The effect of fibre aspect ratio on the stiffness of discontinuous fibre-reinforced composites

The mechanics underlying the stiffness of discontinuous fibre-reinforced composites are well understood. In particular the critical fibre aspect ratio is known to affect the resultant deformation of the composite. This paper will explain how the Cox theory can be used to determine the critical aspect ratio for a given fibre/matrix combination at a given volume fraction. Supporting experimental evidence for the key dependencies influencing the critical aspect ratio are shown at the microscopic level (by a Raman spectroscopic approach) and at the macroscopic level (by a tensile creep approach) for a series of different composite materials.     

The influence of the interface on the strength and elastic properties of low aspect ratio fibre composites

The strength and elastic properties of randomly distributed low aspect ratio fibre composites were investigated. The fibre-matrix interfacial conditions were varied by applying various surface treatments to the fibres. The influence of the interfacial bond on the strengths of such composites was demonstrated.     

Tensile strength of discontinuous fibre-reinforced composites

A stochastic Monte-Carlo approach, based on Eyring's chemical activation rate theory, is used to study the factors controlling the tensile strength of discontinuous fibre-reinforced composites. The model explicitly takes into account the local distribution of stress near fibre ends. Both the fibre and the matrix are allowed to break during fracture of the composite. The stress-strain curves and the modes of failure of the composite are found to be strongly dependent on the volume fraction and aspect ratio of the fibres. The importance of adhesion at the fibre/matrix interface is also studied. The results are compared with available experimental data.     

Complex moduli of aligned discontinuous fibre-reinforced polymer composites

This paper describes recent analytical and experimental efforts to determine the effects of fibre aspect ratio, fibre spacing, and the viscoelastic properties of constituent materials on the damping and stiffness of aligned discontinuous fibre-reinforced polymer matrix composites. This includes the analysis of trade-offs between damping and stiffness as the above parameters are varied. Two different analytical models show that there is an optimum fibre aspect ratio for maximum damping, and that the predicted optimum aspect ratios lie in the range of actual aspect ratios for whiskers and microfibres when the fibre damping is small. When the fibre damping is great enough, however, the optimum fibre aspect ratio corresponds to continuous fibre reinforcement. Experimental data for E-glass/epoxy specimens are presented for comparison with predictions.Nomenclature A _c,A_f,A_m Cross-sectional area of composite, fibre, and matrix, respectively - d Fibre diameter - E _c ^* ,E _f ^* ,E _m ^* Complex extensional modulus of composite, fibre, and matrix, respectively. - E_c,E_f,E_m Extensional storage modulus of composite, fibre, and matrix, respectively - E_c,E_f,E_m Extensional loss modulus of composite, fibre, and matrix, respectively - G_m Complex shear modulus of matrix - G_m Shear storage modulus of matrix - i –1^1/2 - K Defined in Equation A9 - K ₁ Defined in Equation A5 - l Fibre length - r Radial distance from centre of fibre - r ₀ Fibre radius - R Radius of representative volume element, or one-half of centre-to-centre fibre spacing - v _f,v _m Volume fraction of fibre and matrix, respectively - W _c Total strain energy stored in a unit volume of composite - W _f Strain energy stored in volumev _f of fibre - W _m Strain energy stored in a volumev _m of matrix - W _m Shear strain energy stored in a volumev _m of matrix - W _m Extensional strain energy stored in a volumev _m of matrix - w _rm Shear strain energy stored in the matrix inr ₀rR - w _f Extensional strain energy stored in a single fibre - x Distance along fibre from end of fibre - Defined in Equation 12 - Defined in Equation 2 - ^* Defined in Equation A2 - Extensional (longitudinal) strain - _c, _f, _m Extensional loss factor of composite, fibre, and matrix, respectively - _Gm Shear loss factor of matrix - Polar angle measured in a plane perpendicular to fibre axis - ¯gs _c,¯gs _f,¯gs _m Average longitudinal stress in composite, fibre, and matrix, respectively - _f Longitudinal stress in fibre - Shear stress in matrix - Defined in Equation 27     

