Showing papers on "Volume fraction published in 1973"

Effect of Microstructure on Strength of Si3N4‐SiC Composite System

Abstract: The Si3N4-SiC composite system was investigated to better understand the effect of microstructure on the strength-controlling factors, i.e. fracture energy, elastic modulus, and crack size. Silicon carbide dispersions with average particle sizes of 5, 9, and 32 μm were used to form 3 composite series within this system, each containing 0.10, 0.20, 0.30, and 0.40 vol fraction of the dispersed phase. These composites were fabricated by hot-pressing. Fracture energy and strength values were measured for each composite. A linear relation between the elastic modulus of the two phases was assumed. The crack size was calculated for each composite using the appropriate property values. The strength behavior of the 9- and 32-μm series was controlled by the crack size, which, in turn, was controlled by the particle size and volume fraction of the SiC phase. Particle size and volume fraction did not affect the crack size of the 5-μm series, in which strength was controlled by both fracture energy and elastic modulus. Strengths measured at 1400°C and thermal conductivity measurements indicate that several of these composites are promising as high-temperature structural materials.

Modulus reinforcement in elastomer composites. I. Inorganic fillers

Abstract: The effect of various inorganic fillers on the storage modulus of four elastomers was determined experimentally. Results are interpreted using the Kerner equation, modified to include a parameter, B, in the volume fraction terms. This factor combines particle size and specific interaction effects, and in theory can be evaluated from energy dissipation measurements.

A Theory for the mechanical properties of metal-matrix composites at ultimate loading

Abstract: A theory describing the strain, ultimate strength, and work during uniform strain to ultimate loading of metal-matrix composites deformed in tension parallel to the reinforcement is presented. These quantities may be calculated for composites of arbitrary volume fraction using only the component stress-strain curves. The theory is based on the systematic application of a macroscopic principle commonly used to predict the ultimate strength of ductile monolithic materials—namely, that necking occurs when the load borne by the material is maximized. For brittle reinforcing elements, the results are identical to those of previous workers. For ductile reinforcing elements, necking strains intermediate between those of the components and ultimate strengths increasing smoothly with volume fraction from that of the matrix to that of the reinforcement are predicted. The theory can be used to predict the variation of composite ultimate properties with any parameter of interest. In this paper the variation with volume fraction and yield strength of the matrix are studied, with both exact solutions and useful approximations being derived.

Dynamic mechanical properties of epoxy–rubber polyblends

Abstract: The dynamic mechanical properties of the epoxy resin of the diglycidyl ether of bisphenol A cured with varying amounts of a carboxyl-terminated butadiene–acrylonitrile copolymer were determined. Isochronal measurements were made between −90° to 170°C for eight compositions. Mechanical relaxations indicate the degree of interaction and the state of mixing of the two-phase system. Phase reversal occurs at a volume fraction of 0.5, where an intermediate compound is formed. In the low concentration range of the elastomeric phase, the impact strength improvement correlates well with an increase in the energy absorption of the relaxation. The known morphology of the system at this composition range allowed testing of various phenomenological mechanics models proposed to calculate the tensile properties of composite systems.

Superconductivity of copper containing small amounts of niobium

Abstract: Superconductivity of copper containing small amounts of niobium has been investigated by measuring the electrical resistivity, superconducting volume fraction and by metallographic studies. Small amounts of niobium added to copper has a drastic effect on the low temperature resistivity of the alloys, The annealed alloy Cu99.5Nb0.5 shows zero resistance at a current density of 200 A cm−2 below 3K. The estimated superconducting volume fraction of this alloy at 2K is about fifty times the physical volume fraction of the Nb in the alloy.

