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Showing papers on "Elastic modulus published in 1975"


Journal ArticleDOI
TL;DR: In this paper, the authors describe a study of the adhesion between elastic solids and the effect of roughness on their adhesion, showing that roughness which is small compared with the overall deformation occurring at the region of the rubber-Perspex contact can produce an extremely large reduction in adhesion.
Abstract: This paper describes a study of the adhesion between elastic solids and the effect of roughness in reducing the adhesion. The experiments were carried out between optically smooth rubber spheres and a hard smooth flat surface of Perspex which could be roughened to various degrees. The radius of the rubber spheres was varied by a factor of 8, their elastic modulus by a factor of 10, while the centre line average (c.l.a.)of the roughened Perspex surface was varied from 0.12 to 1.5 μm. The results show that c.l.a. roughnesses which are small compared with the overall deformation occurring at the region of the rubber-Perspex contact can produce an extremely large reduction in adhesion. The effect is more marked for rubbers of higher modulus. On the other hand the curvature of the sphere (over the range examined) has little influence. For this reason and because the analytical problem of a sphere on a rough flat is extremely complicated a theoretical analysis has been developed for the simpler case of a smooth flat in contact with a rough flat surface. As in Greenwood & Williamson (1966) the rough surface is modelled by asperities all of the same radius of curvature and with heights following a Gaussian distribution of standard deviation σ. The overall contact force is obtained by applying the contact theory of Johnson, Kendall & Roberts (1971) to each individual asperity. The theory predicts that the adhesion expressed as a fraction of the maximum value depends upon a single parameter, 1/Δ e ,which is the ratio between a and the elastic displacement δ C that the tip of an asperity can sustain before it pulls off from the other surface. The analysis shows that the adhesion parameter may also be regarded as representing the statistical average of a competition between the compressive forces exerted by the higher asperities trying to prize the surfaces apart and the adhesive forces between the lower asperities trying to hold the surfaces together. Although the theory is derived for two nominally plane surfaces it is found to fit the experimental results for a sphere on a flat reasonably well.

838 citations


Journal ArticleDOI
01 Nov 1975-Wear
TL;DR: In this paper, the elastic contact of an isotropically rough surface with a plane is treated by approximating the summits of a random process model by paraboloids with the same principal curvatures and applying the classical Hertzian solution for their deformation.

710 citations


Journal ArticleDOI
TL;DR: In this article, the authors show that the force required to peel an elastic film from a rigid substrate depends not only on the adhesive surface energy but also on an elastic deformation term.
Abstract: An energy balance shows that the force required to peel an elastic film from a rigid substrate depends not only on the adhesive surface energy but also on an elastic deformation term. This elastic term, tending to reduce the adhesion force, can only be significant in two instances: for materials which can support stresses approaching the elastic modulus without fracturing, and for very small peel angles. Experiments using rubber peeling from glass over a range of peel angles support the theory.

687 citations


Journal ArticleDOI
TL;DR: In this paper, a semi-empirical method for the calculation of bulk modulus, shear modulus and Poisson's ratio of glass was proposed, combining Gruneisen's equation with Young's modulus equation of glass.
Abstract: Combining Gruneisen's equation with our Young's modulus equation of glass, new formulae were semi-empirically derived for the calculation of bulk modulus, shear modulus and Poisson's ratio of glass. Considering packing density of atoms and bond energy in unit volume the elastic moduli of glass can be calculated. The agreements between calculated and observed values of the moduli of glass are satisfactory for more than 30 glasses.

490 citations



Journal ArticleDOI
TL;DR: It is shown that the nonlinearI–V characteristics observed at different temperatures can be accurately accounted for with no adjustable parameters, by considerations of the mechanical compression of the membrane due to stresses induced by the electric field.
Abstract: The dielectric breakdown in the membranes of cells ofValonia utricularis was investigated using intracellular electrodes and 500-μsec current pulses. Electrical breakdown, which occurs when the membrane potential reaches a well-defined critical value, is not associated with global damage to the cell or its membranes (the membrane reseals in <5 sec). It was thus possible to investigate the effect of temperature on dielectric breakdown in single cells. It was found that the critical potential for breakdown was strongly dependent on temperature, decreasing from ∼1000 mV at 4°C to ∼640 mV at 30°C. The decrease in the breakdown potential with increasing temperature and the very short rise-time of the breakdown current (∼1 μsec) suggests that the Wien field dissociation does not play a major role in the breakdown process. It is shown that the nonlinearI–V characteristics observed at different temperatures can be accurately accounted for with no adjustable parameters, by considerations of the mechanical compression of the membrane due to stresses induced by the electric field. Electrical breakdown on this scheme results from an electromechanical instability in the membrane. On this basis the present results indicate that the elastic modulus of the region of the membrane where breakdown occurs, decreases by a factor of 2 with increasing temperature from 4 to 30°C. On the assumption of a thickness of 4.0 nm and a dielectric constant of 5, the elastic modulus is estimated to have a value of 5×106 Nm−2 at 20°C.

