Showing papers on "Elastic modulus published in 1992"

An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments

Abstract: The indentation load-displacement behavior of six materials tested with a Berkovich indenter has been carefully documented to establish an improved method for determining hardness and elastic modulus from indentation load-displacement data. The materials included fused silica, soda–lime glass, and single crystals of aluminum, tungsten, quartz, and sapphire. It is shown that the load–displacement curves during unloading in these materials are not linear, even in the initial stages, thereby suggesting that the flat punch approximation used so often in the analysis of unloading data is not entirely adequate. An analysis technique is presented that accounts for the curvature in the unloading data and provides a physically justifiable procedure for determining the depth which should be used in conjunction with the indenter shape function to establish the contact area at peak load. The hardnesses and elastic moduli of the six materials are computed using the analysis procedure and compared with values determined by independent means to assess the accuracy of the method. The results show that with good technique, moduli can be measured to within 5%.

On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation

Abstract: Results of Sneddon's analysis for the elastic contact between a rigid, axisymmetric punch and an elastic half space are used to show that a simple relationship exists between the contact stiffness, the contact area, and the elastic modulus that is not dependent on the geometry of the punch. The generality of the relationship has important implications for the measurement of mechanical properties using load and depth sensing indentation techniques and in the measurement of small contact areas such as those encountered in atomic force microscopy.

Properties of diamond-like carbon

Abstract: This paper revies the preparation and properties of hard forms of amorphous carbon and hydrogenated amorphous carbon, often known as diamond-like carbon. Properties such as the hydrogen content, sp 3 content, optical gap, refractive index, hardness, elastic modulus and friction and their dependence on the deposition conditions are described. Models of the electronic structure and mechanical properties are used to relate the physical properties to the atomic structure.

Resistivities of conductive composites

Abstract: A steady‐state model for the resistivity of composites is presented, based on the idea that the resistance through a composite is the result of a series of a large number of resistors combined in series and parallel. There are three separate contributions to the resistance: constriction resistance at the contacts, tunneling resistance at the contacts, and the intrinsic filler resistance through each particle, with tunneling resistance generally dominating the magnitude of the overall resistance. The model predicts resistivity increases with increasing filler hardness and/or elastic modulus and insulating film thickness, while resistivity decreases with increasing particle size and intrinsic stress. The room‐temperature dc resistivity behavior of conductor‐filled silicone rubber composites was investigated to verify the model. Comparison of the model to this experimental data showed that good agreement could be obtained for filler materials in which the tarnish layer was a known quantity for a given powder...

Elastic constants of single‐crystal transition‐metal nitride films measured by line‐focus acoustic microscopy

Abstract: The elastic constants of single‐crystal NbN, VN, and TiN films were determined from surface acoustic wave (SAW) dispersion curves obtained by the use of an acoustic microscope with a line‐focus beam. Measurements were carried out for single‐crystal nitride films grown on the (001) plane of single‐crystal cubic‐symmetric MgO substrates. The phase velocities measured as functions of the angle of propagation display the expected anisotropy. Dispersion curves of SAWs propagating along the symmetry axes were obtained by measuring the wave velocities for various film thicknesses and frequencies. Using a modified simplex method, an inversion of the SAW dispersion data yielded the elastic constants of cubic symmetry, namely c11, c12, and c44. The Rayleigh surface wave velocities calculated from the determined elastic constants and known mass densities agree well with a result measured by Brillouin scattering spectroscopy reported elsewhere.

Nonlinear Cyclic Behavior of Reinforcing Bars Including Buckling

Abstract: The effects of inelastic buckling on monotonic and cyclic behavior of reinforcing steel bars are studied. Experimental tests show that this phenomenon occurs when the ratio between length and diameter of the bar exceeds 5, and that it leads to a postyield softening branch in compression that strongly influences the cyclic behavior of the bar. An analytical model of rebars accounting for inelastic buckling is presented, suitable for inclusion in programs for the analysis of r/c sections using the fiber type of discretization. The model employs four hardening rules (kinematic, isotropic, memory, and saturation) as functions of four independent parameters (yield stress, elastic modulus, hardening ratio, and a weighing coefficient). An explicit stress‐strain relation in finite terms for loading branches is utilized. The model yields accurate results in predicting the cyclic behavior of rebars, both with and without inelastic buckling, for deformation paths of general nature.

