Showing papers on "Elastic modulus published in 2009"

Effective elastic mechanical properties of single layer graphene sheets.

Abstract: The elastic moduli of single layer graphene sheet (SLGS) have been a subject of intensive research in recent years. Calculations of these effective properties range from molecular dynamic simulations to use of structural mechanical models. On the basis of mathematical models and calculation methods, several different results have been obtained and these are available in the literature. Existing mechanical models employ Euler-Bernoulli beams rigidly jointed to the lattice atoms. In this paper we propose truss-type analytical models and an approach based on cellular material mechanics theory to describe the in-plane linear elastic properties of the single layer graphene sheets. In the cellular material model, the C-C bonds are represented by equivalent mechanical beams having full stretching, hinging, bending and deep shear beam deformation mechanisms. Closed form expressions for Young's modulus, the shear modulus and Poisson's ratio for the graphene sheets are derived in terms of the equivalent mechanical C-C bond properties. The models presented provide not only quantitative information about the mechanical properties of SLGS, but also insight into the equivalent mechanical deformation mechanisms when the SLGS undergoes small strain uniaxial and pure shear loading. The analytical and numerical results from finite element simulations show good agreement with existing numerical values in the open literature. A peculiar marked auxetic behaviour for the C-C bonds is identified for single graphene sheets under pure shear loading.

Nonlinear elasticity of monolayer graphene

Abstract: By combining continuum elasticity theory and tight-binding atomistic simulations, we work out the constitutive nonlinear stress-strain relation for graphene stretching elasticity and we calculate all the corresponding nonlinear elastic moduli. Present results represent a robust picture on elastic behavior and provide the proper interpretation of recent experiments. In particular, we discuss the physical meaning of the effective nonlinear elastic modulus there introduced and we predict its value in good agreement with available data. Finally, a hyperelastic softening behavior is observed and discussed, so determining the failure properties of graphene.

Elastic bending modulus of monolayer graphene

Abstract: An analytic formula is derived for the elastic bending modulus of monolayer graphene based on an empirical potential for solid-state carbon atoms. Two physical origins are identified for the non-vanishing bending stiffness of the atomically thin graphene sheet, one due to the bond-angle effect and the other resulting from the bond-order term associated with the dihedral angles. The analytical prediction compares closely with ab initio energy calculations. Pure bending of graphene monolayers into cylindrical tubes is simulated by a molecular mechanics approach, showing slight nonlinearity and anisotropy in the tangent bending modulus as the bending curvature increases. An intrinsic coupling between bending and in-plane strain is noted for graphene monolayers rolled into carbon nanotubes. (Some figures in this article are in colour only in the electronic version)

Nano-indentation studies on polymer matrix composites reinforced by few-layer graphene.

Abstract: The mechanical properties of polyvinyl alcohol (PVA) and poly(methyl methacrylate) (PMMA)-matrix composites reinforced by functionalized few-layer graphene (FG) have been evaluated using the nano-indentation technique. A significant increase in both the elastic modulus and hardness is observed with the addition of 0.6 wt% of graphene. The crystallinity of PVA also increases with the addition of FG. This and the good mechanical interaction between the polymer and the FG, which provides better load transfer between the matrix and the fiber, are suggested to be responsible for the observed improvement in mechanical properties of the polymers.

Non-Linear Elasticity of Extracellular Matrices Enables Contractile Cells to Communicate Local Position and Orientation

Abstract: Most tissue cells grown in sparse cultures on linearly elastic substrates typically display a small, round phenotype on soft substrates and become increasingly spread as the modulus of the substrate increases until their spread area reaches a maximum value. As cell density increases, individual cells retain the same stiffness-dependent differences unless they are very close or in molecular contact. On nonlinear strain-stiffening fibrin gels, the same cell types become maximally spread even when the low strain elastic modulus would predict a round morphology, and cells are influenced by the presence of neighbors hundreds of microns away. Time lapse microscopy reveals that fibroblasts and human mesenchymal stem cells on fibrin deform the substrate by several microns up to five cell lengths away from their plasma membrane through a force limited mechanism. Atomic force microscopy and rheology confirm that these strains locally and globally stiffen the gel, depending on cell density, and this effect leads to long distance cell-cell communication and alignment. Thus cells are acutely responsive to the nonlinear elasticity of their substrates and can manipulate this rheological property to induce patterning.