199 citations


Journal ArticleDOI
TL;DR: In this paper, the authors describe the behavior of a carbon-fibre reinforced epoxy composite when deformed in compression under high hydrostatic confining pressures and show that the failure strength of the composite increased rapidly with increasing confining pressure, though the elastic modulus remained constant.
Abstract: This paper describes the behaviour of a carbon-fibre reinforced epoxy composite when deformed in compression under high hydrostatic confining pressures. The composite consisted of 36% by volume of continuous fibres of Modmur Type II embedded in Epikote 828 epoxy resin. When deformed under pressures of less than 100 MPa the composite failed by longitudinal splitting, but splitting was suppressed at higher pressures (up to 500 MPa) and failure was by kinking. The failure strength of the composite increased rapidly with increasing confining pressure, though the elastic modulus remained constant. This suggests that the pressure effects were introduced by fracture processes. Microscopical examination of the kinked structures showed that the carbon fibres in the kink bands were broken into many fairly uniform short lengths. A model for kinking in the composite is suggested which involves the buckling and fracture of the carbon fibres.

136 citations


Journal ArticleDOI
TL;DR: The results suggest that the wall architecture at in vivo prestress is such that changes in axial prestress do not affect tangential properties of the wall when prestress increases, however, wall elements become reoriented, taking on a more axial direction and increasing directional interactions.

123 citations


Journal ArticleDOI
TL;DR: In this article, an equation for the mechanical behavior of polyurethane foams as a function of foam density is provided, starting from a model conception and the qualitative microscopic consideration of the deformation and failure mechanism, simple relations are found for the tensile, compressive and shear strength and the elastic modulus.
Abstract: Rigid plastic foams find application in construction mainly as core materials for loaded sandwich structures—in buildings, ground vehicles, and airplanes. This work provides an equation for the mechanical behavior of polyurethane foams as a function of foam density. Starting from a model conception and the qualitative microscopic consideration of the deformation and failure mechanism, simple relations are found for the tensile, compressive and shear strength and the elastic modulus, which sufficiently express the measured results.

117 citations


Journal ArticleDOI
L. R. Testardi1
TL;DR: In this article, the elastic modulus, thermalexpansion coefficient, and specific heat of a transformed phase relative to the untransformed phase are calculated assuming a particular but useful form of the thermodynamic potential.
Abstract: The interrelation of the elastic modulus, thermal-expansion coefficient, and specific heat of a transformed phase relative to the untransformed phase is calculated assuming a particular but useful form of the thermodynamic potential. For second-order phase transitions where this potential applies, measurements of modulus, expansion, and specific heat can yield the general (longitudinal as well as shear) first- and second-order stress (or strain) dependences of the transition temperature and of the order parameter at absolute zero. An exemplary application to one type of phase transition is given. (AIP)

107 citations


Journal ArticleDOI
TL;DR: In this paper, numerical formulae are given for stress relaxation modulus from the known course of the storage and loss modulus with frequency for linear viscoelastic materials.
Abstract: Numerical formulae are given for calculation of stress relaxation modulus from the known course of the storage and loss modulus with frequency for linear viscoelastic materials. The formulae involve values of the storage modulus and/or loss modulus at frequencies equally spaced on a logarithmic frequency scale, the ratio between successive frequencies beeing two. A method is introduced by which bounds for the relative errors of these formulae can be derived. These bounds depend on the value of the damping, tanδ, at the angular frequency,ω, for which the calculation is made. The less the damping, the simpler the calculation of the stress relaxation modulus. This calculation involves either the value of the storage modulus at a frequencyω 0 = 1/t, and the values of the loss modulus in a rather narrow frequency region aroundω 0, or the value of the storage modulus at frequencyω 0 and the derivative of the storage modulus with respect to the logarithm of frequency in a frequency region aroundω 0.