Elastic Behavior of Woven Fabric Composites: II—Laminate Analysis:

Abstract: Two-dimensional models are presented for the elastic analysis of the plain weave fabric laminates. A methodology to generate the laminate configuration from the lamina configuration is given. The effect of lamina configuration and their relative posi tions with respect to each other on the in-plane elastic constants of the woven fabric lami nates is studied. A laminate configuration with optimum shifts gives higher elastic proper ties compared to the other configurations. A comparison between in-plane elastic moduli of the unidirectionally laminated symmetric cross-ply laminates and plain weave fabric laminates is made. The in-plane elastic moduli of plain weave fabric laminates predicted by the models are found to be in good agreement with the experimental results.

High-temperature elasticity of iron-bearing olivines

Abstract: The first high-temperature data on the nine adiabatic elastic moduli for iron-bearing olivine are reported. These measurements are on two single-crystal specimens of natural olivine at ambient pressure and from room temperature to a maximum of 1500 K. The two specimens contain 8 and 9 modal percent fayalite, which required the oxygen fugacity be controlled at high temperature to preserve their chemical stability. The rectangular parallelepiped resonance apparatus was adapted to buffer the specimens from the atmosphere with a mixture of CO and CO2 gas. A small increase (∼1–2 GPa) in the adiabatic bulk modulus of each specimen, over that of end-member forsterite, was found. The data are high quality to extreme temperatures, with good agreement found when comparing the temperature derivatives of the elastic moduli of the two specimens. Neither specimen exhibits measurable nonlinear temperature dependence in the computed isotropic bulk and shear moduli, which is in contrast to published forsterite data. The temperature derivatives of the isotropic bulk modulus KS are (−1.69, −1.80) × 10−2 GPa K−1 for the two olivine specimens, and the shear modulus G derivatives are (−1.38, −1.36) × 10−2 GPa K−1. These derivatives are only slightly larger in magnitude than |(∂KS/∂T)P| = 1.56 × 10−2 and |(∂G/∂T)P| = 1.30 × 10−2 GPa K−1 found previously for iron-bearing olivine over a very small temperature range. There are also no significant differences between the temperature derivatives found here and the average derivatives of end-member forsterite from data retrieved over a slightly larger temperature range. Several dimensionless parameters have been calculated from these results and are discussed in view of systematics which bear on high-pressure phases in Earth's transition zone. One result from these systematics related to the seismic velocities in the Earth, and especially the shear wave velocities, is that an olivine content of less than 50% is implied at the 400-km discontinuity if Earth's upper mantle is isochemical. Furthermore, the substitution of almost 10% iron for magnesium at the forsterite end of the olivine solid solution series has little effect on the dimensionless parameters or on the temperature derivatives of the elastic moduli at high temperature.

Elastic modulus and equilibrium swelling of poly(dimethylsiloxane) networks

Abstract: Model poly(dimethylsiloxane) (PDMS) networks and imperfect networks confining pendant chains and branched structures are prepared by end-linking mixtures of di- and monofunctional PDMS and a tetrafunctional cross-linker. Values of the equilibrium modulus of the networks, obtained from dynamic mechanical experiments, illustrate the importance of the entanglement contribution to the elastic modulus. The extents of equilibrium swelling are determined for the networks in toluene and benzene. The predictions from the c * theorem do not apply to the model networks due to extensive interspersion of the network chains, which leads to entanglements that are not removed by swelling

A model for finite strain elasto-plasticity based on logarithmic strains: computational issues

