Showing papers on "Volume fraction published in 1991"

Strengthening of composites due to microstructural changes in the matrix

Abstract: The addition of discontinuous silicon carbide (SiC) to aluminum (Al) alloys can result in a five-fold increase in the yield stress. The magnitude of the increase is obviously a function of the volume fraction and the particle size of the SiC. Previously, it was proposed that the strength increase due to SiC addition to Al alloys was the result of change in the matrix strength, i.e. an increase in dislocation density and a reduction of subgrain size. The data obtained from a series of experiments indicate that dislocation density increases with an increase in volume fraction of SiC and decreases with an increase in particle size. The subgrain size decreases as the volume fraction increases and increases as the particle size increases. There is a good correlation between the microstructural changes in the matrix and the changes in the yield stress of the composites.

MR Contrast Due to Microscopically Heterogeneous Magnetic Susceptibility: Numerical Simulations and Applications to Cerebral Physiology

Abstract: We calculate the effects of subvoxel variations in magnetic susceptibility on MR image intensity for spin-echo (SE) and gradient-echo (GE) experiments for a range of microscopic physical parameters. The model used neglects the overlap of gradients from one magnetic inclusion to the next, and so is valid for low volume fractions and weak perturbations of the magnetic field. Transverse relaxation is predicted to deviate significantly from linear exponential decay in both SE and GE at a particle radius of 2.5 microns. Calculated changes in transverse relaxation rates for SE and GE increase linearly with volume fraction of high-susceptibility regions of 5 microns diameter, but increase with about the 3/2 power of volume fraction of regions with 15 micron spacing between centers. This sensitivity to the actual size and spacing of magnetized regions may allow them to be measured on the basis of contrast. without being resolved in images. GE and SE decay rates are approximately twice as sensitive to long cylinders of 5 microns diameter than to spheres of the same size, for diffusion constants of 2.5 micron 2/ms. Calculated changes in transverse decay rates increase with approximately the square of field and susceptibility variation for 5-microns spheres and a diffusion constant of 2.5 microns 2/ms. This exponent is smaller for cylindrical magnetized regions of the same size, and also depends on the diffusion constant. We discuss possible applications of our theoretical results to the analysis of the effects of high-susceptibility contrast agents in brain. Experimental data from the literature are compared with calculated signal changes according to the model. The monotonic dependence of decay rates on the volume of distribution of the contrast agent suggests that cerebral blood volume and flow could be measured using MR contrast.

An analysis of the effects of matrix void growth on deformation and ductility in metal-ceramic composites

Abstract: Deformation and failure of metal-matrix composites, by the nucleation and growth of voids within the ductile matrix, are studied numerically and experimentally. The matrix material is modelled as an elastic-viscoplastic ductile porous solid to characterize the evolution of damage from void formation. The material systems chosen for parametric analyses and for quantitative comparisons between numerical analyses and experiments are aluminum alloys discontinuously reinforced with SiC. The brittle reinforcement phase, in the form of spheres, particulates with sharp corners, or cylindrical whiskers, is modelled as elastic or rigid, with the interfaces between the ductile matrix and the brittle reinforcement assumed to be perfectly bonded. The overall constitutive response of the composite and the evolution of matrix failure are analyzed using finite element models within the context of axisymmetric and plane strain formulations. Detailed parametric analyses of the effects of (i) reinforcement shape, (ii) reinforcement volume fraction, (iii) mechanical properties of the matrix, (iv) nucleation strain and volume fraction of void-nucleating particles, and (v) reinforcement distribution on the overall deformation and ductility of the composite are discussed. The numerical predictions of yield strength, strain hardening exponent and ductility for the composites with different volume fractions of SiC particulates are also compared with experimental measurements.

