Showing papers on "Elastic modulus published in 2002"

Direct mechanical measurement of the tensile strength and elastic modulus of multiwalled carbon nanotubes

Abstract: We have conducted pulling and bending tests on individual carbon nanotubes in-situ in a transition electron microscope. Based on our observation of the force required to break the tube, a tensile strength of 0.15 TPa was computed. From corresponding bending studies on such nanotubes, the Young's modulus was estimated to be 0.9 TPa (0.8 TPa after ‘sub continuum’ corrections). These results suggest a strength that is a large fraction of the elastic modulus, although previous measurements of their elastic stiffness have yielded higher modulus values, by as much as a factor of 2. The result does indicate that individual nanotubes can fail as essentially defect-free materials. Furthermore, we observed no obvious reduction in cross-sectional area prior to the failure. In addition, the bending experiments revealed a remarkable flexibility in these tubes. These unique properties support the potential of nanotubes as reinforcement fibers in structural materials.

Fabrication of Carbon Multiwall Nanotube/Polymer Composites by Shear Mixing

Abstract: The dispersion of nanotubes in polymer matrices has been investigated as a means of deriving new and advanced engineering materials. These composite materials have been formed into fibers and thin films and their mechanical and electrical properties determined. The nanotube concentration at which conductivity was initiated (the percolation threshold) varied with host polymer. In poly(propylene), this was as low as 0.05 vol.-%, while higher concentrations were required for polystyrene and particularly for ABS. There was a small increase in elastic modulus and decrease in tensile strength at low nanotube loading, but as the concentration was increased there was a progressive increase in both strength and stiffness.

Aligned multi-walled carbon nanotube-reinforced composites: processing and mechanical characterization

Abstract: Carbon nanotubes have been the subject of considerable attention because of their exceptional physical and mechanical properties. These properties observed at the nanoscale have motivated researchers to utilize carbon nanotubes as reinforcement in composite materials. In this research, a micro-scale twin-screw extruder was used to achieve dispersion of multi-walled carbon nanotubes in a polystyrene matrix. Highly aligned nanocomposite films were produced by extruding the polymer melt through a rectangular die and drawing the film prior to cooling. Randomly oriented nanocomposites were produced by achieving dispersion first with the twin-screw extruder followed by pressing a film using a hydraulic press. The tensile behaviour of the aligned and random nanocomposite films with 5 wt.% loading of nanotubes were characterized. Addition of nanotubes increased the tensile modulus, yield strength and ultimate strengths of the polymer films, and the improvement in elastic modulus with the aligned nanotube composite is five times greater than the improvement for the randomly oriented composite.

Recent Advances in the Theory of Filler Networking in Elastomers

Abstract: The viscoelastic properties of (mostly carbon black) filled elastomers are reviewed with emphasis on the strain-dependence of the complex dynamic modulus (Payne effect) Considerable progress has been made in the past in relating the typical dynamical behavior at low strain amplitudes to a cyclic breakdown and reagglomeration of physical filler-filler bonds in typical clusters of varying size, including the infinite filler network Common features between the phenomenological agglomeration/deagglomeration Kraus approach and very recent semi-microscopical networking approaches (two aggregate VTG model, links-nodes-blobs model, kinetical cluster-cluster aggregation) are discussed All semi-microscopical models contain the assumption of geometrical arrangements of sub-units (aggregates) in particular filler network structures, resulting for example from percolation or kinetical cluster-cluster aggregation These concepts predict some features of the Payne effect that are independent of the specific types of filler These features are in good agreement with experimental studies For example, the shape exponent m of the storage modulus, G′, drop with increasing deformation is determined by the structure of the cluster network Another example is a scaling relation predicting a specific power law behavior of the elastic modulus as a function of the filler volume fraction The exponent reflects the characteristic structure of the fractal filler clusters and of the corresponding filler network The existing concepts of the filler network breakdown and reformation appear to be adequate in describing the deformation-dependence of dynamic mechanical properties of filled rubbers The different approaches suggest in a common manner that there is a change of filler structure with increasing dynamic strain However, in all cases additional assumptions are made about the accompanying energy dissipation process, imparting higher hysteresis to the filled rubber This process may be slippage of entanglements (slip-links) in the transition layer between bound rubber layer and mobile rubber phase, and/or partially release of elastically ‘dead’ immobilized rubber trapped within the filler network or agglomerates