Abstract: In the context of general isothermal processes, issues related to the constitutive modelling and computational treatment of finite deformation elasto-plasticity are examined employing logarithmic stretches as strain measures. A strain-energy function for isotropic elastic materials is proposed, which leads to a linear stress-strain relation and constant and isotropic elastic modulus in material setting. It is assumed that isotropy is maintained in the intermediate configuration which necessitates a representation of the plastic flow based on the scalar internal variables. By exploiting the main features of the present approach, expressed through the simple hyperelastic constitutive model in conjunction with notions of multiplicative decomposition of the deformation gradient and unstressed configuration, a computationally effective framework is formulated. It is pointed out that in this context, an algorithm could be proposed for rate-independent finite strain elasto-plasticity, which is exact for elastic processes and in the limit of non-hardening, deviatoric elasto-plasticity is in accordance with physical observations. Large elasto-plastic deformations at moderate elastic strains are examined within the approximation theory and displacement based finite element formulation of the boundary value problem proposed. Numerical analysis is performed for a realistic example capturing shear band localisation and the results are compared with experimental data.

Compressive mechanical properties of human cancellous bone after gamma irradiation.

Abstract: The effect of gamma irradiation on the mechanical properties of human bone was examined Specimens of cancellous bone were cut from the proximal epiphyseal region of fresh-frozen tibiae and divided into control and irradiated groups according to anatomical region The irradiated groups were exposed to 10,000, 31,000, 51,000, or 60,000 gray (10, 31, 51, or 60 megarad) The specimens were tested in compression to failure to determine failure stress, strain to failure, and elastic modulus Failure stress and elastic modulus were found to be proportional to the square of the density and were normalized with respect to this property Significant differences in normalized failure stress (p less than 0001) and normalized elastic modulus (p = 0003), when compared with the values for matched control specimens, were found only for the specimens that had been irradiated with 60,000 gray (60 megarad)

The elastic moduli of a sheet containing circular holes

Abstract: W e apply computer simulation techniques to obtain the clastic moduli of a matrix containing circular holes. As the area fraction of holes increases, the Young's modulus of the composite decreases from E0 until it eventually vanishes at the percolation threshold. We study three distinct geometries: (a) periodically centered circular holes on a honeycomb lattice, (b) periodically centered circular holes on a triangular lattice, and (c) randomly centered circular holes. All three cases have the same dilute limit that can be calculated exactly. By examining the narrow necks between adjacent circles, we have calculated the critical behavior for the regular cases and obtain critical exponents of 1 2 or 3 2 , depending on the local breakdown mode at the necks. For (c) we compare our results with an effective-medium theory, which predicts that the Poisson's ratio tends to 1 3 as the percolation threshold is approached, independent of its value in the pure system. Our results are also compared with recent experimental results. Based on this work, we propose that the relative Young's modulus E E 0 of a two-dimensional sheet containing circular holes, overlapping or not, is the same for ail materials, independent of the Poisson's ratio v0, for any prescribed geometry.

Relationship between structure and mechanical properties for aramid fibres

Abstract: The relationship between structure and mechanical properties for a series of twelve wellcharacterized aramid fibres has been determined. The fibres were produced under a variety of processing conditions and the fibre structure has been characterized using transmission electron microscopy. In particular, both the overall degree of molecular orientation in the fibres and the difference in structure between the fibre skin and core regions have been investigated in detail. The mechanical properties of the fibres have been evaluated using conventional mechanical testing and molecular deformation followed using Raman microscopy to monitor strain-induced band shifts. It has been shown that the mechanical properties of the fibres are controlled by the fibre structure. In particular, it is shown that the fibre modulus is governed by the overall degree of molecular orientation. It is also demonstrated that the fibre strength is controlled principally by the overall molecular orientation but may also be reduced by the presence of a highly-oriented skin region. It has been found that the rate of shift of the Raman bands per unit strain is proportional to the fibre modulus except for fibres with large differences in molecular orientation between fibre skin and core regions. For these fibres the rate of shift reflects the higher orientation of the skin.

