A multiplanar model for the pore radius distribution in isotropic near-planar stochastic fibre networks

A model is presented for the pore radius distribution in isotropic near-planar stochastic fibre networks. At a given areal density, the mean pore radius of two-dimensional random networks is shown to decrease with increasing fibre width and to increase with increasing fibre linear density.For structures with a structural component in the third dimension the standard deviation of pore radii is shown to be proportional to the mean for changes in areal density and porosity in agreement with data reported in the literature. At a given porosity, near-planar networks exhibit an increase in mean pore radius with increasing fibre width and linear density.     

Statistical geometry of pores and statistics of porous nanofibrous assemblies.

The application of theoretical models to describe the structure of the types of fibrous network produced by the electrospinning of polymers for use in tissue engineering and a number of other applications is presented. Emphasis is placed on formal analyses of the pore size distribution and porosities that one would encounter with such structures and the nature of their relationships with other structural characteristics likely to be important for the performance of nanofibrous materials. The theoretical structures considered result from interactions between randomly placed straight rods that represent fibres with nanoscale dimensions. The dominant role of fibre diameter in controlling the pore diameter of the networks is shown and we discuss the perhaps counter-intuitive finding that at a given network mass per unit area and porosity, increasing fibre diameter results in an increase in mean pore radius. Larger pores may be required for ingrowth of cells to nanofibrous networks, hence this study clarifies that simply making the diameters of the fibres smaller might not be the way to improve cell proliferation on such substrates. An extensive review of structural features of the network such as the distribution of mass, inter-fibre contacts and available surface for cell attachment, fibre contact distributions for integrity of the networks and the porosity and pore size distributions is given, with emphasis placed on nanofibre dimensions for the first time.     

A model for fibre contact in planar random fibre networks

A model is presented for the expected degree of contact between fibres in isotropic near-planar random fibre networks. The statistics of fibre contact in two-dimensional fibre networks are considered and the expressions derived are developed to allow the fractional contact area in structures formed by the superposition of two-dimensional structures to be derived. These expressions allow the fractional contact area to be expressed in terms of the network porosity only. For thin networks, the fractional contact area may be expressed in terms of network porosity and the expected coverage of the network. Theory permitting the determination of the expected area of one contact and hence the expected number of contacts per fibre is presented also. Good agreement is found between the expressions derived for the fractional contact area and data from the literature.     

Does fabric tensor exist for a fabric?

It is shown that the mean intercept length distribution for planar fibre networks or for materials composed of a set of plates is not in general elliptic and cannot be expressed analytically in terms of a second-order tensor. However, our numerical computations indicate that the polar plot of the mean intercept length at the angle of measurement may become nearly ellipsoidal as the microstructure (fibres or plates) become less discretely organized, but yet remain orthotropic. The equations presented in this study may be used to obtain fibre (plate) orientation density functions from the experimental data on mean intercept length distribution.     

Structural characteristics and optical properties of vestan (polyester) fibres

Refractive indices and birefringence for skin and core changes with strain, produced by different stresses in undrawn vestan fibres, were measured interferometrically. Applications were carried out using multiple-beam Fizeau fringes in transmission to determine the Cauchy's constants and dispersive coefficient for the fibre layers. The resulting data were used to calculate the polarizability per unit volume for each layer. The scanning electron microscope (SEM), optical microscope and He-Ne laser beam were applied to estimate the geometrical parameters of the fibre cross-section. A comparative study between the three methods used for measuring the fibre diameter was made. The effect of temperature on the refractive index and birefringence for each fibre layer has been also investigated. The relationship between temperature and birefringence of the fibres was studied and the thermal coefficient of the refractive index was determined. An empirical formula is suggested to relate temperature and birefringence. Illustrations are given using microinterferograms.     

Critical parameters of nylon and other fibres for spalling protection of high strength concrete in fire

This study investigated various types of fibre length, fibre diameter, fibre type and fibre content on the degree of spalling of concrete in fire. Four types of fibres, namely, polypropylene, polyvinyl alcohol, cellulose and nylon with various lengths and diameters were studied. Fibre contents ranged from 0.05 to 0.15% by volume of concrete. Fire tests were conducted according to the ISO 834 standard heating curve. Results showed that when comparing all the fibres under the same fibre content levels (% volume of concrete), the nylon fibre was the most effective in protecting concrete from spalling. This is because the diameter of the nylon fibres were significantly less than the other fibres, hence there were significantly more number of nylon fibres present for the same fibre content (% volume) in concrete. Analysis revealed, regardless of the amount of fibre, the type of fibre, diameter of and length of fibre, there is a strong relationship between the total number of fibres present per unit volume, length of fibres and the degree of spalling observed. Based on this relationship, the authors established a critical minimum for total number of fibres per unit volume for spalling protection in fire.     