Understanding nanoindentation unloading curves

Abstract: Experiments have shown that nanoindentation unloading curves obtained with Berkovich triangular pyramidal indenters are usually welldescribed by the power-law relation P = α(h − hf)m, where hf is the final depth after complete unloading and α and m are material constants. However, the power-law exponent is not fixed at an integral value, as would be the case for elastic contact by a conical indenter (m = 2) or a flat circular punch (m = 1), but varies from material to material in the range m = 1.2–1.6. A simple model is developed based on observations from finite element simulations of indentation of elastic–plastic materials by a rigid cone that provides a physical explanation for the behavior. The model, which is based on the concept of an indenter with an “effective shape” whose geometry is determined by the shape of the plastic hardness impression formed during indentation, provides a means by which the material constants in the power law relation can be related to more fundamental material properties such as the elastic modulus and hardness. Simple arguments are presented from which the effective indenter shape can be derived from the pressure distribution under the indenter.

Elastic modulus measurements of human liver and correlation with pathology.

Abstract: Viral hepatitis causes fibrosis in the liver and may change mechanical properties of the liver. To evaluate the impact of fibrosis on elastic properties of human liver and to investigate potential benefits of ultrasonic elasticity imaging, 19 fresh human liver samples and 1 hepatic tumor (focal nodular hyperplasia) sample obtained during operations were studied. Simple 1-D estimates based on the cyclic compression-relaxation method were performed. Elastic modulus values were derived from the predetermined strain (controlled by a step motor system) and the stress values (measured by an electronic balance). Each specimen subsequently received histologic examination and a grade of liver fibrosis was scored from 0 to 5. Results show that the elastic modulus values were on the order of several hundreds to thousands of Pascals. The elastic modulus generally increased with the fibrosis grade, although some discrepancies existed at the middle grades of fibrosis (scores 1 to 3). The correlation between the fibrosis score and the elastic modulus was significant (p < 0.01) based on the statistical analysis using the Pearson correlation method. In addition, the relation between the elastic modulus and the fibrosis grade generally exhibited a quadratic trend. It was concluded that severity of fibrosis had a good correlation with stiffness of the liver. Results also indicated that the elasticity imaging of the liver may provide significant clinical values if the elastic modulus can be accurately measured. (E-mail: paichi@cc.ee.ntu.edu.tw)

Elastic properties of model random three-dimensional open-cell solids

Abstract: Most cellular solids are random materials, while practically all theoretical structure-property relations are for periodic models. To generate theoretical results for random models the finite element method (FEM) was used to study the elastic properties of open-cell solids. We have computed the density (rho) and microstructure dependence of the Young's modulus (E) and Poisson's ratio (nu) for four different isotropic random models. The models were based on Voronoi tessellations, level-cut Gaussian random fields, and nearest neighbour node-bond rules. These models were chosen to broadly represent the structure of foamed solids and other (non-foamed) cellular materials. At low densities, the Young's modulus can be described by the relation E proportional to rho (n). The exponent n and constant of proportionality depend on microstructure. We find 1.3 < n < 3, indicating a more complex dependence than indicated by periodic cell theories, which predict n = 1 or 2. The observed variance in the exponent was found to be consistent with experimental data. At low densities we found that nu approximate to 0.25 for three of the four models studied. In contrast, the Voronoi tessellation, which is a common model of foams, became approximately incompressible (nu approximate to 0.5), This behaviour is not commonly observed experimentally. Our studies showed the result was robust to polydispersity and that a relatively large number (15%) of the bonds must be broken to significantly reduce the low-density Poission's ratio to nu approximate to 0.33. (C) 2001 Elsevier Science Ltd. All rights reserved.

Thin interphase/imperfect interface in elasticity with application to coated fiber composites

Abstract: The imperfect interface conditions which are equivalent to the effect of a thin elastic interphase are derived by a Taylor expansion method in terms of interface displacement and traction jumps. Plane and cylindrical interfaces are analyzed as special cases. The effective elastic moduli of a unidirectional coated fiber composite are obtained on the basis of the derived imperfect interface conditions. High accuracy of the method is demonstrated by comparison of solutions of several problems in terms of the imperfect interface conditions or explicit presence of interphase as a third phase. The problems considered are transverse shear of a coated infinite fiber in infinite matrix and effective transverse bulk and shear moduli and effective axial shear modulus of a coated fiber composite. Unlike previous elastic imperfect interface conditions in the literature, the present ones are valid for the entire range of interphase stiffness, from very small to very large.

