Showing papers on "Volume fraction published in 1980"
TL;DR: In this paper, the authors extended the classical theory of the coarsening of precipitate particles by competitive growth to include the effect of encounters between growing particles using the method outlined by Lifshitz and Slyosov [J. phys. solids19, 35 (1961)].
328 citations
TL;DR: In this article, the volume fraction φ 0 of the dispersed phase in close-packed, uncompressed emulsions is predicted as a function of the thickness of the film separating neighboring droplets, and of the contact angle between the film and its adjacent Plateau border.
138 citations
TL;DR: In this article, the critical stress intensity factor and other related fracture parameters have been measured in three-point bending for pure Al2O3-TiC composites containing 4 to 35 volume fractions of TiC.
Abstract: The critical stress intensity factor and other related fracture parameters have been measured in three-point bending for pure Al2O3-TiC composites containing 4 to 35 volume fractions of TiC. An increase has been observed for all the parameters with increasing volume fraction of TiC. Following a study of the mode of fracture, the results are explained in terms of a linear variation of the fracture energy with the volume fraction of TiC.
131 citations
TL;DR: The tensile and Izod impact strength of polycarbonate (PC) based polyethylene (PE) and polystyrene (PS) blends has been examined in this paper.
Abstract: The tensile and Izod impact strength of polycarbonate (PC) based polyethylene (PE) and polystyrene (PS) blends has been examined. The tensile strength can best be described as being proportional to an exponential function of the volume fraction of PE and the first power of volume fraction of PS. The variation of Izod impact strength with composition also differs considerably for the two blends, a small amount of PS causing a marked drop in impact strength. The impact strength of the PE/PC blend is related to the area under the tensile stress-strain curve, whereas for PS/PC blends no correspondence is found. The variation in properties is related to the composition, morphology, interfacial adhesion at the phase boundary and failure surfaces of the various blends.
118 citations
TL;DR: In this paper, the isothermal crystallization of isotactic polypropylene at different temperatures in the presence of fibrous substrates has been investigated and it is shown that preferential transcrystalline growth occurs at the fiber surface and that changes in nucleation density in the bulk material adjacent to the fibers also occur, the extent of which is dependent on temperature and fiber volume fraction.
Abstract: The isothermal crystallization of isotactic polypropylene at different temperatures in the presence of fibrous substrates has been investigated. It is shown that preferential transcrystalline growth occurs at the fiber surface and that changes in nucleation density in the bulk material adjacent to the fibers also occur, the extent of which is dependent on temperature and fiber volume fraction. The effects are discussed in terms of the diffusion of heterogeneities in the bulk due to interaction and the adsorption on the fibers.
105 citations
TL;DR: In this article, the effect of stress on the diffusion of water in glassy polymers is analytically treated, and the free volume concept is established and in turn is related to the diffusion coefficient yielding the following formula: Dσ = Doe(6 to 10)σ/G where Dσ and Do are the diffusion coefficients in the presence and absence of stress respectively, G is the shear modulus, and σ is the stress.
Abstract: The effect of stress on the diffusion of water in glassy polymers is analytically treated. Utilizing the free volume concept the effect of stress on the free volume fraction is established and in turn is related to the diffusion coefficient yielding the following formula: Dσ = Doe(6 to 10)σ/G where Dσ and Do are the diffusion coefficients in the presence and absence of stress respectively, G is the shear modulus, and σ is the stress. Experiments are described which demonstrate that in a bent epoxy bar, more water is picked up at the tension side than at the compression side. Theory and experiment are discussed and compared.
92 citations
TL;DR: In this article, a simple analytical method was proposed to predict the residual stress state and the stress strain curves of Nb3Sn composites at 4.2 K. The method requires only a prior knowledge of the volume fraction of the composite components and the percentage of the Nb converted to Nb 3Sn.
