Showing papers on "Volume fraction published in 1974"

A theoretical study of the effect of an interfacial layer on the properties of composites

Abstract: A theoretical analysis using finite element methods has been applied to oriented short-fiber composites and spherical particle composites in order to predict the influence of a finite layer at the interface on mechanical properties. In this study the interfacial layer has been modeled by assuming that a layer surrounds the interface and that this layer has a modulus of elasticity different than both the fiber and the matrix. The stress distribution near the interface has been determined as a function of the elastic constants of the interface layer and the interface layer volume fraction. This analysis has also been performed for two volume fractions of fibers and two fiber length to diameter ratios. From this stress distribution, the composite modulus and toughness have been determined as a function of interface modulus. It is theoretically shown that the toughness, measured by amount of strain energy absorbed, can be maximized by controlling the interface modulus. Furthermore, recent experimental results appear to verify the theory.

The strength of polymeric composites containing spherical fillers

Abstract: A theoretical relationship has been developed which relates the ultimate strength of a composite containing spherical fillers to the size, volume fraction, and surface adhesion of the dispersed phase. The theoretical predictions are compared to experimental data using glass beads of known diameters in polyester resin matrix. Results were compared for the case of poor adhesion between the glass beads and the matrix and for the case of good adhesion. The derived relationships should be useful in helping to optimize the strength properties of particulate reinforced systems.

High-temperature strength of dispersion-hardened single crystals: I. Experimental results

Abstract: The yield stress of copper crystals containing a dispersion of SiO2 particles was measured as a function of temperature (20°-1050°C), strain rate, and volume fraction and diameter of the SiO2 particles. The ratio of the modulus-corrected yield stress at temperatures from 20° to 1050°C, to that at 20°C, was found to be strongly temperature-dependent above about 400°C. But the modulus-corrected yield stress at 1050°C was still about half the value at 20°C. Between 600° and 1000°C, the yield stress was found to vary logarithmically with the strain rate. The theoretical analysis of these results will be the subject of another paper.

Specific permeability of partially solidified dendritic networks of Al-Si alloys

Abstract: Porous dendritic networks of Al-4 pet Si and Al-4 pct Si-0.25 pet Ti alloys with volume fraction solid,gsA > 0.628 were prepared by removing the segregated interdendritic liquid from partially solidified samples of the alloys. In the equiaxed samples, available channels for flow were predominately between the grains. Specific permeabilities of the porous dendritic networks were measured with a triaxial cell permeameter. Measured values of specific permeability were 1 × 10-9 to 3.5 × 10-11 cm2 in the Al-4 pet Si alloy for volume fractions solid of 0.655 to 0.94, respectively. Specific permeabilities in Al-4 pct Si-0.25 pct Ti alloy were 4.82 × 10-10 to 7.6 × 10-11 cm2 for volume fractions solid of 0.628 to 0.837, respectively. For equivalent volume fractions solid, the measured specific permeabilities were consistently lower for the grain refined samples. Flow through the porous dendritic networks obeys D’Arcy’s law and equations derived from the capillaric flow model for volume fraction liquid less than ∼0.35.

Mechanical and thermal expansion properties of a participate filled polymer

Abstract: The use of particulate filled polymer formulations over wide temperature ranges has resulted in a need to understand their mechanical behaviour better. In this investigation, a crosslinked epoxy-urethane polymer filled with Al2O3 particles was studied. Mechanical and thermal expansion properties were determined at ambient and liquid nitrogen temperatures and compared to theoretical predictions. Other parameters under consideration were volume fraction and adhesion between filler and matrix. The theoretical equations employed for predicting mechanical properties appear fairly reliable at ambient temperature but unreliable at liquid nitrogen temperatures. The degree of bonding between filler and matrix influences mechanical properties at ambient temperature but at liquid nitrogen temperature no difference in properties owing to matrix filler bonding was evident. This result is attributed to compressive stresses on the filler particles resulting from the lower thermal expansion of the filler.