Apparent elastic modulus and hysteresis of skeletal muscle cells throughout differentiation

Abstract: The effect of differentiation on the transverse mechanical properties of mammalian myocytes was determined by using atomic force microscopy The apparent elastic modulus increased from 115 +/- 13 kPa for undifferentiated myoblasts to 453 +/- 40 kPa after 8 days of differentiation (P < 005) The relative contribution of viscosity, as determined from the normalized hysteresis area, ranged from 013 +/- 002 to 021 +/- 003 and did not change throughout differentiation Myosin expression correlated with the apparent elastic modulus, but neither myosin nor beta-tubulin were associated with hysteresis Microtubules did not affect mechanical properties because treatment with colchicine did not alter the apparent elastic modulus or hysteresis Treatment with cytochalasin D or 2,3-butanedione 2-monoxime led to a significant reduction in the apparent elastic modulus but no change in hysteresis In summary, skeletal muscle cells exhibited viscoelastic behavior that changed during differentiation, yielding an increase in the transverse elastic modulus Major contributors to changes in the transverse elastic modulus during differentiation were actin and myosin

Characterisation of interphase nanoscale property variations in glass fibre reinforced polypropylene and epoxy resin composites

Abstract: The local microstructure can be altered significantly by various fibre surface modifications, causing property differences between the interphase region and the bulk matrix. By using tapping mode phase imaging and nanoindentation tests based on the atomic force microscope (AFM), a comparative study of the sized fibre surface topography and modulus as well as the local mechanical property variation in the interphase of E-glass fibre reinforced epoxy resin and E-glass fibre reinforced modified polypropylene (PPm) matrix composites was conducted. The phase imaging AFM was found a highly useful tool for probing the interphase with much detailed information. Nanoindentation experiments indicated the chemical interaction during processing caused by a gradient profile in the modulus across the interphase region of γ-aminopropyltriethoxy silane (γ-APS) and polyurethane (PU)-sized glass fibre reinforced epoxy composite. The interphase with γ-APS/PU sizing is much softer than the PPm matrix, while the interphase with the γ-APS/PP sizing is apparently harder than the matrix, in which the modulus was constant and independent of distance away from the fibre surface. The interphase thickness varied between less than 100 and ≈300 nm depending on the type of sizing and matrix materials. Based on a careful analysis of ‘boundary effect’, nanoindentation with sufficient small indentation force was found to enable measuring of actual interphase properties within 100 nm region close to the fibre surface. Special emphasis is placed on the effects of interphase modulus on mechanical properties and fracture behaviour. The interphase with higher modulus and transcrystalline microstructure provided simultaneous increase in the tensile strength and the impact toughness of the composites.

Effects of Creep and Thermal Drift on Modulus Measurement Using Depth-sensing Indentation

Abstract: In modulus measurement by depth-sensing indentation, previous considerations assume elastic recovery to be the sole process during unloading, but in reality creep and thermal drift may also occur, causing serious errors in the measured modulus. In this work, the problem of indentation on a linear viscoelastic half-space is solved using the correspondence principle between elasticity and linear viscoelasticity. The correction term due to creep in the apparent contact compliance is found to be equal to the ratio of the indenter displacement rate at the end of the load hold to the unloading rate. A condition for nullifying the effect of thermal drift on modulus measurement is also proposed. With this condition satisfied, the effect of thermal drift on the calculated modulus is negligible irrespective of the magnitude of the drift rate.

Field dependence of viscoelastic properties of mr elastomers

Abstract: A magnetoactive elastomer made of micronic carbonyl iron particles, structured in elongated clusters and embedded in a silicon elastomer matrix is studied under traction both in static and dynamic modes. The application of a magnetic field of 120 kA/m induces a change in elastic moduli of about 0.6 MPa at strains of 4 to 5%. Still higher changes (4 MPa) are observed in dynamic storage modulus at low strains (10-4 to 10-3). The shape of the stress-strain curves are explained by taking into account the existence of a fiber like structure.