Mori-Tanaka estimates of the overall elastic moduli of certain composite materials

Abstract: Simple, explicit formulae are derived for estimates of the effective elastic moduli of several multiphase composite materials with the Mori-Tanaka method. Specific results are given for composites reinforced by aligned or randomly oriented, transversely isotropic fibers or platelets, and for fibrous systems reinforced by aligned, cylindrically orthotropic fibers.

Tensile properties of polypropylene/kaolin composites

Abstract: Tensile properties of isotactic polypropylene filled with particulate kaolin fillers were evaluated in the composition range 0–60 wt % kaolin. Tensile modulus increased with filler concentration while breaking elongation and tensile strength decreased. The modulus increase was attributed to the restriction on the molecular mobility of the polymer imposed by kaolin particles. The decrease in elongation was also an effect of this restriction coupled with interference to stress transfer by the filler particles. Generation of discontinuity in the composite structure through formation of stress concentration points accounted for the tensile strength decrease. Morphology studies by SEM also indicated the introduction of stress concentration points by the presence of bare and nonadherent kaolin particles and their agglomerates with sharp edges in these composites.

The use of dilute solution viscometry to characterize the network properties of carbopol microgels

Abstract: We used dilute solution viscometry, specifically, measurements of intrinsic viscosity and overlap concentration to characterize two members of the carbopol family, carbopols 940 and 941 These measured quantities were then used to calculate the swollen-to-dry volume ratios for both resins over a range of ionic strengths The variation in this ratio is representative of the swelling equilibria of the micronetwork and is modeled using standard network theory with modifications for non-Gaussian chain statistics and for fixed charges on the chains By fitting to experimental data, the cross-link density is determined as 1450 monomer units between cross-link sites for carbopol 940 and 3300 units for carbopol 941 The shear modulus of the microgel domain is then predicted from the swelling data and found to be an order of magnitude greater than the elastic modulus measured on concentrated carbopol dispersions We argue that this discrepancy is due to a large number of defects which reduce the cycle rank of the network Current microgel technology specifies that their rheological behavior can be predicted once the domain cross-link density is known Simple dilute solution viscometry appears capable of providing this prerequisite

New results in the theory of elasticity for two-dimensional composites

Abstract: We bring together and discuss a number of exact relationships in two-dimensional (or plane) elasticity, that are useful in studying the effective elastic constants and stress fields in two-dimensional composite materials. The first of these dates back to Michell (1899) and states that the stresses, induced by applied tractions, are independent of the elastic constants in a two-dimensional material containing holes. The second involves the use of Dundurs constants which, for a composite consisting of two isotropic elastic phases, reduce the dependence of stresses on the elastic constants from three independent dimensionless parameters to two. It is shown that these two results are closely related to a recently proven theorem by Cherkaev, Lurie and Milton, which we use to show that the effective Young's modulus of a sheet containing holes is independent of the Poisson's ratio of the matrix material. We also show that the elastic moduli of a composite can be found exactly if the shear moduli of the components are all equal; a previously known result. We illustrate these results with computer simulations, where appropriate. Finally we conjecture on generalizations to multicomponent composite materials and to situations where the bonding between the phases is not perfect.

A Numerical Model for the Contact of Layered Elastic Bodies With Real Rough Surfaces

Abstract: A numerical model for the two-dimensional dry, frictionless contact of two elastic bodies with real rough surfaces, where one body has a rigidly bonded surface layer, is presented. The model uses surface profile data directly recorded with a stylus measuring instrument and is suitable for use on a microcomputer. Verification of the accurary of the model by reproduction of test case results is presented. Contact pressure distributions for layers of varying thickness and elastic modulus are presented

Grain boundaries as heterogeneous systems: atomic and continuum elastic properties

