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.     

Time-dependent resistivity in carbon fibre sheets

The electrical properties of sheets of short carbon fibres in resin, glass-fibre and wood-pulp materials have been investigated. For carbon fibre in wood-pulp, a conductor-to-insulator transition was observed at 3 wt % (0.6 vol %) carbon fibre above which conductivity varied linearly with weight fraction. This result is interpreted in terms of a percolation threshold in a system of high aspect ratio. The data agree well with previous measurements on carbon-fibre in polymer composites, and satisfactorily with two-dimensional Monte Carlo calculations. At high concentrations of carbon fibre in all materials, the in-plane resistivity was found to be strongly time-dependent, the fractional change being proportional to Int. A theoretical model is presented which assumes a continuous increase in the number of interconnecting pathways as fibres physically move together under electrostatic attractive forces. Thermal activation over a continous spectrum of energy barriers leads to logarithmic time dependence as observed experimentally. Studies of the effect of external compression support the model for the time dependence. Shell (UK) Ltd Research Fellow in Materials Science.     

Micromechanical characterisation of fibre/matrix interfaces

Theoretical analyses for the single fibre pull-out and push-out models under monotonic loading are given which are based on a shear-lag analysis in a fracture mechanics approach considering non-constant friction at the debonded interface as a result of fibre Poisson contraction (or expansion). The solutions allow the determination of typical fibre/matrix interfacial properties such as the interfacial fracture toughness, G_ic, the coefficient of friction, μ, and the residual clamping stress, q₀. Under cyclic loading the interfacial properties are expected to degrade as a result of repetitive abrasion, and a power law function is assumed between μ and the number of elapsed cycles, N. However, G_ic is assumed to be unaffected and a fracture mechanics based debond criterion is derived for the relationship between the external applied stress, the debond length and the reduced friction coefficient for both fibre pull-out and fibre push-out. In addition, the relative displacements between the free fibre end and the matrix top are obtained for cyclic fatigue when the fibre is loaded and unloaded. A relationship obtained for the protrusion (or intrusion) length in fibre pull-out (or push-out) experiments allows the severity of the interface frictional degradation to be evaluated and characterised. Similarities and differences in the frictional degradation behaviour between fibre pull-out and push-out are also identified.     

Plant fibre composites – porosity and volumetric interaction

Plant fibre composites contain typically a relative large amount of porosity, which considerably influences properties and performance of the composites. The large porosity must be integrated in the conversion of weight fractions into volume fractions of the fibre and matrix parts. A model is presented to predict the porosity as a function of the fibre weight fractions, and to calculate the related fibre and matrix volume fractions, as well as the density of the composite. The model predicts two cases of composite volumetric interaction separated by a transition fibre weight fraction, at which the combination of a high fibre volume fraction, a low porosity and a high composite density is optimal. Experimental data from the literature on volumetric composition and density of four types of plant fibre composites are used to validate the model. It is demonstrated that the model provides a concept to be used in fabrication, process optimisation and design of plant fibre composites.     

Plant fibre composites – porosity and stiffness

Plant fibre composites contain typically a relatively large amount of porosity which influences their performance. A model, based on a modified rule of mixtures, is presented to include the influence of porosity on the composite stiffness. The model integrates the volumetric composition of the composites with their mechanical properties. The fibre weight fraction is used as an independent parameter to calculate the complete volumetric composition. A maximum obtainable stiffness of the composites is calculated at a certain transition fibre weight fraction, which is characterised by a best possible combination of high fibre volume fraction and low porosity. The model is validated with experimental data from the literature on several types of composites. A stiffness diagram is presented to demonstrate that the calculations can be used for tailoring and design of composites with a given profile of properties.     