Effect of yttrium oxide volume fraction and particle size on elevated temperature strength of a dispersic strengthened superalloy

Abstract: The effect of yttrium oxide dispersoid volume fraction and particle size on the 1400†F (1033 K) and 1900†F (1311 K) rupture strength of a dispersion strengthened nickel-base superalloy, made by mechanical alloying, was investigated. Yttrium oxide Contents ranged from 0 pct to 4.5 pct by volume, and average oxide particle sizes varied from about 150A (15 nm) to 580A (15 nm) to 580A (58 nm). High volume fractions and small particle sizes gave low grain aspect ratios and poor 1900†F (1311 K) and 1400†F (1033 K) stress rupture properties following heat treatment. Rupture strengths at 1400†F (1033 K) were otherwise relatively unaffected by dispersoid parameters. At grain aspect ratios less than 6.0, 1900†F (1311 K) rupture strength was controlled by grain geometry while at higher values rupture strength was directly influenced by dispersoid parameters.

The Refractive Indices of Isolated and of Aggregated Soot Particles

Abstract: The optical properties of aerosols of finely divided carbon particles depend on the refractive index of a carbon particle, rather than on that of a macroscopic sample of soot which has a substantial volume fraction of voids. It is shown that, provided the voids are sufficiently small and are evenly distributed, a simple relationship exists between the volume polarizabilities of a carbon particle and of soot. The difficulties in determining the refractive index of carbon from the ellipsometricatly determined values for soot samples are discussed and a new method is proposed which avoids these difficulties.

Concentration dependence of the mean dimension of a polymer chain

Abstract: Computer experiments simulating athermal polymer solutions on a simple cubic lattice have been performed at various concentrations and chain lengths n. The mean-square end-to-end distance 〈r2〉 seems to decrease steadily as the polymer volume fraction φ increases, this effect becoming more pronounced when the chain gets longer. For large n and low φ, a reasonable fit of the data is obtained with 〈r2〉φ/〈r2〉0 ≃ 1 - 0.043n0.72 φ.

The Effects of Carbon Black on Rubber Hysteresis

Abstract: The viscous modulus of oil-extended SBR loaded with carbon black relative to the gum stock increases with volume fraction of carbon black. This increase is much larger than predicted by the Guth-Gold equation and also greater than the increase in the elastic modulus. This behavior reflects the sum of at least three effects: geometrical (strain amplification), changes in the viscoelastic properties of the rubber, and formation of a three-dimensional network of carbon black and rubber. The geometrical effect increases with volume fraction of carbon black. Its per cent contribution to the viscous modulus decreases as the carbon black loading increases because of increased contribution of the viscoelastic effect at low loadings and of the network effect at high loading. The geometrical effect can be described reasonably well by the Guth equation with a shape factor and with the volume fraction increased by the additional immobilized rubber (bonded elastomer). The viscoelastic effect due to 60 phr bla...

Elastic-plastic Poisson's ratio of borsic--aluminum

Abstract: Poisson's ratio as a function of tensile strain has been examined for four volume fractions of unidirectional Borsic-reinforced aluminum composites. Linear relationships were found between Poisson's ratio and filament volume fraction during Stage I (elastic filaments-elastic matrix) and Stage II (elastic filaments-plastic matrix) deformation which could be correlated to filament and matrix values of Poisson's ratio. These results confirm that a simple rule-of-mixtures relationship may be used to predict composite Poisson's ratios as a function of filament volume fraction. The marked increase in the Poisson's ratio of the matrix upon yielding causes an abrupt rise in the slope of the composite Poisson's ratio versus longitudinal strain curve. This sudden increase may be used as an accurate method of determining matrix yield in filament-reinforced, metal-matrix composites.

