Showing papers on "Elastic modulus published in 1977"

Enhanced elastic modulus in composition‐modulated gold‐nickel and copper‐palladium foils

Abstract: The biaxial elastic modulus Y[111] has been measured by bulge testing in Au‐Ni and Cu‐Pd foils containing short‐wavelength one‐dimensional composition modulations produced by vapor deposition. As compared with homogeneous foils of the same average composition, the modulated foils exhibited an appreciable increase in modulus—from 0.21 to 0.46 TPa for Au‐Ni and from 0.27 to 1.31 TPa for Cu‐Pd. For the latter system, the increase was found to be proportional to the square of the amplitude of the modulation. The enhancement of the modulus decreased with increasing wavelength and for wavelengths greater than 3 nm the modulus was the same as that for homogeneous foils. It was also observed that the deformation was non‐Hookian; the slope of the stress‐strain curves decreased with increasing strain.

Model networks of end‐linked polydimethylsiloxane chains. I. Comparisons between experimental and theoretical values of the elastic modulus and the equilibrium degree of swelling

Abstract: Two samples of hydroxyl‐terminated polydimethylsiloxane having molecular weights the order of 2×104 and 1×103 g mol−1 were separated into a total of six fractions of relatively narrow molecular weight distribution. Portions of one of the unfractionated polymers and each of the fractions were cross‐linked by reacting the hydroxyl chain ends, in the undiluted state, with a tetrafunctional orthosilicate. The resulting networks of end‐linked chains were studied with regard to their stress–strain isotherms in elongation at 25°C and their equilibrium swelling in benzene at room temperature. Values of the elastic modulus obtained from the isotherms support theoretical arguments that fluctuations in the network chain vectors reduce the value of the modulus to approximately one‐half of the value predicted for affine deformations of chain vectors constrained in their fluctuations by cross‐links firmly embedded in the network medium. Values of the equilibrium degree of swelling of the networks calculated on this bas...

Elastic properties of zinc: A compilation and a review

Abstract: The elastic constants of zinc are compiled and reviewed; one hundred references are cited. The included elastic constants are: Young’s modulus, shear modulus, bulk modulus, compressibility, Poisson’s ratio, second‐order single‐crystal elastic stiffness and compliances, and third‐order, elastic stiffness. Temperature and elastic‐anisotropy effects are also reviewed. Other topics are: sound velocities, elastic Debye temperature, Cauchy relationships, elastic stability, pressure effects, and theoretical studies. New polycrystalline data are computed from single‐crystal data by tensor‐averaging methods.

Elastic modulus of single wood pulp fibers

Abstract: Careful measurements have been made of the elastic modulus of softwood fibers over a range of fibril angle 0-50°. For fibers of similar fibril angle, the modulus varies appreciably and this is shown to be caused by microcompressions, dislocations, and other inhomogeneities in the structure. For fibers that are free from such defects, the plot of modulus against fibril angle follows a smooth curve. Using orthotropic elasticity theory, an explicit equation for modulus in terms of fibril angle and the orthotropic elastic constants of the cell wall has been derived. The experimental data fit theory excellently. The elastic constants of the cell wall derived from the fit show the wall to be highly anisotropic.

Moisture Effects in Epoxy Matrix Composites

Abstract: : The effect of absorbed moisture on the mechanical properties of a neat epoxy resin and derived graphite/epoxy composites is investigated. Glass transition temperature and modulus as a function of moisture content and temperature is determined for both the neat resin and composite. In addition, elastic modulus for the neat resin, and strength and elastic moduli for unidirectional composites and quasi-isotropic laminates are determined as a function of absorbed moisture and temperature. A method for predicting moisture content and through-the-thickness profile for a laminate exposed to a constant humidity and temperature is discussed. Particular attention is also given to the details of environmental testing. Data indicates that absorbed moisture and temperature effects on the neat resin translate directly to matrix dominated properties of the composite and can lead to a change in failure mode, while filament dominated properties show very little environmental sensitivity. Results also indicate that resin glass transition temperature is a function of processing as well absorbed moisture.

Environmental Effects on the Elastic Moduli of Composite Materials

Abstract: The buckling moduli of Thornel 300/Fiberite 1034 graphite epoxy composites were measured at temperatures ranging from 105 K to 422 K and at moisture contents ranging from 0% (dry) to 1.5% (fully saturated). The measurements were made using 0°, 90° and π/4 laminates. A survey was also made of the existing data showing the effects of temperature and moisture content on the tensile modulus and the compressive modulus of different composite materials.

