Showing papers on "Elastic modulus published in 1990"

Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates

Abstract: A novel strain-energy function which is a simple cubic equation in the invariant (I1−3) is proposed for the characterization of the elastic properties of carbon-black-filled rubber vulcanizates. Conceptually, the proposed function is a material model with a shear modulus which varies with deformation. This contrasts with the neo-Hookean and Mooney-Rivlin models which have a constant shear modulus. The variation of shear modulus with deformation is commonly observed with filled rubbers. Initially, the modulus falls with increasing deformation, leading to a flattening of the shear stress/strain curve. At large deformations, the modulus rises again due to finite extensibility of the network, accentuated by the strain amplication effect of the filler. This characteristic behavior of filled rubbers may be described approximately by the proposed strain-energy function by requiring the coefficient C20 to be negative, while the coefficients C10 and C30 are positive. The use of the proposed strain-energy ...

A new method for analyzing data from continuous depth-sensing microindentation tests

Abstract: A new parameter, hardness/modulus2 (H/E2), has been derived from the equations used to calculate the hardness and elastic modulus from data taken during continuous depth-sensing microindentation tests. This paper discusses the use of this parameter to treat the data obtained from a sample whose surface roughness was of the same scale as the size of the indents. The resulting data were widely scattered. This scatter was reduced when the data were plotted in terms of H/E2 versus stiffness. The effect of surface roughness on the hardness and elastic modulus results is removed via stiffness measurements, provided single contacts are made between the indenter and the specimen. The function relating the cross-sectional area of the indenter versus the distance from its point is not required for calculation of H/E2, but the hardness and modulus cannot be determined separately. The parameter H/E2 indicates resistance to plastic penetration in this case.

Structural properties of ordered high-melting-temperature intermetallic alloys from first-principles total-energy calculations

Abstract: Intermetallic compounds which are ductile at high temperatures are of great technological interest; however, purely experimental searches for improved intermetallic materials are time consuming and expensive. Theoretical studies can shorten the experimental search by focusing on compounds with the desired properties. While current ab initio density-functional calculations cannot adequately determine material properties at high temperature, it is possible to compute the static-lattice equation of state and elastic moduli of ordered binary compounds. Known correlations between equilibrium properties and high-temperature properties such as the melting temperature can then be used to point the way for experiments. We demonstrate the power of this approach by applying the linear augmented-plane-wave method to the calculation of the equation of state and all of the zero-pressure elastic moduli for SbY in the B1 (NaCl) phase, CoAl and RuZr in the B2 (CsCl) phase, and NbIr in the L${1}_{0}$ (Au-Cu I) phase. The calculated equilibrium lattice constants are all within 2% of the experimentally determined values. The only experimentally known elastic moduli in these systems are the bulk and shear moduli for polycrystalline SbY, CoAl, and NbIr. The predicted bulk moduli are with 7% of experiment. Theory enables us to place limits on the experimental polycrystalline shear modulus. The experimental shear moduli of SbY and CoAl are within our theoretical bounds, but the experimental shear modulus of NbIr is 35% smaller than our lower bound. We stress that in the case of CoAl our calculations provided a prediction for the bulk and shear moduli that were subsequently confirmed by the experiments of Fleischer. We also discuss the band structures and electronic density of states for these materials.