Effect of cholesterol on structural and mechanical properties of membranes depends on lipid chain saturation

Abstract: The effects of cholesterol on membrane bending modulus K(C), membrane thickness D(HH), the partial and apparent areas of cholesterol and lipid, and the order parameter S(xray) are shown to depend upon the number of saturated hydrocarbon chains in the lipid molecules. Particularly striking is the result that up to 40% cholesterol does not increase the bending modulus K(C) of membranes composed of phosphatidylcholine lipids with two cis monounsaturated chains, although it does have the expected stiffening effect on membranes composed of lipids with two saturated chains. The B fluctuational modulus in the smectic liquid crystal theory is obtained and used to discuss the interactions between bilayers. Our K(C) results motivate a theory of elastic moduli in the high cholesterol limit and they challenge the relevance of universality concepts. Although most of our results were obtained at 30 degrees C , additional data at other temperatures to allow consideration of a reduced temperature variable do not support universality for the effect of cholesterol on all lipid bilayers. If the concept of universality is to be valid, different numbers of saturated chains must be considered to create different universality classes. The above experimental results were obtained from analysis of x-ray scattering in the low angle and wide angle regions.

Microstructure and mechanical properties of CoCrFeNiTiAlx high-entropy alloys

Abstract: CoCrFeNiTiAl x ( x values in molar ratio, x = 0, 0.5, 1.0, 1.5 and 2.0) high-entropy alloys were prepared using a vacuum arc melting method. The effects of Al addition on microstructure and mechanical properties were investigated. The results show that only a face-centered cubic (FCC) crystal structure phase is observed in the CoCrFeNiTi alloy. The phase composition transforms to stabilized body-centered cubic (BCC) structure phases and typically cast dendrite structure appears when Al is added. The dendrite region is rich in Co, Ni, Ti and Al elements while the interdendrite region is rich in Fe and Cr elements. Subgrains and nanosized precipitates are observed in the as-cast CoCrFeNiTiAl alloy. These CoCrFeNiTiAl x high-entropy alloys exhibit excellent room-temperature mechanical properties. For CoCrFeNiTiAl 1.0 alloy, the compressive strength and elastic modulus reach as high as 2.28 GPa and 147.6 GPa, respectively. High density of dimple-like structure is observed from the fracture surfaces of the Al 0 alloy, while alloys with Al addition show typical cleavage fractures with river-like patterns and cleavage steps.

Local elasticity map and plasticity in a model Lennard-Jones glass.

Abstract: In this work we calculate the local elastic moduli in a weakly polydispersed two-dimensional Lennard-Jones glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarse-grained microscopic expressions for the strain, displacement, and stress fields. This method allows us to calculate the local elasticity tensor and to quantify the deviation from linear elasticity (local Hooke's law) at different coarse-graining scales. From the results a clear picture emerges of an amorphous material with strongly spatially heterogeneous elastic moduli that simultaneously satisfies Hooke's law at scales larger than a characteristic length scale of the order of five interatomic distances. At this scale, the glass appears as a composite material composed of a rigid scaffolding and of soft zones. Only recently calculated in nonhomogeneous materials, the local elastic structure plays a crucial role in the elastoplastic response of the amorphous material. For a small macroscopic shear strain, the structures associated with the nonaffine displacement field appear directly related to the spatial structure of the elastic moduli. Moreover, for a larger macroscopic shear strain we show that zones of low shear modulus concentrate most of the strain in the form of plastic rearrangements. The spatiotemporal evolution of this local elasticity map and its connection with long term dynamical heterogeneity as well as with the plasticity in the material is quantified. The possibility to use this local parameter as a predictor of subsequent local plastic activity is also discussed.

Generalized hooke's law for isotropic second gradient materials

Abstract: In the spirit of Germain the most general objective stored elastic energy for a second gradient material is deduced using a literature result of Fortune ´ & Vallee. Linear isotropic constitutive relations for stress and hyperstress in terms of strain and strain- gradient are then obtained proving that these materials are characterized by seven elastic moduli and generalizing previous studies by Toupin, Mindlin and Sokolowski. Using a suitable decomposition of the strain-gradient, it is found a necessary and sufficient condition, to be verified by the elastic moduli, assuring positive definiteness of the stored elastic energy. The problem of warping in linear torsion of a prismatic second gradient cylinder is formulated, thus obtaining a possible measurement procedure for one of the second gradient elastic moduli.

