The stiffness and strength of a polyamide thermoplastic reinforced with glass and carbon fibres

It has been established that the optimum degree of mechanical property enhancement by fibre reinforcement of a typical thermoplastic material (polyamide 6.6) is achieved if comparatively long fibres are used, the fibre length required being determined by the properties of the interface between the fibre and the thermoplastic matrix. The extent of stiffness improvement at low strains is described by simple modifications to the law of mixtures to allow for fibre orientation and length. The strength enhancement is limited by an embrittlement effect which reduces the strain to fracture as the stiffness of the composite is improved. The cause of this effect has been identified as matrix crack formation at the ends of the reinforcing fibres. At strains of between 0.5% and 1.0%, according to fibre type, length andV _f, cracks form at the tips of the longest fibres aligned in the straining direction. Subsequently as the strain is increased more cracks form progressively at the ends of shorter and/or more misaligned fibres. It has been shown that initially this cracking can be accommodated by load transfer to adjacent fibres which bridge the cracked region. Final failure occurs when the extent of cracking across the weakest section reaches a critical level when the surrounding fibres and matrix can no longer support the increasing load.     

Suppression of crack growth in hybrid fibre composites

A theoretical analysis based on the assumed form of the strain field surrounding a crack bridged by reinforcing elements has been used to examine the growth of a crack propagating transversely to the fibres in hybrid fibre composites. An intermingled carbon fibre/glass fibre polymer matrix system has been considered. Two situations have been investigated. In the first of these the effect of the addition of carbon fibres on the development of cracks resulting from the failure of the glass fibres by stress corrosion has been studied. The analysis indicates that crack growth can be severely inhibited by a 5% volume fraction of type III carbon fibres. The analysis has been used also to investigate the process by which strong high failing strain glass fibres inhibit the growth of cracks caused by the fracture of localized clusters of low failing strain carbon fibres. The predictions of this analysis agree with existing experimental data on glass fibre/carbon fibre hybrids.     

Tensile failure of pultruded glass-polyester composites under superimposed hydrostatic pressure

The tensile properties of five types of pultruded 0·52 V_f glass-fibre-polyester rods were investigated by extending waisted round specimens at atmospheric and superimposed hydrostatic pressures, −H, to 300 MPa. The maximum principal stress at fracture, −700 MPa, decreased, with the superimposition of −H, approximately by its magnitude. As −H increased the failure surfaces became flatter, the amount of fibre pull-out decreased and transverse cracks became shorter or were eliminated. Glass fibres in the failure surfaces were resin free, and failure of the glass fibre bundles appeared to control the fracture process in the entire pressure range for all materials. The decrease in maximum principal tensile stress with increasing −H indicates that the glass fibre failure process is not controlled by a critical tensile stress. Failure criteria are discussed, and in the tension-compression-compression octant of stress space the relevant criteria appear to be strain energy and deviatoric tensile stress, strain and strain energy for these GRPs and glass itself.     

Crack bridging and fibre pull-out in polyethylene fibre reinforced epoxy resins

An investigation has been undertaken of the stress distributions in high-performance polyethylene fibres bridging cracks in model epoxy composites. The axial fibre stress has been determined from stress-induced Raman band shifts and the effect of fibre surface treatment has been followed using untreated and plasma-treated polyethylene fibres. It is found that when the specimen is cracked, the fibres do not break and stress is transmitted from the matrix to the fibre across the fibre/matrix interface. A debond propagates along the fibre/matrix interface accompanied by friction along the debonded interface. The axial stress distributions in the fibres can be analysed using a partial-debonding model based upon shear-lag theory and it is found that the maximum interfacial shear stress at the bond/debond transition is a function of the debond length. The debonding process has been modelled successfully in terms of the interfacial fracture energy-based criterion developed by Hsueh for the propagation of a debond along a fibre/matrix interface accompanied by constant friction along the interface.     