Plastic deformation of crystalline polymers

Abstract: Under uniaxial tensile load, the plastic deformation of unoriented crystalline polymers first transforms the lamellae into a fibrous structure. Usually the drawing is inhomogeneous with a neck propagating through the sample. The higher the draw ratio, the higher the axial elastic modulus as a consequence of the larger fraction of taut tie molecules in amorphous layers connecting the crystalline blocks of each microfibril. As a consequence of the almost 1/(1 − α) times higher strain of amorphous layers under tensile load, the taut tie molecules are much more strained than the chains in crystal blocks. Hence, their contribution to elastic modulus is substantially higher than one would guess from their fraction β. This is more so in polyethylene with higher crystallinity (α = 0.8) than in nylon 6 with low crystallinity (α = 0.5). Even for the highest modulus polyethylene E = 70 GPa ∼ 0.3 × Ec, one needs less than 7.5 percent of taut tie molecules. The plastic deformation of the fibrous structure markedly enhances the number of interfibrillar tie molecules in nylon 6 and to a lesser extent in polyethylene and polypropylene. Homogeneous drawing without a neck transforms the whole sample into a fibrous structure rather uniformly so that for a long while one has the lamellar and fibrillar morphology side by side. The end effect on the structure obtained does not differ appreciably from inhomogeneous drawing with neck propagation. The drawing of polymers with a liquid crystal structure yields a highly aligned fibrous structure with very few chain folds and an exceptionally high elastic modulus and strength. But the axial connection of individual highly oriented and ordered domains is affected by a relatively small fiaction of tie molecules, and this is responsible for reduction of the elastic modulus below the value of the ideal crystal lattice.

Glass bead-filled polypropylene part I: Rheological and mechanical properties

Abstract: Five glass bead-filled polypropylene composites were rheologically characterized at 240°C using two rotational rheometers to obtain low shear-rate data and a capillary rheometer to obtain high shear-rate data. Both steady and dynamic properties were measured at low shear rates. Each composite was also injection molded into tensile and flexural test bars for a mechanical properties profile at 25°C. The tensile modulus was determined from a simple extensional deformation whereas the flexural modulus was determined from a three-point-bend test. The relative shear viscosity and relative loss modulus are different nonlinear functions of the volume fraction of beads at a constant shear rate, while the relative storage modulus appears to be a linear function of bead fraction. The relative viscosity decreases with increasing shear rate and the zero shear-rate data are in very good agreement with the Guth-Gold equation. The relative tensile modulus and relative flexural modulus are each linear functions of bead fraction over the entire range of filler concentration, 0-29 vol percent. From these data it is concluded that a simple correspondence between slow viscous flow and small strain elasticity does not exist for these composites.

Elastic Properties of Randomly Oriented Short Fiber-Glass Composites:

Abstract: Simplified equations are presented for the elastic properties of randomly oriented short fiber-glass composites. The suggested equations for the Young's modulus, the shear modulus and the Poisson ratio are given in terms of the fiber-glass content and the Young's moduli of the constit uents. The equations are applicable for fiber-glass volume fractions in the range 0.1 to 0.4. The theoretical results are compared with experimental values, and the achieved good correlation, shows the utility of the pro posed approximations.

Drawing and annealing of fibrous material

Abstract: The more‐than‐linear increase of elastic modulus with draw ratio, the gradual disappearance of meridional SAXS maximum, the drastic drop of elastic modulus after annealing and its recovery upon standing at room temperature if the sample was annealed with fixed ends so that it did not shrink, and the shape stability of such polyethylene samples and of superdrawn material (polyethylene, polypropylene, polyoxymethylene) during new annealing can be easily explained by the microfibrillar model of fibrous structure which was developed some years ago on the basis of electron microscopy and x‐ray and ir investigation of plastically deformed linear polyethylene and isotatic polypropylene.

High temperature elasticity of rutile-structure MgF2

Abstract: The elastic moduli of single-crystal MgF2 have been determined by the ultrasonic pulse superposition technique as a function of temperature from T=298−650° K. These new data are consistent with those obtained by other ultrasonic pulse techniques at and below room temperature and agree favourably with polycrystalline data above room temperature. The elastic moduli (c) are represented by quadratic functions in T over the experimental temperature range with the curvature in the same sense for all the moduli. For the rutile-structure fluorides and oxides, evaluation of the temperature derivatives of the elastic moduli at constant volume indicates that the dominant temperature effect is extrinsic for (∂K S /∂T) P and intrinsic for (∂μ/∂T) P , where K S and μ are the isotropic bulk and shear moduli, respectively. There appears to be no simple relationship between (∂c/∂T) P and crystallographic parameters for the rutile structure, and |(∂c/∂T) P | for the fluorides is in general very much lower than the corresponding |(∂c/∂T) P | for the oxides. For the pair of compounds MgF2-TiO2, there is no evident analogue relationship for high-temperature elastic properties.