Effects of nanotube waviness on the modulus of nanotube-reinforced polymers

Abstract: Recent experimental results demonstrate that substantial improvements in the mechanical behavior of polymers can be obtained using very small amounts of carbon nanotubes as a reinforcing phase. Here, a method is developed to incorporate the typically observed curvature of the embedded nanotubes into traditional micromechanical methods for determination of the effective modulus of the nanotube-reinforced polymer. Using a combined finite element and micromechanical approach, it was determined that the nanotube curvature significantly reduces the effective reinforcement when compared to straight nanotubes. This model suggests that nanotube waviness may be an additional mechanism limiting the modulus enhancement of nanotube-reinforced polymers.

Mechanical properties and interfacial characteristics of carbon-nanotube-reinforced epoxy thin films

Abstract: Multiwalled carbon nanotubes (MWNT) reinforced epoxy composite thin films were prepared by a microfabrication process and their elastic modulus was determined using a shaft-loaded blister test and linear and nonlinear elasticity models. Compared to net resin thin films, a 20% increase in elastic modulus was seen when 0.1 wt % MWNTs were added, suggesting MWNT alignment by spin coating. Electron microscopic observations of the fracture surfaces suggested high interfacial shear stress between MWNTs and the epoxy matrix, a result supported by both molecular mechanics simulation and micromechanics calculations.

Cell wall properties and their effects on the mechanical properties of fibers

Abstract: The properties of the cell wall are determined by its structure and by the properties of the wood polymers. In this study, the influence of the elastic constants of the three wood polymers on the elastic modulus of the cell wall was investigated. Cellulose was found to dominate the properties in the longitudinal direction. In the transverse direction, the effect of the properties of hemicellulose was more pronounced. The results show that it is possible to reduce the discrepancy between experimental and modeled values of the transverse modulus to a large extent by lowering the assumed values of the elastic constants of hemicellulose and lignin. The thickness and fibril angles of the S1- and S3-layers were also found to be important parameters for the transverse properties of the fiber wall. These two layers should not be neglected when transverse elastic properties are related to cell wall structure.

Extended elastic impedance for fluid and lithology prediction

Abstract: Constant angle projections of seismic sections can be designed to provide maximum discrimination between fluids or lithologies. The optimum projection for a noise‐free, isotropic environment can be obtained using an extension to the elastic impedance concept, which itself is an extension of acoustic impedance (AI) to nonzero angles of incidence. To achieve this, we modify the definition of elastic impedance (EI) beyond the range of physically meaningful angles by substituting tanχ for sin2 θ in the two‐term reflectivity equation. The primary variable now becomes χ rather than θ. We allow it to vary between −90° and +90°, which gives an extension of EI for any combination of intercept and gradient. We refer to this form of elastic impedance as extended elastic impedance (EEI).In this paper we demonstrate that EEI can be tuned using different χ values to be approximately proportional to a number of elastic parameters, and we give EEI expressions for shear impedance (SI), bulk modulus, shear modulus, Lame's ...

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

Abstract: A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

Mechanical properties of Al2O3/ZrO2 composites

Abstract: In the present study, both t-phase zirconia and m-phase zirconia particles are incorporated into an alumina matrix. Dense Al2O3/(t-ZrO2+m-ZrO2) composites were prepared by sintering pressurelessly at 1600 °C. The microstructure of the composites are characterized, the elastic modulus, strength and toughness determined. Because the ZrO2 inclusions are close to each other in the Al2O3 matrix, the yttrium ion originally in t-ZrO2 particles can diffuse to nearby m-ZrO2 particles during sintering, and the m-phase zirconia is thus stabilized after sintering. The strength of the Al2O3/(t-ZrO2+m-ZrO2) composites after surface grinding can reach values as high as 940 MPa, which is roughly three times that of Al2O3 alone. The strengthening effect is contributed by microstructural refinement together with the surface compressive stresses induced by grinding. The toughness of alumina is also enhanced by adding both t-phase and m-phase zirconia, which can reach values as high as two times that of Al2O3 alone. The toughening effect is attributed mainly to the zirconia t–m phase transformation.

Towards the understanding of mechanical properties of super- and ultrahard nanocomposites

Abstract: This article presents an attempt to explain in a simple way, understandable to a broad spectrum of readers, the unusual combination of the mechanical properties of the recently developed new class of superhard nanocomposites, such as high hardness which significantly exceeds that of the rule of mixtures, enhancement of the elastic modulus as measured by the indentation technique, very high elastic recovery which is observed upon the indentation and the absence of crack formation even under elastic deformation corresponding to a strain of more than 10%. Future experimental work is suggested which should bring further progress towards the understanding of these materials.