Showing papers on "Volume fraction published in 1972"

The Aerosol Size Distribution of Los Angeles Smog

Abstract: A total of 342 atmospheric size distributions have been measured at the California Institute of Technology in Pasadena, CA during August and September 1969 over the size range 0.003–6.8 μm using the Minnesota Aerosol Analyzing System in collaboration with other investigators making chemical, meteorological, mass, and optical measurements. This paper presents characteristics of the aerosol size distributions and discusses the significance of these findings. It also presents a new computer-compatible system of nomenclature and a new system for separating and analyzing the size distribution in one decade ranges. In addition to the usual log ΔN/ΔDp versus log Dp plot, it was found that a plot of ΔV/Δ log Dp versus log Dp was very useful for characterizing the distribution of particles larger than 0. 05 μm. From the later volume distribution plot, it was found that the smog aerosol was universally bimodal with the saddle point in the 1- to 2-μm size range and with the volume fraction for the individual size distributions below 1 μm being characterized with a grand correlation coefficient of 0.9719 with log normal distributions. The grand log normal distribution had a geometric mean of 0.302 μm and a geometric standard deviation of 2.25. The grand average volume below 1.05 μm was 34 μm3/cm3 and the volume above 1.05 μm was 24.1 μm3/cm3. For sizes above 1 μm, the volume distribution increases steadily up to 6.8 μm, the largest size measured by the MAAS. Comparisons with Lundgren impactor data suggest that this larger mode peaks at 7–10 μm and then drops sharply at about 15 μm. The grand average number distribution log ΔN/ΔDp vs. log Dp was very similar to the grand average measured by Clark and Whitby in Minneapolis in 1966. The number distribution can be characterized reasonably well in the size range from 0. 2 to 7 μm by ΔN/ΔDp = 0. 4 VTDp−4, where VT = 58. 1 μm3/cm3, the total volume fraction. The volume fraction smaller than 1. 05 μm was found to correlate well with light scattering, solar radiation, and, to a lesser degree, with ozone. Analysis of the data and comparisons with laboratory studies of coagulating aerosols suggest strongly that, during the daytime when there is even light smog, most of the aerosol mass, in the size range smaller than 1 μm, is contributed by condensation of photochemical reaction products on particles larger than 0. 1 μm rather than from coagulation of smaller particles. There is considerable evidence that, while most of the mass of particles smaller than 1 μm is contributed by photochemical reactions during smog periods, most of the mass of particles larger than a few microns comes from other sources. While the aerosol mass of particles smaller than 1 μm peaks at about noon, the maximum in the condensation nuclei count peaked at about 1500 at values on the order of 1. 8 × 105/cm3. On the other hand, in Minneapolis, when there was no volume peak at noon, the condensation nuclei count peaked at 1. 8 × 106/cm3. The third paper in this series shows that, because the coagulation coefficient between 0. 01-μm particles and the 0.3-μm particles of the lower volume mode is much higher than for 0.01-μm particles with themselves, the presence of the relatively large volume below 1 μm in Los Angeles smog decreases the maximum condensation nuclei count observed compared to cities with less severe air pollution.

Creep of Ice Containing Dispersed Fine Sand

Abstract: Cylindrical samples of ice with 0.0 to 0.35 volume fraction fine sand were tested in unconfined uniaxial compression at stresses between 5.3 and 6.4 bar and at temperatures between −7.4 and −9.4° C. Secondary creep rates were obtained from the slope of the total strain vs. time curve and were normalized to 5.6 bar and −9.1° C. Creep rates in ice with low sand concentrations were in some cases higher and in other cases lower than in clean ice. However at higher sand concentrations the creep rate decreases exponentially with increasing volume fraction sand. The latter results are in general agreement with theories developed to explain dispersion hardening of metals, and suggest that each sand grain is surrounded by a tangled network of secondary dislocations which impede passage of primary glide dislocations.

Initial dislocation distributions in tungsten fibre-copper composites

Abstract: Etch-pit studies of composites consisting of small volume fractions of tungsten wires into which a copper matrix had been introduced by vacuum infiltration showed the dislocation density in the single crystal matrix to increase with volume fraction of fibre and to rise to high values toward the fibre-matrix interface. The dislocation distributions, which resulted from strains arising due to differential shrinkage, were interpreted in terms of a contribution, independent of fibre fraction, due to transverse strains which fall off with distance from the fibre and a second one due to axial strain which increases with fibre fraction but is invariant with distance from the fibre. Part of the axial adjustment is accomplished by interface shear.