Abstract: The relation between atomic structure and elastic properties of grain boundaries is investigated theoretically from both atomistic and continuum points of view. A heterogeneous continuum model of the boundary is introduced where distinct phases are associated with individual atoms and possess their atomic level elastic moduli determined from the discrete model. The effective elastic moduli for sub-blocks from an infinite bicrystal are then calculated for a relatively small number of atom layers above and below the grain boundary. These effective moduli can be determined exactly for the discrete atomistic model, while estimates from upper and lower bounds are evaluated in the framework of the continuum model. The complete fourth-order elastic modulus tensor is calculated for both the local and the effective properties. Comparison between the discrete atomistic results and those for the continuum model establishes the validity of this model and leads to criteria to assess the stability of a given grain boundary structure. For stable structures the continuum estimates of the effective moduli agree well with the exact effective moduli for the discrete model. Metastable and unstable structures are associated with a significant fraction of atoms (phases) for which the atomic-level moduli lose positive definiteness or even strong ellipticity. In those cases, the agreement between the effective moduli of the discrete and continuum systems breaks down.

Mathematical modelling of the elastic properties of retina: A determination of Young's modulus

Abstract: The retina can be regarded as an elastic membrane or sheet which stretches and deforms when a force is applied to it. Isolated bovine retina was taken and a graded traction force applied to determine retinal profile as a function of force. The resulting profile can be modelled mathematically and the model then used to determine a value for the elastic constant. The value of the elastic constant obtained by this method is approximately 2 N/m. This value of the elastic constant, combined with the observed retinal thickness, yields a value of Young's modulus for retina of approximately 2 x 10(4) Pa, which is about 2 orders of magnitude weaker than typical rubber. This value can then be used in modelling retinal behaviour in vivo when forces are applied to detached retina.

Measurement of elastic properties of single-crystal CaO up to 1200 K

Abstract: The elastic moduli of a single-crystal calcium oxide, CaO, are measured in the temperature range from 300 to 1200 K (1.8 times of the Debye temperature) by the resonant sphere technique (RST). The lowest 18 modes are identified in the frequency range from 0.6 to 1.4 MHz for the vibrating spherical specimen, which is 5.6564 mm in diameter and 3.3493 g/cm3 in density at room temperature, and the resonant frequencies are traced as a function of temperature. The adiabatic elastic moduli are determined in the present temperature range from the observed frequencies by inversion calculations. Most of the elastic moduli, except forC 12 modulus, decrease as temperature increases. The temperature curves ofC s andC 44 moduli cross at 372 K. This means that the CaO specimen has an isotropic elasticity at the temperature. The temperature derivatives (∂C 11/∂T) P and (∂C s/∂T) P become slightly less negative with temperature increase and (∂C s /∂T) P and (∂C 44/∂T) P are almost constant. Combining the present elastic data with thermal expansion and specimen heat capacity data of CaO, we present the temperature dependence of thermodynamic parameters important in the studies of earth's interior.

Viscoelastic response of electrorheological fluids. II. Field strength and strain dependence

Abstract: In this paper, we elaborated on our previously developed model for the viscoelastic response of electrorheological (ER) fluids. We compared elastic modulus data obtained for a mineral‐type ER fluid over a range of dispersed phase concentrations (0.02–0.10), electric field strengths (0.1–5 kV/mm) and strains (0.2–15%) to model predictions for these parameters. We found that a point dipole approximation underestimated the modulus. Accounting for higher multipoles allowed for a closer prediction of the actual data. The strain dependence data were not rigorously quantitative because of experimental limitations. Here we discussed trends in the data and discussed the implications of the data on the assumptions of our model. We also pointed out similar trends in the work of others, all of which were consistent with the idea that ‘‘free strings’’ are an important microstructural feature of ER fluids which give rise to viscoelasticity. Microscopic observations of a variety of ER fluids were used to illustrate the structural features which we incorporated into our model.