Finite-element analysis of 1-3 composite transducers

Abstract: The vibrational and electromechanical characteristics of a wide range of 1-3 composite structures, comprising ceramic pillars aligned within a polymer phase, are considered using finite-element analysis. The influence of pillar geometry, ceramic volume fraction, and pillar orientation is described in terms of overall transduction efficiency. It is shown that the finite-element method provides a versatile means of analysis and the results obtained permit a set of useful design guidelines to be developed. In general, a small pillar aspect ratio and a relatively high volume fraction provides the most satisfactory performance, in terms of electromechanical efficiency and uniformity of thickness dilation. >

The rheology of a concentrated colloidal suspension of hard spheres

Abstract: The rheology of a model hard-sphere suspension has been studied at high volume fraction. Particular emphasis was placed on observing the transition between liquid-like and solid-like behavior at the maximum packing volume fraction. Capillary viscometry has shown that the suspension viscosity at low concentration agrees well with theory and other experimental work on hard-sphere systems. At higher concentrations the rheological properties, measured using steady shear, oscillatory shear, and creep techniques, change rapidly from viscous Newtonian to shear-thinning viscoelastic. When the volume fraction is greater than the maximum packing volume fraction the behavior is like that of an elastic solid, and a yield stress can be measured using cone and plate instruments and the vane method. At high volume fractions the product of a characteristic shear rate (or Peclet number) and the low shear limiting viscosity is found to be almost independent of concentration. It is possible to superimpose all the steady shear data using a scaling based on the Cross equation.

Effect of reinforcement on the aging response of cast 6061 Al-Al2O3 particulate composites

Abstract: The effect of 10 and 15 vol pct alumina particulate addition on the age hardening behavior of cast 6061 Al-matrix composites was studied using microhardness, electrical resistivity, differential scanning calorimetry, and transmission electron microscopy (TEM). It was found that the kinetics of precipitation in the matrix alloy are significantly accelerated due to the presence of reinforcements. This acceleration is attributable to the decrease in incubation time required for nucleation and the increase in solute diffusivity and hence precipitate growth rate resulting from the increase in the matrix dislocation density due to coefficient of thermal expansion (CTE) mismatch between the matrix and the reinforcements. The relative amounts of the various phases were also observed to be affected by reinforcement addition. Increasing reinforcement content decreased the volume fractions of the Β’ and Β precipitates while increasing the volume fraction of the GP-I zones. The volume fraction of silicon clusters (which are the precursors to GP zones in 6061 Al) formed during postsolution treatment aging was found to decrease with increasing reinforcement addition. The above effects have been discussed with respect to the associated mechanisms, and plausible explanations have been offered.

Dewatering of flocculated suspensions by pressure filtration

Abstract: Pressure filtration is an important method for removing liquids from a suspension. Previous work used linear models or applied to stable suspensions. Nonlinear models for flocculated suspensions are studied here. The equations governing the consolidation of flocculated suspensions under the influence of an applied pressure are based on the assumption that when the volume fraction is high enough, the network formed from the aggregation of flocs possesses a compressive yield stress Py(φ) that is a function of local volume fraction φ only. There are two modes of operation of the pressure filter—the fluid flux or the applied pressure is specified—and both of these are studied. The resulting nonlinear partial differential equations involve the time‐dependent piston position, and in the case of the suspension being initially unnetworked, another internal moving boundary below which the suspension is networked. The small time behavior of these systems is obtained with an asymptotic method. In general, at later times, the solution can only be found numerically and an algorithm for doing this is discussed. The important parameters and properties of the filter cake are described. The results suggest various ways of controlling the filtration process, which may be useful in the manufacture of ceramics.

Air‐based system for the measurement of porosity

Abstract: An experimental system for the measurement of porosity, the volume fraction of air contained in a material, is described. Porosity is important as one of several parameters required by acoustical theory to characterize a porous material. As with the technique described by Beranek [J. Acoust. Soc. Am. 13, 248–260 (1942)], the isothermal pressure change in a closed volume containing a sample material is measured for a known change in the volume. The volume of air contained in the sample, and hence the porosity, is inferred from these two quantities. The new system, though, avoids the use of liquids, either directly in the technique or for temperature stabilization. Instead, a piston of accurately known diameter is used to produce the change in volume, and the change in pressure is measured with an electronic pressure transducer. Model calculations and measurements on real materials confirm that porosity can be measured rapidly and conveniently with this apparatus, with an accuracy of better than 1% over a broad range of sample volumes and porosities.