Nonlinear elasticity and pressure-dependent wave speeds in granular media

Abstract: Following is an analysis of the small-strain nonlinear elasticity of granular media near states of zero stress, as it relates to the pressure-dependent incremental linear elasticity and wave speeds. The main object is elucidation of the p ½ dependence of incremental elastic moduli on pressure p , a dependence observed in numerous experiments but found to be at odds with the p ½ scaling predicted by various micromechanical models based on hertzian contact. After presenting a power-law continuum model for small-strain nonlinear elasticity, the present work develops micromechanical models based on two alternative mechanisms for the anomalous pressure scaling, namely: (1) departures at the single-contact level from the hertzian contact, due to point-like or conical asphericity; (2) variation in the number density of hertzian contacts, due to buckling of particle chains. Both mechanisms result in p ½ pressure scaling at low pressure and both exhibit a high-pressure transition to p ½ scaling at a characteristic transition pressure p *. For assemblages of nearly equal spheres, a non-hertzian contact model for mechanism (1) and percolation-type model for (2) yield estimates of p * of the form p * = c μ ˆ ∝ 3 . Here c is a non-dimensional coefficient depending only on granular-contact geometry, while α ≪ 1 is a small parameter representing spherical imperfections and μ ˆ is an appropriate elastic modulus of the particles. Then, with R representing particle radius and h a characteristic spherical tolerance or asperity height, it is found that α = ( h / R ) ½ for mechanism (1) as opposed to α = h / R for (2). Limited data from the classic experiments of Duffy & Mindlin on sphere assemblages tend to support mechanism (1), but more exhaustive experiments are called for. In addition to the above analysis of reversible elastic effects, a percolation model of inelastic ‘shake-down’ or consolidation is given. It serves to describe how prolonged mechanical vibration, leading to the replacement of point-like or inactive contacts by stiffer Hertz contacts may change the pressure-scaling behaviour of particulate media. The present analysis suggests that pressure-dependence of elasticity may provide a useful means of characterizing the state of consolidation and stability of dense particulate media.

Mechanical properties of trabecular bone from the proximal femur: a quantitative CT study.

Abstract: We have investigated the relationships between trabecular bone compressive strength and elastic modulus and the directly measured apparent density and noninvasively measured CT equivalent mineral density for 49 cylindrical specimens harvested from fresh human proximal femora. Compressive strength demonstrated a high positive correlation with both densities, being proportional to the apparent density raised to the 1.8 power (R2 = 0.93) and equivalent mineral density to the 1.5 power (R2 = 0.89). Similarly, the compressive modulus demonstrated a high correlation with both density measures, being proportional to the apparent density raised to the 1.4 power (R2 = 0.91) and CT equivalent mineral density to the 1.2 power (R2 = 0.90). Though variations in architecture and bone marrow fat were observed to influence trabecular properties, the data presented here demonstrate that apparent density, compressive strength, and elastic modulus can be determined accurately using single energy quantitative CT. We expect that the use of these noninvasive data will result in improved estimates of that component of hip fracture risk that is attributable to bone strength.

Theory of spontaneous vesicle formation in surfactant mixtures.

Abstract: The curvature elastic energy of bilayer vesicles formed by a mixture of two surfactants, which individually form either micelles or lamellar bilayer phases is described theoretically. In the limit of large bending elastic modulus K being much greater than the temperature T, the free energy is minimized by vesicles with different concentrations of the two surfactants in each monolayer of the bilayer. Vesicles are more stable than lameliar structures only when interactions or complexing of the two surfactants is taken into account.

Electronic, elastic, and fracture properties of trialuminide alloys: Al3Sc and Al3Ti

Abstract: The electronic mechanism behind the brittle fracture of trialuminide alloys is investigated using the full-potential linearized augmented plane-wave (FLAPW) total-energy method within the local density functional approach. To this end, the bulk phase stability, the elastic constants, the anti-phase boundary (APB) energy, the superlattice intrinsic stacking fault (SISF) energy, and the cleavage energy on different crystallographic planes have been determined. A small energy difference (=0.10 eV/unit formula) is found between the DO22 and L12 structures of Al3Ti. In general, the trialuminide alloys have large elastic modulus, small Poisson's ratio, and small shear modulus to bulk modulus ratio. An extremely high APB energy (=670 mJ/m2) on the (111) plane is found for Al3Sc, indicating that the separation between ½(110) partials of a (110)(111) superdislocation is small. Since the total superdislocation has to be nucleated essentially at the same time, a high critical stress factor for dislocation emission at the crack tip is suggested. The high APB energy on the (111) plane is attributed to the directional bonding of Sc(d-electron)-Al(p-electron). The same type of directional bonds is also found for Al3Ti. In addition, moderately high values of SISF energy (=265 mJ/m2) on the (111) plane and APB energy (=450 mJ/m2) on the (100) plane are found for Al3Sc. The brittle fracture of trialuminide alloys is attributed to the higher stacking fault energies and a lower cleavage strength compared to those of a ductile alloy (e.g., Ni3Al). While the (110) surface has the highest surface energy, the cleavage strength (=19 GPa) of Al3Sc is found to be essentially independent of the crystallographic planes. The directional Sc—Al bond becomes even stronger on the (110) surface, which may explain the preferred (110) type cleavage observed by experiment.