Creep strength of discontinuous fibre composites

A unidirectional, discontinuous fibre composite is considered under conditions of steady state creep in the direction of reinforcement. The composite consists of noncreeping, discontinuous, perfectly aligned, uniformly distributed fibres which are perfectly bonded to a matrix obeying a power relation between stress and strain rate. Expressions for the interface stress, the creep velocity profile adjacent to the fibres and the creep strength of the composite are derived. Previous results for the creep strength,σ _c obtained for composites of the same type are briefly reviewed and compared with the present result. It is shown that all results reduce to the same general expression $$\sigma _c = \alpha V_{f^{\sigma _0 } } \left( {\frac{{\dot \in }}{{\dot \in _{0 } }}} \right)1/n_{\rho ^{1 + 1/n} }$$ in whichρ is the fibre aspect ratio, \(\dot \in\) is the composite creep rate,V _f is the fibre volume fraction,σ ₀,ε ₀ andn are the constants in the matrix creep law. The creep strength coefficient α is found to be very weakly dependent onV _f and practically independent ofn whenn is greater than about 6.     

The effect of aspect ratio on toughness in composites

Much information now exists on factors affecting toughness in composites. Theoretical expressions for fracture energy also abound, in response to the many factors that have been identified as contributing to toughness in fibre reinforced materials. This material is reviewed from the point of view of the effect of aspect ratio on toughness. Expressions relating fracture energy to aspect ratio are derived and compared with experimental data. It is shown that in many cases aspect ratio should be as large as possible. There are a few cases, however, where the aspect ratio should be as close to the critical value as possible.     

Effect of fibre misalignment on the fracture behaviour of fibre-reinforced composites

Deviations from ideal parallel packing in a unidirectional fibre-reinforced composite affect its resistance to splitting. In order to relate, quantitatively, the failure processes to such misorientation, it is necessary to characterize the departure from ideality and to measure the resistance to failure. Experimental observations are presented relating to: (i) a tendency for the carbon fibres in a tow to group into bundles that deviate somewhat from being parallel with each other, and (ii) the fracture toughness for the splitting of several imperfectly aligned composites. Statistical representations are offered for quantifying or modelling the degree of misalignment.     

Effect of fibre misalignment on fracture behaviour of fibre-reinforced composites

