Showing papers on "Young's modulus published in 1975"

Calculation of bulk modulus, shear modulus and Poisson's ratio 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.

Tough thermoplastic polyester compositions

Abstract: Toughened multi-phase thermoplastic composition consisting essentially of one phase containing 60 to 99 percent by weight of a polyester including polycarbonate matrix resin of inherent viscosity of at least 0.35 deciliter/gram, and 1 to 40 percent by weight of at least one other phase containing particles of at least one random copolymer having a particle size in the range of 0.01 to 3.0 microns and being adhered to the polyester, the at least one random copolymer having a tensile modulus in the range of 1.0 to 20,000 p.s.i., the ratio of the tensile modulus of the polyester matrix resin to tensile modulus of said at least one polymer being greater than 10 to 1. Said at least one polymer is either a branched or straight chain polymer. The toughened compositions are useful for making molded and extruded parts. Such parts possess greater ductility, less reduction in toughness from scratches and molded in notches and reduced susceptibility to catastrophic failure when compared to known melt fabricated materials.

Significance of cyclic confining stress in repeated-load triaxial testing of granular material

Abstract: A number of research projects have been concerned with determining the nonlinear stress-strain characteristics of granular materials by using repeated-load triaxial tests. Improvements in materials testing equipment have lead to experiments in which the confining stress and the vertical stress were applied cyclically. There is an apparent difference in the resilient Poisson's ration determined under constant and under variable confining stresses. This difference is best explained by considering the behavior of granular materials in terms of volumetric stress-strain and shear stress-strain relationships. By doing this, one can show that Poisson's ratio is a function of the ratio of volumetric strain to shear strain. Resilient strains were investigated separetely from permanent strain because the permanent strain developed depended on the loading history of the sample and because the resilient behavior was not affected by any previous subfailure stress applications. To keep materials testing techniques simple, a constant confining stress equal to the mean value of a cyclic confining stress can be considered to be equal to the cyclic confining stress for determining the resilient modulus and permanent deformation.

Numerical calculation of stress relaxation modulus from dynamic data 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.

Fiber reinforced rubber modified polypropylene

Abstract: Reinforcement can improve the modulus, heat distortion temperature and thermal expansion coefficient of rubber modified polypropylene. These improvements canbe obtained with a minimum sacrifice in resin ductility and impact toughness. Our studies have shown that reinforcement with small discontinuous fibers can provide a material with a good balance of stiffness and impact strength. The combination of small potassium titanate fiber reinforcement, polypropylene homopolymer and an impact modifier can produce a material with a tensile modulus of 470,000 psi, a notched Izod impact strength of 4.6 ft-lb/in. and a Gardner imact strength of 320 in-lb. Glass fiber reinforcement produces similar improvements in stiffness and retains Izod impact strength but drastically reduces Gardner impact strength. Polypropylene resin viscosity has a profound effect on composite impact strength. Transmission electron microscopy showed that a correlation exists between EPDM rubber particle size and impact strength: as rubber particle size is reduced, impact strength is increased. A 5 melt flow rate polypropylene was found to have the viscosity required to adequately shear and disperse the impact modifier. The paper describes an approach to broadening the utility of polypropylene homopolymers. The properties and flow of these materials compare very favorably with medium impact ABS.

Properties of polypropylene-polyethylene blends

Abstract: High-density polyethylene (PE) and isotactic polypropylene (PP) were melt-blended in the following percentages of PE by weight: O, 10, 33.3, 40, 50, 66.6, 90, and 100. For these blends we obtained data on shear stress vs shear rate; tensile modulus and strength; density; and rates of water-vapor transmission for films. The shear-rate/shear-stress data at 190 and 210°C are well fitted by the Ellis model with a maximum relative error of 5 percent. At 190°C all the mixtures were found to exhibit flow instabilities at high shear rates except the 90 percent and pure PE compositions. These, however, were unstable at 140, 150, and 160°C. The 10, 33.3, 40, 50, and 66.6 percent PE mixtures ruptured at elongations of less than 15 percent at the maximum tensile stress. The maximum tensile strength and modulus pass through maxima at 10 percent PE. Density is given by the equation ρ = 0.9029 + 0.0544 (wt fraction PE). Water-vapor permeability was measured using wax-sealed permeability cups, according to ASTM E96-66. Valid results were obtained for only a few compositions because of faulty seals that could be detected only during careful dismantling of the specimen dishes. Faulty seals could account for the value, about ten times ours, reported in the literature for linear PE.