Effective elastic moduli of porous solids

Abstract: The principles of continuum mechanics can be extended to porous solids only if the effective moduli are known. Although the effective bulk modulus has already been determined by approximating the geometry of a porous solid to be a hollow sphere, bounds could only be established for the other moduli. This problem of indeterminacy of the moduli is solved in this study using a particular model from the variation of the effective Poisson's ratio. In addition to this, the results are extended for the hollow sphere to real geometry by introducing a porositydependent factor. These results are compared with experimental data and the agreement is found to be good. As the effective Poisson's ratio cannot be determined accurately using experiments, the derived equation is verified using finite element analysis.

The effect of substrate on the elastic properties of films determined by the indentation test — axisymmetric boussinesq problem

Abstract: T he elastic solution of an axisymmetric mixed boundary value problem is considered. An elastic layer is assumed to be either in frictionless contact or perfectly bonded to a semi-infinite elastic half-space. The elastic field caused by the indentation of the elastic layer, by a rigid indenter is solved for spherical, conical and flat-ended cylindrical indenters. The results are obtained by solving a Fredholm integral equation of the second kind with a continuous symmetrical kernel which depends on the bonding conditions. Numerical results are given for several combinations of film and substrate elastic moduli and film thicknesses. These results provide a guideline for selecting the appropriate film thickness and substrate in order to determine the elastic constants of thin films.

Mechanical Properties of Hardened Cement Paste Exposed to Temperatures up to 700 C (1292 F)

Abstract: Temperatures of significance are identified in the range 20 to 700 C (68 to 1292 F) for changes in strength and elastic modulus both static and dynamic) of unsealed hardened cement paste measured at the various temperaturues as well as after cooling. These changes are correlated with chemical microstructural changes reported in the literature. The beneficial effects of thermal drying and loading, within limits, upon these mechanical properties are observed. It is concluded that these properties are dependent primarily on the maximum temperature of exposure as opposed to the temperature at testing.

The effect of cell size on the mechanical behavior of cellular materials

Abstract: The Young's modulus, strength and fracture toughness, of a brittle reticulated vitreous carbon foam, was measured as a function of cell size at a constant density and compared to a theoretical model Image analysis was used to characterize the macrostructure of the samples and provided a basis for evaluating the mechanical behavior It was determined that both the compressive and bend strength scale inversely with cell size The change in compressive strength is due to a change in the strut strength with cell size The bend strength behavior may be due to a reduction in the critical flaw size, as well as the increasing strut strength at smaller cell sizes The fracture toughness and elastic modulus were found to be independent of cell size Comparison of these results with previous work on open cell alumina clearly indicates a very different behavior and is attributed to a change in the microstructure of the solid phase with cell size in the alumina materials

Effect of coarse-aggregate characteritics on mechanical properties of high-strength concrete

Abstract: An experimental study investigated the influence of 4 coarse aggregate types available in Northern California on the compressive strength and elastic behavior of a very high-strength concrete mixture. Using identical materials and similar mix proportions, it was found using diabase and limestone aggregates produced concretes with significantly higher strength and elastic modulus than those using granite and river gravel. The mineralogical differences in the aggregate types are considered to be responsible for this behavior.