Importance of slip mode for dispersion-hardened β-titanium alloys

Abstract: The mechanical properties of Ti-7 Mo-7 Al and Ti-7 Mo-16 Al (in at. pct) were correlated to the microstructure. The mechanical properties of the alloy with low aluminum content, consisting of α+ β phases, were dependent on the size of the α particles. Although the α phase is softer than the β phase, the small α particles, upon plastic deformation of the alloy, functioned as typical hard agents in a dispersion-hardened system and the volume fraction of the particles controlled the macroscopic ductility. A rapid strain-hardening behavior of the small α particles seemed to be responsible for this effect. Large α particles behaved like soft, incoherent particles, the volume fraction having little effect on the inherent ductility of the alloy. The two phase (β+ Ti3Al) microstructure of the alloy with high aluminum content resulting from high temperature aging to 900°C exhibited a yield stress of 130 ksi and an elongation to fracture of 5 pct. The ductility of this microstructure was controlled by the volume fraction of the Ti3Al particles inducing homogeneous slip. The favorable ductility properties of the microstructures with low Ti3Al volume fraction were lost if the slip mode was changed from homogeneous slip to planar slip.

The Effect of Size and Distribution of Second Phase Particles and Voids on Sintering

Abstract: The equations for the kinetics of diffusion controlled coarsening were solved with no restrictions on the size or spacial distribution of the particles in the system. In the limit of very small volume fractions, approximately parts per million of second phase, the treatment reduces to that of Lifshitz-Wagner. As the volume fraction is increased there is a deviation from the predictions of Lifshitz-Wagner, this deviation can be more than an order of magnitude at moderate volume fractions and it may be either positive or negative. The deviation tends to be positive if particles of greatly different radii are near neighbors, and tends to be negative if particles of only slightly different radii are near neighbors. This treatment of diffusion controlled coarsening can be applied to give a better understanding of how voids coarsen during sintering. The treatment can also be used to better understand the coarsening of second phase particles in the sintering of two phase composites.

The particle-to-matrix bond in dispersion-hardened austenitic and ferritic iron alloys*

Abstract: The bonding strength, or ‘work of adhesion’, W, between particle and matrix in a number of austenitic and ferritic iron alloys has been determined from electron micrographs of the solid/solid contact angle, θ, at cavities formed by cold working and annealing. The critical strain to bring about cavitation, ec, was measured by plotting the strain corresponding to a sudden fall in rate of work-hardening. In deriving an equation to predict ec, account must be taken of the dependence of the equilibrium shape of the cavity on θ. Good correlation between experimental and predicted ec, as a function of W, was found. Brittle fracture of the matrix is likely to occur if θ is very low and the volume fraction is high. A criterion for brittle fracture, based on θ, is suggested which successfully predicts brittle fracture in one of the alloys studied.

Effects of Thermal Loading on Fiber-Reinforced Composites With Constituents of Differing Thermal Expansivities

Abstract: Estimates of the magnitudes of elastic stresses and elastoplastic stresses and strains were made for tungsten fiber-reinforced 80Ni + 20Cr matrix composites Heating or cooling between 80 and 2000 F was assumed The calculated elastic stresses exceeded representative or estimated strengths of constituents For composites with less than 065 volume fraction of fiber, plastic flow was considered possible, and elastoplastic solutions indicated that stresses would be reduced but with the concomitant occurrence of sufficiently large strain ranges, particularly in the matrix, to pose a possible thermal fatigue problem Limited experimental studies on tungsten fiber-copper matrix composites heated and cooled a number of times between 80 and 1600 F in a conventional furnace and then heated from 80 to 1652 F in a hot-stage microscope resulted in matrix microfracture for a 70 volume fraction fiber composite and substantial matrix strain for a 40 volue fraction fiber composite

Dependence of the free volume fraction at the glass transition temperature on the molecular parameters of linear polymers

Abstract: Various definitions of the fractional free volume fg at the glass transition temperature Tg were used to test the original Fox-Flory concept of Tg as an “iso-free volume state” for polymers with a simple backbone structure. It was demonstrated that the fg values obtained by a linear extrapolation of liquid and glassy volumes below Tg for various polymers are not constant, but appear to decrease with a decrease in packing efficiency of polymer molecules in the bulk phase. Some arguments were advanced to support the idea that the glassy state of polymers might still be regarded as an iso-free volume one if the value of the intrinsic, or Van der Waals, volume of the chain repeat unit was taken for an occupied volume at Tg Peculiarities of the chain segmental motion at Tg in polymers with bulky aromatic substituents in the backbone are briefly discussed.