The Effective Conductivity of Random Suspensions of Spherical Particles

Abstract: The effective conductivity of an infinite, random, mono-disperse, hard-sphere suspension is reported for particle to matrix conductivity ratios of ∞, 10 and 0.01 for sphere volume fractions, c, up to 0.6. The conductivities are computed with a method previously described by the authors, which includes both far- and near-field interactions, and the particle configurations are generated via a Monte Carlo method. The results are consistent with the previous theoretical work of D. J. Jeffrey to O(c^2) and the bounds computed by S. Torquato and F. Lado. It is also found that the Clausius-Mosotti equation is reasonably accurate for conductivity ratios of 10 or less all the way up to 60 % (by volume). The calculated conductivities compare very well with those of experiments. In addition, percolation-like numerical experiments are performed on periodically replicated cubic lattices of N nearly touching spheres with an infinite particle to matrix conductivity ratio where the conductivity is computed as spheres are removed one by one from the lattice. Under suitable normalization of the conductivity and volume fraction, it is found that the initial volume fraction must be extremely close to maximum packing in order to observe a percolation transition, indicating that the near-field effects must be very large relative to far-field effects. These percolation transitions occur at the accepted values for simple (sc), bodycentred (BCC) and face-centred (FCC) cubic lattices. Also, the vulnerability of the lattices computed here are exactly those of previous investigators. Due to limited data above the percolation threshold, we could not correlate the conductivity with a power law near the threshold; however, it can be correlated with a power law for large normalized volume fractions. In this case the exponents are found to be 1.70, 1.75 and 1.79 for sc, BCC and FCC lattices respectively.

The permeability and compressibility of aligned and cross‐plied carbon fiber beds during processing of composites

Abstract: Two of the most important input parameters needed to simulate the processing of continuous fiber laminated composites are the fiber bed permeability and the portion of the autoclave load borne by the consolidating fiber network (compressibility). In this study we have experimentally examined how both these parameter change with resin volume fraction as pressure is applied and consolidation proceeds. For a unidirectional fiber bed, the Kozeny-Carman equation can be used to predict both the transverse (perpendicular to the laminate plies) permeability (Kozeny constant, K′z = 11) and the axial (parallel to the fibers) permeability (Kozeny constant, K′X = 0.57). The axial permeability was found to be dependent on the surface tension of the permeant. For a unidirectionally aligned fiber, the measured transverse permeabilities varied from 1.1 × 10−10 cm2 to 12. × 10−9 cm2 while the axial values varied from 2.1 × 10−9 to 4.4 × 10−8 cm2 for a liquid volume fraction range of 0.25 to 0.5. Axial permeability measurements indicate that the permeability decreases with increasing off-axis angle × (measured from the laminate axial direction). The off-axis permeability behavior can be described by a modified Kozeny-Carman equation. The fiber network compressibility can be described with a logarithmic relation which has been found valid for a large number of consolidated soils.

Elastoplastic finite element analysis of short-fiber-reinforced SiC/Al composites: effects of thermal treatment

Abstract: Elastoplastic finite element analyses of realistic models of short-fiber-reinforced composites were extended to include the effects of prior thermal treatments on predictions of subsequent mechanical properties. Two three-dimensional models were used, one in which the fiber ends were transversely aligned and another in which they were staggered. Both models were found to be necessary for accurate predictions of the behavior of higher volume fraction composites. The temperature dependence of the yield stress of the matrix material was explicitly included in the analysis. The spatial and temporal history of calculated. The room temperature residual stresses were also predicted. Both the plastic deformation and the residual stresses in the matrix were spatially non-uniform and varied rapidly from the regions near the ends of the fiber to those near the midpoint. Predictions of subsequent tensile stress-strain properties were in good quantitative agreement with experiments. The presence of residual stresses and locally deformed regions caused the tensile behavior to differ from the compressive behavior. These differences were complex and depended on the volume fraction and aspect ratio of the reinforcement. The analyses provide detailed insight into the deformation mechanisms of these composites.

Ion condensation on solid particles: Theory and simulations

Abstract: For polyelectrolytes the Manning theory predicts an effective charge density, which increases with the bare charge density up to the point where the thermal energy of an ion balances the reversible work necessary to remove the ion from the polymer. From that point on, the effective charge remains constant, as no more ions will desorb. For spherical colloidal particles, a similar maximum effective charge can be expected, which indeed is predicted by the Poisson–Boltzmann theory. To check these predictions quantitatively, Monte Carlo simulations have been performed on the ionic distribution of a salt‐free colloid at a volume fraction of 36%, both in the spherical cell model and in a periodic system of cubic symmetry. In the latter system the interactions were evaluated using the Ewald summation method. These simulations show that the effective charge of a colloid at this volume fraction does not reach a plateau value for large bare charges, but instead the effective charge passes through a maximum, and decr...