Abstract: The critical current Ic as a function of applied tensile strain depends upon the residual stress state that exists in Nb3Sn bronze‐process composite conductors after cooling from the reaction temperature to 4.2 K. This paper presents a simple analytical method to predict the residual stress state and the stress‐strain curves of Nb3Sn composites at 4.2 K. The method requires only a prior knowledge of the volume fraction of the composite components and the percentage of Nb converted to Nb3Sn. Experimental results and analytically derived values are compared and good agreement is generally found.
73 citations
TL;DR: In this article, the rubber phase volume fraction (RPVF) was used as a variable in the synthesis of impact polystyrene and it was found that notched Izod impact strength increased linearly with RPVF, while tensile yield strength was inversely proportional.
66 citations
TL;DR: In this paper, the effect of isothermal aging 14°C below the glass transition temperature on these mechanical properties was examined for its devitrification characteristics at temperatures both above and below Tg Tensile tests and Knoop microhardness experiments were conducted to determine the effect.
59 citations
TL;DR: In this article, the abrasive wear rates of quartz and glass particle-reinforced PMMA have been measured as a function of filler volume fraction for silicon carbide, quartz and calcite abrasives.
Abstract: The abrasive wear rates of quartz and glass particle-reinforced PMMA have been measured as a function of filler volume fraction for silicon carbide, quartz and calcite abrasives. The wear rates were found to exceed those predicted by a simple series model. Abraded surfaces were studied by surface profile measurement and SEM. The excess wear is attributed to rapid wear of the filler at the matrix interface and to particle pulls-outs.
56 citations
TL;DR: In this paper, the particle growth rate in Ni-Co-Al alloys has been studied using X-ray diffraction, scanning electron microscopy, and transmission electron microscope.
Abstract: Continuous precipitation of γ′ in Ni-Co-Al alloys has been studied using X-ray diffraction, scanning electron microscopy and transmission electron microscopy The precipitation sequence is observed to be a change of morphology from spheres → cube → plates The γ∣γ′ lattice parameter mismatch is of the order of 03% The γ′ particle growth rate has been determined over a range of temperatures for alloys containing a range of cobalt contents from 0 to 55 at % In all cases the particle size varies att1/3 and the particle number density ast−1 The growth rate varies very little with increasing volume fraction of γ′ The measured particle growth rate decreases with increasing cobalt content, probably as a result of partitioning of cobalt between particle and matrix Electron micro-probe analysis, volume fraction measurements and X-ray analyses were used to determine the γ∣(γ + γ′) boundary in the Ni-Co-Al ternary system at temperatures between 973 and 1073 K It is clear from the position of the boundary that a significant beneficial effect of cobalt is in decreasing the solubility of the γ′ phase in γ for any temperature up to 1073 K Histograms of particle size were constructed and compared with both the Lifshitz-Slyozov-Wagner and the Lifshitz-Slyozov encounter modified (LSEM) predicted distributions The LSEM theory for particle coarsening was shown to be a much better fit to the experimental particle size distributions
TL;DR: In this article, a nonlinear version of the theory was used for boundary value problems corresponding to gravity flow in a closed vertical channel and in a channel with a free surface inclined at various angles from the vertical.
Abstract: A theory of flowing granular materials with incompressible grains is presented which is similar to one proposed by Goodman and Cowin in 1972. Using a nonlinear version of the theory, boundary‐value problems corresponding to gravity flow in a closed vertical channel and in a channel with a free surface inclined at various angles from the vertical are considered in detail. In analyzing these problems, the dependence of the free energy and viscosity on the volume fraction are specialized to agree with those proposed as a result of recent experimental work. Solutions of these problems demonstrate many of the characteristics normally assumed in other treatments of granular materials. In particular, for vertical flow, when the volume fraction is greater than (less than) the critical volume fraction, a compressive (tensile) force must be exerted on the walls to maintain isochoric flow. Pluglike regions in which the velocity is almost constant develop, and there is a relatively thin shear region near the wall. For the flow with a free surface, as grain size or angle of inclination increases, the solutions tend to two rigid motions separated by a thin shear layer.
TL;DR: The steady-state creep rate of amorphous Fe40Ni40P14B6 has been measured under stresses, σ, ranging between 0.12 GPa and 1.41 GPa at temperatures between 524 and 646 K as discussed by the authors.