Strain-sensitive Raman spectroscopy and electrical resistance of carbon nanotube-coated glass fibre sensors

This paper presents the development of glass fibres coated with nanocomposites consisting of carbon nanotubes (CNTs) and epoxy. Single glass fibres with different CNT content coating are embedded in a polymer matrix as a strain sensor for composite structures. Raman spectroscopy and electrical response of glass fibres under mechanical load are coupled for in situ sensing of deformation in composites. The results show that the fibres with nanocomposite coating exhibit efficient stress transfer across the fibre/matrix interface, and these with a higher CNT content are more prone to fibre fragmentation at the same matrix strain. A relationship between the fibre stress and the change in electrical resistance against the fibre strain is established. The major finding of this study has a practical implication in that the fibres with nanocomposite coating can serve as a sensor to monitor the deformation and damage process in composites.     

Effects of inter-fibre spacing and matrix cracks on stress amplification factors in carbon-fibre/epoxy matrix composites. Part I: planar array of fibres

When the loading on a composite is sufficient to cause fracture of an individual fibre, the resulting stress amplification in the adjacent intact fibres may be large enough to cause failure of these fibres. In this work, 3D elasto-plastic finite element analysis was used to investigate the effect of inter-fibre spacing on the stress amplification factor in a composite comprising a planar array of fibres. A Progressional Approach was used in the FE analysis to simulate the constituent non-linear processes associated with the generation of thermal residual stresses from fabrication, the fibre fracture event and the subsequent initiation and propagation of conical matrix cracks induced with incremental tensile loading. As the inter-fibre spacing increases, the effect of fibre fracture on the stress distribution in the neighbouring intact fibres is reduced, whereas the effect on the matrix material is increased, thereby inducing localised yielding. The presence of a conical-shaped matrix crack was found to increase both the stress amplification factor and the positively affected length in neighbouring fibres. For a large inter-fibre spacing, a longer matrix crack is required to obtain good agreement with LRS measurements of fibre stress.     

Evaluation of fibre bridging stress of short fatigue cracks in SCS-6/Ti-15-3 composite

Single‐edge notched specimens of a unidirectional SiC long fibre reinforced titanium alloy, were fatigued under four point bending. The propagation behaviour of short fatigue cracks from a notch was observed on the basis of the effects of fibre bridging. The branched fatigue cracks were initiated from the notch root. The fatigue cracks propagated only in the matrix and without fibre breakage. The crack propagation rate decreased with crack extension due to the crack bridging by reinforced fibres. After fatigue testing the loading and residual stresses in the reinforced fibres were measured for the arrested cracks by the X‐ray diffraction method. The longitudinal stresses in the reinforced fibres were measured using high spatial resolution synchrotron radiation. A stress map around the fatigue cracks was then successfully constructed. The longitudinal stress decreased linearly with increasing distance from a location adjacent to the wake of the matrix crack. This region of decreasing stress corresponded to the debonding area between the fibre and the matrix. The interfacial frictional stress between the matrix and the fibre could be determined from the fibre stresses. The bridging stress on the crack wake was also measured as a function of a distance from a notch root. The threshold stress intensity factor range, corrected on the basis of the shielding stress, was similar to the propagation behaviour of the monolithic matrix. Hence the main factor influencing the shielding effect in composites is fibre bridging.     

Reference stress approach for predicting creep deformation of metal matrix composites

Abstract

A sound, mechanics based approach, using the reference stress concept, has been provided to allow the effects of volume ratio, fibre aspect ratio, and fibre spacing on the creep behaviour of uniaxial metal matrix composites to be quickly assessed. It is shown that fibres are much more effective than particles in reducing creep deformations. In addition, volume ratio and fibre aspect ratio have a large effect on creep properties, while fibre spacing has a relatively small effect. The existence of cracks at the ends of fibres is shown to reduce seriously the effectiveness of the reinforcement. The creep properties for loading in transverse directions are much lower than for loading in longitudinal directions.

MST/2059     

Non-linear compression stress-strain curve of pitch-based high modulus carbon fibre composites and structural responses

The longitudinal compression behaviour of unidirectional composites is studied to understand the role of the fibre compressive property in deformation and failure by systematically varying the tensile modulus of reinforcing high modulus carbon fibre. As the composites deform, their softness increases with increasing compressive strain, and the loading path is traced back when the load is removed. The intensity of softening is correlated to the fibre's tensile modulus and possible softening mechanisms are discussed in conjunction with fibre and matrix properties. Further, it is investigated how the non-linear stress-strain relation affects the stress and strain distributions and deformation when plates fabricated from these fibres are tested by the three-point bending test.     