Mechanical properties of particulate composites

Abstract: The mechanical properties of glass bead (30 micron diameter glass spheres) filled epoxy and polyester resins have been studied as a function of volume fraction of filler and the strength of the interfacial bond. The bonding between glass and resin was varied by chemically surface treating the glass using a silicone mold release to prevent chemical bonding at one extreme and a silane coupling agent to maximize bonding at the other extreme. Theoretical predictions of the elastic modulus and tensile strength have been made utilizing a finite element method. Excellent agreement is obtained with the experimental results. Izod impact energies have been measured for these composites as a function of filler content and interface treatment.

The Strength and Fracture Toughness of Polycrystalline Magnesium Oxide Containing Metallic Particles and Fibres

Abstract: The transverse rupture strength of hot-pressed and annealed composites of magnesium oxide and dispersed metallic phases (nickel, iron, cobalt) increases with increasing volume fraction of metal and annealing temperature. The strengthening effect of the metal is attributed to an inhibition of grain growth while flaw healing occurs during the annealing of the composites.

Bound rubber in elastomers: Analysis of elastomer-filler interaction and its effect on viscosity and modulus of composite systems

Abstract: Bound rubber measurement may be very misleading as a measure of elastomer–carbon black interaction because sometimes only part of the apparently bound rubber is truly adsorbed on the carbon black surface. A theory is proposed which utilizes bound rubber measurements, but separates truly adsorbed rubber from other insoluble gel and enables calculation of the adsorbed elastomer layer thickness, a numerical value of interaction. Measurements of interaction were obtained for many different rubbers, including polybutadienes, styrene–butadienes, EPDMs, and butyl, with several different furnace blacks. An equation for viscosity of a rubber–carbon black composite is proposed, based on the degree of interaction obtained from the theory and the possible varying degree of orientation of the composite as the rate of shear is changed. This has been applied experimentally both to soluble elastomers and to an elastomer containing a nonrigid gel. The modulus of a vulcanized composite is shown to be related to the effective volume fraction of filler, which is equivalent to the volume fraction of filler plus adsorbed rubber, at temperatures above the glass transition temperature, regardless of the type of rigid filler. Below the glass transition temperature, the modulus depends only on the filler volume concentration.

Effect of Crystallization on the Mechanical Properties of Li2O‐SiO2 Glass‐Ceramics

Abstract: Variations in the thermal expansion coefficients, elastic moduli, and fracture strengths of Li2O-SiO2 glass-ceramics were determined as a function of nucleation treatment and volume fraction of crystals present. Strength enhancement was attributed to a decrease in the mean free path between crystals as crystallization proceeds. It is postulated that the eventual reduction in strength in some glass-ceramics is caused by the development of localized cracks at the crystal-glass interface as a result of the volumetric changes which occur during crystallization.

Multiple fracture in a steel reinforced epoxy resin composite

Abstract: Specimens of an epoxy resin reinforced by steel wires have been made to fail by a process which involves extensive cracking of the matrix before the UTS of the composite is reached. Such behaviour can result in energy being absorbed by the composite under constant or rising load conditions even when the composite is composed of two brittle phases. The influence of fibre size and volume fraction on the cracking process have been examined, and it has been shown that for low fibre volume fractions and large fibre sizes, the cracking process is governed by a simple relationship. When the fibre size becomes small, or the volume fraction becomes large, the cracking process is hindered, and this relationship breaks down. Under extreme conditions, cracking of the matrix can be completely suppressed and the matrix can be forced to exhibit properties markedly better than it would have shown when tested by itself. The design of materials which behave in this way may provide an important means for producing ceramic-matrix compositions with very good mechanical properties.

Viscous flow of aligned composites

Abstract: The case is considered of an aligned composite subjected to tensile creep in the direction of the fibres. A geometrical argument shows that shear strain in the composite is amplified l/2s times compared with unsupported matrix, where l/2s ∼ aspect ratio of the inter-fibre spaces. The shear stress is amplified (l/2s)1/n times, where n is the exponent in the matrix creep law. Consequently the rate of energy expenditure is amplified Vm(1/2s)1+1/n times, as is therefore the tensile flow resistance of the composite (Vm is the volume fraction of matrix). The potential increase in flow resistance is thus enormous. However, the fibre end-stress, which is calculated, ∝ fibre diameter, and may be large enough to initiate rupture unless the fibres are very thin (e.g. 1 μm diameter). The tensile load is roughly equally divided between matrix and fibres irrespective of volume fractions.