Journal ArticleDOI
TL;DR: In this paper, the dynamic elastic moduli of Zircaloy-2, Zr-1.15 wt% Ci-0.1 wt % Fe and Zr 2.5wt% Nb have been determined over the temperature range 293-773 K.


Journal ArticleDOI
TL;DR: Studies of muscle function indicate that the smooth muscle of the media does not contribute significantly to the static elastic properties of the vessel wall, and the value of the incremental elastic modulus does not change after 12 weeks.
Abstract: The static mechanical properties of the aorta have been examined in rats, aged between 4 weeks and 2 years. Internal radius, relative wall thickness, circumferential incremental strain, and circumferential incremental elastic modulus have been measured at pressures between 1.33 and 33.3 kPa (10 and 250 mm Hg). The results show that the value of the incremental elastic modulus does not change after 12 weeks. Changes observed in younger animals are related to alterations in relative wall thickness. The findings correlate with previously observed chemical and morphological changes. Studies of muscle function indicate that the smooth muscle of the media does not contribute significantly to the static elastic properties of the vessel wall.

Journal ArticleDOI
TL;DR: In this article, the composites have a relatively high density (1.70 g/cm3), a crystallite size LC = 150 A and an interlayer spacing d002 = 3.35 A.
Abstract: Composites of boron nitride (BN) have been made by the chemical vapor deposition (CVD) of a BN matrix on a BN felt fiber substrate. Reactant gases were boron trifluoride and ammonia. The composites have a relatively high density (1.70 g/cm3), a crystallite size LC = 150 A and an interlayer spacing d002 = 3.35 A. Measurements of elastic modulus and thermal conductivity and expansion showed some anisotropy as a result of the preferred fiber orientation of the substrate.

Journal ArticleDOI
TL;DR: In this article, the behavior of the twist elastic modulus K22 of a lyotropic liquid crystal formed by the α-helical polypeptide polyγ-benzyl-glutamate of three molecular weights in three solvents (dioxane, dichloromethane, and chloroform) was investigated as a function of concentration and temperature.
Abstract: Aspects of the behavior of the twist elastic modulus K22 of a lyotropic liquid crystal formed by the α‐helical polypeptide poly‐γ‐benzyl‐L‐glutamate of three molecular weights (MW= 300 000, 310 000, and 550 000) in three solvents (dioxane, dichloromethane, and chloroform) were investigated as a function of concentration and temperature. We find that K22 in this system may be made to vary over a wide range by adjustment of solvent and polymer molecular weight. Only a slight concentration dependence of K22 throughout the liquid crystal range was, however, noted. The variations can be at least partially understood in terms of changing macromolecular interactions and recent statistical hard‐rod theoretical treatments of liquid crystal elasticity. The functional form for the temperature dependence of the order parameter was also determined for the system through the clearing point.

Journal ArticleDOI
TL;DR: In this paper, a theory has been developed to explain crack propagation through a long elastic lap joint held under constant load, which has been verified by direct observation of cracks through lap joints made from smooth, transparent rubber strips pressed together to give reproducible autohesion.
Abstract: A theory has been developed to explain crack propagation through a long elastic lap joint held under constant load. Verification of the theory has been achieved by direct observation of cracks through lap joints made from smooth, transparent rubber strips pressed together to give reproducible autohesion. Lap-joint strength was found to depend in the theoretically predicted manner on the adhesive energy of the bonded surfaces, measured by peeling tests, and on the thickness, width and elastic modulus of the adherend sheets. Application of these results to the design of practical lap joints has been discussed.

Journal ArticleDOI
TL;DR: In this article, the elastic properties of four austenitic stainless steels (AISI 304, AISI 310, A ISI 316, and A286) are reported over the temperature range 300-4 K.
Abstract: The elastic properties of four austenitic stainless steels—AISI 304, AISI 310, AISI 316, and A286—are reported over the temperature range 300–4 K. These properties include longitudinal modulus, shear modulus, Young’s modulus, bulk modulus (reciprocal compressibility), Poisson’s ratio, and elastic Debye temperature. Elastic constants were determined from measurements of longitudinal and transverse sound‐wave velocities using an ultrasonic (10 MHz) pulse‐superposition method. Measurements were made in the absence of a magnetic field; these alloys undergo paramagnetic‐to‐antiferromagnetic transitions at low temperatures. For all four alloys, the shear modulus behaves regularly with respect to temperature. The other elastic constants, all of which have a dilatational component, decrease anomalously at temperatures below 80 K. The largest anomaly, about 3%, is in the bulk mudulus of the 304 alloy; this modulus is lower at 0 K than at 300 K. Results are interpreted on the basis of the Doring effect, which resul...