PROGRESSIVE MICROCRACKING IN UNIDIRECTIONAL BRITTLE MATRIX COMPOSITES

Abstract

In this work we investigate the initiation of microcracking in a unidirectional Nicalon^TMfibre, glass-ceramic (CAS) matrix composite under flexural loading. We find that damage develops and grows in these composites as a continual initiation of new transverse cracks in a more-or-less random manner, as well as growth of existing cracks, within the matrix. Initial cracks are usually of limited extent, being stopped when they encounter the nearest fibres, in a mode idealized by the so-called full-cell cracking model. Each new crack that initiates under increasing load yields another data point, provided the precracked state of stress and crack geometry at the initiation site can be determined. The latter conditions are satisfied since the zone of influence of each crack can be determined analytically and the full-cell cracking mode geometry receives at least partial validation. Analysis is accomplished by use of an axisymmetric micro mechanical model based on Reissner's variational principle in which variable fibre spacing can be recognized. In a semi-empirical failure model, the matrix axial stress just prior to crack initiation is computed and assumed to act on an unbounded matrix containing a penny-shaped crack having a radius dictated by the local fibre spacing, s. This model is geometrically appropriate for the case of large localized fibre spacings. Statistical information on s and the critical matrix mode I stress intensity factor is presented, and the average value seems to be consistent with expectation based upon measurements on monolithic samples of the matrix material. Application of the micromechanical model shows that, at least for the predominant range of s, sufficient energy is available to mobilize annular matrix cracks at stresses predicted by the semi-empirical model, and also that interfacial crack deflection is expected rather than fibre penetration. In accordance with this observation, very few fibre breaks were seen in the test programme. Finally, some comments regarding the practical consequences of this work are offered and the conventional view of a constant microcracking stress level in a steady-state model is dismissed, at least for the class of composites considered.     

In situ observations of microscale damage evolution in unidirectional natural fibre composites

Synchrotron X-ray tomographic microscopy (XTM) has been used to observe in situ damage evolution in unidirectional flax fibre yarn/polypropylene composites loaded in uniaxial tension at stress levels between 20% and 95% of the ultimate failure stress. XTM allows for 3D visualization of the internal damage state at each stress level. The overall aim of the study is to gain a better understanding of the damage mechanisms in natural fibre composites. This is necessary if they are to be optimized to fulfil their promising potential. Three dominating damage mechanisms have been identified: (i) interface splitting cracks typically seen at the interfaces of bundles of unseparated fibres, (ii) matrix shear cracks, and (iii) fibre failures typically seen at fibre defects. Based on the findings in the present study, well separated fibres with a low number of defects are recommended for composite reinforcements.     

A MODEL TO PREDICT THE FATIGUE LIFE OF FIBRE-REINFORCED TITANIUM MATRIX COMPOSITES UNDER CONSTANT AMPLITUDE LOADING

A model based on micro-mechanical concepts has been developed for predicting fatigue crack growth in titanium alloy matrix composites. In terms of the model, the crack system is composed of three zones: the crack, the plastic zone and the fibre. Crack tip plasticity is constrained by the fibres and remains so until certain conditions are met. The condition for crack propagation is that fibre constraint is overcome when the stress at the location of the fibre ahead of the crack tip attains a critical level required for debonding. Crack tip plasticity then increases and the crack is able to propagate round the fibre. The debonding stress is calculated using the shear lag model from values of interfacial shear strength and embedded fibre length published in the literature. If the fibres in the crack wake remain unbroken, friction stresses on the crack flanks are generated, as a result of the matrix sliding along the fibres. The friction stresses (known as the bridging effect) shield the crack tip from the remote stress, reducing the crack growth relative to that of the matrix alone. The bridging stress is calculated by adding together the friction stresses, at each fibre row bridging the crack, which are assumed to be a function of crack opening displacement and sliding distance at each row. The friction stresses at each fibre row will increase as the crack propagates further until a critical level for fibre failure is reached. Fibre failure is modelled through Weibull statistics and published experimental results. Fibre failure will reduce the bridging effect and increase the crack propagation rate. Calculated fatigue lives and crack propagation rates are compared with experimental results for three different materials (32% SCS6/Ti-15-3, 32% and 38% SCS6/Ti-6-4) subjected to mode I fatigue loading. The good agreement shown by these comparisons demonstrates the applicability of the model to predict the fatigue damage in Ti-based MMCs.     

