Showing papers on "Volume fraction published in 1983"

Rheology of foams and highly concentrated emulsions

Abstract: Expressions are derived for certain rheological properties, such as the stress vs strain relationship, yield stress, and shear modulus, of monodisperse foams and highly concentrated emulsions for the model of infinitely long cylindrical drops (or bubbles). The variables considered are the volume fraction of the dispersed phase, the drop radius, the interfacial tension, the thickness of the films separating adjacent drops, and the films' associated contact angle. Both the yield stress and the shear modulus are proportional to the interfacial tension and inversely proportional to the drop radius. The yield stress increases sharply with increasing volume fraction, while the shear modulus varies as its square root. The effect of a finite contact angle, θ, is to decrease the shear modulus and, in most cases, to increase the yield stress. Finally, the effect of a finite film thickness is to always increase both the yield stress and the shear modulus. The implications of these results to real emulsions and foams are discussed.

Formation kinetics and control of microcrystallite in μc-Si:H from glow discharge plasma

Abstract: The formation kinetics of μc-Si:H has been investigated through the film depositions and plasma diagnoses in widely-scanned glow discharge plasma conditions; RF power density, SiH 4 /H 2 ratio and substrate temperature. The roles of H and SiH x adsorbed on the surface as well as impinging ions have been discussed in relation to volume fraction and crystallite size of μc films, and continuous control of crystallite size has been demonstrated using a triode system. Hall mobility of the deposited μc-Si:H films has also been presented as a function of the volume fraction of μc.

Fiber fracture in reinforced thermoplastic processing

Abstract: The length reduction of reinforcing fibers in short-fiber reinforced plastics during processing has been studied experimentally. It has been shown that fiber volume fraction, initial length, and initial state of dispersion have little effect on the final fiber length. In dilute suspension theory based on shearing flow conditions and fiber properties the flow stresses are found to be compatible with the experimental results and results which are found in the literature.

Microstructure, tensile deformation, and fracture in aged ti 10V-2Fe-3Al

Abstract: In the /3-Ti alloy Ti-10V-2Fe-3Al a variety ofα-andω-aged microstructures with different yield stresses was established by combinations of forging and heat treatment. Tensile tests have shown that plastic deformation and fracture are strongly influenced by the morphology, size, and volume fraction of the different types of a-phase (primary a, secondaryα, grain boundaryα), as well as by the-phase. A detailed microscopical study revealed several deformation and fracture modes. It appears that at several sites stress and strain concentrations and subsequent void nucleation can occur and that the quantitative combinations of the differentα-types determine which sites are active. The dominant deformation mode for the (α +gb) solution treated andα-aged conditions was a strain localization in theα-aged matrix leading to voids at the interface between aged matrix and primary a-phase. In case of theβ-solution treated andα-aged microstructures the grain boundaryα leads to a strain localization in the softα-film and to void nucleation at grain boundary triple points at low macroscopic strains. Based on the above mechanisms it is discussed in detail how varying size, volume fraction, and morphology of theα-phase affect the ductility. The embrittling effect ofω-particles can be largely reduced by a grain refinement.

Dielectric constant of a composite inhomogeneous medium

Abstract: We derive an expression for the effective dielectric constant of a composite medium considering the contributions from both the electric and the magnetic dipole terms. We show that the form of the size distribution of small metallic particles determines the value of the volume fraction at which a sharp increase in ac absorption of a composite material occurs. Depending on the width and mode radius of the size distribution, the effective dielectric constant of a composite medium can be increased by several orders of magnitude.

