Showing papers on "Elastic modulus published in 1974"
TL;DR: The elastic moduli for human and bovine bone specimens were determined by compression and tension tests and compared and no statistically significant difference was found between the moduli determined in the two loading modes.
509 citations
TL;DR: In this paper, the authors conducted compressive plastic deformation experiments between 77°K and 520°K on a bulk Pd0.775 Cu0.06 Si0.165 glass.
252 citations
TL;DR: In this paper, the elastic properties of copper have been compiled and reviewed, including Young's modulus, the shear modulus and the bulk modulus of copper, and a few theoretical numbers are included.
Abstract: The elastic properties of copper have been compiled and reviewed. Polycrystalline elastic constants included are: Young's modulus, the shear modulus, the bulk modulus, and Poisson's ratio. Single‐crystal constants of second‐, third‐, and fourth‐order are included. Over 200 references to the experimental literature are given. A few theoretical numbers are included. When sufficient data exist, best values are recommended together with their standard errors. Effects on the elastic constants of temperature, pressure, and mechanical (plastic) deformation are included. The Cauchy (central‐force) relationships and the single‐crystal—polycrystal relationship are also discussed.
211 citations
TL;DR: In this paper, the fourth-order finite strain expressions for the effective elastic moduli of a solid under hydrostatic stress are derived from a general expression for effective elastic models, which is then written in terms of the moduli and their pressure derivatives evaluated at an arbitrary reference state.
201 citations
TL;DR: Aqueous dispersions of homoionic sodium montmorillonite have been studied under compressive and decompressive conditions in order to determine the internal pressure of the system as a function of the clay and electrolyte concentrations as mentioned in this paper.
Abstract: Aqueous dispersions of homoionic sodium montmorillonite have been studied under compressive and decompressive conditions in order to determine the internal pressure of the system as a function of the clay and electrolyte concentrations. Complementary measurements were also made of the electrokinetic properties of the montmorillonite particles. Compression of a sodium montmorillonite dispersion from ca. 2 % to ca. 65 % w/w gave a continuous curve of pressure against distance of plate separation up to pressures greater than 100 atmospheres. On subsequent decompression, however, a different curve was obtained and a hysteresis effect was found to occur in the pressure against distance curves. It is considered that the initial curve represents the behaviour of a disordered clay system, i.e., the initial gel, whereas the decompression curve represents the behaviour of a system in which the plates have become ordered into a parallel array. The elastic modulus of the latter system was determined. The results strongly suggest that the gel properties of montmorillonite dispersions are the consequence of long range electrostatic interactions.
201 citations
TL;DR: In this paper, the theory of elastic moduli of composite materials in which an inversion of the phases can occur is reviewed and the applicability of the theoretical equations is illustrated for four systems of block polymers and polyblends.
Abstract: The theory of the elastic moduli of composite materials in which an inversion of the phases can occur is reviewed. The morphology of the system and the packing fraction of the dispersed phase are important in determining the moduli. The applicability of the theoretical equations is illustrated for four systems of block polymers and polyblends. In three of the systems, phase inversion occurs. Agreement between theory and experiment is good, and where the morphology of the composites is known, the moduliagree with the values expected for that morphology.
121 citations
TL;DR: In this article, it is shown that conservative failure prediction based on an equivalence between inclusion size and crack size is usually acceptable if the shear modulusμ or thermal expansion coefficientα for the inclusion is larger than the matrix values.
Abstract: The stress concentrations that occur at inclusions due to thermal expansion and elastic modulus mismatch are discussed and the stress intensity factors at interface cracks that result from these stresses are calculated. It is shown that conservative failure prediction based on an equivalence between inclusion size and crack size is usually acceptable if the shear modulusμ or thermal expansion coefficientα for the inclusion is larger than the matrix values. If, however,μ andα are smaller for the inclusion than the matrix, extensive cracking can develop at the inclusions which may lead to premature failure. For this case the only effective methods for failure prediction are techniques which give directly the maximum stress intensity factor, i.e., proof testing and/or acoustic emission.