Low‐temperature elastic properties of four austenitic stainless steels

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...

Radial tire having sidewalls reinforced with a rubbery mixture having a high modulus

Abstract: A tire with a radial carcass and a top belt under the tread, has sidewalls which are reinforced by layers of a rubbery mixture exhibiting a high modulus of elasticity and extending over the entire height of the sidewalls. The upper edges of these reinforcement layers are inserted between the carcass and the lateral edges of the belt.

Thrust chamber life prediction. Volume 1: Mechanical and physical properties of high performance rocket nozzle materials

Abstract: Pertinent mechanical and physical properties of six high conductivity metals were determined. The metals included Amzirc, NARloy Z, oxygen free pure copper, electroformed copper, fine silver, and electroformed nickel. Selection of these materials was based on their possible use in high performance reusable rocket nozzles. The typical room temperature properties determined for each material included tensile ultimate strength, tensile yield strength, elongation, reduction of area, modulus of elasticity, Poisson's ratio, density, specific heat, thermal conductivity, and coefficient of thermal expansion. Typical static tensile stress-strain curves, cyclic stress-strain curves, and low-cycle fatigue life curves are shown. Properties versus temperature are presented in graphical form for temperatures from 27.6K (-410 F) to 810.9K (1000 F).

Young's modulus of lignin from a continuous indentation test

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.

Construction material for stringed musical instruments

Abstract: Improved construction material especially suitable for use in the manufacture of soundboards and panels used in stringed instruments which equal or surpass the sound radiation qualities and physical properties of wood. The construction material of the invention includes fibers having a Young's modulus of elasticity greater than 18×10 11 dynes/cm 2 and a density less than 2 g/cc bonded to a material having a density lying within the range of 0.15 g/cc and 1 g/cc, the said fibers of the composite are oriented in such manner so as to provide a final material having a bending stiffness ratio of at least 4:1.

Tensile properties of ultradrawn polyethylene

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.

Storage and loss moduli in discontinuous composites

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.

Low-temperature elastic properties of four wrought and annealed aluminium alloys

Abstract: The elastic properties of four annealed polycrystalline commercial aluminium alloys were studied between 4 and 300 K using a pulse-superposition method. Results are given for longitudinal sound velocity, transverse sound velocity, Young's modulus, shear modulus, bulk modulus (reciprocal compressibility), Poisson's ratio, and elastic Debye temperature. The elastic stiffnesses of the alloys increase 4 to 13% on cooling from room temperature to liquid helium temperature. The elastic constant-temperature curves exhibit regular behaviour.

Strength and Elastic Modulus of a Randomly-Distributed Short Fiber Composite:

Abstract: Experimental results for tests of strength and elastic modulus of a randomly-distributed short fiber composite are reported in this paper. Three different tests were employed: tension, 3-point flexure, and 4-point flexure. A statistical approach based on Weibull distribution was applied to account for the difference between tensile and flexural test results. Mate rial variation, as exhibited in the experimental scatter for elastic modulus, and its effect on strength were shown not to be negligible. Test results also showed wider experimental scatter than observed with continuous fiber composites. Consequently considerable penalty had to be paid by reducing the design strength in order to assure the same level of confidence and reliability.

Reed type valve formed of high modulus fiber reinforced composite material

Abstract: The specification discloses a reed type valve formed of a composite material having a coherent matrix reinforced with fibers of high strength and high modulus of elasticity aligned along given directions to provide reinforcement against loads to be applied to the valve during operation thereof. The high modulus fibers may be of carbon or boron and preferably have an average modulus of elasticity greater than 18 × 106 psi.

