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.     

Stress disturbances arising from cut fibre and matrix in unidirectional metal matrix composites calculated by means of a modified shear lag analysis

A useful method to calculate stress disturbances arising from cut fibres is the so-called shear lag analysis, in which it is assumed that fibres act to carry tensile stress without transferring applied stress to the matrix, and the matrix acts to transfer stress to the fibres without carrying tensile stress. This assumption gives a limit for application. In the present work, with unidirectional metal matrix composites in mind, the usual two-dimensional shear lag analysis was modified to express the situation where both fibres and matrix act to carry applied stress and also to transfer stress. By using this modified method, tensile strain concentration in the fibres and matrix adjacent to cut fibres and matrix, and shear stresses at the interface between fibres and matrix, were calculated for some examples.     

Tensile strength of fibre-reinforced metal matrix composites with non-uniform fibre spacing

The influence of non-uniform fibre spacing on the strength of unidirectional fibre-reinforced metal matrix composites was studied by means of a Monte-Carlo computer simulation experiment. The influence of yield stress of the matrix and scatter of the fibre strength on the strength of composites were also studied for both uniform and non-uniform fibre spacings. It was demonstrated that (1) the strength of composites with non-uniform fibre spacing is lower than that with uniform spacing due to the high stress concentration arising from the breakage of fibres, and (2) the reduction in strength of composites due to the non-uniformity increases with increasing scatter of fibre strength. For both cases of uniform and non-uniform spacings, the following tendencies were observed : (a) the strength of composites increases but then decreases with increasing yield stress of matrix, (b) it is very sensitive to yield stress of the matrix when the scatter of fibre strength is large but not when it is small, and (c) it decreases but then increases with increasing scatter of fibre strength when the yield stress of the matrix is high, while it decreases monotonically with increasing scatter of fibre strength when the yield stress is low.     

Failure mechanisms and fracture energy of hybrid materials

A shear-lag model of hybrid materials is developed. The model represents an alternating arrangement of two types of aligned linear elastic fibres, embedded in a linear elastic matrix. Fibre and matrix elements are taken to fail deterministically when the axial and shear stresses in them reach their respective strengths. An efficient solution procedure for determining the stress state for arbitrary configurations of broken fibre and matrix elements is developed. Starting with a single fibre break, this procedure is used to simulate progressive fibre and matrix failure, up to composite fracture. The effect of (1) the ratio of fibre stiffnesses, and (2) the ratio of the fibre tensile strength to matrix shear strength, on the composite failure mechanism, fracture energy, and failure strain is characterised. Experimental observations, reported in the literature, of the fracture behaviour of two hybrid materials, viz., hybrid unidirectional composites, and double network hydrogels, are discussed in the framework of the present model.     

Cavitation instabilities between fibres in a metal matrix composite

Short fibre reinforced metal matrix composites (MMC) are studied here to investigate the possibility that a cavitation instability can develop in the metal matrix. The high stress levels needed for a cavitation instability may occur in metal–ceramic systems due to the constraint on plastic flow induced by bonding to the ceramics that only show elastic deformation. In an MMC the stress state in the metal matrix is highly non-uniform, varying between regions where shear stresses are dominant and regions where hydrostatic tension is strong. An Al–SiC whisker composite with a periodic pattern of transversely staggered fibres is here modelled by using an axisymmetric cell model analysis. First the critical stress level is determined for a cavitation instability in an infinite solid made of the Al matrix material. By studying composites with different distributions and aspect ratios of the fibres it is shown that regions between fibre ends may develop hydrostatic tensile stresses high enough to exceed the critical level for a cavitation instability. For cases where a void is located in such regions it is shown that unstable cavity growth develops when the void is initially much smaller than the highly stressed region of the material.     

Silicon carbide (NicalonTM) fibre-reinforced borosilicate glass composites: mechanical properties