Tensile yield stress of polypropylene composites filled with ultrafine particles

Abstract: For polypropylene composites filled with ultrafine or particles of the order of microns, (SiO2 and glass, respectively), yield stress was measured as functions of temperature, the rate of strain and filler content. The yield stress of the composites filled with ultrafine particles increased with the filler content and decreased with the filler size, while for the composites filled with glass particles, these relations were reversed. For SiO2 filled composites, the tensile yield stress was found to be reducible with regard to temperature, the rate of strain and the filler content. The Arrhenius plot of the shift factors for composing the logarithmic strain rate — temperature master curve formed a single curve irrespective of the filler content and size. The curve comprised three linear regions with breaks appearing at 60 and 110° C, where the transition of the matrix polymer took place. The master curves obtained for different contents of a given size filler could be further reduced into a grand composite curve by shifting them along the axis of logarithmic strain rate, with the logarithmic second shift factors proportional to the square root of the volume fraction of the filler. The dependence of the filler volume fraction on the second shift factor was related to the dispersion state of fillers in PP matrix, namely, the promotion of the aggregation with filler content. The dependences of the yield stress on the filler volume fraction and size were explained by a modified equation based on the dispersion strength theory, with an aggregation parameter incorporated.

The effect of grain size on deformation twinning in a textured zinc alloy

Abstract: The incidence of deformation twinning in samples of a commercial rolled zinc-0.1% aluminium-0.05 wt % magnesium alloy has been measured at room temperature as a function of strain, grain size and direction of loading relative to the rolling direction. The volume fraction of twinned material has been measured at the surface and in the bulk. It is shown that this volume fraction is a linear function of both strain and grain size in most cases. Bands of heavily twinned grains are found to form inhomogeneously across the gauge length of tensile specimens, by an autocatalytic mechanism. Several examples are given of the interaction of twins and slip bands at grain boundaries which illustrate the formation and the accommodation of twins. The smaller volume fraction of twins found at the surface compared with the bulk reflects a relaxation of Von Mises criterion.

Mechanical properties of ductile Fe-Ni-Zr and Fe-Ni-Zr (Nb or Ta) amorphous alloys containing fine crystalline particles

Abstract: Melt-quenched Fe60–80Ni10–30Zr10 and Fe70Ni20Zr10−x(Nb or Ta) x (x≲2 at %) alloy ribbons with the duplex structure consisting of amorphous and bcc phases were found to exhibit hardness and tensile strengths higher than those of the totally amorphous alloys. The volume fraction of the bcc phase was intentionally allowed to alter in the range 0% to 60% by changing the composition and sample thickness. The bcc phase has an average particle size of 75 nm for the Fe-Ni-Zr alloys and 50 nm for the Fe-Ni-Zr-Nb alloys, and the lattice parameter is much larger than that of pure α-Fe because of the dissolution of large amounts of zirconium, niobium and/or tantalum. The hardness and tensile strength of the duplex alloys increase with amount of bcc phase and reach about 880 DPN and 2580 MPa, which are higher by about 20% to 30% than those of the amorphous single state, at an appropriate volume fraction of bcc phase. As the volume fraction of the bcc phase increases further, the duplex alloys become brittle and the tensile strength decreases significantly. The enhancement of strength was considered to be due to the suppression of shear slip caused by fine bcc particles dispersed uniformly in the amorphous matrix. It was thus demonstrated that an optimum control of melt-quenched structure results in the formation of ductile Fe-based amorphous alloys containing fine crystalline particles.

Properties of concentrated polystyrene latex dispersions

Abstract: In order to understand the properties of concentrated dispersions it is necessary to obtain the spatial and temporal locations of the particles in the system as a function of both the volume fraction and the electrolyte concentration and to correlate this with theoretical models. A useful experimental technique for examination of the static structure factor is provided by small-angle neutron scattering, using cold neutrons with a wavelength of ca. 10 A, since the scattering vectors then available are appropriate for systems containing small particles over a wide range of volume fractions. Polystyrene latices consisting of spherical particles of radius 157 A, with a narrow distribution of particle sizes, provide an excellent system for such studies. Structures are reported for these latices covering a range of volume fractions from 0.01 to 0.14 and electrolyte concentrations from very low values, ion-exchanged systems, up to 5 × 10–3 mol dm–3 sodium chloride. The structure factors obtained are compared with various theoretical models for electrostatically interacting systems.