119 citations
TL;DR: In this paper, the authors describe a mechanism of load transfer from matrix to fibre about single short fiber models. And they predict Young's modulus of short fibre-reinforced materials provided that the orientation of the fibres obeys a certain rule.
114 citations
TL;DR: In this paper, a theoretical relation between the elastic modulus of amorphous rubber and the concentrations of potential entanglements, random tetrafunctional crosslinks, and chain ends was proposed and verified experimentally.
Abstract: The theory of rubber elasticity relates the elastic modulus of unfilled amorphous rubber to the concentration of elastically effective strands. A theoretical relation between this concentration and the concentrations of potential entanglements, random tetrafunctional crosslinks, and chain ends was proposed recently. In the present work, the new relation was combined with the theory of rubber elasticity and verified experimentally. Polydimethylsiloxane samples were cured by 60Co irradiation and were extensively extracted to determine gel fraction, which was used to calculate concentrations of crosslinking and scission due to irradiation. Equilibrium modulus values determined from creep tests were in excellent agreement with those calculated using the new relation if the average spacing between potential entanglements is 116 (CH3)2SiO units. Thus, in typical commercial silicone rubbers, the contribution to the modulus from trapped entanglements is greater than the direct contribution from crosslinks. The new relation allows the calculation of crosslink concentrations from modulus measurements on other unfilled rubbers once the potential entanglement spacing of the polymer is determined.
109 citations
TL;DR: A new kind of acetal fiber has been discovered which has a tensile strength of 1.7 GPa (250,000 psi) and an elastic modulus of 35 GPa(5 × 106 psi) as mentioned in this paper.
Abstract: A new kind of acetal fiber has been discovered which has a tensile strength of 1.7 GPa (250,000 psi) and an elastic modulus of 35 GPa (5 × 106 psi). This fiber is produced by a special two-stage drawing process in the solid state which requires careful control of deformation rate and temperature. Previously known drawn fibers are reported to consist of folded-chain blocks joined by a limited number of tie-molecules. It is hypothesized that the second stage of the novel drawing process eliminates the lamella (block) surfaces which act as strength-limiting stress concentrators. A new type of fiber is created in which any remaining chain-folds are distributed as defects in a continuous crystal matrix. It is the continuity of the crystal matrix which is believed responsible for the remarkable properties of the fiber.
01 Nov 1974
TL;DR: In this paper, an isotropic elastic material containing a random distribution of identical spherical particles of another elastic material is considered, where the bonding between the spheres and the matrix is imperfect, so that slip may occur at interfaces when stress is applied to the medium.
Abstract: An isotropic elastic material containing a random distribution of identical spherical particles of another elastic material is considered. The bonding between the spheres and the matrix is imperfect, so that slip may occur at interfaces when stress is applied to the medium. The shear stresses at the interface is assumed to be proportional to the amount of slip. The velocity and attenuation of the average harmonic elastic waves propagating through such a medium are calculated. The results are valid to the lowest order in frequency for wave lengths long compared with the radius of the sphere. The dynamic elastic moduli are obtained from these results and are compared with available results for welded contact. The variations in the P and S wave velocities for propagation across earthquake faults is discussed.
TL;DR: In this article, a composite material consisting of a dilute suspension of initially spherical inclusions embedded in a matrix of different material is considered and an expression for the overall bulk modulus of the composite material is obtained in terms of the moduli of the constituents.
Abstract: F rom the work of R. Hill on constitutive macro-variables it is known that for an inhomogeneous elastic solid under finite strain an overall elastic constitutive law may be defined. In particular, the volume average of the strain energy of the solid is a function only of the volume-averaged deformation gradient. In view of the importance of this result it is re-derived in this paper as a prelude to a discussion of composite materials. A composite material consisting of a dilute suspension of initially spherical inclusions embedded in a matrix of different material is considered. For second-order isotropic elasticity theory an expression for the overall bulk modulus of the composite material is obtained in terms of the moduli of the constituents. When the inclusions are vacuous a known result for the bulk modulus of porous materials is recovered. In certain situations the strengthening/ weakening effects of the inclusions are less pronounced in the second-order theory than in the linear theory.
