Showing papers on "Young's modulus published in 1984"
TL;DR: In this article, the influence of aspect ratio α, from zero to infinity, on the effective elastic moduli of a transversely isotropic composite was examined, where the reinforcing inclusions, which could be flakes or short fibers, are assumed to be spheroidal and unidirectionally aligned.
Abstract: This paper examines the influence of aspect ratio α, from zero to infinity, on the effective elastic moduli of a transversely isotropic composite. The reinforcing inclusions, which could be flakes or short fibers, are assumed to be spheroidal and unidirectionally aligned. Of the five independent elastic constants, the longitudinal Young's modulus E11 and in-plane shear modulus μ12 appear to increase with increasing aspect ratio, while the transverse Young's modulus E22, out-plane shear modulus μ23, and plane-strain bulk modulus K23, generally decrease. It is further noted that E11 is more sensitive to α when α > 1 but the others are more so when α < 1. The present analysis was carried out by the combination of Eshelby's and Mori-Tanaka's theories of inclusions.
636 citations
TL;DR: Analytical solutions have been obtained for the internal deformation and fluid-flow fields and the externally observable creep, stress relaxation, and constant strain-rate behaviors which occur during the unconfined compression of a cylindrical specimen of a fluid-filled, porous, elastic solid, such as articular cartilage, between smooth, impermeable plates.
Abstract: Analytical solutions have been obtained for the internal deformation and fluid-flow fields and the externally observable creep, stress relaxation, and constant strain-rate behaviors which occur during the unconfined compression of a cylindrical specimen of a fluid-filled, porous, elastic solid, such as articular cartilage, between smooth, impermeable plates. Instantaneously, the "biphasic" continuum deforms without change in volume and behaves like an incompressible elastic solid of the same shear modulus. Radial fluid flow then allows the internal fluid pressure to equilibrate with the external environment. The equilibrium response is controlled by the Young's modulus and Poisson's ratio of the solid matrix.
559 citations
TL;DR: The adoption of different degrees of mineralization by different bones, leading to different sets of mechanical properties, is shown to be adaptive in most cases studied, but some puzzles still remain.
Abstract: There is a considerable variation in the mineralization of bone; normal, non-pathological compact bone has ash masses ranging from 45 to 85% by mass. This range of mineralization results in an even greater range of mechanical properties. The Young modulus of elasticity can range from 4 to 32 GPa, bending strength from 50 to 300 MPa, and the work of fracture from 200 to 7000 Jm-2. It is not possible for any one type of bone to have high values for all three properties. Very high values of mineralization produce high values of Young modulus but low values of work of fracture (which is a measure of fracture toughness). Rather low values of mineralization are associated with high values of work of fracture but low values of Young modulus and intermediate values of bending strength. The reason for the high value for the Young modulus associated with high mineralization is intuitively obvious, but has not yet been rigorously modelled. The low fracture toughness associated with high mineralization may be caused by the failure of various crack-stopping mechanisms that can act when the mineral crystals in bone have not coalesced, but which become ineffective when the volume fraction of mineral becomes too high. The adoption of different degrees of mineralization by different bones, leading to different sets of mechanical properties, is shown to be adaptive in most cases studied, but some puzzles still remain.
354 citations
TL;DR: In this paper, a relationship between porosity and Young's modulus is obtained theoretically for porous materials made by powder metallurgy and an approximate solution with a wide applicable porosity range is given.
Abstract: A relationship between porosity and Young's modulus is obtained theoretically for porous materials made by powder metallurgy. The relationship is applicable to the entire range of porosity and is capable of treating the transition of pore structure from interconnected to isolated. The exact solution is presented graphically. An approximate solution with a wide applicable porosity range is given.
228 citations
TL;DR: In this paper, a systematic experimental study was carried out of two distinct failure phenomena, cavitation and debonding, in an elastomer containing a rigid spherical inclusion, and several elastomers were employed containing glass beads of various diameters, ranging from 60 to 5000 μm, and with chemically different surfaces.
Abstract: A systematic experimental study has been carried out of two distinct failure phenomena, cavitation and debonding, in an elastomer containing a rigid spherical inclusion. Several elastomers were employed containing glass beads of various diameters, ranging from 60 to 5000 μm, and with chemically different surfaces. The critical stress for cavitation was found to depend upon both Young's modulus, E, of the elastomer and the diameter of the bead. By extrapolation, it was found that the stress for cavitation near an infinitelylarge bead is given by 5E/12, as predicted by theory. In contrast, the critical stress for debonding decreased somewhat with increasing Young's modulus of the elastomer. This is attributed to a concomitant decrease in the strength of adhesion between the elastomer and the bead surface, due to rheological effects. The stresses for both cavitation and for debonding were found to vary approximately with the negative half-power of the bead diameter. This suggests that a similar Griffith mechanism governs both failure processes when the bead size is small. A study of cavitation and debonding in the presence of two glass beads was also carried out. As predicted from theoretical considerations, both stresses were found to decrease as the distance between the two beads was decreased, irrespective of the diameter of the bead and Young's modulus of the elastomer. At higher strains, however, a second cavitation process was found to take place at a point midway between the beads. Tensile fracture of the specimen resulted from the unrestrained lateral growth of the second cavity.