A new constitutive model for fibre suspensions: flow past a sphere

Abstract: A new phenomenological constitutive equation for homogeneous suspensions of macrosized fibres is proposed. In the model, the local averaged orientation of the fibres is represented by a director field, which evolves in time in a manner similar to the rotation of a prolate spheroid. The stress is linear in the strain rate, but the viscosity is a fourth-order tensor that is directly related to the director field. In the limit of low-volume fractions of fibres, the model reduces properly to the leading terms of the constitutive equation for dilute suspensions of spheroids. The model has three parameters: the aspect ratio R of the fibres, the volume fraction Φ, and A, which plays the role of the maximum-volume fraction of the fibres. Experimental shear data are used to estimate the parameter A, and the resulting model is used in a boundary-element program to study the flow past a sphere placed at the centre line of a cylinder for the whole range of volume fractions from 0.01 to near maximum volume fraction. The agreement with experimental data from Milliken et al. [1] is good.

Dual phase continuity in polymer blends

Abstract: The literature on formation of immiscible polymer blends with dual phase continuity is shortly reviewed. When the volume fraction of one phase is low, nearly spherical discrete domains may be formed in flow fields. The critical volume fraction for formation of infinite structures: φcr = 0.156, predicted by percolation theory for monodisperse spherical domains, is in reasonable accordance with experimental data for samples with spherical domains. In simple shear flow and low volume fraction the coalescence and break up processes may lead to the coexistence of long nearly cylindrical domains (large) oriented in the flow direction and (small) spherical domains. A hypothesis predicting a decrease of the percolation threshold value when φL* · φS* · P · 4 is large, is shown to be in accordance with experimental observations. φL* and φS* are the relative volume fraction of large and small domains, respectively, and P is the aspect ratio of the elongated (cylindrical) drops. The applicability of general (scaling) relations based on percolation theory are discussed.

The influence of microstructure on the fracture behaviour of particulate metal matrix composites

Abstract: Fracture processes have been studied in a range of model particle-reinforced metal matrix composite systems: commercially pure aluminium matrices reinforced with silicon carbide particles of two volume fractions and three particle sizes. The fracture micromechanisms have been identified by a combination of fractography and in situ experiments. A transition in fracture mechanisms from decohesion at the particle-matrix interface to particle cracking has been observed on increasing both the particle size and the volume fraction. Fracture nucleation criteria have been developed to explain these phenomena as a function of the microstructural parameters.

The rheology of adhesive hard sphere dispersions

Abstract: The influence of an attractive interparticle potential on the rheology of a sterically stabilized silica dispersion was investigated. Using a marginal solvent, there was an effective attraction between the particles which depended on the temperature. Three experiments in which different properties of the dispersion were probed showed that a square well model can be used to describe the temperature dependence of the pair potential. The turbidity of a dilute dispersion was measured as a function of the volume fraction and the temperature. Using dynamic light scattering techniques, the effect of the strength of the interparticle attraction on the diffusion coefficient was investigated. Furthermore, the steady shear viscosity was measured as a function of the volume fraction and the temperature. A microscopic theory for the low shear viscosity of a semidilute dispersion of adhesive hard spheres was successfully used to determine the interaction parameters. Viscosity measurement on dense suspensions showed tha...

Diffusion in fluid-bearing and slightly-melted rocks: experimental and numerical approaches illustrated by iron transport in dunite