The abrasive wear behaviour of continuous fibre polymer composites

The dry abrasive-dominant wear behaviour of several composite materials consisting of uni-directional continuous fibres and polymer matrices was investigated. Seven materials were examined: neat epoxy (3501-6), carbon fibre epoxy (AS4/3501-6), glass fibre/epoxy (E-glass/ 3501-6), aramid fibre/epoxy (K49/3501-6), neat polyetheretherketone (PEEK), carbon fibre/PEEK (APC2) and aramid fibre/PEEK (K49/PEEK). The wear behaviour of the materials was characterized by experimentally determining the friction coefficients and wear rates with a pin on-flat test apparatus. First, the effects of the operation variables apparent normal pressure, sliding velocity and apparent contact area were observed. The dimensionless wear rate increased linearly as the apparent normal pressure increased and decreased as the apparent contact area increased. Second, through microscopic observations of the worn surfaces and subsurface regions, basic wear mechanisms were identified as a function of fibre orientation. Observations of fibre-abrasive particle interactions allowed for the differentiation of the dominating wear mechanisms. Finally, a network of data was compiled on the wear behaviour in terms of the three material parameters: fibre orientation, fibre material and matrix material. This enabled the systematic selection of an ideal low wear composite material which would consist of a PEEK matrix reinforced with aramid fibres oriented normal to the contacting surface and carbon fibres oriented parallel to the contacting surface.     

Comments on the pore radius distribution in near-planar stochastic fibre networks

The pore radius distribution in near-planar stochastic fibre networks is known to be influenced by changes in the mean number of fibres per unit area and their distribution in the plane. Experimental data is presented that confirms the established result that the standard deviation of pore radii is proportional to the mean. The data shows also that this proportionality is the same for changes in the number of fibres per unit area and for changes in the uniformity of their in-plane distribution. Data from the literature suggests that processes that increase the mean pore radius, increase also the coefficient of variation of pore radii. Theoretical considerations and experimental data are presented that show that the coefficient of variation of pore radii is in fact constant for near-random and non-random stochastic fibre networks.     

Wigner distribution moments in fractional Fourier transform systems

It is shown how all global Wigner distribution moments of arbitrary order in the output plane of a (generally anamorphic) two-dimensional fractional Fourier transform system can be expressed in terms of the moments in the input plane. Since Wigner distribution moments are identical to derivatives of the ambiguity function at the origin, a similar relation holds for these derivatives. The general input-output relationship is then broken down into a number of rotation-type input-output relationships between certain combinations of moments. It is shown how the Wigner distribution moments (or ambiguity function derivatives) can be measured as intensity moments in the output planes of a set of appropriate fractional Fourier transform systems and thus be derived from the corresponding fractional power spectra. The minimum number of (anamorphic) fractional power spectra that are needed for the determination of these moments is derived. As an important by-product we get a number of moment combinations that are invariant under (anamorphic) fractional Fourier transformation.     

A higher-order triangular plate bending element revisited

A new formulation of an eighteen-degrees-of-freedom higher-order triangular plate bending element using triangular area co-ordinates is presented. The displacement function w is taken as the complete fifth-order polynomial in area co-ordinates. The normal slope along an edge of the triangle is constrained to vary cubically. The twenty-one constants are expressed explicity in terms of eighteen degrees of freedom. The element stiffness matrix is expressed as a product of component matrices for which explicit expressions are developed and presented. No numerical inversion or integration is necessary. The formulation is expected to be useful specially for microcomputers.     

Contact angle measurement on xerogel sensitive layer for optical fibre sensor

This paper deals with approach for the detection of chemical vapours based on refractive-index changes of a silica xerogel layer deposited as an optical cladding on the fibre core. The fibre is multimode fibre excited with an inclined collimated beam. The refractive-index changes are evaluated by means of changes of the output power at the end put of the fibre. The optical properties of the sensitive cladding (refractive index and absorption coefficient) can be obtained with modelisation program. The sensitivities of tetraethoxysilane (TEOS) and methyltriethoxysilane (MTEOS)-based xerogel layers to toluene and water are presented in the paper. The hydrophobicity of the two-xerogel layers and their surface-free energy has been determined with contact angle measurements. A correlation between optical detection results and contact angle measurements can be done.     