TL;DR: In this paper, the intrinsic coercivity of the equilibrium component was found to depend on whether a given percent of equilibrium phase is produced by directional solidification or post-solidification heat treatment anneal.
Abstract: Eutectic Bi/MnBi composites (3.2 volume percent MnBi) have been plane-front directionally solidified using the Bridgman-Stockbarger method. For the growth velocity range investigated, the morphology of the composites consists of an aligned ensemble of MnBi rods with mean rod diameters lying below the theoretical size for single domain behavior. Magnetization as a function of temperature, applied field and angle with respect to the solidification direction was used to characterize the magnetic properties. These measurements have been correlated with particle size distributions and volume fraction data. Previous studies have shown that solidification processing conditions and post-solidification heat treatment significantly affect the magnetic properties due to the presence of a nonequilibrium magnetic phase. The nonequilibrium phase has been isolated by varying the processing parameters and the temperature dependence of its magnetization determined. In addition, the transformation kinetics of the nonequilibrium to the equilibrium MnBi phase was investigated by monitoring the magnetization change during isothermal annealing. The intrinsic coercivity of the equilibrium component was found to depend on whether a given percent of equilibrium phase is produced by directional solidification or post-solidification heat treatment anneal.
TL;DR: The porosity measured for two series of diluent-modified styrene copolymers (10 and 20 wt.-% of DVB) was found to depend on sample pre-treatment as discussed by the authors.
Abstract: The porosity measured for two series of diluent-modified styrene (S) — divinylbenzene (DVB) copolymers (10 and 20 wt.-% of DVB) was found to depend on sample pre-treatment. A correlation between the volume fraction of the polymer in the swollen gel and the volume fraction of octane used as diluent has been established assuming the isotropic swelling of the sample pretreated with water before porosity determination.
TL;DR: In this paper, the optimum composition profiles for maximum solar absorptance of selective surfaces consisting of cermet layers with graded refractive index were found, and linear grading of metal volume fraction with depth gave normal absorptances close to optimum for both a dielectric and an air matrix.
TL;DR: In this article, the tensile strength and ultimate strain of polypropylene fibers were measured by the creep fracture method at various temperatures, which were plotted on log-log scales and superposed by shifting the curves along the logarithmic time-to-break axis.
Abstract: The tensile strength and ultimate strain of polypropylene fibers were measured by the creep fracture method at various temperatures. The tensile strength against time-to-break curves at various temperatures, which were plotted on log–log scales, were superposed by shifting the curves along the logarithmic time-to-break axis, and the composite curve of the tensile strength as a function of a reduced time to break was obtained. On the other hand, to construct the composite curve of ultimate strain from the ultimate strain against time-to-break curves at various temperatures, shifting the curves along the logarithmic ultimate strain axis was required in combination with shifting along the logarithmic time-to-break axis. The temperature dependence of the shift factor aT followed an equation of the Williams–Landel–Ferry (WLF) form. The volume fraction of free volume at the glass transition temperature and the coefficient of thermal volume expansion, which were calculated from the WLF coefficients determined for the polypropylene fibers, are almost the same as those known as “universal values” for amorphous polymers.
TL;DR: In this article, a single ply of unidirectional composite is modeled as a two-dimensional al-close packed lattice of circular fiber cross sections of infinite width and finite thickness, and the effect of lattice thickness on the critical fiber fraction for percolation is calculated.
Abstract: A single ply of unidirectional composite is modeled as a two-dimension al close packed lattice of circular fiber cross sections of infinite width and finite thickness. To introduce randomness fibers are removed at random from the lattice, leaving vacant lattice sites of matrix material, until a certain fiber volume fraction is reached. The effect of lattice thickness on the critical fiber fraction for percolation is calculated for this random, close packed fiber model. For a typical ply thickness of 24 fiber diameters, the critical fiber fraction for percolation is reduced by 20% from the infinite lattice value of 0.45 to a smaller value of 0.36. The percolation versus thickness results of the random square lattice of fibers are compared with those of the random close packed fiber model. Experimental measure ments of the increase in electrical conductivity of a single ply of graphite/ epoxy composite with decrease in ply thickness predicted by the random close packed fiber model, are presented.