The effect of fibre diameter on the dynamic properties of glass-fibre-reinforced polyester resin

Abstract: The effect of fibre diameter on the mechanical properties of unidirectional composites was investigated using a glass/polyester system. The specimens were vibrated in flexure and longitudinal shear, and finally tested to destruction in interlaminar shear. To allow for changes in fibre diameter at constant fibre volume fraction, the surface area of fibre per unit volume, Af, was defined. It was found that the fibre diameter had no significant effect on Young's modulus in flexure, nor on the longitudinal shear modulus and damping. However, there was a pronounced variation of flexural damping with fibre diameter and fibre volume fraction, and hence with Af. The interlaminar shear strength was low for small values of Af, but rapidly tended to an average of about 56 MN m−2.

Predicting the stress-strain behavior of polycrystalline α-lron containing hard spherical particles

Abstract: Recent interest in the work hardening of metal crystals containing a dispersion of hard particles has resulted in analytical expressions relating the work hardening to strain, particle diameter, and volume fraction as well as other material parameters. In this study, these models have been used to calculate the tensile stress-strain behavior of polycrystalline α iron containing dispersions of the intermetallic compound Fe2Ta. The structural characteristics of the Fe-Ta alloys were thoroughly evaluated. The particle morphology was measured for randomness, mean particle diameter, standard deviation of the particle diameter, volume fraction, and planar interparticle spacing. Also, the matrix flow strength, composition, crystallographic randomness, dislocation morphology and grain size were evaluated. It was found that an Orowan type relationship as modified by Ashby satisfactorily described the yield strength as a function of the interparticle spacing and particle diameter. An experimental slope of 11.1 x 10-5 kg-cm/mm2 and a calculated slope of 9.75 x 10-5 kg-cm/mm2 were found. Both the Hart revised FHP work hardening model and Ashby’s model based on the generation of secondary dislocations were in good agreement with the experimental data. Hart’s revised FHP model required the use of empirically obtained values for the particle volume fraction which differed by a factor of 10 from the measured volume fraction and therefore is not suitable for predictive purposes. At tensile strains greater than 5 pct, the work hardening was characteristic of the matrix without particles; therefore, deviation between the experimental and calculated results based on Ashby’s model occurred at large strains. It is hoped that this study represents a step towards applying work hardening models to more complex polycrystalline alloys.

One‐dimensional radiative energy transfer in thin layers of fibrous materials

Abstract: A general model for one‐dimensional radiative energy transfer through a bed of fibrous materials is presented. The end result is the radiative thermal conductivity as a function of bed thickness, fiber emittances, volume fraction occupied by the fibers, and the average fiber diameter. Any general geometrical model of the arrangement of the fibers in the bed can be used in this model. For comparison purposes, a bed with randomly oriented fibers is considered.

Ultrasonic absorption studies of poly‐benzyl‐L‐aspartate in mixed solvents, in relation to the helix–coil transition

Abstract: Ultrasonic absorption measurements were carried out on solutions of polybenzyl-L-aspartate (PBLA) in chloroform–dichloroacetic acid (DCA) and in 1,2-dichloroethane (DCE)–DCA, in the range 3.9–155 MHZ. The helix–coil transition of PBLA produces an increase of absorption which is larger in CHCl3–DCA than in DCE–DCA solutions. The influence of the solvent on the excess ultrasonic absorption suggests that solvation processes may be involved in these changes of absorption. The plots of the absorption vs. the volume fraction of DCA do not show any absorption maximum. This indicates that the ultrasonic absorption is not sensitive to the helix–coil equilibrium of PBLA in the frequency range investigated. A maximum value of 109S−1 has been obtained for the rate constant of growth of a helix region.