Crack propagation in metal-matrix/ metal-fibre composites: I. Strength and toughness

Abstract: The strength and toughness of composites consisting of an aluminium-4% copper alloy reinforced with tungsten wires has been studied by conventional mechanical testing methods and with the aid of fracture mechanics techniques. The effects of fibre volume fraction and of the plastic deformation behaviour of the matrix alloy are shown. Values of the fracture energy, measured in a variety of ways, are compared with each other and with the predictions of existing theoretical models. One of these, modified to take account of the actual shape of the plastic zone developed during crack propagation, has been found to agree reasonably satisfactorily with the experimental results for intermediate fibre volume fractions - ie for composites in which Vf is not sufficiently high to cause splitting and not so low as to permit matrix plasticity to control the composite behaviour. The effect of the matrix work-hardening rate is found to be insignificant in composites containing more than about 12 volume% of fibres.

Apparent Tensorial Conductivity of Layered Composites

Abstract: A lamination theory is proposed to treat a multilayered composite material as an anisotropic but homogeneous equivalent material. The conductivity tensor and the governing differential equations of the equivalent material are derived. A sample heat conduction problem for a laminated cylindrical body is solved by the present approach and results compared favorably with the exact solution. Nomenclature K = conductivity KLj — conductivity tensor qi = heat flux in the direction of x, Rij = resistivity tensor T — temperature V = volume fraction 4> = dimensionless temperature defined in Eq. (21) r\ = dimensionless temperature defined in Eq. (27) Sij = Kronecker delta Superscripts "p" = pth layer or component (") = dimensionless quantities defined in Eqs. (21) and (27).

Stress relaxation in carbon‐black‐filled styrene–butadiene rubber

Abstract: The tensile stress relaxation of carbon-black-filled SBR was studied in the linear viscoelasticity region as a function of temperature and volume fraction of fillers. Time—temperature superposition was valid, and master relaxation curves were obtained. Carbon black increases the modulus of the compound, especially in the rubbery region, and the time range over which the glass-rubber transition occurred. The shift factor is divided into three regions; an Arrhenius dependence in rubbery and glassy states, and Williams-Landel-Ferry (WLF) dependence in the transition region. The apparent activation energy in the rubbery state increases with the volume fraction of carbon black (or silica) and is unaffected by the structure of the filler. The increase in activation energy is caused by the attachment of rubber chains to the carbon surface. At 30% elongation, the activation energy for carbon-black-filled rubber has a value of 32 kcal/mole, independent of structure and concentration of the filler.

Metallographic characterization of rubber‐modified poly(methyl methacrylates)

Abstract: The microstructure of rubber-modified samples of poly(methyl methacrylates) was characterized by depositing a thin layer of gold on a polished surface and then applying the conventional techniques of metalography. Samples were prepared with a known volume fraction of rubber comprising particles of known size. It was shown that the methods of quantitative microscopy were successful in estimating these parameters. The method was also shown to provide information about crazing or cracking, which was viewed near the tip of an arrested crack. It is recommended that adoption of the metallographic method be extended to characterize other polymeric systems.

Effect of the interface on the mechanical properties of composite materials.

Abstract: In previous papers (1, 2) we have analyzed the internal stresses in spherical particle composites for the cases where the particle is softer than the matrix (1), as in rubber particle filled polymers, or for the case where the particle is harder than the matrix as in ceramic filled glasses (2). Also, the analysis has been applied to porous composites such as foams in which case spherical voids simply replace the particles (2). A finite element analysis has been used for the calculation of internal stresses and for the prediction of elastic constants and strength of the composite with a suitable model geometry and proper boundary conditions. The results have been presented as a function of the volume fraction of particles or inter-particle spacing.

Transverse properties of three-phase composites comprising continuous glass fibre, glass microspheres, and epoxy resin

Abstract: Some transverse mechanical properties of composites comprising uniaxially aligned continuous glass fibres embedded in a glass microsphere-reinforced expoxy resin matrix have been determined from three-point bending experiments. For a constant fibre volume fraction, the transverse modulus, strength, fracture surface energy for crack initiation and work of fracture are investigated as a function of microsphere content and compared with the equivalent two-phase composites without beads. Modification of composite transverse properties are attributed to corresponding changes in matrix properties and comparisons are made with boundary expressions established for two-phase particulate systems. The effects of voids, microsphere size and surface treatment on the properties are also examined.