TL;DR: The deformation response of paving asphalts to small-amplitude sinusoidal loading in shear is linear and thermorheologically simple so that master curves relating the dynamic shear modulus to the (reduced) frequency can be constructed.
Abstract: The deformation response of paving asphalts to small‐amplitude sinusoidal loading in shear is linear and thermorheologically simple so that master curves relating the dynamic shear modulus to the (reduced) frequency can be constructed. A simple analytical expression which gives a good fit to these master curves is proposed. Data were obtained for the response of 14 different asphalts over a range of frequencies and temperatures, and master curves relating the absolute value of the modulus to the reduced frequency were constructed. These were found to fit closely to an equation which is one arm of an hyperbola whose asymptotes represent the purely viscous and purely elastic behavior expected at infinitely low and infinitely high frequencies, respectively. The rapidity with which an asphalt changes from a viscous to an elastic response as the frequency of loading increases (shear susceptibility parameter) is indicated by the distance between the point at which the hyperbola crosses its “modulus” axis and its origin. The phase angle is approximately proportional to the slope of the hyperbola, and the equation relating the phase angle with reduced frequency obtained using this relationship gave an adequate fit to the data. From this equation, and that of the hyperbola, the relaxation spectra of the materials were calculated. Shear susceptibility parameters, limiting viscosities, and moduli at a very high frequency of the materials are given and the increase of these parameters when a Kuwait asphalt was air blown in the refinery is indicated. The method used to fit the hyperbola equation to the data and an indication of the precision of fit are given in the Appendix.
TL;DR: In this article, the density, elastic moduli, creep and fracture properties of Ni 0.76 P 0.24 and Co 0.75P 0.25 have been measured for both the glassy and crystalline states.
TL;DR: In this article, an account of the experimental determination of the transverse elastic moduli and yield behavior of some commercially available organic and graphite high-modulus filaments is given.
Abstract: An account is given of the experimental determination of the transverse elastic moduli and yield behavior of some commercially available organic and graphite high-modulus filaments. The experimental technique involves transverse compression of single cylindrical filaments between two parallel flat platens and concurrent measurement of the platen- relative displacements and contact forces on the filaments. A theoretical discussion of the transverse compressional behavior of a linear elastic, homogeneous, orthotropic cylinder is presented. Using the theoretical results and the trans verse load-displacement measurements, a technique is developed for calculating the elastic moduli and maximum shear stresses at yield or fracture.
TL;DR: In this article, the wear behavior of polyoxymethylene and 20% PTFE-filled polyoxide-monoethylene sliding against a metallic surface was studied and an experimental setup capable of measuring sliding friction and providing wear under variable conditions was designed and fabricated.
01 May 1974
TL;DR: The use of even-order isotropic tensors in non-linear elasticity theory is discussed in this paper, where a notation is adopted through which these tensors can be represented conveniently so that their interdependence is clearly shown.
Abstract: The use of even-order isotropic tensors in non-linear elasticity theory is discussed in this paper. A notation is adopted through which these tensors can be represented conveniently so that their interdependence is clearly shown. Information about the number of independent elastic constants required is then readily available for use in an expansion of the stress to various orders in the strain relative to the undistorted configuration of the elastic material in question.For an incompressible isotropic hyperelastic solid, it is shown that each principal component of the distortional part of the stress is expressible as a function only of the corresponding principal component of strain to the fourth order. Under certain conditions, which are not too restrictive, this result can be extended to higher orders.
TL;DR: Calcium ion causes the development of a higher elastic modulus in fibrinogen solutions clotted by thrombin, and covalent crosslinking of α-chains causes an increase of the modulus, while covalents of γ-chains does not.
TL;DR: In this paper, two ultrasonic methods are presented for the measurement and monitoring of the elastic moduli of polymers and other liquids undergoing solidification, which are thought to be most sensitive to the buildup of the real component of the modulus of rigidity of the material.