Effect of microstructure on strength of si3n4-sic composite system

Abstract: The Si3N4-SiC composite system was investigated to better understand the effect of microstructure on the strength-controlling factors, i.e. fracture energy, elastic modulus, and crack size. Silicon carbide dispersions with average particle sizes of 5, 9, and 32 μm were used to form 3 composite series within this system, each containing 0.10, 0.20, 0.30, and 0.40 vol fraction of the dispersed phase. These composites were fabricated by hot-pressing. Fracture energy and strength values were measured for each composite. A linear relation between the elastic modulus of the two phases was assumed. The crack size was calculated for each composite using the appropriate property values. The strength behavior of the 9- and 32-μm series was controlled by the crack size, which, in turn, was controlled by the particle size and volume fraction of the SiC phase. Particle size and volume fraction did not affect the crack size of the 5-μm series, in which strength was controlled by both fracture energy and elastic modulus. Strengths measured at 1400°C and thermal conductivity measurements indicate that several of these composites are promising as high-temperature structural materials.

Properties of alloys on the tie-line between the copper-CuZrGe pseudo-binary eutectic and the copper-Cu5Zr eutectic

Abstract: The electrical conductivity of copper-CuZrSi alloys is shown to be improved by making them zirconium-rich; however, the volume fraction of the strengthening phase is thereby reduced. To counteract the loss of strength, the isotypic copper-CuZrGe system with its higher volume fraction of second phase was studied. The UTS was found to be higher, the high elongation to failure being retained. To study the variation of conductivity, alloys on the tie-line to the copper-Cu5Zr eutectic were investigated. It was found that conductivity values which are proportional to the volume fraction of copper can be achieved. The tensile properties follow a law-of-mixtures pattern as control of failure passes from the weaker, ductile copper-CuZrGe eutectic to the stronger, much less ductile ternary eutectic. This ternary eutectic is found to be close to the copper-Cu5Zr eutectic; the tensile properties of the two eutectics are similar, being controlled by the Cu5Zr phase which is present in both to about the same volume fraction.

X-ray determination of the volume fraction of retained austenite in quenched carbon steels

Abstract: A new method for x-ray determination of the volume fraction of phases in a sample has been developed This method is characterized by the accurate and rapid determination of these phases by analysing a single reflection from each phase, regardless of the condition of the sample This new method was applied to the determination of the quantity of retained austenite in some quenched carbon steels; it was found that the quantity of retained austenite increased with quenching temperature, becoming almost constant, and depended on the carbon content of the matrix and the quenching procedure

Void size distribution of wet-spun acrylic fibers

Abstract: Void size distributions of wet-spun acrylic fibers were studied by means of mercury porosimetry, X-ray small angle scattering and combined measurement of surface area and density:1. Measurements of the porosimetry revealed that first the void size distributions depend on the polymer compositions; the peaks of the distribution curve are at the radii of about 1000 A for fibers from acrylonitrile (AN) and methyl acrylate (MEA) copolymer, about 400 A for polyacrylonitrile fibers and fibers from AN, MEA and styrene sulfonate (SSS) terpolymer, about 100 A for fibers from AN and SSS or allyl sulfonate (SAS) copolymer, secondly the position of the peak shift to the small radius by stretching.2. The results obtained from the X-ray small angle scattering based on Fankuchen's method are similar to that obtained by porosimetry.3. Assuming that the frequency distribution of the void size takes gamma distribution, the mean radius (R_??_) and the number (N_??_) of the spherical voids are obtained by the following equations. where p is a parameter of gamma distribution function, d1 is toluene density, d2 is mercury density, A is surface area of fibers.Using the relationship between gamma distribution and x2 distribution, volume fraction of voids having radii larger than a certain value (Pr) can be estimated.4. The results obtained from applying the analytical method mentioned at (3) are as follows; first, R_??_is nearly equal to the radius at which void size distribution curve from porosimetry takes a maximum value. Secondly logarithm of the number of voids having smaller radii than 1000 A is linearly related to the X-ray small angle scattering power.

Gas–liquid chromatography measured activity coefficients in non-electrolyte solutions

Abstract: Measurements of infinite dilution activity coefficients of six aromatic solutes in each of eighteen solvents at 60°C are reported. It is shown that a combination of Hildebrand–Scatchard and Flory–Huggins equations allows a reasonably quantitative description of the mole fraction based coefficients. The corresponding molarity based coefficients, which may commonly be identical with the volume fraction based coefficients, show substantial independence of solute for a given solvent and, for a given type of solvent the variation is sufficiently small that solute type-solvent type averaged coefficients allow prediction of infinite dilution activity coefficients to better than 10 %. It is suggested that volume fraction based coefficients are likely, for particular solute and solvent types, to be even more closely solute and solvent independent.