228 citations
180 citations
TL;DR: The results from the first phase of a 6-university study are presented in this article, which includes specimen size, fiber volume content, fiber type, and the effect of a notch as the primary parameters of investigation.
Abstract: The results from the first phase of a 6-university study are presented in this article. This first phase includes specimen size, fiber volume content, fiber type, and the effect of a notch as the primary parameters of investigation. Results from the tests, including toughness, and other important properties such as stress at first-crack, ultimate strength, and the elastic modulus as influenced by the specified parameters, are presented and discussed. The importance of making accurate deflection measurements and the influence of these measurements on the toughness and other flexural characteristics are disscussed. Conclusions are made with regard to lessons learned from the inter-university testing program, drawbacks of some currently used measures of toughness, observed material property trends, and a possible alternate measure of toughness.
151 citations
TL;DR: In this article, a simple formula was established to estimate the fracture toughness of concrete in terms of specimen dimensions, maximum aggregate size and notch depth, together with the mix compressive strength and modulus of elasticity.
Abstract: Synopsis Tests were performed on cement mortar and concrete beams, in two stages, with a view to studying the influence of several specimen and mix variables upon the fracture behaviour of concrete. On the basis of the results from the first stage of tests, in which a single water/cement ratio and type of coarse aggregate were used, a simple formula was established to estimate the fracture toughness of concrete in terms of specimen dimensions, maximum aggregate size and notch depth, together with the mix compressive strength and modulus of elasticity (determined from separate standard cylinder tests). It was found to predict, with sufficient accuracy, the results from the second stage of tests in which, besides variation of the type of coarse aggregate and water/cement ratio, some of the specimen sizes were outside the range used in the first series.
131 citations
TL;DR: In this paper, the relationship between the chemical and physical network structure, the deformation and failure processes and the tensile mechanical properties of polyethertriamine-cured bisphenol-A-diglycidyl ether epoxies are reported for a series of epoxy glasses prepared from a range of polyethyltriamine concentrations.
120 citations
TL;DR: Vacuum mixing improved the flexural and compression strength and the modulus of elasticity by 15-30 per cent, especially for high viscosity cement.
Abstract: The mechanical strength of high and low viscosity gentamicin-containing cement was analysed using three different mixing procedures: hand, vibration, and vacuum stirring. Vacuum mixing improved the flexural and compression strength and the modulus of elasticity by 15-30 per cent, especially for high viscosity cement.
106 citations
TL;DR: In this article, a simple and convenient method to overcome the difficulty is by conducting intermittent unloading tests during a conventional tensile test and by measuring the modulus from the unloading curve.
TL;DR: In this article, anomalies were observed in electrical resistivity components, Hall coefficient and Young's modulus of semimetallic ZrTe 3 near 63K, suggesting that a structural phase transition, e.g. the onset of a charge density wave, occurs.
TL;DR: In this paper, the Young's modulus and internal friction dependence on temperature in alumina, silicon nitride, and partially stabilized zirconia (Y-PSZ) ceramics were investigated.
Abstract: A study is conducted of the Young's modulus and internal friction dependence on temperature in alumina, silicon nitride, and partially stabilized zirconia (Y-PSZ) ceramics. While little change in internal friction was noted in the case of alumina, an increase was found for silicon nitride ceramics above 700 C. The internal friction of Y-PSZ markedly increased with temperature, up to a peak at about 200 C. 7 references.
TL;DR: The modulus of elasticity (E) was determined in simple three- and four-point bending for an 0.0175" (3 X 0.008") stainless steel arch wire and corroborated the metallurgical literature in which E spanned 27.8-30.2 X 10(6) psi.
