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.     

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

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

Deterministic method for predicting the strength distribution of a fibre bundle

Owing to the non-strain hardening plastic behaviour of the aluminium matrix and the weak fibre/matrix interface, it has been shown that the strength of a carbon fibre-reinforced aluminium matrix composite made by diffusion bonding of prepreg layers can be derived from the corresponding fibre bundle strength. Application of Coleman's model to predict bundle strength leads to the conclusion that the composite must break when 15% of the fibres are broken. This greatly overestimates the experimental composite strength. Overestimations made by using the Coleman model are due to some implicit assumptions which are not valid in the case under consideration and which may consequently not describe our material. A new approach is proposed for the calculation of the strength distribution of a fibre bundle, based on the same fracture mechanism (fibres fracture progressively until the catastrophic fracture) but without restrictive assumptions. The real interpolated experimental fibre strength distribution (and not the Weibull distribution) is taken into account to predict bundle strength. The proposed method clearly shows the limit of strength prediction, in term of bundle size (number of fibres and gauge length). The risk of making predictions following the Weibull distribution out of the range of the observations (through single-fibre tensile tests) is demonstrated.     

Compressive and tensile behaviour of carbon fibres

Attempts have been made to discuss the fibre axial tensile and compressive behaviour of several carbon fibres prepared from different precursors, and surface- and/or sizing-treatments. With all fibres, the number of breaks increased with increasing tensile or compressive strain, and remained constant beyond a certain strain. The constant number of breakages based on the precursor differed remarkably in compression, whereas those based on the surface- and/or sizing-treatments differed remarkably in tension. In tension, the PAN-based fibre could be broken with a somewhat greater ease than the pitch-based fibre, while in compression, the pitch-based fibre could be broken with somewhat greater ease than the PAN-based fibre. © 1998 Chapman & Hall     

Fibre strain mapping in aramid/epoxy microcomposites

Two-dimensional microcomposites, comprising regular arrays of Kevlar 49 fibres embedded in an epoxy resin, were fabricated and subjected to incremental tensile loading up to fracture. The strain along individual fibres at different levels of applied load was monitored using a laser Raman spectroscopic technique. A strain magnification of 80% maximum was measured in an intact fibre as a result of a fibre fracture in an adjacent fibre. The exact distribution of the strain increase within the transfer length of the broken fibre was obtained. The experimental stress concentration factor is compared with that derived from existing analytical models.     

Assessment of the tensile properties of coir,bamboo and jute fibre

Natural fibres are studied as alternatives for man-made fibres to reinforce composites while keeping the weight lower. The assessment of the value of some commonly available tropical fibres for the composite industry starts with the determination of the strength, E-modulus and strain to failure through single fibre tensile tests. The mean strength and standard deviation is calculated following the normal and Weibull distribution resulting in the questionable benefit of applying the Weibull distribution. Furthermore, a correction method assesses the real fibre elongation from the measured clamp displacement. This procedure seems to be useful for strong, brittle fibres to produce more reliable results for the E-modulus and strain to failure.     

Weibull strength statistics for graphite fibres measured from the break progression in a model graphite/glass/epoxy microcomposite

Recent statistical theories for the failure of fibrous composities focus on the initiation and growth of clusters of broken fibres within the composite. These theoreis require the probability distribution for fibre strength at the length scale of micromechanical load transfer around a cluster of broken fibres. Such lengths are of the order of 10 to 150 fibre diameters, and thus the associated strengths have previously been unmeasurable by direct means. Using Weilbull/weakest-link rules, researchers have resorted to extrapolation of tension test results from gauge lengths two orders of magnitude longer. In this paper, a technique is developed to study the break progression of a single graphite fibre in an epoxy microcomposite tape, where the graphite fibre is flanked by two, proof-tested, glass fibres. These results are interpreted using a Weibull/Poisson model of the break progression, the number of breaks in the graphite fibre as a function of applied strain, which accounts for stress decay at the fibre ends. It is shown that such extrapolations of tension test data are too optimistic. In addition, different fibres from the same yarn cross-section, apparently have different flaw populations, unlike that which occurs at longer gauge lengths.     

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.     

Tensile properties of real unidirectional Kevlar/epoxy composites

Mechanical behaviour, tensile strength and failure modes in real unidirectional Kevlar/epoxy composites, loaded parallel to the fibres, at volume fraction (V_f) range 0.26–0.73, were investigated. It was found that the measured tensile strengths deviated from the expected values calculated from the Rule of Mixture. The deviation, which was minimal at V_f of about 0.5, was mainly due to geometrical deficiencies typical of real composites. At V_f<0.5 it could be explained by non-homogeneous fibre spread and distribution of fibres. At V_f>0.5 the deviation was explained by the increasing lack of matrix between some adjacent fibres and by squeezing of fibres. The initial part of loading was typified by straightening out of non-axial fibres, accompanied by fibre/matrix debonding. The straightening process was completed at a stress level of about 0.6–0.7 of the composite strength. Matrix damage began at this stress level and continued to develop up to final failure. Failure of Kevlar fibres was noted to occur only at an extremely short loading interval coinciding with the catastrophic final failure. This was due to the small scatter of Kevlar fibre 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%.     

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.     