Elastic Moduli of Refractory Spinels

Abstract: Elastic moduli of spinel phases in the system Mg(Al, Cr, Fe)2O1 were determined from sonic analyses of porous, polycrystalline specimens prepared by hot-pressing. A special iterative least-squares technique (ILS) and standard curve-fitting techniques were used to obtain moduli at zero porosity by extrapolation. A minimal standard error of estimate was achieved in all cases by using an exponential form for the porosity dependence and the ILS technique. Moduli were checked for self-consistency. Extrapolated moduli for MgAl2O1 agreed well with respective moduli calculated from single-crystal elastic constants and Birch's law. Longitudinal and shear sound velocities decreased with increasing phase density in the solid-solution systems and systematics indicate that elastic moduli of arbitrary solid solutions can be estimated to lt; ± 10% from the phase density.

Influence of elastic and thermal mismatch on the local crack-driving force in brittle composites

Abstract: An expression is derived for the change of localK 1 value of a crackfront near circular and spherical inclusions with elastic moduli and thermal expansion coefficient different from those of the matrix. The derivation is based on the concept of an “image stress” which is imposed on the crack, to illustrate the interaction between elastic and thermal stress concentrations developed around inclusions in a composite material and the crack-tip stress field.

Ultrasonic Measurement of Some Mineral Filled Plastics

Abstract: Absrroct-Several composite systems such as vinyl-tungsten, polymethylmethacrylatecrystabolite, and epoxycrystabolite have been examined for the variation of the longitudinal velocity as a function of volume fraction of the hard constituent. When the Voigt and Reuss velocity bounds rather than elastic bounds are plotted for these composite systems, the bounds are widely divergent and the V-bound is concave downward, while the R-bound is concave upward and has a well-defined minimum velocity. The experimental data for all the systems conform to the R-bounds indicating that the composite systems are families of true Reuss solids. The velocity minimum occurs because the density increases more rapidly than the elastic modulus. C OMPOSITE materials, where the matrix is soft and the filler is hard, are encountered in many situations. Our experience includes backing materials for ultrasonic transducers, dental restorative materials, and hard biological tissues like bone and teeth. Composites are materials made of two or more constituents in intimate contact. The composite is homogeneous and isotropic when the filler is a powder uniformly distributed throughout the matrix. When the filler is fibrous, the composite can exhibit anisotropic behavior and hard tissues are fibrous and anisotropic. In this paper only homogeneous isotropic composites will be discussed and only with respect to the performance of the longitudinal sonic velocity as it is affected by the amount of the hard filler included in the solid. The ultrasonic transducers employed in the measurements emitted well-damped pulses. For the vinyl-tungsten composite system listed in Table 11, the pulse duration was about one microsecond, but for the other materials it was 100 nanoseconds. Hence in all instances, the use of ultrasonics ensured that the measurements were made at high strain rates with very little displacement, so that only the elastic properties affected the measurements and plastic deformation was negligible. The samples could be retested since there was no deformation or destruction. Moreover, the ultrasonic tests could be repeated with little variation on the same sample and the results were repeatable for similar samples. What is desired is a technique for predicting the velocity characteristics of the composite system as a function of the volume fraction of the hard filler constituent. In a 1973 paper [l] it was shown that the longitudinal sonic velocity of the tungsten-vinyl composite decreased markedly to a

The elastic modulus of lignin as related to moisture content

Abstract: In previous papers, a theory was developed relating Young's modulus of hydrogenbond dominated solids to the density of this bond and to its parameters, and also to the moisture content of the solid. In this paper, the theory is applied to experimental results reported by Cousins on periodate lignin. The theory fits the observations and, furthermore, predicts that this particular lignin has 6.84 potential H-bonding sites per repeating unit of an assumed molecular weight of 1,000. No data for periodate lignin exist, but a Freudenberg constitutional scheme for lignin postulates a little over 7 potential sites for H-bonding per repeating unit of 1,000 molecular weight.