Fatigue behaviour related to interface modification during load cycling in ceramic-matrix fibre composites

Ceramics reinforced with continuous fibres exhibit delayed failure under pulsating load. A micromechanical model describing the fatigue effects is proposed. It is based on a decrease in shear stress at the fibre/matrix interfaces, as a result of interfacial wear caused by see-saw sliding. The main features of this model are as follows. During the first load cycle, the material exhibits multiple matrix cracking and some fibre breaks. The system is then a serial set of matrix cracks, each of them bridged by a parallel set of intact or broken fibres. During subsequent cycles the interfacial shear stress decreases, leading to an increase in the failure probability of the bridging fibres. These changes give both a reduction of stiffness and a widening of the hysteresis loops. For a critical fraction of broken bridging fibres, instability occurs and the specimen fails, thus defining the lifetime. The higher the applied load, the higher is the initial damage on the first cycle and the faster the instability condition is reached. For peak stresses that are lower, but still higher than the proportionality limit, the material also changes but no failure occurs (up to 10⁶ cycles), indicating that the interfacial shear stress decreases to a non-zero value; this limiting value controls the fatigue limit in the lifetime diagram.     

Analysis of cellulose networks by the finite element method

Paper can be regarded as a network of cellulosic fibres, especially at lower basis weights. When the elastic behaviour of paper sheets is modelled, it is normally essential to know or to assume how the stresses (and strains) are distributed at the fibre level. This article presents an attempt to estimate how the stresses are transferred throughout a simple fibre network using the finite element method (FEM). Attention is mainly focused on the axial fibre stress distribution when the network is uniaxially deformed. The presence of fibre ends is found to induce local stress increases (stress concentrations) in the deformed network, which presumably have a bearing on the ultimate properties of the sheet. The influence of the properties of the bonds between crossing fibres on the mechanical properties is also investigated. It is noted that the bond stiffness has no significant effect on the stress transfer between fibres provided that the stiffness is above a critical value. Below this value the stress transfer deteriorates rapidly.     

Influence of interfacial stress transfer on fatigue crack growth in SiC-fibre reinforced titanium alloys

An important damage mechanism during fatigue of unidirectional SiC-fibre reinforced titanium alloys is the formation of matrix cracks transverse to the fibre direction. Due to the relatively low fibre/matrix bond strength these matrix cracks initially do not break the fibres, so that matrix cracks bridged by fibres develop. It is shown experimentally, that the strong drop in fatigue strength is caused by the formation of a bridged crack of a critical size and the crack propagation rate (da/dN) for a single load level has been determined. A prediction of da/dN on the basis of finite element calculation of the stress intensity factor range of the bridged matrix crack ΔK_m and the ΔK_m–da/dN relationship of the used titanium alloy (Timetal 834) has been performed. Calculation of ΔK_m assuming a negligible fibre/matrix bond strength and considering shear load transfer at the fibre/matrix interface due to Coulomb friction (coefficient of friction μ=0.5 and μ=0.9) led to a large discrepancy between the measured and predicted crack growth rate. It can be concluded, that the assumed conditions of stress transfer at the fibre/matrix interface neglecting bonding is the reason for this discrepancy.     

Local stress concentration and the prediction of tensile failure in unidirectional composites

The aim of this paper is to present a new representation of the tensile failure of a composite material which accounts for the normal stress supported by the matrix and allows a study of the influence of constituent material properties and fibre volume fraction on the stress-concentration factors. This is done by micromechanical analysis which allows the stress and strain in the fibres and the matrix to be related to the applied stress or strain on the composite. Stress-concentration factors are calculated in the composite transverse section and are found to be smaller than previously published analytical solutions. The difference is essentially due to the normal stress supported by the matrix which is neglected by the shear-lag analysis but is taken into account in our model. The tensile strength is calculated firstly by numerical simulations and secondly by Batdorf's methodology which addresses the formation and propagation of fibre fractures. Comparisons with experimental measures are satisfactory.     