Porous Ti6Al4V scaffolds directly fabricated by 3D fibre deposition technique: Effect of nozzle diameter

3D porous Ti6Al4V scaffolds were successfully directly fabricated by a rapid prototyping technology: 3D fibre deposition. In this study, the rheological properties of Ti6Al4V slurry was studied and the flow rate was analyzed at various pressures and nozzle diameters. Scaffolds with different fibre diameter and porosity were fabricated. ESEM observation and mechanical tests were performed on the obtained porous Ti6Al4V scaffolds with regard to the porous structure and mechanical properties. The results show that these scaffolds have 3D interconnected porous structure and a compressive strength which depends on porosity at constant fibre diameters and on the fibre diameter at constant porosity. These Ti6Al4V scaffolds are expected to be constructs for biomedical applications.     

Modelling cyclic shear deformation of fibre/epoxy layers in fibre metal laminates

Relations for a theoretical model were derived describing the shear deformation of uni-directional fibre/epoxy layers in Fibre Metal Laminates. The shear deformation is induced by the cyclic shear stresses at the interface that result from the cyclic load transfer from aluminium to the bridging fibre/epoxy layers during fatigue loading of the laminate. With the presented relations the crack opening contribution as result of shear deformation can be calculated. As the shear deformation is hard to measure experimentally, the theoretical model has been validated by comparing the model with finite element analysis. A good correlation has been obtained between the presented theoretical model and the FE-model representing the complex reality.     

Determining the minimum,critical and maximum fibre content for twisted yarn reinforced plant fibre composites

The effect of fibre volume fraction on the physical and tensile properties of aligned plant fibre composites (PFCs) produced via vacuum infusion has been investigated. There is no clear correlation between fibre volume fraction and porosity. However, low fibre content PFCs are prone to intra-yarn voids, while high fibre content PFCs are prone to inter-yarn voids. This is due to changing resin flow dynamics with increasing fibre content.     

Assessment of the electrochemical behavior of two-dimensional networks of single-walled carbon nanotubes

Scanning electrochemical microscopy (SECM) has been employed in the feedback mode to assess the electrochemical behavior of two-dimensional networks of single-walled carbon nanotubes (SWNTs). It is shown that, even though the network comprises both metallic and semiconducting SWNTs, at high density (well above the percolation threshold for metallic SWNTs) and with approximately millimolar concentrations of redox species the network behaves as a thin metallic film, irrespective of the formal potential of the redox couple. This result is particularly striking since the fractional surface coverage of SWNTs is only approximately 1% and SECM delivers high mass transport rates to the network. Finite element simulations demonstrate that under these conditions diffusional overlap between neighboring SWNTs is significant so that planar diffusion prevails in the gap between the SECM tip and the underlying SWNT substrate. The SECM feedback response diminishes at higher concentrations of the redox species. However, wet gate measurements show that at the solution potentials of interest the conductivity is sufficiently high that lateral conductivity is not expected to be limiting. This suggests that reaction kinetics may be a limiting factor, especially since the low surface coverage of the SWNT network results in large fluxes to the SWNTs, which are characterized by a low density of electronic states. For electroanalytical purposes, significantly, two-dimensional SWNT networks can be considered as metallic films for typical millimolar concentrations employed in amperometry and voltammetry. Moreover, SWNT networks can be inexpensively and easily formed over large scales, opening up the possibility of further electroanalytical applications.     

Design and structural applications of stress-crack width relations in fibre reinforced concrete

The stress-crack width relationship has been shown to be the key to an understanding of fracture propagation in and mechanical behaviour in tension of fibre reinforced concrete materials and structures. A model is derived for the stress-crack width relationship for randomly oriented short fibre composites which takes hybrid fibre systems and possible fibre rupture into account. It is shown how this stress-crack width relationship can be included in a structural model for the prediction of crack widths in reinforced concrete structures. With this combination of models a rational design tool for the design of composite materials and structures has been established. It is shown how different fibre systems can be tested for structural applicability and how combined material and structural optimization can take place.     