Dynamic Response of Sand Reinforced with Randomly Distributed Fibers

Abstract: Laboratory resonant-column and torsional shear tests are performed to determine the dynamic response (i.e., shear modulus and damping) of sands reinforced with discrete, randomly distributed fibers. The effect of fiber inclusion is evaluated as a function of shearing-strain amplitude, confining stress, prestrain, number of cycles, fiber content, aspect ratio, and modulus. The dynamic modulus increases with increasing fiber aspect ratio, modulus, and with increasing fiber content to a limiting weight fraction. The presence of fibers reduces prestrain effects often observed in unreinforced sands. The increase in dynamic modulus of fiber-reinforced sand is decidedly more pronounced at high shearing-strain amplitudes. The maximum percentage increase in modulus as a result of fiber inclusions occurred over a narrow range of confining stresses from 3 to 10 psi (21 to 48 kPa). Damping was less affected by the inclusion of fibers tan shear modulus. The dynamic response of sands reinforced with vertically oriented fibers is very similar to that of randomly distributed fibers.

Calculated elastic and thermal properties of MGO at high pressures and temperatures

Abstract: Using the potential-induced breathing model, we calculate the pressure and temperature dependence of the thermoelastic properties of MgO. These calculations represent the first attempt to obtain a consistent set of thermodynamic elastic moduli for an oxide from an ab initio model over a wide range of pressure and temperature. By assuming the quasi-harmonic approximation for the free energies, we find excellent agreement between the temperature dependence of calculated elastic moduli and those obtained from experiments. Comparison of the calculated athermal and isothermal elastic moduli shows approximations using athermal values to be unreliable at high temperature. The elastic moduli for MgO are presented for pressures and temperatures appropriate for the lower mantle, a regime in which elastic moduli cannot be obtained by direct measurement.

Rigid polymer network models

Abstract: A model is presented for the elasticity of networks composed of rigid chains. The elastic modulus as a function of polymer volume fraction is determined for two cases : (a) the chains are rigidly crosslinked to each other i.e. the network may only deform by bending the chains (energetic network) and, (b) the chains are allowed to rotate freely about the crosslink points so that there is entropy associated with the crosslinks. A crossover concentration between the two behaviours Φc is defined. The reinforcement of a rigid network, by introducing a small concentration cp of straight rod-like elements of length P (much greater than the mesh size of the lattice) is found to increase the modulus by a factor, GP ∝ cP P. Finally we discuss how rigid networks may swell, and « de-swell » if the solvent quality is changed and calculate a possible form of the swelling ratio, as a function of the length of the network chains. The system is found to be unstable for a swelling ratio greater than v 2 eq = (5/4)3.

Elastic constants of MoSi2 and WSi2 single crystals

Abstract: Single crystals of MoSi2 and WSi2 with a body-centred-tetragonal C 1 1b structure were fabricated using a floating-zone method. The elastic wave velocity was measured for samples with various orientations using a simple pulse echo method at room temperature, and six elastic stiffness constantsc ij were calculated. The stiffness constants were a little higher for WSi2 than for MoSi2.c 11 andc 33 of these compounds were approximately equal toc 11 of tungsten and molybdenum, respectively, althoughc ij (i ≠j) was a little higher for these compounds than for molybdenum and tungsten. Young's modulus 1/s 11 was the highest in the direction, and the lowest in the direction. The shear modulus 1/s 66 was high on the {0 0 1} plane and independent of shear direction. It was generally low on the close-packed {1 1 0} plane and largely dependent on shear direction. The elastic constants for the polycrystalline materials were estimated fromc ij ands ij . Poisson's ratiov was 0.15 for MoSi2 and for WSi2, and these values were much lower than for ordinary metals and alloys. The Debye temperature θD was estimated using the elastic-wave velocity of the polycrystalline materials via the elastic constants such as Young's modulus and shear modulus: it was 759 K for MoSi2 and 625 K for WSi2.

Crosslinked biopolymers: Experimental evidence for scalar percolation theory

Abstract: Rheological measurements have been performed on pectin biopolymers close to the sol-gel transition. From these measurements scaling exponents were determined independently for the viscosity, s=0.82(5), for the elastic modulus, t=1.93(8), for the frequency-dependent modulus, \ensuremath{\Delta}=0.71(2), and for the relaxation times below and above the transition, \ensuremath{ u}z=2.67(12) and \ensuremath{ u}z'=2.65(9). The exponents satisfy the scaling relations predicted by the theory and their numerical values agree with those from scalar elasticity percolation. Universal scaling functions were constructed from the data for the complex modulus and the dynamic viscosity.