Deformation micromechanics in high-modulus fibres and composites

It is demonstrated that Raman spectroscopy can be used to study the deformation micromechanics of aramid fibres and of the fibres in a model single-fibre composite with an epoxy resin matrix. It is shown that the peak position of the 1610cm⁻¹ aramid Raman band shifts to lower frequency under the action of stress or strain as a result of the macroscopic deformation leading to direct stretching of the aramid molecules. The strain-induced band shifts can be used to follow the deformation of the aramid fibres in a composite matrix. This allows the distribution of strain to be mapped along a fibre, and it is shown that the behaviour is consistent with that predicted by the classical shear-lag analysis. It is also demonstrated that the interfacial shear stress can be calculated from the distribution of strain along the fibre. Finally, the technique is extended to measure the strain in fibres in a single-fibre composite which are aligned at an angle to the tensile axis. In this case it is shown that the strain in the centre of the fibres is identical to that predicted by classical elasticity theory.     

Fibre interactions in two-dimensional composites by micro-Raman spectroscopy

In the study of fracture processes in composite materials, the interactions between broken and intact fibres are of critical importance. Indeed, the redistribution of stress from a failed fibre to its unfailed adjacent neighbours, and the stress concentration induced in these, determine the extent to which a break in one fibre will cause more breaks in neighbouring fibres. The overall failure pattern is a direct function of the stress concentration factors. In this paper we use laser micro-Raman spectroscopy to study the extent of stress transfer and redistribution caused by fibre fracture in two-dimensional Kevlar 149 based microcomposites. The strain along the fibres was mapped at different levels of load, and specimens with different inter-fibre distances were used to study the fibre content effect. The experimental stress concentration factors were compared with values predicted from various theoretical models. The stress concentration factors generally agreed with those literature models that include interfibre distance and matrix effects. The overall failure pattern was found not to be a direct function of the stress concentration factors in this system, as fracture propagates from fibre to fibre even at large interfibre distances, and is apparently accompanied by relatively low values of the stress concentration factors. The critical cluster size, beyond which final fracture of the composite occurs in a catastrophic manner, was found to be larger than five adjacent fibre breaks in the present system, for all interfibre distances studied.Visiting Stein Fellow at Drexel University, July-September 1994.     

Stress transfer in the fibre fragmentation test: Part III Effect of matrix cracking and interface debonding

A theoretical stress analysis has been developed for the fibre fragmentation test in the presence of matrix cracks at sites of fibre breaks. The strain energy release rates for both matrix cracking and interface debonding are calculated for a carbon fibre/epoxy matrix composite. By comparing these strain energy release rates with the corresponding specific fracture resistances, the competition between matrix crack growth and interface debonding has been studied. The distributions of fibre axial stress and interfacial shear stress obtained from the present analysis show that the matrix crack substantially reduces the efficiency of stress transfer from the matrix to the fibre. This revised version was published online in November 2006 with corrections to the Cover Date.     

Properties of glass fibre cement — the effect of fibre length and content

The properties of glass fibre reinforced cement composites (grc) containing alkali-resistant fibres of lengths 10 to 40 mm and volume fractions 2 to 8% have been studied. At 28 days the optimum properties of the composite were achieved with 6 vol % fibre addition. These were 4 to 5 times the bending strength, 3 to 4 times the tensile strength and 15 to 20 times the impact strength of the unreinforced cement paste. Further increase in the fibre content increases the porosity of the composite resulting in the lowering of bending and tensile strengths. The stress and strain of the composite at matrix cracking increased with increasing fibre contents. No significant improvements in the modulus of the composite were observed over the range of fibre additions investigated. The trends in the properties of grc as affected by the variations in volume fraction and length of the fibre, and environmental conditions of curing of the composites, are qualitatively related to the degree of cement hydration, changes in porosity of the composites and fibre/matrix interfacial effects. The properties of grc change with time, (strengths tend to decrease) and long term studies are in progress.