When a matrix crack encounters a fibre that is inclined relative to the direction of crack opening, geometry requires that the fibre flex is bridging between the crack faces. Conversely, the degree of flexing is a function of the crack face separation, as well as of (1) the compliance of the supporting matrix, (2) the crossing angle, (3) the bundle size, and (4) the shear coupling of the fibre to the matrix. At some crack face separation the stress level in the fibre bundle will cause it to fail. Other bundles, differing in size and orientation, will fail at other values of the crack separation. Such bridging contributes significantly to the resistance of the composite to crack propagation and to ultimate failure. The stress on the composite needed to produce a given crack face separation is inferred by analysing the forces and displacements involved. The resulting model computes stress versus crack-opening behaviour, ultimate strengths, and works of failure. Although the crack is assumed to be planar and to extend indefinitely, the model should also be applicable to finite cracks.Glossary of Symbols a radius of fibre bundle - C 2 _f /aE _f - ^* critical failure strain of fibre bundle - _b bending strain in outer fibre of a bundle - _c background strain in composite - _f axial strain in fibre - _s strain in fibre bundle due to fibre stretching = _f - () strain in composite far from crack - E Young's modulus of fibre bundle - E _c Young's modulus of composite - E _f Young's modulus of fibre - E _m Young's modulus of matrix - f() number density per unit area of fibres crossing crack plane in interval to + d - F total force exerted by fibre bundle normal to crack plane - F _s component of fibre stretching force normal to crack plane - F _b component of bending force normal to crack plane - G _m shear modulus of matrix - h crack face opening relative to crack mid-point - h _m matrix contraction contribution to h - h _f fibre deformation contribution to h - h _max crack opening at which bridging stress is a maximum - I moment of inertia of fibre bundle - k fibre stress decay constant in non-slip region - k ₀ force constant characterizing an elastic foundation (see Equation 7) - L exposed length of bridging fibre bundle (see Equation 1a) - L _f half-length of a discontinuous fibre - m, n parameters characterizing degree of misalignment - N number of bundles intersecting a unit area of crack plane - P _b bending force normal to bundle axis at crack midpoint - P _s stretching force parallel to bundle axis in crack opening - Q() distribution function describing the degree of misalignment - s _f fibre axial tensile stress - s _f ^* fibre tensile failure stress - S stress supported by totality of bridging fibre bundles - S _max maximum value of bridging stress - v fibre displacement relative to matrix - v elongation of fibre in crack bridging region - u _coh non-slip contribution to fibre elongation - U fibre elongation due to crack bridging - v overall volume fraction of fibres - v _f volume fraction of bundles - v _m volume fraction matrix between bundles - w transverse deflection of bundle at the crack mid-point - x distance along fibre axis, origin defined by context - X distance between the end of discontinuous fibre and the crack face - X ^* threshold (minimum) value of X that results in fibre failure instead of complete fibre pullout - y displacement of fibre normal to its undeflected axis - Z() area fraction angular weighting function - tensile strain in fibre relative to applied background strain - ^* critical value of to cause fibre/matrix debonding - angle at which a fibre bundle crosses the crack plane - (k ₀/4EI)^1/4, a parameter in cantilever beam analysis - v_m Poisson's ratio of matrix - L (see Equation 9) - shear stress - _* interlaminar shear strength of bundle - _d fibre/matrix interfacial shear strength - _f frictional shear slippage stress at bundle/matrix interface - angular deviation of fibre bundle from mean orientation of all bundles - angle between symmetry axis and crack plane     

Computational assessment of the influence of load ratio on fatigue crack growth in fibre-reinforced metal matrix composites

A three-dimensional finite element model of a composite tensile specimen consisting of a Ti–6Al–4V matrix reinforced with unidirectional, continuous SiC fibres under cyclic loading has been developed. The model includes the fibre/matrix morphology, with the interface interaction being governed by the Coulomb friction law. The influence of the applied load ratio on the true crack-tip load ratio has been investigated for three different applied load ratios. The results from the model show that due to a combination of thermal residual stresses from processing and fibre bridging, the crack-tip load ratio becomes independent of the applied load ratio after a small amount of crack growth. With the fatigue threshold depending strongly on the load ratio, crack arrest occurs at a later stage than would be predicted from the applied load ratio.     

The effect of pre-softened wood chips on wood fibre aspect ratio and mechanical properties of wood–polymer composites

The objective of this work was to study the effect of chemical pre-treatment and moisture content of wood chips on the wood particle aspect ratio after compounding in a twin-screw extruder and on the mechanical properties of wood–polymer composites (WPCs). Composites with 50 wt.% wood content were manufactured using pre-treated and untreated wood chips. The effect of wood moisture content on composite properties was studied by using dried and undried wood chips. The mechanical properties and fracture surfaces of the composites as well as the microstructure and aspect ratio of wood particles after compounding were studied. The highest wood particle aspect ratio after extrusion was achieved by using pre-treated, undried wood chips as raw material. The chemical pre-treatment was found to enhance the defibration of wood chips as well as the mechanical properties of the composites.     

The weather and its influence on the creep of glass fibre-reinforced cement composites

This paper describes an unusual programme of long-term creep tests on glass-fibre reinforced cement (GRC) boards. The specimens were mounted out-of-doors and loaded in tension. The deformations were monitored continuously by means of special weatherproof extensometers. The recording system is shown to operate in a reliable and consistent manner. The effects of weather and of stress can be separated by comparing the responses of stressed and unstressed specimens. Humidity variations have a dominant effect on the results, but a numerical relationship between humidity and strain remains to be found. Stress causes strains which follow well-defined creep curves once the effects of weather have been allowed for. The experiments are continuing.     