Compressibility of heterogeneous powder mixtures in rolling

Abstract: 1. The relative density of composites consisting of a ductile matrix and brittle fillers whose yield stress exceeds that of the matrix is inversely proportional to the surface area of unit volume of the inclusion particles. The coefficient of proportionality is a structure-sensitive magnitude and depends on the volume fraction of the filler in the mixture, the shape and strength of its particles, and the isotropy of the mixture. 2. The factor influencing the compressibility of composite materials most is, other things being equal, the strength of the inclusion particles. Rupture of filler particles creates a situation in which further densification of the mixture becomes possible. 3. In the case of fillers whose strength characteristics are lower than those of the matrix, stress concentration may increase up to its critical value, which depends on the volume fraction of the filler and the external stress. Exceeding this critical value is accompanied by local stress relief, which results in strip rupture — spontaneous growth of a large crack.

Interaction terms in gas-solid two-phase flows

Abstract: From both experimental data and theoretical results of the two-phase flow, the complete expression of the interaction force between a gas and solid particles at low Reynolds number flow is obtained. The interaction force contains two terms: one is proportional to the difference between the velocities of the gas and the solid particle with a coefficient as a function of volume fraction Z and the other is proportional to the product of the total pressure of the mixture and the gradient of solid volume fraction. The second term is new. When Z tends to 0, the completion expression of interaction force reduces to the well-known Stokes formula.

Decrease of the Specific Conductivity of Electrolyte Solutions by Addition of Nonionic Solutes and the Measurement of Hydration Amount of the Latter

Abstract: Walden's rule predibts that the specific conductivity, k, of solution of an electrolyte of a low molecular weight decreases with increasing viscosity of the solution, n. By analysing the experimental data, it was concluded that the hydrated volume of neutral substances added as visous-forming agent interrupts the transport of ions.When the viscous-forming agent is of a low molecular weight substance, the specific conductivity, k, decreases linearly, regardless of the kind of added substances, with the volume fraction of the hydrated solute, o, calculated from Einstein's equation, as shown in Fig. 5.This means that the hydrated substance hinders the ionic transport.This theory is extended to the case of nonionic polymers, poly(vinyl pyrrolidone)(PVP) and poly(vinyl alcohol)(PVA), the hydration numbers, N(mole H2O/base mole), were calculated to be 2-5 and 1.5-2.0, respectively, as shown in Fig. 8.It has been concluded that ions are transferred thr ugh the poly er coil and that only the volume occupied by hydrated polymers disturbs the transport of the ions and decreases the ionic mobility, while the velume of expanded polymer coils contributes to the viscosity of these polymer solutions.Both hydration number, N, and intrinsic viscosity, [n], decrease in accordance with the lyotropic series as shown in Figs. 9 and 10. ln the case of LiCl'and Na2SO4, however, the ppparent.abnormality of hydration number was observed because the radii .of these hydrated.ions are large.

Tensile (Compressive) Properties of Glass-Epoxy Composites as a Function of Volume Fraction

Abstract: : The mechanical performance of unidirectionally reinforced glass epoxy composites is studied as volume fraction filler is varied over the range 30-70 percent. Experimentally determined quantities include: longitudinal and transverse tensile strength, ultimate strain, modulus; and Poisson's ratio; and longitudinal and transverse compressive strength. Data analysis indicate that all properties vary linearly with volume fraction. Longitudinal properties and Poisson's ratio are interpreted in terms of the rule of mixtures.

The effect of an electric field on the solidification of off-eutectic tin-lead composite alloys

Abstract: The influence of an electric field upon the directional solidification of hypoeutectic and hypereutectic Sn-Pb composite alloys was studied. Equations were derived to account for the effect of electrotransport of solute in the liquid upon the solid composite composition. Experimental results support the theoretical predictions. Mixing in the liquid is more strongly influenced by unstable solute gradients than by current induced convection. Electrotransport shows limited promise as a method for control of the volume fraction fibre phase in the preparation of aligned composites by directional solidification.