The objective of this study was to assess the applicability of an extrinsic carbon coating to tailor the interface in a unidirectional NicalonTM–borosilicate glass composite for maximum strength. Three unidirectional NicalonTM fibre-reinforced borosilicate glass composites were fabricated with different interfaces by using (1) uncoated (2) 25 nm thick carbon-coated and (3) 140 nm thick carbon coated Nicalon fibres. The tensile behaviours of the three systems differed significantly. Damage developments during tensile loading were recorded by a replica technique. Fibre–matrix interfacial frictional stresses were measured. A shear lag model was used to quantitatively relate the interfacial properties, damage and elastic modulus. Tensile specimen design was varied to obtain desirable failure mode. Tensile strengths of NicalonTM fibres in all three types of composites were measured by the fracture mirror method. Weibull analysis of the fibre strength data was performed. Fibre strength data obtained from the fracture mirror method were compared with strength data obtained by single fibre tensile testing of as-received fibres and fibres extracted from the composites. The fibre strength data were used in various composite strength models to predict strengths. Nicalon–borosilicate glass composites with ultimate tensile strength values as high as 585 MPa were produced using extrinsic carbon coatings on the fibres. Fibre strength measurements indicated fibre strength degradation during processing. Fracture mirror analysis gave higher fibre strengths than extracted single fibre tensile testing for all three types of composites. The fibre bundle model gave reasonable composite ultimate tensile strength predictions using fracture mirror based fibre strength data. Characterization and analysis suggest that the full reinforcing potential of the fibres was not realized and the composite strength can be further increased by optimizing the fibre coating thickness and processing parameters. The use of microcrack density measurements, indentation–frictional stress measurements and shear lag modelling have been demonstrated for assessing whether the full reinforcing and toughening potential of the fibres has been realized. This revised version was published online in November 2006 with corrections to the Cover Date.     

Theory of multiple fracture of fibrous composites

The theoretical stress-strain behaviour of a composite with a brittle matrix in which the fibre-matrix bond remains intact after the matrix has cracked, is described. From a consideration of the maximum shear stress at the fibre-matrix interface, the extent of fibre debonding and the crack spacing in a partially debonded composite are derived. The energetics of cracking and the conditions leading to an enhanced matrix failure strain are then discussed and, finally, the crack spacing expected in composites containing fibres isotropically arranged in two or in three dimensions is derived for the case of very thin and hence very flexible fibres.     

Investigation into stress transfer characteristics in alumina-fibre/epoxy model composites through the use of fluorescence spectroscopy

In composite materials, fibre/fibre interaction phenomena due to fibre failure are crucial in determining the composite fracture behaviour. Indeed, the redistribution of stress from a failed fibre to its intact neighbours, and stress concentration induced in the neighbouring fibres, determine the extent to which a break in one fibre will cause more breaks in others. In this paper, we have used fluorescence spectroscopy to study the stress transfer and redistribution induced by fibre fracture in two-dimensional Nextel-610 fibres/epoxy-resin micro-composites. The stress along the fibres was mapped at different load levels, and specimens with different inter-fibre distance were used to study the fibre content effect. The interfacial shear stress distribution along broken and intact fibres was derived by means of a balance of shear-to-axial forces argument. The experimental stress concentration factors (SCF) were smaller than values predicted from our model based on the cell assembly approach. As expected the 2D configuration allows access to the upper bound of the SCF in real composites. For the several specimens tested, a region of matrix yielding was observed behind the fibre fracture and no-debonding at the interface was detected. The measured SCF values agree well with those reported in recent study for carbon-fibre/epoxy model composites.     

MODELLING THE TENSILE FRACTURE BEHAVIOUR OF THE REINFORCING FIBRE YARNS IN CERAMIC MATRIX COMPOSITES

Abstract— Using experimentally determined data on fibre radius distributions, yarn geometry, matrix and fibre elastic moduli and frictional shear stress at the matrix/fibre interface (obtained by nano-indentation experiments), the failure probability of the composite fibre yarns (after matrix cracking) is estimated. Each fibre is divided into a fixed number of segments above and below the matrix crack. The failure probability on every segment of each fibre is computed using Weibull fibre strength statistics. A fibre is assumed to be broken when the cumulative failure probability for the complete yarn reaches a value of 0.5. The segment and fibre are then selected at "random", according to their individual failure probabilities. After fibre failure, the broken fibre can only carry the frictional load and the load drop is transferred to its neighbours according to their distances to the broken fibre. The remote stress is then modified to match again the cumulative failure probability of 0.5 and a new fibre is broken. This procedure is repeated until all the fibres are broken. In this way, it is possible to obtain the "characteristic" load carried by the yarn and its corresponding elongation. Fibre extraction and pull-out behaviour are also considered. The roles of different load-transfer laws (from global to highly localised) are examined. The model is applied to simulate the fracture tensile behaviour of individual yarns of SiC/SiC ceramic-matrix composites. The results are compared with those obtained from tensile experiments on SiC/SiC individual yarns. The computed fracture morphology, in terms of individual pull-out lengths, is also compared to the actual SEM fractography of a woven SiC/SiC composite.     

Matrix cracking with frictional bridging fibres in continuous fibre ceramic composites

Matrix cracking bridged by intact fibres, which debond from the matrix and then slip against the matrix in friction, has been analysed for unidirectional fibre-reinforced ceramic composites under tensile loading parallel to the fibre axis. The effect of bonding at the fibre-matrix interface, Poisson's effect of the fibre, and residual stresses were included in the analysis. Both the crack-opening displacement and the displacement of the composite due to interfacial debonding have been analytically related to the fibre bridging stress. The critical stress for matrix cracking was also analysed. The existing solutions can be recovered by considering a special case in the present generalized solution.     