Templated pores in hydrogels for improved size selectivity in gel permeation chromatography

The pore structures of cross-linked polyacrylamide gels can be altered by polymerizing in the presence of high concentrations of unreactive, micellar surfactant cosolutes which act as "templates". Removal of surfactant after polymerization is expected to leave pores with the approximate shape and dimensions of the surfactant micelles. A simple model was developed to simulate gel permeation chromatography (GPC) separations of globular proteins on templated gels. The model assumes that the partition coefficient for sieving of a protein is equal to the fraction of gel volume accessible to a sphere with a radius equal to the protein Stokes radius. The total gel volume is considered to include a fraction that is a conventional, random gel matrix and a remaining fraction contributed by templated pores. The pore size distribution of the conventional gel was estimated using the Ogston equation, which approximates the matrix as a random collection of long, thin, rigid fibers. Templated pores were assumed to have a Gaussian distribution of radii centered about some mean determined by the micelle radius. In comparison to conventional media, gels with templated pores are predicted to exhibit more sharply defined exclusion limits and improved resolution over a narrow size range centered on the mean templated pore size. Selectivity and resolution are expected to increase as the volume fraction of templated pores is increased and as the dispersion of templated pore radius is decreased. Small changes in template radius lead to large changes in the molecular weight range of optimal separation of globular proteins. It should be possible to create a series of GPC media that collectively offer high resolution over the molecular weight range of most globular proteins of interest.     

Probabilistic aspects of strength of short-fiber composites with planar fibre distribution

The study of the fracture of short-fibre composites must involve statistics as an integral part. Two components of composite strength, each with probabilistic aspects, are described in this paper: fibre crossover reinforcement, and fibre gap bridging before fracture. The fibre crossover density is proposed as a measure of mutual fibre strengthening. and simulations are performed to estimate this density. Several different fibre orientations are proposed which have identical elastic properties but different crossover densities, indicating that more information is required for strength prediction than for elastic property prediction. The crossover density is a random variable whose average increases roughly as a fibre length squared function, and whose coefficient of variation decreases with increasing fibre length. The phenomenon of fibres bridging microcrocks is also examined as a fracture mechanism for fibres whose length well exceeds their critical length. General probabilistic expressions are derived which give the distribution of the number of fibres bridging a gap perpendicular to the applied load. These formulae are applied to the distribution of strength of an aligned fibre system.     

X-ray measurements and the structure of polyacrylonitrile- and pitch-based carbon fibres

X-ray measurements were carried out on polyacrylonitrile- and pitch-based carbon fibres. The crystallites, disordered regions and microvoids in these carbon fibres were evaluated quantitatively by applying the methods previously proposed by the present authors. The structural parameters evaluated are the 1 1 plane spacing of the carbon layer, the average, standard deviation and asymmetry of the distribution of interlayer spacing, the stacking regularity parallel to the layer plane, the layer extents parallel and perpendicular to the fibre axis, the stacking height, the crystallite orientation, the volume fractions of crystallites, disordered regions and microvoids, the variation of the electron density in a microvoid, and the size parameters of the void cross-section perpendicular to the fibre axis, such as the area, radius of gyration, chord length and thickness. The mutual relationships of these structural parameters are presented, and parameters sensitive to the nature of the starting materials are pointed out.     

Development of composite coaxial cylinder stress analysis model and its application to SIC monofilament systems

An analytical model is presented allowing prediction of the principal stresses in a system composed of a set of coaxial cylinders, subject to temperature change or applied stress. The materials must exhibit transverse isotropy of stiffness and thermal expansivity. The model represents a development of an analysis published by Mikata and Taya, the modification allowing any number of component cylinders and a finite outer radius. Use of the model is illustrated by means of a series of examples involving SiC monofilaments. Application to the behaviour of composites containing many aligned fibres is demonstrated, using cylinder radii appropriate for the fibre volume fraction in the composite. It is shown by comparison with predictions from an Eshelby model that this is an acceptable approximation, preferable to the surrounding of fibre and matrix by an outer composite layer of infinite radius.     