Abstract: The modulus of elasticity (E) was determined in simple three- and four-point bending for an 0.0175" (3 X 0.008") stainless steel arch wire. Using variable light loads (10-160 g) to limit the elastic deflection of a wire to less than 5% of its beam length, the force-deflection profiles were determined for three nominal span lengths (L = 0.35", 0.75", and 1.00") in three-point bending and three nominal inner span lengths (L2 = 0.17", 0.40", and 0.50") in four-point bending (single outer span length, L = 1.00"). By assuming that each wire could be considered as a bundle of frictionless, tightly wound helical springs (i.e., strands), in which both the Young's modulus (E) and the shear modulus (G) contribute to the overall stiffness, values for E equaled 28.6 +/- 0.6 X 10(6) and 29.6 +/- 0.9 X 10(6) psi in three- and four-point bending, respectively. In addition, by using simple beam theory, the values of E for the 0.010" and 0.018" single-stranded wires were measured and equaled 27.2 +/- 0.3 X 10(6) and 27.8 +/- 0.7 X 10(6) psi in three-point bending, and 27.9 +/- 0.7 and 27.8 +/- 1.2 X 10(6) psi in four-point bending, respectively. Despite the fact that the elastic moduli of all three wires were significantly different (p less than 0.001), the results corroborated the metallurgical literature in which E spanned 27.8-30.2 X 10(6) psi. This was in contrast to the dental literature, in which a broader range of values has been reported, i.e., 18.3-38.0 X 10(6) psi.
TL;DR: In this paper, the storage modulus of nylon-CR and PET-CR composites with unidirectional short fibers was studied as a function of temperature by using a Rheovibron.
Abstract: The dynamic moduli, E′ and E″, and tan δ for nylon–CR and PET–CR composites with unidirectional short fibers were studied as a function of temperature by using a Rheovibron. The temperature dependence of tan δ showed two dispersion peaks for nylon–CR composite. The peak at −28°C corresponded to the main dispersion of CR and the peak at 100°C to the α-dispersion of nylon 6. For a PET-CR composite, in addition to the individual dispersion of CR and PET, a small and broad peak was observed at about 90°C. The angular dependence of E′ indicated that the short fibers assumed good orientation. The storage modulus for the composites was given by the parallel model as E′ = Vf′Ef + VmE′m., where E′c, E′f and E′m were the storage modulus for the composite, fiber, and matrix and Vf and Vm were the volume fraction of fiber and matrix, respectively. In the transverse direction of fiber, the peak values of tan δ at −28°C were given by the following equation; tan δc = tan δm − δVf, where tan δc and tan δm are the loss tangent for the composite and matrix, respectively, and α is coefficient depending on fiber type. The results indicated that a region with strong interaction was formed between fibers and CR matrix.
TL;DR: In this article, four microcracking-modulus theories are rewritten in terms of the macroscopic, observable parameters of Young's modulus and Poisson's ratio, eliminating the specific dependence on the difficult to measure, microscopic quantities.
Abstract: Microcracking-elasticity theories typically relate a decrement in elastic moduli to the number density,N, and the mean microcrack radius 〈a〉. In this paper, four microcracking-modulus theories are rewritten in terms of the macroscopic, observable parameters of Young's modulus and Poisson's ratio, eliminating the specific dependence on the difficult to measure, microscopic quantitiesN and 〈a〉. The rewritten microcracking elasticity theories are then compared to elasticity data on a variety of microcracked, polycrystalline ceramics.
TL;DR: In this article, a theoretical expression for the initial shear modulus of a plain-woven fabric is derived and compared with the moduli of a range of woven fabrics.
Abstract: A theoretical expression for the initial shear modulus of a plain-woven fabric is derived and is then compared with the moduli of a range of woven fabrics.
TL;DR: The difference between flexural and tensile Young's modulus, as experienced experimentally, is analyzed theoretically in this paper, and it can be explained by large shear deformation and a heterogeneous section, making the formulae from elementary bending of beams incorrect.
TL;DR: In this paper, the tensile drawing behavior of a range of selected polyethylene copolymers has been studied and it was found that even at the very low concentration of one side branch per 1000 carbon atoms there was a very marked effect on the strain hardening behavior and the maximum draw ratio that could be achieved.
Abstract: The tensile drawing behavior of a range of selected polyethylene copolymers has been studied. Sheets were prepared by quenching molten polymer into cold water. Two-centimeter-gauge-length samples were then drawn in air at 75 or 115°C in an Instron tensile testing machine at a crosshead speed of 10 cm/min. It was found that even at the very low concentration of one side branch per 1000 carbon atoms there was a very marked effect on the strain hardening behavior and the maximum draw ratio that could be achieved. The reduction in draw ratio increased with increasing branch concentration, and long branches were more effective than short branches in limiting the draw ratios achieved. The similarity between these effects and the effects of increasing Mw or radiation crosslinking is noteworthy. This suggests that even a very small concentration of branches can significantly reduces the moleculer motions required for the process of plastic deformation. The Young's modulus/draw ratio relationship follows a pattern virtually identical to that observed in the case of homopolymers.