Thermal Conductivity Measurement of Granular Materials by Dispersion Method (II)

Abstract: For determining thermal conductivity of granular materials, the equations for the thermal conductivity of two-phase media were examined by the measurement on the specimens composed of glass particles and silicon rubber.The results are summarized as follows:(1) In two-phase mixture where spherical or irregular glass particles were dispersed into silicon rubber, thermal conductivity agreed well with Maxwell-Eucken's relation when volume fraction of particles was low.(2) Maxwell-Eucken's formula was not affected by the size and shape of the dispersed particles.(3) On the basis of Maxwell-Eucken's formura, two equations for determination of thermal conductivity when volume fraction was high and the granule was closely packed were derived.Through these equations, determination of thermal conductivity of the granular part is possible within an error of ±5-±8%.

Heat of Fusion of Crystalline Polypropylene by Volume Dilatometry and Differential Scanning Calorimetry

Abstract: Heat of fusion measurements on stereoregular forms of polypropylene have been the subject of a great number of investigations. The techniques most commonly used have been volume dilatometry, specific heat, DTA, TGA, DSC, empirical calculations, and copolymer studies. Furthermore, the published values for the heat of fusion of isotactic polypropylene using these methods have ranged all the way from 15.5 to 62 cal./g. Thus, an accurate value of ΔHU for the hypothetical 100% crystalline polypropylene remains a subject of some uncertainty. The results of this work present information on a simultaneous study of identical samples using two of the techniques, namely, volume dilatometry and differential scanning calorimetry. The melting points of the pure homopolymer and binary mixtures of it with high purity transdecalin have been carefully determined in a series of dilatometers using mercury as the confining fluid. At the same time, a DSC technique has been employed to obtain the melting point depression as a function of the volume fraction of diluent. The Flory theory for melting point depression is applied to both data and results for ΔHU thus obtained are compared to other estimates based on crystallinity calculated from density measurements and the actual heat of melting for the semi-crystalline samples.

Tensile properties to 650° C and deformation structures in a precipitation-strengthened Ti-Al Alloy

Abstract: Appreciable strength levels were retained up to 650°C in a Ti-10 Al-1 Si alloy aged in the (α + α2) phase field to yield best room-temperature strength and ductility. The aging treatment precipitated such a uniform distribution of the α2 particles that at room temperature, dislocations bypassed instead of shearing the particles at low strains. Specimens fractured at room temperature exhibited fine uniform dimples even for those aging conditions that imparted no macroscopic ductility. A two-step aging process produced a higher volume fraction of bimodally distributed α2 particles that led to higher strength levels at elevated temperatures. Both for the single-size and the bimodal α2 particle distributions, elevated-temperature deformation structures consisted mainly of planar slip bands that sheared through the α2 particles.

Superplasticity of Fe-Ni alloys

Abstract: In the two phase alloys which exhibit superplasticity, strain rate sensitivitym, in the relationship σ =Kem, has been known to be strongly dependent on the volume fraction of the second phase. It, however, has not been necessarily confirmed experimentally on various two phase alloys. In this paper we present an experimental evidence showing that the largestm is obtained when the volume fraction of the second phase is around 0.5.

Relationship between the heat resistance and structural parameters of dispersion-strengthened nickel

Abstract: 1 The Orowan strengthening mechanism in dispersion-strengthened alloys remains operative up to high temperatures For alloys processed under the same conditions a linear relationship is observed between their long-time rupture stress and the reciprocal of the mean interparticle spacing 2 In the determination of the mean interparticle spacing it is necessary to take into account the volume fraction distribution of particles 3 For a qualitative evaluation of the heat resistance of an alloy, use may be made of the relative volume fraction of coarse strengthening particles