Effects of strain rate, mixing ratio, and stress-strain definition on the mechanical behavior of the polydimethylsiloxane (PDMS) material as related to its biological applications.

Abstract: Tensile tests on Polydimethylsiloxane (PDMS) materials were conducted to illustrate the effects of mixing ratio, definition of the stress-strain curve, and the strain rate on the elastic modulus and stress-strain curve. PDMS specimens were prepared according to the ASTM standards for elastic materials. Our results indicate that the physiological elastic modulus depends strongly on the definition of the stress-strain curve, mixing ratio, and the strain rate. For various mixing ratios and strain rates, true stress-strain definition results in higher stress and elastic modulus compared with engineering stress-strain and true stress-engineering strain definitions. The elastic modulus increases as the mixing ratio increases up-to 9:1 ratio after which the elastic modulus begins to decrease even as the mixing ratio continues to increase. The results presented in this study will be helpful to assist the design of in vitro experiments to mimic blood flow in arteries and to understand the complex interaction between blood flow and the walls of arteries using PDMS elastomer.

Elastic Moduli of Organic Electronic Materials by the Buckling Method

Abstract: Mechanical moduli of common organic electronic materials are measured by the buckling method. The organic layers were prepared on the elastomer polydimethylsiloxane (PDMS) substrate by transfer, direct spin-coating, or thermal evaporation. When a small (∼2%) compressive strain is applied to organic/PDMS film samples, the layer becomes buckled with a characteristic wavelength. Fitting the experimentally measured data of buckling wavelength as a function of layer thickness with a model equation yields the mechanical modulus of the organic layer. The measured values compare well with those from theoretical predictions for materials such as poly(3-hexylthiophene) (P3HT) and its blend with [6,6]-phenyl C61-butyric acid methyl ether (PCBM). The modulus of poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) is similar to that of pure PSS, which is contrary to the common expectation that the ionic interaction between PEDOT and PSS chains may lead to a modulus value 2−3 times larger than that of th...

Link between surface elasticity and foam stability

Abstract: We have measured the surface dilational elastic moduli of bubbles immersed in water and soap bubbles in air. The short time response was obtained by submitting the bubbles to a rapid expansion after which the surface tension evolution was monitored, using either image analysis or pressure measurements. It was possible with this method to measure directly the Gibbs elasticity. The longer time response was obtained by submitting the bubbles to low frequency oscillations. Experiments were performed with solutions of non-ionic surfactants, C12E6, C12G2, their 1:1 mixture, Pluronic F-68 and 127 and the surface elastic moduli were compared with the stability of foams made with these surfactants. The foams evolve with time, first by Ostwald ripening, controlled by the low frequency elasticity, and then by bubbles coalescence, controlled by the high frequency elasticity.

Size effects in mechanical deformation and fracture of cantilevered silicon nanowires.

Abstract: Elastic modulus and fracture strength of vertically aligned Si [111] nanowires (o ) 100-700 nm) in an as-grown state have been measured using a new, multipoint bending protocol in an atomic force microscope. All wires showed linear elastic behavior, spring constants which scale with (length) 3 , and brittle failure at the wire-substrate junction. The “effective” Young’s modulus increased slightly (100 f 160-180 GPa) as wire diameter decreased, but fracture strength increased by 2-3 orders of magnitude (MPa f GPa). These results indicate that vapor-liquid-solid grown wires are relatively free of extended volume defects and that fracture strength is likely controlled by twinning and interfacial effects at the wire foot. Small wires (100 nm) grown with a colloidal catalyst were the best performers with high modulus (∼180 GPa) and fracture stress >1 GPa. One-dimensional nano-objects (nanowires, tubes, rods, springs, etc.) have attracted considerable interest lately as building blocks for electromechanical systems (oscillators, sensors, actuators), circuit interconnects, and composite materials of the future. Manipulation and exploitation of these new structures for technological applications requires detailed knowledge of material properties at the single nanostructure level. Previous studies have shown that the “effective” elasticity, strength, and plasticity of materials can all be influenced by size, shape, and “surface effects” (surface stress, oxide layers, roughness, and defects) when nanometer dimensions are involved. 1-5 Given the importance of such issues, it is no surprise that many interrogation techniques have been used to explore these effects: nanoindentation, tensile/bending (static and dynamic) tests, and resonant excitation. 1-16 In particular, atomic force microscope (AFM)based bending experiments on nanobeams and nanowires (NW) are very popular. These approaches typically measure the force required to deform a “beam” fabricated via topdown techniques, 6,7 NWs that have been artificially “fixed” to a surface with metallic pads, 8 or NWs positioned across a gap 9-12 (with and without surface pinning of the wire ends).