TL;DR: In this article, the dynamic shear modulus of casein gel was measured slightly above the gelation concentration as functions of frequency and concentration, and it was shown that the shear exponent t is constant at lower frequency region and is close to the value expected from the percolation theory.
Abstract: Dynamic shear modulus of casein gel was measured slightly above the gelation concentration as functions of frequency and concentration The results show that the shear modulus G is expressed by G = C · e t , where e is the reduced concentration in reference to the gelation concentration The exponent t is found to be constant at lower frequency region and is close to the value expected from the percolation theory
Patent•
12 Sep 1984TL;DR: In this paper, the first layer on the fiber consists of UV cured acrylate resin having a modulus of elasticity at 25° C. The second layer is also a UV cured ACrylate resin resin, but has a higher modulus at 50° C, and the ratio of the thickness of the first and second layers is between 0.5 and 2.
Abstract: Glass optical fiber having a primary coating constructed from two layers (having a total thickness 50-70 μm), in which the first layer on the fiber consists of UV cured acrylate resin having a modulus of elasticity at 25° C. less than or equal to 5 N/mm2. The second layer is also a UV cured acrylate resin, but has a modulus of elasticity at 25° C. of from 25 to 1500 N/mm2. The ratio of the thickness of the first layer to the thickness of the second layer is between 0.5 and 2.
Journal Article•
TL;DR: In this article, the static and dynamic elastic moduli of particulate composites, consisting of two phases, one of which has isotropic-elastic and the other linear viscoelastic properties, were studied.
Abstract: The static and dynamic elastic moduli of particulate composites, consisting of two phases, one of which has isotropic–elastic and the other linear viscoelastic properties, were studied. For this purpose a model defining the approximate equations for determining the elastic modulus of a composite from the properties of the constituent materials was used. Classical theory of elasticity was applied to this simplified model of a composite-unit cell. The following assumptions are made: (i) filler particles are spherical; (ii) fillers are completely dispersed; and (iii) the volume fraction of fillers is sufficiently small, so that any interaction among fillers may be neglected. A class of iron-filled epoxy composites was subjected to tests in order to compare the theoretical values with the experimental results. The elastic modulus calculated by the expression derived in this study seems to corroborate with the experimental results fairly well. Finally, by applying the correspondence principle to this expression, theoretical relationships for the dynamic storage and loss moduli were also derived.
TL;DR: In this paper, a model of junction network is used to calculate maximum attainable draw ratios (X) and corresponding values of tensile strength (F) for different conditions of polymer film and fiber forming.
Abstract: A model of junction network that is deformed upon drawing has been used to calculate maximum attainable draw ratios (X) and corresponding values of tensile strength (F) for different conditions of polymer film and fiber forming. Experimental data for melt-spun samples of polyethylene (PE), polycaproamide and polyoxymethylene and solution-cast films of polyvinylalcohol appeared to be in good agreement with calculated values. Considered also are methods for the increase of X and F due to polymer molecular weight enhancement in samples forming from “poor” solvent with subsequent orientation drawing under optimal conditions. Values of X=130–230 and those of F = 7 GPa with a Young's modulus E=144 and sonic modulus Es=200 GPa, approximating theoretical, have been obtained for monofilaments of PE with m.w. 2.106.
TL;DR: The general elastic property ratio equations for nth-stranded wires are derived and then specified for the case of a triple-stranding arch wire, showing differences which can be explained on the basis of the mechanical property values and/or the geometric modeling assumed.
TL;DR: In this paper, a model of the micro-structure and the associated compressive strength law for Portland cement pastes is presented, where the most important parameter influencing the strength is the capillary porosity.
TL;DR: In this paper, the relaxation time of extruded thermotropic liquid-crystal polymers is much longer than that of conventional polymers, and the initial modulus and elongation of sheets extruded with liquid crystal polymers were found to be strongly dependent on the gauge length.
Abstract: Using two types of thermotropic liquid-crystal polymers, experimental results reconfirmed previous reports that the relaxation time of extruded liquid-crystal polymers is much longer than that of conventional polymers The initial modulus and elongation of sheets extruded with liquidcrystal polymers were found to be strongly dependent on the gauge length In addition, it was observed, for the first time, that the mechanical properties of the extruded thermotropic copolyesters follow the general equations for fiber-reinforced composites such that the angular dependence of the tensile strength of the extruded liquid-crystal polymeric sheets obeys the Tsai-Hill theory, while the angular dependence of the initial modulus follows the Lees equation These results suggest that the highly oriented liquid-crystal domains may be considered as reinforcing fibers in the extruded articles, and their mechanical properties can be predicted using existing composite theories