Abstract: Bulk diffusion of iron in synthetic dunites containing 1–6 vol.% fluid or melt at 10 kbar (1 GPa) and 900°–1300° C was examined by encapsulating the samples in platinum, which served as a sink for iron. The rate of iron loss from the dunite was found to depend strongly upon the identity of the fluid, which was varied from CO2 and H2O to melts of basaltic and sodium carbonate composition. Carbon dioxide in amounts up to 4 vol.% has no effect upon bulk iron diffusion because it exists in the dunite are isolated pores. The interconnected nature of H2O, basaltic melt, and carbonate melt, on the other hand, results in marked enhancement of bulk-rock Fe diffusion that is correlated with the diffusivity and solubility of olivine components in the fluid. At 1300° C, 4–5 vol.% of either water or basaltic melt increases the effective bulk diffusivity from the fluidabsent value of ≈10-10 cm2/s to ≈10-8 cm2/s. A single experiment involving a similar volume fraction of carbonate melt yielded a minimum bulk diffusivity of 10-7–10-6 cm2/s. This remarkably high value is attributable to the concurrent high diffusivity and high solubility of olivine components in molten carbonate H2O has a high diffusivity, estimated at ≈10-4 cm2/s in this study, and basaltic melt can dissolve large amounts of olivine, but neither possesses these two qualities in combination. Bulk transport of Fe in dunite containing <2 vol.% of pure H2O is independent of olivine grain size for samples having an average grain diameter of <10 μm to ≈60 μm. This is probably because bulk diffusion specifically in these H2O-bearing samples is ratelimited by the flux (which is proportional to concentration) of olivine components in the fluid. Given a constant fluid volume fraction, the effect of reducing the grain size is to increase the number of fluid-filled channels, but at the same time to decrease their average aperture, thus keeping constant the cross-sectional area through which the diffusional flux occurs. (Independence of bulk diffusivity from grain size is not anticipated for rocks containing melt, in which the silicate components are much more soluble.) In numerical (finite difference) simulations of selected laboratory experiments, the bulk Fe transport process was modeled as diffusion in fluid-filled tubules of triangular cross-section that are supplied by volume diffusion from contacting olivine grains with which they are in surface equilibrium. Applying a tortuosity factor of 1.7 brings the numerically computed diffusional loss profiles for experiments containing basaltic melt into near-coincidence with the experimentally-determined curves. This success in reproducing the experimental results lends credence to the interpretation of the bulk diffusional loss profiles as composites of gradients due to volume, grain-boundary and fluid-phase diffusion.

A.c. electrical properties of composite solid electrolytes

Abstract: An improved effective-medium model to describe a.c. electrical properties of composite electrolytes is proposed in the light of its microstructure. Three characteristic volume fractions, two percolation thresholds ( ν 2 ′, ν 2 ″ ) for percolation of interface bondsand disruption of conducting paths, and ν 2 ∗ corresponding to the maximum enhancement in conductivity, are obtained from this model. The effect of microstructure parameters, such as grain size and size distribution, and grain volume fraction on the three characteristic volume fractions and a.c. electrical properties is discussed in detail. The results obtained by the theoretical model are consistent with the present experimental results.

Rubber‐Modified epoxies. IV. Influence of morphology on mechanical properties

Abstract: The mechanical properties of a system consisting of a bisphenol A diglycidylether (DGEBA) expoxy, cured with a cycloaliphatic diamine (4,4′-diamino-3,3 dimethyldicyclohexyl-methane, 3DCM), in the presence of an epoxy-terminated butadiene-acrylonitrile random copolymer (ETBN), was studied as a function of the cure schedule and the initial rubber concentration. Fracture toughness (KIc) and fracture energy (GIc) were increased, while Young's modulus and yield strength decreased slightly with increasing volume fraction of the dispersed phase. We show that there is no significant influence of the precure schedule and of the various observed particle diameters on the mechanical properties for a constant rubber volume fraction. In our case, the main deformation process in the rubber-modified epoxy networks is shear yielding while cavitation is negligible.

Localized deformation of SiCAl composites

Abstract: Tensile tests of SiC-6061 Al composites containing various volume fractions of whiskers or particles (20, 5 and 0 vol.%) showed that for samples containing a high volume fraction (20 vol.%) the fracture process was very localized, i.e. a very narrow neck. As the volume fraction of whiskers or particles decreased, the deformed region spread out. One might expect that the microstructure should correspond to the macroscale changes. In the highly deformed region the dislocation density is expected to be higher, in the less deformed regions the dislocation density should be lower, and if the deformation is very localized, then the high dislocation density should also be limited to a very narrow region. Overall, there is good agreement between the microstructure (dislocation density) change and the macroscale deformation of SiCAl composite tensile samples. The mechanism proposed to account for this change in deformation behavior as a function of volume fraction of SiC in aluminum is related to the expansion of the plastic zone (due to differences in thermal coefficients of expansion between SiC and aluminum) when the external stress is applied. Also, the localized deformation is related to localized clusters of SiC particles. There is a cooperative effect which leads to a region of very localized plastic deformation.