Analysis of fibre wrinkling during squeezing flows of fibre-reinforced composites

An analysis of the stability of squeezing flows between flat plates (consolidation flows) of viscous liquids reinforced by continuous fibres is presented. The ideal linear fibre-reinforced fluid model is used to model the composite as an incompressible Newtonian fluid reinforced with inextensible fibres. The development of small fibre wrinkles initially present in the preimpregnated plies is analysed using linear stability theory. It is shown that when the flows are lubricated by resin rich layers, two perturbation modes are possible. In the first mode, the wrinkles are of the same form throughout the thickness of the sample while in the second mode they vary linearly with distance from the platens. In both cases the stability depends on the normal components of the applied stress. If the only traction acting in addition to hydrostatic pressure is that due to the squeezing force then the first perturbation mode is stable. This prediction is in agreement with experimental results.     

Effect of fibre volume on tensile properties of real unidirectional fibre-reinforced composites

A simple theoretical model is proposed to account for the effect of high fibre loading on the tensile properties of real, unidirectionally reinforced fibre composites. Based on the reduction of interfacial surfaces due to fibre-fibre interaction, a modification to the rule of mixtures is proposed. The experimentally observed non-linear variation of tensile strength with fibre volume can be predicted by the modified rule. Experimental data from the literature are used to validate and verify the model and show good agreement with the predictions.     

A probabilistic theory for the strength of discontinuous fibre composites

The strength of discontinuous fibre-reinforced composites is often reduced due to local stress concentrations at large fibre-end-gaps. A theoretical prediction of the strength of unidirectional fibre composites is performed based upon a probabilistic model of the fibre configuration. This work further develops the concepts of Bader, Chou and Quigley, and Fukuda and Chou. A limiting case of the present analysis shows good agreement with the results of Smith. Emphases are placed on the effect of matrix stress transfer properties including matrix plasticity. For a matrix deforming elastically, the strength is reduced as the composite size (N) increases. As compared with the rule-of-mixtures prediction for continuous fibre composites with identical fibre volume fraction, the reduction is shown to be proportional to (In N)^–P , with the exponent P being between 0.5 and 1 for two-dimensional composites and between 0.25 and 0.5 for three-dimensional composites. For a matrix deforming plastically, the local stress concentrations are reduced. Based upon the analytical expression of the local load sharing rule for a plastically deformed matrix, the composite strength is shown to approach the modified rule-of-mixtures of Kelly and Tyson as the matrix yield stress decreases.This work was done on leave from Applied Mechanics Section, Central Research Laboratories, Sumitomo Metal Industries, Ltd., Nishinagasuhumdori, Amagasaki, Japan.     

Numerical simulation of the effects of volume fraction,aspect ratio and fibre length distribution on the elastic and thermoelastic properties of short fibre composites

In this paper a new numerical procedure by Gusev, for predicting the elastic and thermoelastic properties of short fibre reinforced composites, is described. Computer models, comprising 100 non-overlapping aligned spherocylinders, were generated using a Monte Carlo procedure to produce a random morphology. Periodic boundary conditions were used for all the generated structures. Where necessary, the generated microstructures were based on measurements of real materials: for example a measured fibre length distribution was used to seed the Monte Carlo generator to produce a computer model with an equivalent fibre length distribution (FLD). The generated morphologies were meshed using an intelligent 3 dimensional meshing technique, allowing the elastic and thermo-elastic properties of the microstructures to be calculated. The numerical predictions were compared with those from three commonly used micromechanical models, namely those attributed to Halpin/Tsai, Tandon/Weng and Cox (shear lag). Firstly, the effect of volume fraction and aspect ratio were investigated, and the numerical results were compared and contrasted with those of the chosen models. Secondly, the numerical approach was used to investigate what effect a distribution of fibre lengths, as seen in real materials, would have on the predicted mechanical properties. The results were compared with simulations carried out using a monodispersed fibre length, to ascertain if the distribution of lengths could be replaced with a single length, and whether this length corresponded to a particular characteristic of the distribution, for example the first moment or average length.