TL;DR: In this article, the tear strength of several thermoplastic polymers filled with colloidal silica has been determined as a function of polymer molecular weight, and two regimes of behaviour were found: low molecular weight materials were embrittled by a small amount, around 10% volume fraction, of filler, while high molecular weight polymers, on the other hand, were not degraded at low filler concentrations, and some thermoplastics were actually reinforced, that is toughened, by the colloidal particles with a peak in crack resistance at 12% volumetric fraction.
Abstract: The tear strength of several thermoplastic polymers filled with colloidal silica has been determined as a function of polymer molecular weight. There were two regimes of behaviour. Low molecular weight materials were embrittled by a small amount, around 10% volume fraction, of filler. High molecular weight polymers, on the other hand, were not degraded at low filler concentrations, and some thermoplastics were actually reinforced, that is toughened, by the colloidal particles with a peak in crack resistance at 12% volume fraction. There was found to be a characteristic transition in toughness, similar to that observed with environmental stress cracking, between the low and high molecular weight regimes. It was concluded that a polymer molecular weight above the transition value was a necessary but not sufficient condition for colloidal reinforcement.
TL;DR: In this article, the convergence of an acoustic wave due to the interaction with the microbubbles produced in the cavitation zone is shown experimentally, and the theoretical analysis shows that the self-focusing primarily depends on the effective microbubble volume fraction.
TL;DR: In this article, the authors analyzed the creep of polycrystalline NaCl contaning a fine dispersion of Al2O3 particles in terms of dependence on stress, temperature, volume fraction and size of dispersion, and grain size of samples.
Abstract: The creep of polycrystalline NaCl contaning a fine dispersion of Al2O3 particles is analysed in terms of dependence on stress, temperature, volume fraction and size of dispersion, and grain size of samples. Compressive creep experiments around 0.8 Tm show that the dispersion inhibits diffusive creep. The creep is characterized by a threshold stress above which the creep rate increased linearly with applied stress. The threshold stress decreases with increasing temperature and is proportional to the volume fraction of the dispersion in agreement with a model proposed by Burton. The activation energy corrected for the temperature dependence of the threshold stress falls within a narrow range consistent with grain-boundary diffusion of chlorine in sodium chloride. The grain-size dependence is not consistent with a modified diffusive creep model but it is suggested that it may be controlled by inhibited grain-boundary sliding according to a new model.
TL;DR: In this article, the inner structure of a unidirectional composite was approximated by symmetric, rectangular arrangement of fibers, and the composite thermal con ductivity was calculated with the use of different theoretical methods and compared to experimental data obtained from a model of the composite.
Abstract: The effective thermal conductivity of a unidirectional composite was determined. Inner structure of the composite was approximated by symmetric, rectangular arrangement of fibers. The composite thermal con ductivity was calculated with the use of different theoretical methods and compared to experimental data obtained from a model of the composite and the composite itself. Good agreement was found between theory and experiment. Temperature fields in the composite were also calculated. The results of the effective thermal conductivity occurred to be lower than the analogical values obtained by Adams and Doner. It was found that for isotropic composite having up to 50% fiber volume fraction, Hashin and Rosen's formula for "random arrangement" of fibers could be successfully used. Two pairs of bounds on the composite thermal conductivity were studied. Each of them was found to be narrower for different range of fiber volume fraction.
TL;DR: In this article, a theoretical model has been formulated which describes how the strain in a tensile bar can localize to a thin sheet of material with a higher volume fraction of particles than the surrounding material.
TL;DR: Viscosities of γ-Fe2O3 dispersions in epoxy resin, phenol resin, and polyvinyl butyral solutions are measured at shear rate D from 192 to 384 sec−1 as discussed by the authors.