Influences of interfacial bonding strength and scatter of fibre strength on tensile behaviour of unidirectional metal matrix composites

The influences of interfacial bonding strength and scatter of strength of fibres on tensile behaviour of unidirectional metal matrix composites, whose matrix has low yield stress in comparison to the strength of fibres, were studied using the Monte-Carlo simulation technique using two-dimensional model composites. The following results were found. The strength of composites increases with increasing bonding strength, especially when the bonding strength exceeds the shear yield stress of the matrix and then remains nearly constant. The strength of composites is very sensitive to bonding strength when the scatter of fibre strength is large, but not when it is small. The fracture mode varies from non-cumulative to cumulative with increasing scatter of fibre strength for both cases of weak and strong interfacial bondings. The fracture surface becomes irregular when bonding strength becomes low and scatter of fibre strength becomes large. The applicability of the Rosen and Zweben models and the rule of mixtures to predict the strength of composites was examined.     

Eigenspannung im mit gasdruckunterstütztem Feingussverfahren hergestellten langfaserverstärkten Aluminium‐Matrix‐Verbundwerkstoff

Residual Stress in Continuous Fibre Reinforced Aluminium Matrix Composites Prepared by Modified Investment Casting The residual stresses between matrix und fibres in the continuous γ‐Al₂O₃ fibre reinforced aluminium alloy (AlZn6Mg1Ag1) matrix composites prepared by modified investment casting were measured with x‐ray diffraction as well as simulated with FEM. It was indicated as expected that tensile residual stress exists in the Matrix und compressive residual in the fibre. The average value of the residual stress in both matrix and fibre in the composites is not very significant. However it is distributed very unevenly. Next to the interface between matrix and fibre there is a small zone in the matrix with relative great tensile residual stress. The effect of fibre volume percentage on the residual stress in the composite was also analysed. With increase of the fibre volume percentage the tensile residual stress in the matrix increases while the compressive residual stress in the fibre decreases. If the fibre volume percentage in the composite exceeds 65 %, the maximal tensile residual stress will reach the yield stress of the matrix alloy and local plastic deformation will occur.     

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.     

The durability of controlled matrix shrinkage composites

During fatigue of aligned fibre pultrusions, the flexural modulus decreases continuously when the applied stresses are tensile and directed along the fibres (R=0.1). In addition, the Poisson's ratio increases continuously, and so does the energy absorbed during the fatigue cycle. Holes in the specimens continuously increase in size in a direction at right angles to the applied stress, but change little in the stressing direction. These effects are enhanced by including compressive stresses in the cycle (R=–0.3) and are reduced by reducing the polymer cure shrinkage pressure. There are notable similarities between fatigue failure and compressive failure in aligned fibre composites, and evidence that matrix stresses are produced at right angles to the fibres, which are probably large enough to cause matrix fatigue failure. These observations lead to the conclusion that the fatigue failure may well originate from misaligned fibres, which generate off-axis stresses. These cause interface failure and polymer fragmentation, which can then lead to fibre failure (and thus composite failure) even when the applied stresses are always tensile.     

Correlation of injection moulding parameters with mechanical and morphological aspects of natural fibre reinforced thermoplastics

The mechanical behaviour of fibre reinforced composites depends – amongst other things – on the morphological structure. This in turn is greatly affected by the processing conditions. In this study a 10 weight % flax fibre reinforced high density polyethylene composite is prepared by extrusion compounding followed by injection moulding. The effect of injection temperature, speed and rotational screw speed on the morphology of fibres and matrix are studied and related to the tensile and impact behaviour of the composites. Results indicate that fibre length is easily affected by all parameters under consideration. Whereas a higher injection temperature allows the preservation of fibre length, an excessive increase in temperature, however, leads to their thermal degradation. Increased injection and rotational speeds further introduce excessive shear stresses on the fibre, causing their breakage, similarly leading to reduced mechanical performance. Matrix structure is mainly affected by the injection temperature, where its increase leads to the reduction in the degree of crystallinity and thus also a decrease in tensile strength. Other processing parameters prove to have minor effect on matrix morphology.     