The fibre pull-out energy of misaligned short fibre composites

A theoretical study on the fibre pull-out energy has been carried out for short fibre-reinforced composites. Two probability density functions were introduced for modelling the fibre-length distribution and the fibre-orientation distribution. By taking into account the effect of snubbing friction between fibres and matrix at the fibre exit point during fibre pull-out, and that of the fracture stress of fibres obliquely crossing the fracture plane (i.e. the inclined strength of fibres), the fibre pull-out energy of composites has been derived as a function of fibre-length distribution and fibre-orientation distribution, as well as interfacial properties. The previously existing fibre pull-out energy theories can be deduced from the present model. The effects of fibre-length distribution, fibre-orientation distribution, interfacial properties, snubbing-friction coefficient and parameter A for determining the inclined strength of fibres on the fibre pull-out energy, have been studied in detail. The present study provides the necessary information as to which fibre-length distribution, fibre-orientation distribution and interfacial property are required to achieve a desired fibre pull-out energy and hence a desired composite toughness. High-strength fibres, a large fibre-volume fraction and a large fibre diameter for a comparatively large mean fibre length, are shown to be favourable for achieving a high fibre pull-out energy. This revised version was published online in November 2006 with corrections to the Cover Date.     

The effect of fibre length on fracture toughness and notched strength of short carbon fibre/epoxy composites

The effect of radius of curvature on the tensile notched strength of random short carbon fibre/epoxy composites containing 1, 5 and 15 mm length fibres is studied. The strength of all laminates showed a sensitivity to the radius of curvature, with the tensile strength decreasing at smaller radii of curvature. A model is developed to predict notched strength based on assumed evolution and propagation of damage from the tip of the notch. The predictions of the model depend principally on two material properties: the unnotched tensile strength and fracture toughness. Reasonable agreement is achieved between the predicted notched strength and experimental data.     

Influence of geometrical parameters on the elastic response of unidirectional composite materials

A numerical approach to predict the elastic properties of composite materials departing from the properties of the individual constituents is presented. Using a recently proposed algorithm which generates a random distribution of fibres emulating the real distribution in the transverse cross-section of composite materials, an estimate of the elastic properties is obtained by performing volumetric homogenisation of the results from micromechanical analyses. The influence of different geometrical parameters used in the generation of the random distribution of fibres is analysed, namely, the dimensions of the representative volume element, the fibre radius, and the interval between neighbouring fibres.     

Round-robin analysis of the RILEM TC 162-TDF uni-axial tensile test: Part 2

Plain and steel fibre reinforced concrete cylinders were tested uni-axially in tension under closed-looped conditions in a round robin test programme. During the test, three deformation readings around the notched plane were measured. It was found that during the course of the test, rotations were occurring and thus a fibre counting exercise was initiated. This was to investigate the influence of fibre distribution within the cylinder specimens on the observed rotations of the specimens. The results of the investigation could not detect any strong correlation between the fibre distribution and the observed rotations and a more likely source for the variations observed is the boundary conditions of the tests. Significant variations were found in the number of fibres with coefficients of variation in the range of 30% to 50%. Additionally, it was found that toughness is approximately linearly related to the number of fibres in the fracture surface up to a certain limiting value where the toughness appears to plateau in relation to the mumber of fibres.     

Effects of the process conditions during dry-defibration on the properties of cellulosic networks

The influence of structural changes caused by dry-defibration of the pulp on the mechanical properties of dry-formed cellulosic networks has been investigated. The effects of fibre length, fibre curl and content of fine material on these properties are discussed. The fluff pulps used were one CTMP-grade and two kraft pulps. The primary parameters used to describe the networks were the storage modulus, G0 (measured at low strain amplitudes), and the critical strain, c (at which the network yields), obtained from dynamic-mechanical measurements, and the maximum force, Fmax, sustained by the network and the maximum strain, max (at Fmax), measured with a specially constructed shear tester. It was noted that the storage shear modulus, G0, and maximum force, Fmax, were affected in the same manner by the defibration conditions. To improve the deformability of the cellulosic network before rupturing, the ideal dry-defibration process should provide a greater number of free fibres per unit volume without producing fine material, at the same time as the curl index of the fibres should increase. Long and curled fibres are thus to be preferred. © 1998 Chapman & Hall     