Journal ArticleDOI
TL;DR: In this paper, the contribution of the temperature dependent elastic modulus to the apparent activation energy can be very large and the modulus correction is particularly important at high temperatures and for materials with high stress exponents.
Abstract: Creep studies on dispersion strengthened metals have often resulted in inexplicably high creep activation energies and high stress exponents. An analysis is presented which shows that the contribution of the temperature dependent elastic modulus to the apparent activation energy can be very large. Two cases are examined in which the difference between the apparent activation energy and the activation energy of self diffusion is almost entirely accounted for by the contribution of the temperature dependent elastic modulus. The modulus correction is particularly important at high temperatures and for materials with high stress exponents.

Journal ArticleDOI
TL;DR: The rigidity modulus of dentine determined by the torsion of rectangular prisms was 0.62GN/m2, which led to the calculation of Poisson's ratio values of −0.025 to 0.26 which are very low, and the bulk modulus is 1 3 Young's modulus.

Journal ArticleDOI
TL;DR: In this article, the singlecrystal elastic constants, their temperature coefficients, and the thermal expansion coefficients of natrual nepheline, (KAlSiO4)(NaAlSi O4)3, have been measured.
Abstract: The single‐crystal elastic constants, their temperature coefficients, and the thermal expansion coefficients of natrual nepheline, (KAlSiO4)(NaAlSiO4)3, have been measured. The longitudinal modulus c11 and the shear modulus c66 have positive temperature coefficients. Since this implies the existence of a wide range of directions with a zero temperature coefficient of the ultrasonic travel time, nepheline may be a suitable substrate for ultrasonic surface‐wave signal processing devices.

Journal ArticleDOI
TL;DR: The deformation of lignin in a continuous ball indentation test was almost entirely elastic up to a stress of 2.2 × 108 Pa (22 kg mm−2).
Abstract: The deformation of lignin in a continuous ball indentation test was almost entirely elastic up to a stress of 2.2 × 108 Pa (22 kg mm−2). The load versus depth of indentation curve of the lignin followed closely the classical Hertz equation thus enabling the Young's modulus of lignin to be calculated. From these results a stress-strain curve for lignin was drawn.

Journal ArticleDOI
TL;DR: In this article, the elastic modulus is strain-dependent and the ultimate tensile strength increases with decreasing crystal size, which corresponds to exceptionally high per-chain properties, nearly as high as that of diamond.
Abstract: The mechanical properties (Young's modulus, ultimate tensile strength, deformation processes) of extended-chain polydiacetylene crystals are investigated. The properties observed are similar to those of metal and ceramic whiskers. The elastic modulus is strain-dependent and the ultimate tensile strength increases with decreasing crystal size. The maximum tensile strength observed was 1700 Nmm−2. The ultimate tensile strength seems to be controlled by the presence of a small number of defects near the surface at which fracture nucleates. Irreversible deformation of the crystals was observed to occur by crack propagation normal and parallel to the direction of the macromolecules. The observed mechanical behavior corresponds to exceptionally high per-chain properties. The per-chain modulus obtained for these crystals is nearly as high as that of diamond. A chain-aligned polyethylene fiber with the same per-chain mechanical properties would have an ultimate strength as high as 0.9 × 104 Nmm−2.

Journal ArticleDOI
TL;DR: In this article, the effect of strain rate and frequency on modulus has also been evaluated by a combination of stress-strain data and dynamic tension plus sonic measurements over nine decades of time.
Abstract: : High density polyethylene filaments, prepared by a solid-state deformation in an Instron Capillary Rheometer, show unusually high crystal orientation, chain extension, axial modulus and ultimate tensile strength. The Young's modulus and ultimate tensile strength have been determined from stress-strain curves. Gripping of this high modulus polyethylene has been a problem heretofore. Nevertheless, the measurement of ultimate tensile strength has become feasible by a special gripping procedure reported in this study. Tensile moduli show an increase with sample preparation temperature and pressure. The effect of strain rate and frequency on modulus has also been evaluated by a combination of stress-strain data and dynamic tension plus sonic measurements over nine decades of time.