The impact strength of fibre composites

Two models have been developed which predict the crack initiation energy, notched impact strength and unnotched impact strength of fibre composites. One is applicable to composites containing short fibres and the other to composites containing long fibres. Data obtained with randomly oriented short fibre composites were consistent with the one model. The other model has been verified using composites containing uniaxially oriented long fibres and long fibres oriented randomly in a plane. The success of the model demonstrates that the high notched impact strength with long fibres is due to the redistribution of stress away from the stress concentrating notch, the extra stress that can be held by the fibre relative to the matrix and the work required to pull fibres out of the matrix during crack propagation. The parameters which have been shown to control the fracture energy are composite modulus, fibre length, fibre volume fraction, effective fibre diameter, fibre tensile strength and the coefficient of friction during fibre pull-out from the matrix. The matrix toughness on the other hand usually has no effect at all for composites containing fibres randomly oriented in two dimensions and only a minor effect in exceptional cases. The shear strength of the fibre-matrix bond has only an indirect effect in that it controls the number of fibres which pull out rather than fracture.     

Failure phenomena in two-dimensional multi-fibre microcomposites. Part 4: a Raman spectroscopic study on the influence of the matrix yield stress on stress concentrations

Raman spectroscopy was used to study the influence of the shear yield stress of the matrix on the stress situation in carbon/epoxy model composites containing a planar fibre array. The fibre used was a surface-treated high-modulus Tenax® HMS-40 carbon fibre showing good fibre/matrix adhesion. Three matrices were used, all consisting of a common epoxy resin and a mixture of a di-functional and a tri-functional aliphatic amine-based curing agent. By varying the ratio of the di-functional to the tri-functional curing agent, the shear yield stress of the matrix was varied. For all three matrices, it was found that in the area immediately neighbouring a fibre fracture, stress transfer takes place through a locally yielding matrix. More importantly, it was shown that the maximum interfacial shear stress approximately equals the shear yield stress of the bulk matrix. In addition, it was found that an increase in the shear yield stress of the matrix results in a decrease of both the ineffective length and the positively affected length. Further, the experimental results show that the shear yield stress of the matrix does not significantly influence the stress concentration in the fibres adjacent to a broken fibre.     

An evaluation of acoustic emission from fibre-reinforced composites

An analysis of acoustic emission (AE) from model composites consisting of a single aramid fibre and different epoxy matrix systems has been carried out to identify the source of acoustic emission. The AE activity was observed in a narrow range of strain when fibre fracture occurred, whereas in a relatively wide range of strain, debonding occurred at the fibre-matrix interface. Ion-etched fibres showed a good adhesion of the fibres to the matrix so as to produce fibre fracture in place of interfacial debonding. The total number of AE events has one to one correspondence with the number of broken fibres. The effect of surface treatment and matrix systems on the shear fracture strength between the fibre and matrix were described based on the critical length of the broken fibres using AE results.     

Plasma surface modification of advanced organic fibres

The interlaminar shear strength, interlaminar fracture energy, flexural strength and modulus of extended-chain polyethylene/epoxy composites are improved substantially when the fibres are pretreated in an ammonia plasma to introduce amine groups on to the fibre surface. These property changes are examined in terms of the microscopic properties of the fibre/matrix interface. Fracture surface micrographs show clean interfacial tensile and shear fracture in composites made from untreated fibres, indicative of a weak interfacial bond. In contrast, fracture surfaces of composites made from ammonia plasma-treated fibres exhibit fibre fibrillation and internal shear failure as well as matrix cracking, suggesting stronger fibre/matrix bonding, in accord with the observed increase in interlaminar fracture energy and shear strength. Failure of flexural test specimens occurs exclusively in compression, and the enhanced flexural strength and modulus of composites containing plasma-treated fibres result mainly from reduced compressive fibre buckling and debonding due to stronger interfacial bonding. Fibre treatment by ammonia plasma also causes an appreciable loss in the transverse ballistic impact properties of the composite, in accord with a higher fibre/matrix interfacial bond strength.     

Three-dimensional finite element analysis of the stress concentration at a single fibre break

A linear elastic analysis is performed of a single broken fibre surrounded by six equally spaced fibres. These fibres and the surrounding epoxy matrix are modelled separately whilst the rest of the composite is treated as a homogeneous, orthotropic material. The distance of the adjacent fibres is fixed based on an assumed fibre volume fraction of 0·60. The analysis shows that the stress concentration in the adjacent fibres is 1·058, much lower than the value of 1·104 predicted by Hedgepeth and van Dyke (J. Comp. Mater., 1 (1967) 294–309). The positively affected length where there is an increase in stress is only about half the ineffective length of the broken fibre. Further away from the break the axial stress in the adjacent fibres actually drops below the nominal axial stress. This results in a very small enhanced probability of failure in the adjacent fibres. Very close local fibre spacing around the broken fibre increases the maximum stress in the adjacent fibres by less than 3%.