Abstract: Two ultrasonic methods are presented for the measurement and monitoring of the elastic moduli of polymers and other liquids undergoing solidification. The methods are thought to be most sensitive to the buildup of the real component of the modulus of rigidity of the material. Ultrasonic traveling waves are used to interrogate a boundary between the solid body transmitting the wave and the sample under test. Data on epoxy resins are given. During the hardening process, the measured modulus includes contributions from viscoelastic and glass transition effects which are not separated from the total modulus by the measurement methods.
TL;DR: In this article, a general theory for the calculation of the second order effective elastic moduli of porous materials in which the porosity is in the form of isolated cavities is presented.
Abstract: Summary A general theory for the calculation of the second order effective elastic moduli of porous materials in which the porosity is in the form of isolated cavities is presented. The particular case of spherical cavities distributed randomly within an isotropic matrix in such a manner that the material is macroscopically isotropic is then considered in detail and an expression for the first pressure derivative of the effective shear modulus of such a material is obtained correct to first order in the porosity. 1. Introduction In a paper by Walton (1973), hereafter referred to as Paper I, the first pressure derivative of the effective bulk modulus of a porous material was calculated. The particular porous medium considered was that of a homogeneous isotropic matrix containing a dilute distribution of spherical cavities, not necessarily of the same size but such that the total porosity c (that is, the ratio of cavity volume to total volume) is so small that terms of order c2 may be neglected in comparison with unity. Furthermore, the distribution was assumed to be random and such that the material is macroscopically homogeneous and isotropic. The aim of the present paper is to extend the method used in Paper I to the calculation of the first pressure derivative of the effective shear modulus of such a material. 2. Second order effective moduli The method is based on considerations of the overall constitutive law and, in the spirit of Hill (1963), the problem of the calculation of the effective elastic moduli of porous materials may be formulated as follows. The model to be considered is that of a large volume V of some porous material subjected to a uniform strain in its outer boundary. The matrix material is assumed both perfectly elastic and homogeneous, although not necessarily isotropic. The porosity, on the other hand, is assumed to be in the form of isolated cavities distributed throughout the matrix in such a manner that the material is macroscopically homogeneous, although not necessarily isotropic. Finally, there is no restriction at this stage on the size of the porosity c. With the 9-vectors S and D denoting the nominal stress and displacement gradient respectively and with superscripts (m) and (c) referring respectively to the solid matrix and the cavities, the constitutive law for the matrix material may be written, correct to second order in D(m),
TL;DR: In this article, sound velocities and elastic constants were determined semi-continuously for two annealed polycrystalline titanium alloys between 4 and 300 K. A pulse-superposition technique was used.
TL;DR: In this paper, the pressure and temperature derivatives of the elastic moduli of single crystal LiH have been determined at room temperature, by the ultrasonic pulse echo method, using a non-central force model.
TL;DR: In this paper, a torsion pendulum was used to measure the shear modulus of a range of polymers as a function of applied hydrostatic pressure at 20° C. The pressure medium was usually nitrogen gas and the maximum pressure 20000 psi.
Abstract: A torsion pendulum has been used to measure the shear modulus of a range of polymers as a function of applied hydrostatic pressure at 20° C. The pressure medium was usually nitrogen gas and the maximum pressure 20000 psi. The results show that the shear modulus of each polymer is increased by the application of pressure, and the magnitude of the increase is greatest for experiments carried out at temperatures just above an atmospheric relaxation temperature. The increase in shear modulus takes a finite time, of the order of minutes, to be achieved, the equilibrium value being reached in a shorter time at higher temperature.
TL;DR: The elastic modulus and the viscous modulus of hydrated and airdried cortical bone were determined and both moduli showed no change of value in tensile and compressive loading modes.
TL;DR: In this article, a composite resonator was used to determine polycrystalline elastic moduli for TiC, TiC-26% VC, VC-22% TiC and VC with carbon content close to 0.84.