Journal ArticleDOI
TL;DR: In this article, energy release rates for cracks propagating in media with spatially varying elastic moduli, this variation being in a direction perpendicular to the crack growth direction, are derived for transient problems of semi-infinite cracks in infinite media for certain special forms of the variation in shear modulus.
Abstract: Energy release rates are calculated for cracks propagating in media with spatially varying elastic moduli, this variation being in a direction perpendicular to the crack growth direction. Results are given for transient problems of semi-infinite cracks in infinite media for certain special forms of the variation in shear modulus. Steady state crack propagation in a displacement loaded strip is also considered and it is shown by the use of a certain path independent integral that a simple formula for the energy release rate can be obtained for quite general variations in clastic moduli provided these variations are in a direction perpendicular to the crack. Other path independent integrals are derived which may be of use for transient crack tip stress analysis in strips in a similar way to that used in [4] for the homogeneous elastic problem.

Journal ArticleDOI
TL;DR: In this paper, a viscoelastic, rubber-like material unidirectionally reinforced with discontinuous fibres is considered and the longitudinal storage modulus is calculated not only from an equation based on an existing force balance treatment but also from the elastic strain energy stored in matrix and fibres, using two different models to derive the stress and strain distributions from which the stored energy is calculated.
Abstract: The paper deals with viscoelastic, rubber-like material unidirectionally reinforced with discontinuous fibres. The longitudinal storage modulus is calculated not only from an equation based on an existing force balance treatment but also from the elastic strain energy stored in matrix and fibres, using two different models to derive the stress and strain distributions from which the stored energy is calculated. There is very good agreement between all the calculations. The energy calculations reveal that loss modulus is also greatly increased by discontinuous reinforcement and enable its value to be estimated. Experiments on storage and loss modulus are reported and show that the calculations underestimate storage modulus and overestimate loss modulus. In both cases the factor of error ∼ 2, and arises because the amplified matrix strain is underestimated and is partly hydrostatic; the hydrostatic strain is non-dissipative and therefore does not contribute to the loss modulus. Discontinuous reinforcement can increase loss modulus as well as storage modulus by more than 100 times, and this should help sound and vibration deadening. An estimate is made of the wide ratio of compliance ÷ breaking strength available with discontinuous but not with continuous reinforcement, which opens up new design latitude for components hitherto reinforced with continuous fibres.

Journal ArticleDOI
TL;DR: In this article, the elastic constants of polycrystalline silicon nitrides with densities between 2.37 and 3.18 g/cm3 were reported and they were in approximate agreement with the prediction of a theory of composites.
Abstract: Elastic constants are reported for several polycrystalline silicon nitrides with densities between 2.37 and 3.18 g/cm3 in the temperature range 0–1000 °C. The density dependence of the elastic constants is in approximate agreement with the prediction of a theory of composites.


Journal ArticleDOI
TL;DR: In this paper, the curvature of the curved fibres is considered as a wave producing shear or extensional strains in the matrix, and the analysis and conclusions distinguish between various sources of misalignment, and include consideration of fibre straightening.
Abstract: There are many processes in the manufacture of industrial continuous-fibre composites which may result in slight buckling of the fibres. The measured values of their tensile elastic moduli will be below those of carefully prepared laboratory test-pieces. This phenomenon is analysed, by considering the curved fibres as waves producing shear or extensional strains in the matrix. The analysis and conclusions distinguish between various sources of misalignment, and include consideration of fibre straightening.

Journal ArticleDOI
TL;DR: In this article, it was shown that the presence of an interlayer on the fiber at a thickness which is a small fraction of the fiber diameter can significantly affect the stress concentrations in the matrix.
Abstract: Numerical results are given of calculations of the radial, transverse, and shear stresses in the matrix surrounding a cylindrical inclusion in plane strain perpendicular to the cylinder axis, this being taken as a model of a fiber composite under transverse loading. It is shown that the presence of an interlayer on the fiber at a thickness which is a small fraction of the fiber diameter can significantly affect the stress concentrations in the matrix. The interlayer-fiber ‘composite’ can be ‘matched’ to the matrix by suitable choice of interlayer elastic moduli. In particular, if the shear modulus of the interlayer is smaller than that of the matrix and its Poisson's ratio is very small, the stress concentrations in the matrix are considerably reduced and the composite should be less subject to failure by delamination.