Estimation of subgrade resilient modulus from standard tests

Abstract: Mechanistic pavement design procedures based on elastic layer theory require the specification of elastic moduli for each material in the pavement section. Repeated load tests yielding a resilient modulus are frequently used to characterize the soil subgrade. Due to difficulties associated with cyclic testing, approximate methods are often used for design estimates of resilient modulus. These approximations are often based only on shear strength measures and do not account for the dependence on the magnitude of cyclic deviator stress. A procedure is described to relate the soil-index properties and the moduli obtained from unconfined compression tests, to resilient modulus. Two statistical models are described and demonstrated for 11 soils from throughout the state of Tennessee. One model provides an estimation of the breakpoint resilient modulus, or the modulus at a deviator stress of 6 psi (41 kPa). The second model provides a general nonlinear relationship for the modulus of fine-grained soils as a function of deviator stress. Both models are demonstrated for a range of soils and are shown to provide a good characterization of the response for the soils investigated. Similar relationships can be developed for other subgrade soils, and may prove useful to agencies that use deterministic pavement design procedures, but lack the capability for high-production repeated-load testing.

Anchor ring-vesicle membranes.

Abstract: A family of the exact and analytical solutions of the equilibrium shape equation of vesicle membranes is found. They are anchor rings with generating circles of radii in the ratio 1/ \ensuremath{\surd}2 . It is shown that these ring vesicles are stable for some negative values of their spontaneous curvatures, such that experimental construction of such vesicles seems possible. A discussion shows that a positive Gauss-curvature elastic modulus favors the formation of these special vesicles.

Effective Elastic Moduli of Ribbon-Reinforced Composites

Abstract: Based on the Eshelby-Mori-Tanaka theory the nine effective elastic constants of an orthotropic composite reinforced with monotonically aligned elliptic cylinders, and the five elastic moduli of a transversely isotropic composite reinforced with two-dimensional randomly-oriented elliptic cylinders, are derived. When the aspect ratio approaches zero, the elliptic cylinders exist as thin ribbons, and these moduli are given in very simple, explicit forms as a function of volume fraction. These results are in direct contrast to those of circular fibers

Dynamic viscoelastic characterization of sol-gel reactions

Abstract: The evolution of the storage and loss dynamic shear module during the acid-catalyzed hydrolysis and condensation of tetraethoxysilane is studied from mixing through the gel point. Reaction time dependant shift factors for the frequency and modulus are determined which allow creation of a modulus. Frequency master curve. The scaling of these shift factors with the extent of reaction yields critical exponents for zero shear viscosity, elastic modulus and cluster radius

Tensile Properties of Short Fiber-Reinforced SiC/AI Composites: Part I. Effects of Matrix Precipitates

Abstract: The tensile behavior of aluminum matrix composites reinforced with 8 and 20 pet SiC whiskers or paniculate was characterized. Two matrix alloys were employed, a solution-hardened Al-Mg alloy (5456) and a precipitation-hardened Al-Cu-Mg alloy (2124). The precipitation-hardened alloy was aged to develop a variety of precipitate microstructures. It was found that additions of SiC caused monotonie increases in the elastic modulus, 0.2 pct offset yield stress, work-hardening rate, and ultimate tensile stress. The proportional limit, however, was found to first decrease and then increase with SiC content. Whiskers caused a greater increase in the longitudinal elastic modulus than particles. For the 2124 alloy, it was found that the proportional limit could be varied between 60 and 650 MPa by changing the precipitate microstructure, while changes in the SiC content had much smaller effects. These observations are discussed in relation to current theories of the strengthening of short fiber composites, with primary emphasis being placed on the effects of SiC additions on the elastic modulus and the work-hardening rate.