Fatigue and resilient characteristics of asphalt mixtures by repeated-load indirect tensile test

Abstract: The mixtures studied contained crushed limestone or rounded gravel aggregates and an AC-10 asphalt cement ranging from 4 to 8 percent by weight of total mixture. The fatigue and repeated-load tests were conducted at 50, 75, and 100 F, with the stress level ranging between 8 and 120 psi. From the static tests, an equation which predicts indirect tensile strength in terms of testing temperature and mixture properties was developed. In addition, a strong relationship was found to exist between static modulus of elasticity and indirect tensile strength. From the fatigue study, relationships between fatigue life and various test variables and mixture properties were evaluated and equations were developed for predicting fatigue life from initial strain and from the ratio of repeated tensile stress to the average indirect tensile strength.

The modulus of elasticity of human cortical bone: an in vivo measurement and its clinical implications.

Abstract: The modulus of elasticity was derived by combining the velocity of ultrasound measurements and photon absorption (Norland-Cameron method) in human cortical bone (proximal radius) in vivo. The results compare favorably with published values of the elasticity modulus obtained in vitro. Values obtained for a heterogeneous group of patients with bone and joint complaints differed from those of normal volunteers.

The Response of Frozen Soils to Vibratory Loads

Abstract: This study was conducted to provide reliable values of the stiffness and damping properties of frozen soils subjected to vibratory loads and to define the significant factors affecting these parameters. A laboratory test was conducted on prepared specimens of frozen soils where a right circular cylinder was subjected to steady-state sinusoidal vibration. The material was considered to be linearly viscoelastic. Analysis of test data based on one-dimensional wave propagation yielded the complex Young's modulus, the complex shear modulus, the phase velocity of wave propagation, the shear velocity, the damping property expressed as the angle representing time lag between stress and strain, an attenuation coefficient, and a complex Poisson's ratio. The frequency of vibration was varied for 500 to 10,000 Hz, and the peak dynamic stress was varied from 0.1 to 5.0 psi. Specimens were remolded or cored in-situ, frozen, and tested at 0,15, and 25 F(-17.8, -9.4, and -3.9 C). A few tests were conducted on identical soils nonfrozen. Test results from a limited number of tests on selected soils indicate that the stiffness of these soils varies with the volume of ice/volume of soil ratio, and that ice is less stiff than saturated frozen soils. Frozen soils have stiffnesses up to 100 times those of identical soils nonfrozen. Depending upon the degree of ice saturation, the stiffness of non-saturated frozen soils varies from that of the saturated soils to nearly that of the nonfrozen soils. Stiffness increases with decreasing temperature but the rate is relatively low. As temperature rises and approaches the freezing point, stiffness abrupty decreases. Damping, as a property of the material does not differ greatly for frozen soil versus nonfrozen soil. This indicates that the mechanism influencing damping for frozen soil is quite different from that for nonfrozen soil. In the range of frequencies and stress studied, the use of linear biscoelastic theory appears to be adequate for frozen soils, as only slight evidence to nonlinearity was observed. /Author/

A flexible circular plate on a heterogeneous elastic half-space: influence coefficients for contact stress and settlement

Abstract: To predict the stresses and displacements in soil beneath a flexible foundation it has been found that a better agreement with observed results is obtained by assuming that Young's modulus increases with depth. An outline is given of a finite element method which has been used to study the behaviour of a rigid circular plate on a half-space together with an extension of the method to allow for plate flexibility. In this note, the authors provide influence coefficients from which the contact stress and settlement may be computed. /TRRL/

Testing Procedure Effects on Dynamic Soil Behavior

Abstract: Cyclic triaxial tests were performed on dry and saturated undrained sands using stage testing methods to investigate the influence of repeated cyclic straining and specimen reconsolidation on equivalent linear modulus and damping values on both a total stress and on an effective stress basis. It was found that: (1) Modulus and damping values for dry sand are not significantly affected by stage testing; (2) damping values are not significantly higher for saturated specimens than for dry specimens; (3) volume changes in saturated specimens induced by stage testing can be severe and can severely change initial testing densities; and (4) modulus values for saturated sands are significantly higher for stage tested specimens than for fresh specimens at the same shear strain levels after the same number of cycles. It was concluded that stage testing methods may not give reasonable values of dynamic soil properties for saturated undrained sands for shear strain levels greater than about 0.1% or for more than about 25 strain cycles.