Statistical aspects of cleavage fracture in steel

Abstract: The fracture of mild steel in the cleavage range has been evaluated using a weakest link statistical model, assuming the preexistence of a distribution of cracked carbides. The model provides a rationale for the critical fracture distance, viz., the distance from the crack tip at which the probability of cleavage cracking exhibits a maximum. The critical distance depends on the size distribution and volume fraction of carbides. The model also predicts trends in K,ic with material properties: flow strength, cracked carbide size and volume fraction, and grain size. The resultant temperature dependence of K,ic is shown to derive exclusively from the temperature dependence of the flow stress, as in prior models. The effects of microstructure on K,ic depend primarily on the size distribution of cracked carbides, with additional influences of the grain size and of the volume fraction of carbides.

Pressure dependence of newtonian viscosity

Abstract: Recently, a new method of generalization of the zero shear viscosity of liquids has been proposed. The method utilizes a modified Doolittle formula and the temperature-dependent volume, as expressed by the corresponding states theory of liquids. Furthermore, the glass-transition temperature has been employed as the scaling parameter. The proposed treatment allowed prediction of the correlation between: (i) viscosity, η, and temperature, T, (ii) η and the molecular weight of polymer, (iii) η and concentration, and (iv) the combined effect of these variables. At present, the method is extended to the pressure, P, effect. Furthermore, by substituting the free volume fraction in the Doolittle formula by the theoretical “hole fraction,” a master-relation is proposed that provides means for predicting η = h(T, P) dependence.

The classical pressure vessel problems for linear elastic materials with voids

Abstract: The traditional problems of the thick walled spherical and circular cylindrical shells under internal and external pressure are solved in the context of the theory of linear elastic materials with voids. The solutions are quasi-static. The stress distributions are those predicted by isotropic linear elasticity. The displacement and solid volume fraction charge fields exhibit a volumetric viscoelasticity induced by a rate dependence of the volume fraction change.

The inhibition of grain-boundary motion by a dispersion of particles

Abstract: The resistance to grain-boundary motion provided by a dispersion of spherical particles has been calculated for primary and secondary recrystallization (normal grain growth). Specific account has been taken of grain-boundary flexibility, and of those forces, which aid and those which hinder motion. When neither the intrinsic surface energy of particles nor that of grain boundaries is changed by the presence of the other, the resistance decreases markedly with increasing volume fraction of the particulate phase. Where there is interaction this resistance can be markedly larger, particularly at the highest volume fractions.

An optical method for studying the properties of ordered latices

Abstract: A method is described to study the properties of ordered latices, which consists of normally illuminating and observing a latex dispersion covered by a flat glass plate. In this way a hexagonal pattern of diffraction spots, a ring-shaped halo, and a dark ring in the halo region are observed. The size of the hexagonal pattern of diffraction spots depends on the volume fraction of the latex and on the particle size. Observed diffraction angles agree within experimental error with those calculated from the Laue theory. Also, the dependence of the hexagon size on the volume fraction of the latex is in agreement with theory. It is found, both experimentally and by numerical calculations, that the thickness of the latex sample does not significantly affect the angle and intensity of the diffraction spots, and thus the diffraction spots contain no information about the three-dimensional structure of the latex. From the inner and outer radius of the ring-shaped halo, the mean refractive index of the latex can be determined. This new method is much simpler than the Bragg diffraction method which has been employed by other workers. The volume fraction dependence of the refractive index of the latex was found to be in good agreement with literature results. The dark ring occurs at a radial distance corresponding to an angle which satisfies the Bragg condition. From the radius of the dark ring and the refractive index of the latex, the size of the latex particles can be determined and is found to be in good agreement with the size determined by electron microscopy. Although this darkening effect has not been observed in other materials, it seems to be a general optical phenomenon associated with crystal structure.

Stengthening of polyphase Si3N4 materials through oxidation

Abstract: Specimens of various polyphase Si3N4 materials fabricated in the Si-Mg-O-N system, and a commercial Si3N4 material were subjected to oxidation treatments prior to flexural strength determinations at 1400° C. It was demonstrated that a pre-oxidation treatment could significantly improve the high-temperature strength. The compositional change induced by oxidation which can decrease the volume fraction of the viscous phase present in these materials at high temperatures is believed to be responsible for the observed strengthening.