Abstract: Polycrystalline elastic moduli have been determined for TiC, TiC-26% VC, VC-22% TiC and VC using a composite resonator. Carbon to metal ratios were in all cases close to 0.84. Room temperature moduli variations with alloy composition are discussed and by comparison with other data the order of magnitude of modulus variation with carbon content is determined for TiC. The temperature dependence of Young's modulus for TiC and VC are determined in the range 20 to 1600° C. Correlations are sought with hardness data.
TL;DR: In this article, the mechanical behavior of polyurethane, polyoxymethylene and branched low density polyethylene is evaluated at various levels of hydrostatic pressure from atmospheric up to 6.9 Kb.
Abstract: The mechanical behavior of polyurethane, polyoxymethylene and branched low density polyethylene is evaluated at various levels of hydrostatic pressure from atmospheric up to 6.9 Kb. Polyurethane undergoes a “ductile-brittle-ductile” transition accompanied by decreased strain hardening and also exhibits intrinsic yield behavior in compressive tests at higher pressures. A study was made of polyoxymethylene with emphasis below 1.4 Kb and in the vicinity of 5.5 Kb. The effect on the mechanical behavior in the 5.5 Kb region is attributed to a possible pressure-induced shift of a β-transition. Additional data not reported by Sardar et al. are discussed. Tests on branched low density polyethylene show that it behaves under pressure in a way similar to that of medium density polyethylene. With increased pressure, failure of the specimens tested, occurs by necking to a fine point. The elastic modulus versus pressure data indicates a possible pressure-induced shift of a β-transition up to room temperature....
TL;DR: In this article, the deformation and flow properties of solid polymers under uniaxial tensile and compressive loading have been determined for a variety of both crystalline and amorphous polymers at hydrostatic pressures to about 7, kb.
Abstract: The deformation and flow properties of solid polymers under uniaxial tensile and compressive loading have been determined for a variety of both crystalline and amorphous polymers at hydrostatic pressures to about 7 , kb. For some polymers, like polytetrafluoroethylene, cold drawing is inhibited by increasing pressure, and scanning electron micrographs show that local plastic deformation is greatly reduced. However, the true flow stress and the true fracture stress both increase with pressure, as does, also, the elastic modulus. The increase is greatest in the low-pressure range below 2 kb. This behavior is attributed to the pressure-induced shifting of a lowtemperatureβ′-transition. The influence of polymer composition and of the initial elastic constants on the pressure dependence of the elastic modulus and the yield stress is discussed. The observed behavior can be analyzed in terms of finite strain effects and a pressure-dependent yield criterion. It is shown that some amorphous polymers undergo a pressure-induced brittle-ductile transition, and these findings are used to explore the hydrostatic extrusion of polyimide and polysulfone at room temperature.
TL;DR: In this paper, the authors evaluated the Beran-Molyneux and McCoy bounds on the effective bulk modulus of two-phase materials using the correlation functions developed in Paper II of this series.
Abstract: The Beran‐Molyneux bounds on the effective bulk modulus and the McCoy bounds on the effective shear modulus of a statistically homogeneous and isotropic heterogeneous material require a knowledge of several three‐point correlation functions. These correlation functions are contained within integrals which must be evaluated. Both sets of bounds are here evaluated for two‐phase materials, using the correlation functions developed in Paper II of this series. The method of evaluation includes a simplification of the integrals containing the correlation functions and a numerical evaluation of the simplified integrals. The resultant bounds are compared with experimental data on the effective shear modulus of three two‐phase systems: aluminum‐lead, iron‐lead, and tungsten‐lead. The bounds are also compared with the less restrictive Hashin‐Shtrikman bounds which do not require any knowledge of correlation functions. It is shown that both sets of bounds are a significant improvement over the Hashin‐Shtrikman bound...
TL;DR: In this paper, the authors indicate certain limitations to the elastic moduli and flexoelectric coefficients of liquid crystals in terms of their elasticity and elasticity properties, and their properties are discussed.
Abstract: Phenomenological and molecular considerations indicate certain limitations to the elastic moduli and flexoelectric coefficients of liquid crystals.