Creep of discontinuous fibre composites I. Experimental behaviour of lead-phosphor bronze

Abstract: Measurements of the creep rate of specimens of lead containing alined rods of phosphor bronze of constant length (either 4.5 cm or 2.25 cm) and diameter (0.45 mm) are described. The rate of steady-state creep has been measured for composites in which the fibres creep, and for those in which they do not, and these are compaied with the rates of creep measured for the fibres and matrix alone. The deformation is very non-uniform due to small variations in volume fraction or arrangement of the wires. Voids form early in the creep test but do not immediately lead to fracture. The rate of creep is not sensitive to surface preparation of the wires. The rate of creep is compared with that predicted by a simple theory developed in paper II + + , which appears to be in accord with experiment.

Properties of Poly(dimethylsiloxane) Networks Prepared in Solution, and Their Use in Evaluating the Theories of Rubberlike Elasticity

Abstract: Poly(dimethylsiloxane) networks were prepared by γ irradiation of solutions of the polymer in cyclohexane; concentrations employed corresponded to volume fractions ν2,s of polymer ranging from 0.3 to 1.0. The moduli of these networks were obtained by stress—elongation measurements on the extracted, dried networks, and the relative degrees of crosslinking were obtained by swelling equilibrium experiments. These data were used to calculate the dependence of the modulus on the volume at which the crosslinking had been carried out. Comparison of experimental and theoretical values of this quantity lends strong support to the theory of rubberlike elasticity developed by Flory and coworkers. In addition, for samples having equal moduli, deviations from the form of the theoretical stress—elongation relationship decrease with decreasing ν2,s, with the strongest such dependence apparently occurring at small values of this volume fraction. In contrast, non-equilibrium effects exhibited by these networks al...

Isotropic fiber coarsening in unidirectionally solidified eutectic alloys

Abstract: A theory of coarsening has been developed for the case of fibers of circular cross section in unidirectionally solidified eutectic alloys. The fibers are assumed to be randomly distributed throughout the unoccupied space in the matrix (uniformly distributed), and diffusion of solute is assumed to occur under steady-state conditions with cylindrical symmetry. The theory predicts that the cube of the average fiber radius increases linearly with time for all fiber volume fractions. As the volume fraction increases, the coarsening rate increases and the theoretical distribution of fiber radii becomes broader. It is shown that isotropic fiber coarsening occurs at approximately half the rate at which the same phase would coarsen if it were in the form of spherical precipitates for volume fractions up to 0.6. It is also demonstrated that the fibers will coarsen at a faster rate when they are uniformly distributed than when they are arranged on an hexagonal lattice.

Properties of Poly(dimethylsiloxane) Networks Prepared in Solution, and Their Use in Evaluating the Theories of Rubberlike Elasticity

Abstract: Poly(dimethylsiloxane) networks were prepared by γ irradiation of solutions of the polymer in cyclohexane; concentrations employed corresponded to volume fractions ν2,s of polymer ranging from 0.3 to 1.0. The moduli of these networks were obtained by stress—elongation measurements on the extracted, dried networks, and the relative degrees of crosslinking were obtained by swelling equilibrium experiments. These data were used to calculate the dependence of the modulus on the volume at which the crosslinking had been carried out. Comparison of experimental and theoretical values of this quantity lends strong support to the theory of rubberlike elasticity developed by Flory and coworkers. In addition, for samples having equal moduli, deviations from the form of the theoretical stress—elongation relationship decrease with decreasing ν2,s, with the strongest such dependence apparently occurring at small values of this volume fraction. In contrast, non-equilibrium effects exhibited by these networks al...

Strength of short‐fiber reinforced composites

Abstract: The structural utility of short, glass fiber-reinforced epoxy composities is experimentally investigated for fiber volume fractions from 0.15 to 0.5. The strength and stiffness of systems with randomly oriented fibers are compared with those of similar composites with aligned fibers. The ultimate strength of both types of material increses in a reasonably linear fashion with volume fraction up to 0.5. For all volume fractions in this range, strength of the random composites is slightly higher than the longitudinal and much higher than the transverse strength of equivalent compsites with aligned fibers. The modulus of the random system is approximately two-thirds the longitudinal and twice the transverse modulus of the unidirectional material. The structural utility of the flow molded material is greatest in uniaxial, stiffness critical situations. The greater strength and planar isotropy of the random composites make them preferable in all strength limited or multiaxial applications.