Deformation rate controls elasticity and unfolding pathway of single tropocollagen molecules.

Abstract: Collagen is an important structural protein in vertebrates and is responsible for the integrity of many tissues like bone, teeth, cartilage and tendon. The mechanical properties of these tissues are primarily determined by their hierarchical arrangement and the role of the collagen matrix in their structures. Here we report a series of Steered Molecular Dynamics (SMD) simulations in explicit solvent, used to elucidate the influence of the pulling rate on the Young's modulus of individual tropocollagen molecules. We stretch a collagen peptide model sequence [(Gly-Pro-Hyp)(10)](3) with pulling rates ranging from 0.01 to 100 m/s, reaching much smaller deformation rates than reported in earlier SMD studies. Our results clearly demonstrate a strong influence of the loading velocity on the observed mechanical properties. Most notably, we find that Young's modulus converges to a constant value of approximately 4 GPa tangent modulus at 8% tensile strain when the initially crimped molecule is straightened out, for pulling rates below 0.5 m/s. This enables us for the first time to predict the elastic properties of a single tropocollagen molecule at physiologically and experimentally relevant pulling rates, directly from atomistic-level calculations. At deformation rates larger than 0.5 m/s, Young's modulus increases continuously and approaches values in excess of 15 GPa for deformation rates larger than 100 m/s. The analyses of the molecular deformation mechanisms show that the tropocollagen molecule unfolds in distinctly different ways, depending on the loading rate, which explains the observation of different values of Young's modulus at different loading rates. For low pulling rates, the triple helix first uncoils completely at 10%-20% strain, then undergoes some recoiling in the opposite direction, and finally straightens for strains larger than 30%. At intermediate rates, the molecule uncoils linearly with increasing strain up to 35% strain. Finally, at higher velocities the triple helix does not uncoil during stretching.

Elastic modulus of amorphous polymer thin films: relationship to the glass transition temperature.

Abstract: Understanding the mechanical properties of polymers at the nanoscale is critical in numerous emerging applications. While it has been widely shown that the glass transition temperature (Tg) in thin...

Tensile properties of carbon nanotube reinforced aluminum nanocomposite fabricated by plasma spray forming

Abstract: Uniaxial tensile tests were performed on plasma spray formed (PSF) Al–Si alloy reinforced with multiwalled carbon nanotubes (MWCNTs). The addition of CNTs leads to 78% increase in the elastic modulus of the composite. There was a marginal increase in the tensile strength of CNT reinforced composite with degradation in strain to failure by 46%. The computed critical pullout length of CNTs ranges from 2.1 to 19.7 μm which is higher than the experimental length of CNT, leading to relatively poor load transfer and low tensile strength of PSF nanocomposites. Fracture surface validates that tensile fracture is governed strongly by the constitutive hierarchical microstructure of the plasma sprayed Al–CNT nanocomposite. The fracture path in Al–CNT nanocomposite occurs in Al–Si matrix adjacent to SiC layer on CNT surface.

General Properties of Hydrogels

Abstract: In the application areas of polymer hydrogels, precise information on their molecular constitution as well as their elastic properties is required. Several interesting molecular features control the elastic properties of the hydrogels. In this chapter, we describe general properties of hydrogels formed by free-radical cross-linking copolymerization of vinyl/divinyl monomers in aqueous solutions. Special attention is paid to the relationships between the formation conditions of hydrogels and their properties such as swelling behaviour, elastic modulus, and spatial inhomogeneity. New developments achieved in the design of hydrogels with a good mechanical performance and a fast response rate is also presented.