Viscoelastic response of model epoxy networks in the glass transition region

Abstract: Six epoxy networks with various structures built up from a diepoxy prepolymer, DGEBA, and three different diamines or mixtures of a monoamine and a diamine were studied by dynamic mechanical analysis in the glass transition region. The systems were designed in order to investigate the dependence of glass transition Tg on both crosslink density and network chain flexibility. The time (frequency)—temperature superposition principle (WLF equation) was used to determine the viscoelastic coefficients Cg1 and C which are related to some free volume characteristics on the molecular scale. Cg1, related to the free volume fraction available at Tg depends mainly on crosslink density, even though the product Cg1C, related to the free volume expansion coefficient, is dependent on both chain flexibility and crosslink density. Thus, viscoelastic properties determined over large temperature and frequency ranges are shown to yield more precise information on epoxy network structure than the simple analysis of glass transition temperature.

KR‐Curve Behavior of Duplex Ceramics

Abstract: The fracture toughness behavior during crack growth (KR-curve behavior) of duplex ceramics is investigated. Different types of KR-curves can be distinguished depending on the microstructural designs of these materials which are characterized by the volume fraction and size of the dispersed pressure zones, and by their effective volume expansion. According to their KR-curve behavior, duplex ceramics can be subdivided into two groups consisting of “short-range” and “long-range” toughened materials. The experimental results are discussed regarding the appearance of different toughening mechanisms which are documented by crack path micrographs. An unusual toughening effect, a “crackbranching chain reaction,” is documented by in situ observations. The critical stress to nucleate the observed process zone development is calculated and compared with the internal stress intensity factor Ki which has been previously proposed for these materials and with the material strength.

HREM investigation of homogeneous decomposition in a Ni-12 at. % A1 Alloy

Abstract: Using HREM γ′-precipitates in Ni Al of radii down to 0.7 nm are imaged. This enables us to see undercritical nuclei and to observe the nucleation process in a Ni-12 at.% Al alloy. The kinetics of decomposition of this alloy ay 773 K was followed. The time dependence of the precipitates' size distribution, their volume density, their mean radii and the volume fraction of the γ′-precipitates were measured on HREM micrographes. The results are compared quantitatively with classical nucleation theory and with the LSW-theory for Ostwald-ripening.

Rheology of semisolid Al-4.5%Cu-1.5%Mg alloy

Abstract: The rheological behavior of semisolid Al-4.5%Cu-1.5%Mg alloy slurry was investigated by using a slightly modified Couette viscometer to conduct three different types of experiments. In continuous cooling experiments the apparent viscosity of the sheared slurry increased with increasing volume fraction solid and increasing cooling rate, and decreased with increasing shear rate. The average particle size of the α phase decreased with increasing shear rate, increasing cooling rate, and increasing copper content in the alloy. The rate of decrease in particle size with increasing shear rate decreased with increasing cooling rate. In isothermal experiments at constant volume fraction solid and shear rate, the apparent viscosity decreased with increasing isothermal holding time, reaching a “steady state” value after about 1000s. The normalized specific particle surface area also decreased with isothermal holding time, reaching “quasisteady state” values. In isothermal experiments at constant volume fraction solid and variable shear rate, the steady state apparent viscosity of a semisolid alloy slurry decreased with increasing shear rate and decreasing volume fraction solid, while the normalized steady state specific particle surface area decreased and the normalized steady state average particle size increased. A state equation is proposed which fits reasonably well the experimental points obtained in this third group of experiments.

Diffusion and interaction in gels and solutions

Abstract: The diffusion of monodisperse polyethylene glycols (PEGs) in gels and solutions of the polymers κ-carrageenan and polystyrene sulfonate (NaPSS) has been studied experimentally and theoretically. It was found that the diffusion quotient D/D 0 (ratio between diffusion coefficients of the PEGs in systems with and without polymer) was higher in gels than in solutions of κ-carrageenan at the same total polymer volume fraction. Also, D/D 0 of a PEG was lower in NaPSS solutions at low ionic strengths compared to the diffusion in solutions where NaPSS had a higher degree of flexibility (induced by added salt, which had no influence on D 0). Further, it was found that D/D 0 for each PEG was a convex declining function of the total polymer volume fraction, while at constant volume fraction the D/D 0 quotient was a concave function of the radius of the PEGs. — The results are discussed by means of a novel theory. The basic concepts and equations of this theory are outlined in the paper, and it is shown that the main hindrance to the diffusion of molecules like PEG is the result of sterical obstruction due to the presence of the polymer chains. The crucial parameters determining the diffusion are the size of the diffusing molecule, the polymer radius, the persistence length of the polymer, and the total polymer volume fraction.

