, an energy criterion based on the material's ultimate tensile strength and fracture toughness is developed to limit the maximum contact forces and inter-element relative displacement This paper also addresses the issue of numerical stability in DEM computations and provides a theoretical method for the determination of a stable time-step The method developed herein is validated by modelling several test problems having analytic solutions and results show that indeed convergence is obtained Moreover, a very good agreement with the theoretical results is obtained in both elastic behaviour and fracture An example application of the method to high-speed penetration of a concrete beam is also given Copyright © 2006 John Wiley & Sons, Ltd

Three-Dimensional Linear Behavior of Bituminous Materials: Experiments and Modeling

Abstract: The linear viscoelastic properties of bituminous mixtures are used to design pavement structure. Usually, only complex moduli E* (complex Young modulus) or G* (complex shear modulus) characterizing the stiffness of the materials in one direction (1D) are measured by classical tests. In this paper, the three-dimensional (3D) behavior is investigated. The complex Poisson's ratio ( ν* ) is introduced. Its evolution with temperature and frequency is studied for a bitumen, a mastic, and a mix. Experimental results show that the time–temperature superposition principle is applicable in the 3D case. The same shift factor applies for E* and ν* . The Di Benedetto–Neifar model developed at Ecole Nationale des Travaux Publics de l’Etat to simulate so far the 1D thermo-elastoviscoplastic behavior of bituminous materials has been extended to simulate their 3D isotropic behavior. Calibration of the model and comparison between simulations in the linear viscoelastic domain and experimental data are proposed.

Composite Materials with Viscoelastic Stiffness Greater Than Diamond

Abstract: We show that composite materials can exhibit a viscoelastic modulus (Young's modulus) that is far greater than that of either constituent. The modulus, but not the strength, of the composite was observed to be substantially greater than that of diamond. These composites contain bariumtitanate inclusions, which undergo a volume-change phase transformation if they are not constrained. In the composite, the inclusions are partially constrained by the surrounding metal matrix. The constraint stabilizes the negative bulk modulus (inverse compressibility) of the inclusions. This negative modulus arises from stored elastic energy in the inclusions, in contrast to periodic composite metamaterials that exhibit negative refraction by inertial resonant effects. Conventional composites with positive-stiffness constituents have aggregate properties bounded by a weighted average of constituent properties; their modulus cannot exceed that of the stiffest constituent.

Robust Strategies for Automated AFM Force Curve Analysis—II: Adhesion-Influenced Indentation of Soft, Elastic Materials

Abstract: In the first of this two-part discourse on the extraction of elastic properties from atomic force microscopy (AFM) data, a scheme for automating the analysis of force-distance curves was introduced and experimentally validated for the Hertzian (i.e., linearly elastic and noninteractive probe-sample pairs) indentation of soft, inhomogeneous materials. In the presence of probe-sample adhesive interactions, which are common especially during retraction of the rigid tip from soft materials, the Hertzian models are no longer adequate. A number of theories (e.g., Johnson-Kendall-Roberts and Derjaguin-Muller-Toporov), covering the full range of sample compliance relative to adhesive force and tip radius, are available for analysis of such data. We incorporated Pietrement and Troyon's approximation (2000, "General Equations Describing Elastic Indentation Depth and Normal Contact Stiffness Versus Load," J. Colloid Interface Sci., 226(1), pp. 166-171) of the Maugis-Dugdale model into the automated procedure. The scheme developed for the processing of Hertzian data was extended to allow for adhesive contact by applying the Pietrement-Troyon equation. Retraction force-displacement data from the indentation of polyvinyl alcohol gels were processed using the customized software. Many of the retraction curves exhibited strong adhesive interactions that were absent in extension. We compared the values of Young's modulus extracted from the retraction data to the values obtained from the extension data and from macroscopic uniaxial compression tests. Application of adhesive contact models and the automated scheme to the retraction curves yielded average values of Young's modulus close to those obtained with Hertzian models for the extension curves. The Pietrement-Troyon equation provided a good fit to the data as indicated by small values of the mean-square error. The Maugis-Dugdale theory is capable of accurately modeling adhesive contact between a rigid spherical indenter and a soft, elastic sample. Pietrement and Troyon's empirical equation greatly simplifies the theory and renders it compatible with the general automation strategies that we developed for Hertzian analysis. Our comprehensive algorithm for automated extraction of Young's moduli from AFM indentation data has been expanded to recognize the presence of either adhesive or Hertzian behavior and apply the appropriate contact model.