Fabrication, morphology, and dynamic mechanical properties of a model composite system containing in situ-grown filler

Abstract: The technique of in situ crystallization was utilized to fabricate a model composite system in which the filler morphology is variable under constant interface conditions. A butadiene-acrylonitrile copolymer was chosen as the matrix from which acetanilide was crystallized in two distinctly different crystal morphologies for filler volume loadings up to 0.35. At the same volume fraction filler, the shape of the relative modulus-filler loading curve is sensitive to the filler crystallization temperature and, thus, to the filler size and shape. For a given crystallization temperature (25°C), the data in the low-volume loading region (>0.2) can be represented reasonably well with the Mooney equation which indirectly yields a filler aspect ratio in agreement with scanning electron micrographs. When the observed morphological parameters are utilized for the entire filler loading range, the 25°C data are best predicted by the Halpin-Tsai equation in conjunction with lamination theory. In general, filler...

Effects of microstructure on the radiation stability of amorphous semiconductors

Abstract: The influence of phase separated and crystalline regions on the fast neutron and X-ray damage thresholds of germanium chalcogenides and vanadia-phosphate semiconducting glasses has been established. Damage thresholds are shown to be a function of volume fraction and size of heterogeneities, and the bond energies of the glass. A theoretical model interpreting structure-dependent radiation damage is presented based on heterogeneous semiconductor theory and the destruction of interfacial Schottky barriers. Applications of the results to predicting the radiation sensitivity of amorphous semiconductor devices are suggested.

Solute absorption into molten polystyrene

Abstract: The equilibrium volatilities at near infinite dilution of various solutes absorbed in molten polystyrene have been determined by a gas chromatographic technique. This method is much more rapid, although, with the present apparatus, probably less accurate than conventional static techniques. The primary parameters obtained from measurements of retention volumes are the Henry's law constants, from which are derived the weight and volume fraction activity coefficients, the Flory-Huggins interaction parameters, and the heats of dilution and solution. Of the solutes investigated, 2-butanone (MEK) was the least, and benzene the most compatible (highest and lowest volume fraction activity coefficients, respectively) with molten polystyrene. A small, but definite, variation of the activity coefficients with polystyrene molecular weight was observed.

Elastic Behavior of Polymer‐Impregnated Porous Ceramics

Abstract: The effect of polymer impregnation on the elastic behavior of porous ceramics was investigated. Large increases in the Young's, shear, and bulk moduli and Poisson's ratio were observed. On the basis of a two-dimensional model containing elliptical inclusions, it was shown that the primary role of the polymer on impregnation is to significantly offset the original reduction in elastic moduli caused by the pore phase. The relative effect of polymer impregnation on elastic behavior increases with increasing pore volume fraction and pore ellipticity. These conclusions are also expected to explain the elastic behavior of polymer-modified cements and concretes.

Critical opalescence of polymer solutions

Abstract: The light scattering of polymer solutions is calculated with a simple model based on a local description of the polymer segment density. The following eqn (3.10) is found for finite concentrations of a single polymer in a solvent Kc(1 + cos2θ)/Rθ= dΠ/RT dc+(16π2〈r2〉/3λ2)M–12 sin2θ/2. It is consistent with experiments of Benoit and Picot at the theta point. The same equation also describes the critical opalescence. The Debye-l-parameter is much smaller than predicted by earlier theories and is in much better agreement with experiment. It is also suggested that the critical volume fraction found from light scattering is in fact the volume fraction at the maximum of the spinodal. This explains the discrepancy which is found between critical volume fractions of polydisperse polymers as determined by light scattering and phase-separation studies.The light scattering of a symmetrical system containing two polymers in a common solvent is also formulated. Two types of fluctuations are found: an asymmetrical one in which both polymers fluctuate as a whole and a symmetrical one in which only the composition fluctuates. The last type shows critical opalescence near the point of incompatibility. The predicted Debye l parameter for the range of molecular interaction is much larger than for a single polymer in a solvent.