Theory and simulation of hard‐chain mixtures: Equations of state, mixing properties, and density profiles near hard walls

Abstract: A combination of theoretical modeling and computer simulation is used to study the equation of state of binary mixtures of hard chains, where each chain is modeled by a series of freely jointed, tangent, hard spheres Three approximate equations of state are derived, based on our previous work on one‐component fluids These equations contain no adjustable parameters and relate properties of the chain mixture to properties of pure monomer and dimer fluids at the same total volume fraction Their predictions are tested against Monte Carlo results for the pressure of mixtures of 8‐mers and monomers and mixtures of 8‐mers and 4‐mers, obtained using a hard‐wall technique Very good agreement is obtained using an equation of state developed here, in which the compressibilty factor of the mixture is set equal to the molar average of the compressibility factors of the pure components at the same overall volume fraction, as well as from Wertheim’s second‐order thermodynamic theory of polymerization (TPT2) Using the equations developed here, we also examine the mixing properties of hard‐chain fluids For mixing at constant pressure, the free energy and entropy of mixing range from ideal‐solution behavior at low pressures to Flory–Huggins behavior at high pressures For mixing at constant volume fraction, the free energy and entropy of mixing reduce directly to the Flory–Huggins result without recourse to the usual lattice approximations Site‐density profiles obtained from the simulations indicate that chains are depleted near the walls at low densities and are enhanced near the wall at high densities; monomers, by contrast, are enhanced near the walls at all densities

Structure and properties of rapidly solidified ultrahigh strength AlZnMgCu alloys produced by spray deposition

Abstract: A high solute, ultrahigh strength 7XXX series aluminium alloy (EURA1 alloy) with solute contents close to the equilibrium solid solubility limits of the AlZnMgCu system has been produced by rapid solidification using a new process of spray deposition (Osprey process) which yields massive preforms directly from the liquid state. The same alloy was also produced following the traditional powder metallurgy (PM) route. The microstructures and resulting mechanical and corrosion properties of the extruded products in the T6 and T7X conditions were evaluated and compared. Under peak-aged conditions only the spray-deposited (SD) products exhibited an acceptable strength-ductility combination, with strengths in excess of 800 MPa and fracture elongations of 4.9%. The EURA1 SD products also exhibited the largest increase in fatigue strength compared to the commercial IM 7075-T6 alloy, while maintaining a comparable crack propagation resistance as well as similar corrosion behaviour. The maximum strength was mainly associated with a very high volume fraction of plate-like η′ precipitates (ranging up to 50 A in diameter), which were identified as having a hexagonal structure with lattice parameters a = 0.489 nm and c = 1.374 nm. Nevertheless, within the T6 microstructure, small spherical, possibly ordered, zones (5–10 A in diameter) were also observed. The EURA1 extrusions exhibited a loss in fracture toughness associated with predominantly intergranular dimpled ruptures. However, the structural and fractographic observations suggested that the properties of the EURA materials could be considerably improved and some preliminary results from the ongoing optimization work are presented.

Packing Density of Composite Powder Mixtures

Abstract: A model of particle packing in binary composite systems is developed. The effects of both inclusion surfaces and touching inclusions on the packing density are taken into account. To implement the model, a statistical approach is used to determine the number of inclusion contacts as a function of inclusion content. The statistical approach indicates that the average number of inclusion contacts is a linear function of the inclusion volume fraction, a result which agrees very well with independent computer simulations. The model suggests that the packing efficiency, defined by the ratio of the packing density to the ideal packing density (as originally derived by Furnas), is governed by the inclusion volume fraction (fi) and the particle to inclusion size ratio (r). Good agreement is obtained between the theory and experimental literature data.