Temperature dependence of the dynamic mechanical properties of filled polymers

Abstract: A theory has been developed to explain the jump in the relative modulus of filled polymers near the glass transition temperature Tg and the subsequent decrease in relative modulus at temperatures above the glass transition temperature. The theory is based upon the concept that there are some particle–particle contacts in doublets and in agglomerates containing a larger number of particles. Below Tg motion of particles at the contact points is possible because of the high modulus of the polymer. At Tg particle–particle motion mostly ceases because of the low modulus of the polymer. At higher temperatures, the mismatch in the coefficients of expansion allows some motion to occur at points of contact and slippage may occur at the polymer–particle interfaces, so the modulus decreases. It is shown theoretically and experimentally that both the elastic modulus and the mechanical damping depend upon the nature of the surface of the particles.

Elastic moduli of filled polymers: The effect of particle shape

Abstract: Eshelby’s theory is known for its simplicity in the treatment of the elastic moduli of a composite filled with spheres. His approach is utilized in this paper to estimate the five elastic constants of a filled polymer containing aligned ellipsoids. The anisotropy‐particle‐shape effect is characterized by the aspect ratios (ρ) of an ellipsoid. Because Eshelby’s theory is limited to dilute dispersions, we have to confine the present derivation to the intrinsic moduli. The basic definition and method are outlined in the discussion of shear moduli which have the form analogous to that of spherical filler and have also been investigated by several authors relating explicitly to disk‐ and needle‐shaped particles. Equations on the bulk, longitudinal, and transverse Young’s moduli are the new results which are valid for all values of ρ. Orienting fibers (ρ≳1) parallel or disks (ρ<1) perpendicular to the stretch direction has the similar reinforcing effect and is illustrated with data on glass and boron in epoxy resins.

Reduction in the Modulus of Elasticity in Orthodontic Wires

Abstract: The modulus of elasticity of stainless steel orthodontic wires was found to be 20% below the normally assumed range of 19.3 to 20.0 X 104 MPa (28.0 to 29.0 × 106 psi). Use of the latter value can result in significant computational errors in orthodontic applicance mechanics. The lower modulus was attributed to severe cold drawing.

Elastic Moduli of Carbon-Epoxy Composites and Carbon Fibers

Abstract: All independent elastic moduli of unidirectional carbon-epoxy com posites were measured in the tensile and torsional tests of co-axis and off-axis specimens. The experiments were motivated to estimate the unmeasurable elastic moduli of carbon fiber itself. The experimental results were incorporated with the authors' preceding analytical results which describe the relationships between the moduli of composites and consti tuents. According to several results, the fact that the hexagonal array packing is more favorable as an idealized model was obtained. It should be noted that carbon fiber is highly anisotropic and that the estimated values of those moduli are reasonable in comparison with those in a few existing references. Some of the basic assumptions employed in the analysis were confirmed by the observation of the transverse and longitudinal sections of the specimens through an electron-scanning-beam microscope (ESM).

Polymeric composite systems with two continuous phases

Abstract: A general mixture rule, which has the correct type of phase symmetry, is proposed for estimating the properties of composites having two continuous phases. The form of this equation is different from the equations used to predict the properties of composites with one continuous phase and one dispersed phase. The proposed equation for property P is where the volume fractions of components A and B are oA and oB, respectively, and n is a constant. A simple model is used to correlate the morphology of systems having two continuous phase with the parameter n of the mixture rule. The connectivity of the phase varies with concentration. The properties, such as elastic modulus, depend primarily upon the modulus of the material with the higher modulus. In general, the properties depend very little on the morphology of the system.

Correlation effects in the bulk modulus and equilibrium lattice spacing of the transition metals

Abstract: 2014 The role of correlations in the bulk modulus and equilibrium lattice spacing of the transition metals is studied using a perturbation method related to Gutzwiller’s approximation and is found to decrease the bulk modulus and increase the lattice spacing, the effect being greatest in the middle of the 3d series in agreement with experiment. LE JOURNAL DE PHYSIQUE LETTRES TOME 38, .ler JUILLET 1977, Classification Physics Abstracts 62.20D 71.45 As is seen in figure 1 the bulk modulus in the 4d and 5d transition metal series varies regularly with the

Automatic internal friction and modulus measurement apparatus utilizing a phase‐locked loop

Abstract: An inexpensive apparatus for the continuous and automatic measurement of internal friction and elastic modulus is described. This apparatus is regenerative, maintaining a specimen in resonance at constant amplitude, unless interrupted by the experimenter. A vital component of this system, generally absent in such devices, is a phase‐locked loop.