Secondary Phase Separation in Lead Borate Glasses

Abstract: The effect of secondary phase separation on the apparent volume fraction of second phase was examined in the immiscible region of the PbO-B2A3 system. The volume fraction, V2, of the PbO-rich phase agreed well with theoretical expressions relating V2 to density and composition, except for 0.2

Theoretical approach to the fracture of two-phase glass-crystal composites

Abstract: This paper proposes a fracture theory for two-phase glass-crystal composites. It is hypothesized that the fracture mechanisms of such solids consist of the processes of crack nucleation and of crack propagation round the dispersed particles. At lower volume fractions of dispersed phase, macroscopic fracture will occur as a result of the growth of the micro-cracks originating in the vicinity of the pre-existing structural imperfections through a heterogeneous nucleation process; in this case, strength decreases with the proportion of the dispersed phase. At higher volume fractions where further crack propagation is prohibited by the hard crystalline particles, the process of crack propagation round the dispersed particles may be responsible for the macroscopic fracture of the composite; in this case, strength is an increasing function of the volume fraction. Expressions are formulated for mechanical strength of the glass-crystal composites, based upon the nucleation theory and Griffith's criterion. The published data on the strength of glass-alumina composites are used for the verification of the theory. The proposed theory explains well the strength behaviour of glass-alumina composites, and in particular, the dependence of the strength reduction on particle size at lower volume fractions.

Effect of Crosslinking Density and Dilution during Polymerization on the Stress-Strain and Viscoelastic Behaviour of (2-Hydroxyethyl Methacrylate) Networks in Dry and Swollen States filled with SiO2

Abstract: Linear viscoelastic and stress-strain behaviour of poly(2-hydroxyethyl methacrylate) PHEMA networks filled with SiO2 and prepared by crosslinking copolymerization has been investigated. The main attention was devoted to the effect of the volume concentration of the filler within the range v f = 0 –0.194, concentration of the crosslinking agent (ethylene dimethacrylate) within the concentration range c = 0.13 – 7.84 %, and water present during polymerization with the volume fraction of water ranging from 0.0 to 0.75. It was established that an increasing concentration of the filler had as its consequence a rapid increase in the modulus in the rubberlike region; this effect is more pronounced than in the case of natural rubber filled with active fillers. The effect of the filler decreases with swelling, which is in accordance with the assumption that the polymer-water interactions are stronger than the polymer-filler interactions. The presence of water during polymerization also leads to a decrease...

The matrix fatigue behaviour of fibre composites subjected to repeated tensile loads

Abstract: In a fibre/metal matrix composite the mechanical properties of the matrix itself are changed by the presence of the reinforcing fibres. This changed behaviour of the metal is referred to asin situ behaviour, and a phenomenological model is developed to evaluate thein situ plastic stress-strain properties of a metallic matrix containing fibres, from a study of the properties of the composite. The model is based upon the idealised behaviour of the two components of the system. The application of the model to B/Al alloy composites shows that the plastic stress-strain behaviour of the matrix containing fibres varies strongly with the fibre volume content, and also that the matrixin situ cyclic stress-strain behaviour can be approximately described by a power law of the type: where the strength coefficient and the exponent increase with the fibre volume fraction. It also predicts that in the steady state fatigue behaviour of the composites, the fraction of load amplitude carried by the fibres decreases with increasing applied stress amplitude, and is also dependent on the fibre volume fraction. The effect of the applied stress on the damping capacity is established through expressions derived from the basic ideas involved in the model.

Ostwald ripening during solidification of nondendritic spherical structures

Abstract: A theoretical model was introduced for the study of Ostwald ripening during solidification of the nondendritic spherical structure observed in Mg-Zn alloys grain-refined with Zr. This model assumed that: (1) particles are spherical; (2) each particle receives during solidification a mass increment proportional to its volume fraction with respect to the total volume of the particles in the system; (3) the Scheil equation applies. Experimental results agreed with analytical predictions on the time variation of the total solid-liquid interface area per unit volume and of the relative number of particles per unit volume.

UV dielectric constants of a-Ge as a function of film density

Abstract: The reflectance of a-Ge has been measured in situ on thin films deposited at various substrate temperatures Ts. Kramers-Kronig analysis of this data yields the uv dielectric constants as a function of film density. Trends in the dielectric constants are consistent with the presence of submicroscopic voids whose volume fraction decreases as s increases. These voids are partially aligned and will therefore lead to anistropy in several physical properties.