Influence of fibre taper on the work of fibre pull-out in short fibre composite fracture

A model has been formulated to determine the work of pull-out, U, of an elastic fibre as it shear-slides out of a plastic matrix in a fractured composite. The fibres considered in the analysis have the following shapes: uniform cylinder and ellipsoidal, paraboloidal or conical tapers. Energy transfer at the fibre–matrix interface is described by an energy density parameter which is defined as the ratio of U to the fibre surface area. The model predicts that the energy required to pull out a tapered fibre is small because the energy transfer at the fibre–matrix interface to overcome friction is small. In contrast, the pull-out energy of a uniform cylindrical fibre is large because the energy transfer is large. The pull-out energies of the paraboloidal and ellipsoidal fibres lay between those for the uniform cylindrical and the conical fibres. With the exception of the uniform cylindrical fibre which yields a constant energy density, tapered fibres yield expressions for the energy density which depend on the fibre axial ratio, q. In particular, the energy density increases as q increases but converges at large q. By defining the critical axial ratio, q ₀, as the limit beyond which u is independent of the fibre slenderness, our model predicts the value of q ₀ to be about 10. These results are applied to explain the mechanisms regulating fibre composite fracture.     

The mechanical properties of carbon fibre reinforced Pyrex glass

The mechanical properties of carbon fibre reinforced Pyrex glass are discussed in terms of the volume fraction of fibre, the orientation of the fibres, fibre damage during fabrication, matrix porosity, matrix critical strain, interface properties and the mode of failure in bend tests. The stress at which matrix cracking occurs increases with fibre concentration indicating that the critical strain of the matrix increases as the fibre separation decreases. The ultimate strength of the composite is considerably greater than the stress at which the matrix begins to crack. Preliminary stress cycling experiments at stresses above that at which matrix cracks are formed suggest that propagation of these cracks is inhibited by the fibres.     

Fretting of glass fibre reinforced composites

Favourable specific mechanical properties of polymer matrix composites make them an attractive material for application in many engineering structures for which they offer substantial improvements over metals. The paper deals with fretting behaviour of unidirectional glass epoxy composites/metal contacts. Fretting is a plague for many industries: failures, loss of matter, loss of function can be induced by fretting. It occurs in all quasi-static contacts and appears as a complex wear phenomenon where a lot of parameters have been studied. From the interface tribology concept, the velocity accommodation mechanisms are discussed for different fibre orientations versus the contact surface of the glass fibre reinforced epoxy material. Results were analysed in two steps. From friction logs, Running Conditions Fretting Maps (RCFM) were first plotted in order to give an analysis of contact conditions and determine the associated material responses. The tribological degradations were then analysed. Differences between the different fibre orientations are mainly discussed on the basis of the stiffness of the anisotropic material and the velocity accommodation in the contact.     

Effect of consolidation pressure on volumetric composition and stiffness of unidirectional flax fibre composites

Unidirectional flax/polyethylene terephthalate composites are manufactured by filament winding, followed by compression moulding with low and high consolidation pressure, and with variable flax fibre content. The experimental data of volumetric composition and tensile stiffness are analysed with analytical models, and the composite microstructure is assessed by microscopy. The higher consolidation pressure (4.10 vs. 1.67 MPa) leads to composites with a higher maximum attainable fibre volume fraction (0.597 vs. 0.530), which is shown to be well correlated with the compaction behaviour of flax yarn assemblies. A characteristic microstructural feature is observed near the transition stage, the so-called local structural porosity, which is caused by the locally fully compacted fibres. At the transition fibre weight fraction, which determines the best possible combination of high fibre volume fraction and low porosity, the high pressure composites show a higher maximum performance in terms of tensile stiffness (40 vs. 35 GPa). The good agreement with the model calculations (fibre compaction behaviour, and composite volumetric composition and mechanical properties), allows the making of a property diagram showing stiffness of unidirectional flax fibre composites as a function of fibre weight fraction for consolidation pressures in the range 0–10 MPa.