Abstract: Viscosities of γ-Fe2O3 dispersions in epoxy resin, phenol resin, and polyvinyl butyral solutions are measured at shear rate D from 192 to 384 sec−1 Volume fraction of γ-Fe2O3 in these dispersions ranges from about 0002 to 003 The concentration dependence of relative viscosity η/ηs is closely represented by the Mooney equation From this equation, intrinsic viscosity [η] of suspensions is found to decrease from 461 at D = 192sec−1 to 14 at D = 384 sec−1 for epoxy resin solution The high [η] value indicates the existence of flocs containing immobilized liquid By increasing the shear rate, the average floc size is reduced to point where at an infinite shear rate, only small clusters or possibly particles remain Of the three polymers, the lowest [η] value is obtained in the dispersion of the phenol resin solution
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TL;DR: In this article, it was shown that the presence of a solvent preferential for one of the blocks tends to produce the morphology according to the volume fraction of the solvated block.
Abstract: Publisher Summary This chapter reports the experimental techniques and results obtained in the study of polymeric alloys. Polymeric alloys are formed when two polymers are thoroughly mixed in one body. The lattice model for liquid–polymer mixtures was extended to the mixture of two polymers. A thermodynamic theory, which considers the free energy change on mixing two infinitely long completely separated blocks without consideration of domain morphology, gives for the mean free energy of mixing per segment. It is found that during casting from solution, the presence of solvent at the point of polymer immobilization may influence the type of morphology that is thermodynamically favored. The presence of a solvent preferential for one of the blocks tends to produce the morphology according to the volume fraction of the solvated block. The use of the solubility parameter is restricted to polymer pairs whose interactions are determined solely by dispersion forces. It is observed that in the metastable region, between the binodal and spinodal, phase separation is expected to proceed by nucleation and growth.
TL;DR: In this paper, a method for measuring and calculating the planar interparticle distance between plate-like precipitates has been developed, which utilizes transmission electron microscopy of thin foils: no information of the volume fraction of the particles is needed.
TL;DR: In this article, the slender body theory was extended to cover the bulk thermal properties of composite materials and the increase in the thermal conductivity along the direction of the fibres was found to be of the order φ f K 2 ln2/K, where φ is the volume fraction of the fibre and K is the slenderness ratio of the inclusion.
01 Apr 1980
TL;DR: In this paper, a variety of aged microstructures with different volume fractions and morphologies of primary and secondary alpha and also grain boundary alpha has been tensile tested and the results can be summarized as follows: (1) for a constant volume fraction of primary alpha, it is possible to vary the yield stress in a wide range; it is also possible to reach comparable yield stress levels for different volume ratios of alpha by an appropriate choice of aging temperatures and times as well as heating up rates to the aging temperatures.
Abstract: : In Ti-10-2-3 a variety of aged microstructures with different volume fractions and morphologies of primary and secondary alpha and also grain boundary alpha has been tensile tested. The results can be summarized as follows: (1) For a constant volume fraction of primary alpha it is possible to vary the yield stress in a wide range; it is also possible to reach comparable yield stress levels for different volume fractions of alpha by an appropriate choice of aging temperatures and times as well as heating up rates to the aging temperatures; (2) Increasing the volume fraction of primary alpha reduces the ductility at comparable yield stresses for the alpha-aged conditions. Only the beta-ST conditions with no primary alpha are an exception. They have lower ductilities than the (alpha + beta) ST conditions. The omega-aged microstructures have the lowest ductilities at comparable yield stresses; (3) The differences in ductilities between the (alpha + beta) ST and alpha-aged, the beta-ST and alpha-aged and the omega-aged microstructures are qualitatively related to different fracture modes; and (4) Microstructures from a different forging which instead of the above tested globular primary alpha have elongated primary show lower ductilities at comparable yield stresses.
TL;DR: In this paper, a characterization of the processes observed by adding an inert filler into an elastomer, hysteresis and wave-propagation meaurements were carried out which indicate that dewetting is the main factor that causes an increase in the damping, and is responsible for the softening effect observed in PBCT filled with spherical Al powder.