Alkali-free bioactive sol-gel compositions

Abstract: Sol-gel processing techniques are used to produce alkali-free bioactive glass compositions based on SiO2, CaO and P2O5. By varying the SiO2 content, a range of hydroxyapatite production rates can be obtained; conversely, varying the time of exposure to actual or simulated in vivo solutions permits use of a range of allowable proportions of SiO2. The sol-gel derived compositions can be chosen to achieve target values for thermal expansion coefficient, elastic modulus and volume electrical resistivity.

High elastic modulus bandage

Abstract: A high elastic modulus, cohesive bandage comprising partially extended spaced aligned elastic yarns sealed between two thin nonwoven fibrous webs by means of a polymeric binder is disclosed. The bandage provides joint support without imposing undue constriction. A method of supporting and/or providing compressive force to a mammalian limb including supporting suspensory ligaments and flexor tendons in the leg of a horse is also described.

Elasticity, shear‐mode softening and high‐pressure polymorphism of wüstite (Fe1‐xO)

Abstract: Elastic wave travel times have been determined as functions of hydrostatic pressure to 3 GPa for five modes of propagation in synthetic single-crystal wustite Feo.943O by ultrasonic phase comparison. The measured travel times, corrected for transducer-bond phase shifts, constrain very accurately the zero-pressure elastic moduli (GPa) and, for the first time, their first pressure derivatives (dimensionless) as follows: C11∶218.4, dC11/dP∶9.65, C12∶123.0, dC12/dP∶2.77, C44∶45.5, dC44/dP∶−1.03. The zero-pressure moduli are in good agreement with the results of previous determinations by ultrasonic wave propagation but not with all of the moduli determined by resonance techniques. The variation of bulk modulus with pressure calculated from the Cij (P) is extrapolated to much higher pressures via third-order Eulerian isotherms and isentropes based on K0S = 154.9 GPa and (dKs/dP)0T = 4.90. The resulting isothermal and shock compression curves satisfactorily reproduce the experimental data to ∼70 GPa, thereby providing a unified description of essentially all data bearing on the compressibility of wustite. At higher pressures, published shock compression studies provide clear evidence for the existence of a different phase of much greater density and incompressibility. Metallic values of electrical conductivity have been reported for pressures >70 GPa under conditions of shock and high-temperature static loading. Polyhedral face-sharing in either the B8(NiAs) or B2(CsCl) (or derivative) structures would result in shorter Fe-Fe distances, allowing greater 3d orbital overlap conducive to metallic conductivity. However, none of these possibilities satisfactorily accounts for the large inferred increase (14–20%) in zero-pressure density unless the Fe-O distance is also reduced by 3–5% by electron delocalization or spin-pairing. The marked violation of the Cauchy condition associated with the very low value of C44 and its unusual temperature and pressure derivatives are attributable mainly to exchange coupling between nearest and next-nearest neighbor spins.

Bending elasticity and thermal excitations of lipid bilayer vesicles: Modulation by solutes

Abstract: We present high-precision measurements of the bending elastic moduli of bilayers of a variety of different lipids and of modifications of the flexural rigidity by solutes. The measurements are based on the Fourier analysis of thermally excited membrane undulations (vesicle shape fluctuations) using a recently developed dynamic image processing method. Measurements of the bending modulus as a function of the undulation wave vector provide information on the limitation of the excitations by the constraint of finite membrane area (surface tension effects) and by transient lateral tensions arising in each monolayer by restricted diffusion at high wave vectors. Measurements of the autocorrelation function of the undulation amplitudes provide a further test of the theoretical models. Studies of the effect of solutes show that cholesterol increases the bending modulus of dimyristoylphosphatidylcholine from Kc = 1. 1 × 10−12 erg to 4.2 × 10−12 erg (at 30 mol%). Incorporation of a short bipolar lipid reduces Kc to the order of kT. Finally we present a variety of shape changes of vesicle and provide evidence for the stabilization of metastable non-equilibrium shapes by lateral phase separation.