Psuedo-affine behaviour of collagen fibres during the uniaxial deformation of leather

Chromium tanned bovine leather has been dried under uniaxial strain and its collagen fibre distribution examined using high-angle X-ray diffraction. Microstructural modelling of the fibre kinematics showed that under large-strain deformation (30%) the fibres behave in a psuedo-affine manner. At decreasingly lower strains the fibre re-orientation is seen to progressively deviate from the pseudo-affine prediction; an observation which can be understood in terms of a combination of fibre-fibre adhesion and changes in fibre substructure. The material was also subjected to mechanical testing and tensile data is presented here which indicates how fibre orientation affects tensile modulus. This work represents the first quantitative microstructural model for collagen fibre distribution in strained leather.     

Fibre cross-section determination and variability in sisal and flax and its effects on fibre performance characterisation

The results of a study on the measurement of fibre cross-section and its variability in flax and sisal fibres are presented. Cross-section values obtained from fibre “diameter” measurements were more than double the values obtained from actual observation of cross-sections of the same individual fibres. The overall conclusion is that fibre “diameter” measurement is not an attractive method for accurate estimation of cross-sectional area of these natural fibres. This conclusion is significant for researchers engaged in micromechanical investigation of natural fibre composites since differences in fibre cross-section translate directly into differences of the same magnitude in the values obtained for the fibre modulus and strength. The error in fibre cross-section introduced by the “diameter” method scales with the average fibre “diameter” which may also result in erroneous observations of fibre modulus and strength scaling inversely with natural fibre “diameter”. The difference in average cross-section observed from fibre to fibre was significantly greater than the variation along the length of each individual fibre. The minimum to maximum cross-section variability of individual flax fibres was found to be approximately twice that observed for sisal fibres.     

The effective chemical vapour deposition rate of diamond

The effective chemical vapour deposition (CVD) rate of diamond, defined as the total thickness of diamond or as the mass of diamond deposited per unit time, may be increased by orders of magnitude by increasing the substrate area per unit volume. To obtain these high deposition rates, novel substrate designs are proposed that exploit three-dimensional arrays of small diameter wires or fibres. The analysis suggests that the increased diamond output should be achieved with no increase in the net gas flow or power consumption, which could lead to the more economic production of solid diamond shapes and of composites containing continuous or short diamond fibres, or particulate diamond. Estimates for the cost of CVD diamond made by the fibre array technique are compared with reported current and predicted costs for CVD diamond and estimates for the cost of CVD SiC.     

Stress disturbance due to broken fibres in metal matrix composites with non-uniform fibre spacing

Premature fracture of weaker fibres causes stress disturbances in composites. These disturbances are affected by non-uniformity of fibre spacing. In order to evaluate quantitatively how the disturbances in metal matrix composites are affected by the extent of non-uniformity of fibre spacing, a method of calculation is presented on the basis of two-dimensional shear lag analysis. Static tensile stress concentrations in the intact fibres to broken fibres, tensile stress distribution along the fibre axis in the broken and intact fibres and shear stresses between broken and intact fibres were calculated by the method presented, using some examples. It is shown quantitatively that the spacing between broken and intact fibres and that between intact and next fibres has a significant influence on tensile stress concentrations in intact fibres and also on the shear stresses between broken and intact fibres: the narrower the former spacing and the wider the latter spacing, the higher become both tensile and shear stress concentrations. This tendency is enhanced when the number of broken fibres is large and when the strain hardening of the matrix is high.     

Thermal diffusion of radon in porous media

Based on the non-intersection model of cylindrical capillaries, the mean radius of the pores of some soils and building materials are estimated. In size, the above-mentioned radii are usually of the order of the free path of gas molecules at atmospheric pressure. A review of pore size distribution data also reveals that a large fraction of concrete pores belong to Knudsen's region. This fact indicates that the thermal gradient in these media must cause gas (radon) transport. The interpretation of the experimental data concerning the rate of emanation of 222Rn from a concrete-capped source subjected to a sudden increase in temperature is given, based on irreversible thermodynamics theory. The calculations given here for radon flux, caused by concentration and thermal gradients, are in satisfactory agreement with the experimental data. It is shown that thermodiffusion can significantly contribute to radon flux in concrete. The need to include the thermodiffusion radon flux in the radon entry model is discussed.