Rheological properties of Y-Si-Al-O-N glasses — elastic moduli, viscosity and creep

Abstract: Three oxynitride glasses from the Y-Si-Al-O-N system and differing in their N/O ratio were studied in the 800–1000 °C temperature range. Their viscosities were measured using a threepoint bending test through the glass transition domain. For a given temperature, 4.8 wt % N2 enhances the viscosity by three orders of magnitude in comparison with the corresponding oxide glass. Nitrogen also improves creep resistance. The activation enthalpy for creep, aboveT g, is of the same order as those measured for silicon nitride ceramic (∼900 kJ mol−1). The elastic moduli were determined by ultrasonic techniques, from room temperature up to 1200 °C, which allowed calculation of the free activation enthalpy for viscous flow. Owing to the sharp decrease of shear modulus in the glass transition domain, the free activation enthalpy (∼500 kJ mol−1) greatly differs from the activation enthalpy usually measured in creep studies.

Relationships between the effective properties of transversely isotropic piezoelectric composites

Abstract: We consider two-phase fibre-reinforced piezoelectric composites of arbitrary transverse phase geometry wherein both the constitutents and the composite exhibit transverse isotropy. Such a material is described by a total of 10 overall elastic moduli, piezoelectric constants and permittivities. It is shown that five universal relationships which are independent of geometry at given volume fractions connect six of these effective physical constants. The result is a generalization of the relations found by Hill [J. Mech. Phys. Solids 12, 199 (1964)] for the purely elastic case. An additional relationship between three of the other constants is also known to exist.

The Effect of Sucrose on the Thermo-Reversible Gel-Sol Transition in Agarose and Gelatin

Abstract: The effects of sucrose on the elasticity and thermoreversible gel-sol transition in agarose and gelatin gels were studied. The concentration and temperature dependence of the elastic modulus was analysed by current theories of gel elasticity. The gel-sol transition observed by differential scanning calorimetry was discussed or the basis of a zipper model approach. It was suggested that the number of junction zones increased, the size of each junction zone decreased, and the rotational freedom of a link in a zipper decreased by the addition of sucrose.

Single‐crystal elastic properties of omphacite‐C2/c by Brillouin spectroscopy

Abstract: Single-crystal Brillouin scattering measurements of elastic moduli were performed on an eclogitic omphacite (space group C2/c) with chemical composition close to the diopside (CaMgSiO2O6, 29.9 mol %)-jadeite (NaAlSi2O6, 57.8 mol %) join. Prom the 13 elastic moduli measured under ambient conditions we calculate the adiabatic bulk modulus, KS = 130.8 ±0.5 GPa, and the shear modulus, μ = 79.2 ± 0.2 GPa. The magnitudes of all longitudinal elastic moduli (C11, C22, and C33) are inferred to be influenced primarily by the MgO6 and CaO8, or M polyhedra. Although the silica tetrahedra are extremely stiff, the great rotational freedom of these polyhedra yields a mechanical unit (tetrahedral chains) which is relatively compliant. Virtually all of the omphacite moduli are intermediate in value to those for diopside and Jadeite. Most of the moduli for omphacitic pyroxene can be estimated to within several percent by interpolation between the end member elastic moduli weighted according to the molar percentages of diopside and Jadeite.

A study of some properties of mineralized turkey leg tendon.

Abstract: Several macroscopic physical properties of mineralized turkey leg tendon were measured including wet density, composition, volume fractions of the major components, sonic velocity in three axes, longitudinal modulus and dimensional changes on drying. Where possible the properties were related to density. Typically the wet density of unmineralized tissue is 1.09 g/cc, where for fully mineralized tissue it is 1.6 g/cc (compared with 2.06 to 2.10 g/cc for compact cow bone). Longitudinal sonic velocity axially is 3.22 km/sec, 2.57 km/sec transversely and 2.21 km/sec in thickness. The axial longitudinal modulus is 16.7 GPa compared to the axial Young's modulus of 8.53 GPa. MTLT shrinks 0.5% axially, 4.75% transversely and 4.15% in thickness. The anisotropy is equally exhibited in its microscopic structure when observed optically.Least squares second order curves were fitted to the water, mineral and organic component experimental values. Apparently the water in MTLT is replaced by mineral, unlike the process i...