A Fickian Diffusion Model for Permeable Fibre Polymer Composites

Abstract: A brief description of the Fickian diffusion behavior in polymer composites, containing impermeable fibres (glass and graphite) is presented. The applicability of such a model to composites based on a permeable fibre phase (jute) is verified, both under the influence of varied internal (fibre volume fraction) and external (ambient temperature) factors. Very good correlations are found between the experimental data and a modified Fickian diffusion plot. The significance of a resin impregnated fibre volume fraction in such a composite is highlighted.

Microwave properties of saturated reservoirs

Abstract: Dielectric properties of saturated, porous geologic materials reflect the large difference in dielectric constant e of typical saturating fluids such as water (e = 78) or oil and gas (e = 1–3). The deconvolution of in‐situ dielectric properties of saturated porous materials into the component parts requires a detailed model of the composite material. Defining aspects of this model in the microwave frequency regime is the primary purpose of this investigation. A model is examined in which the dielectric constant of the composite is equal to the sum of the dielectric constants of the components weighted by the volume fraction occupied by each. That model is compared to measurements at microwave frequencies made on systems consisting of glass beads, quartz, or sand saturated with chlorobenzene, 1,2‐dichloroethane, methanol, or air, and find satisfactory agreement. When water is the saturant an interaction between water and the solid matrix has an important effect on the composite dielectric constant. This in...

The time-dependent behavior of aerosols with growth and deposition. I. Without coagulation

Abstract: We have formulated an equation for the particle volume density distribution function n(v, t) describing an aerosol undergoing condensational growth and deposition to surfaces. Coagulation is ignored, thereby rendering the balance equation linear. The forms of the growth and deposition laws may be very general, and explicit analytical solutions are obtained. Both the initial value and source problems are solved. From the solutions it is possible by quadrature to obtain the number of particles in suspension and the volumetric fraction of material at a given time. To illustrate the solutions, a growth law of the form FαVα has been employed together with a deposition law of the form RmVm. Values of m and α are chosen to correspond to realistic conditions. As a measure of the lifetime of an aerosol, we have defined the time moments with respect to particle number and volume fraction. These parameters are evaluated numerically for a range of deposition to growth rate ratios. The knowledge of an exact solution has enabled us to study, extensively, the value of using a similarity approximation for this problem. It is found that a simple form yields acceptable results over a useful range of parameters, although it breaks down at large times and for strong deposition.

Lyotropic and thermotropic liquid-crystalline phase formation from fractions of a semiflexible cellulosic polymer

Abstract: The benzoic acid ester of (2-hydroxypropyl)cellulose (BzPC) was prepared and fractionated from acetone solution by precipitation with methanol-water (85:15, by volume). The fractions were characterized by low-angle laser light scattering in tetrahydrofuran, and by size exclusion chromatography with a low-angle laser light scattering detector. Dilute solution viscosities were measured in acetone and benzene, and the results were interpreted on the basis of a worm-like chain model for BzPC. The critical concentrations of polymer necessary to form lyotropic cholesteric phases in acetone and benzene were found to decrease as the molar mass of the polymer increased, reaching a limiting volume fraction of ≈ 0,35 for high molar mass fractions. The experimental results were compared with the prediction of recent theories for the formation of liquid crystalline phases from semiflexible polymers; the chain parameters required by the theories were estimated from dilute solution viscosities. The fractions of BzPC also showed a thermotropic transition from liquid crystalline phase to isotropic melt. The transition temperature increased sharply with increasing molar mass to reach a limiting value of 176°C.

Effect of fine second phase particles on stored energy and recrystallization kinetics of cold rolled copper single crystals

Abstract: ( 111 ) [ 1 1 ¯ 0 ] crystals of pure Cu–Al203 (particle size < 200 nm) have been strained between 5 and 204% by rolling. Stored energy measurements have been made by differential scanning calorimetry, and the recrystallization kinetics established. The stored energy of cold work is found to increase linearly with prior strain up to a saturation value. The presence of the second phase raises the stored energy by an amount proportional to the volume fraction of particles and also to the magnitude of the applied strain. Internal oxidation of pure Cu leads to the acceleration of recrystallization. Cu–Al203 crystals exhibit a change from suppressed to retarded to accelerated recrystallization as the strain is increased. To explain this a model based on nucleation at microbands is proposed.