Deformation micromechanics of a model cellulose/glass fibre hybrid composite

Interfacial stress transfer in a model hybrid composite has been investigated. An Sm³⁺ doped glass fibre and a high-modulus regenerated cellulose fibre were embedded in close proximity to each other in an epoxy resin matrix dumbbell-shaped model composite. This model composite was then deformed until the glass fibre fragmented. Shifts of the absolute positions of a Raman band from the cellulose fibre, located at 1095 cm⁻¹, and a luminescence band from a doped glass fibre, located at 648 nm, were recorded simultaneously. A calibration of these shifts, for both fibres deformed in air, was used to determine the point-to-point distribution of strain in the fibres around the breaks in the glass fibre. Each break that occurred in the glass fibre during fragmentation was shown to generate a local stress concentration in the cellulose fibre, which was quantified using Raman spectroscopy. Using theoretical model fits to the data it is shown that the interfacial shear stress between both fibres and the resin can be determined. A stress concentration factor (SCF) was also determined for the regenerated cellulose fibre, showing how the presence of debonding reduces this factor. This study offers a new approach for following the micromechanics of the interfaces within hybrid composite materials, in particular where plant fibres are used to replace glass fibres.     

Pre- and post-peak toughening behaviours of fibre-reinforced hot-mix asphalt mixtures

Recycled plastic fibre-reinforced hot-mix asphalt (HMA) mixtures have better fatigue resistance than plain HMA. The toughening effects of recycled plastic fibre-reinforced HMA were characterised using direct tensile loading tests. Adding a small quantity of recycled plastic fibres to HMA was found to significantly increase the mixture's fracture energy and toughness, which were calculated using the pre- and post-peak stages of tensile force–displacement curves. A theoretical model representing the pre-peak behaviour of fibre-reinforced HMA with direct tension-softening curves for various fibre contents is presented here. The enhanced toughness through post-peak analysis was also observed using toughness indices associated with fibre-bridging effect after the pre-peak composite stress. The pre-peak fracture energy model and post-peak toughness indices appeared to be governed by the direct tensile toughening of fibre-reinforced HMA's enhanced fibre-bridging effects. The pre-peak fracture energy model demonstrates the effect of fibre content on the strain energy density during the pull-out process within the pre-peak composite stress region. The maximum pre-peak fracture energy of a coarse-graded HMA mixed with recycled plastic fibres is achieved at a fibre content of 0.4% of the total weight of the HMA. The increases in the toughness indices within the post-peak composite stress region indicate that the fatigue resistance of fibre-reinforced HMA is at least 30% greater than that of control HMA.     

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.     

Fracture mechanism of unidirectional carbon-fibre reinforced epoxy resin composite

The object of this study was to investigate the fracture mechanism of unidirectional carbon-fibre reinforced epoxy resin composite. For this purpose, the failure process of the composite under load was observedin situ by scanning electron microscopy and the matrix deformation around the broken fibre tip was examined by polarized transmission optical microscopy using a thin section of the composite. The failure process was shown to proceed through the following four stages: (1) fibre breakage began to occur at a load of about 60% of the failure load; (2) as the applied load was increased, plastic deformation occurred first from the broken fibre tip along the fibre sides, followed by final matrix cracking in the plastic region; (3) just before failure, partial delamination occurred, originating from fibre breakage and matrix cracking; (4) finally, a catastrophic crack propagation occurred from the delamination, leading to composite failure. Acoustic emission monitoring was also carried out for non-destructive evaluation, which indicated that internal failure began to occur at a load of 60% of the failure load and propagated remarkably before composite failure. A close correspondence between the acoustic signal and crack formation was obtained. The acoustic signal at lower amplitude, occurring over whole load range, corresponded to fibre breakage and matrix cracking while that at higher amplitude, occurring only just before failure, corresponded to partial delamination. From these experimental studies, the fracture mechanism of the composite has been clarified.     

Multi-scale fatigue behaviour modelling of Al–Al2O3 short fibre composites

Using very heterogeneous materials in structural parts submitted to cyclic loadings, this paper presents an elasto-plastic micromechanical model. After recalling the homogenisation principle based on a mean field theory, non-linear kinematic and isotropic strain hardening is introduced into the matrix. Validation is made on an Al–3.5%Cu/SiC particle composite, and an Al–Si7Mg/Al₂O₃ fibre composite is treated as a first application. Damage is introduced into the model using a fibre failure criterion. It is based on the evolution of the volume fraction of broken fibres as a function of the maximum principal stress in the fibre family. The damage law is identified by means of in situ tensile tests performed inside the scanning electronic microscope. The number of broken fibres is determined as a function of the applied load and the number of cycles. The model predicts the fatigue behaviour, the loss of stiffness, the volume fraction of broken fibres for different volume fractions, aspect ratios, distributions of orientation and distributions of strength of the fibres. The effect of the mechanical fatigue properties of the matrix is also studied.     

Fracture response of fibre-reinforced materials with macro/microcrack damage using the Boundary Element Technique

The Boundary Element Method (BEM) incorporating the Embedded Cell Approach (ECA) has been used to analyse the effects of constituent material properties, fibre spatial distribution and microcrack damage on the localised behaviour of transversely fractured, unidirectional fibre-reinforced composites. Three specific composites, i.e., glass fibre reinforced polyester, carbon fibre reinforced epoxy and a glass-carbon hybrid, are considered. The geometrical structures examined were perfectly periodic, uniformly spaced fibre arrangements in square and hexagonal embedded cells. In addition, numerical simulations were also conducted using embedded cells containing randomly distributed fibres. The models involve both elastic fibres and matrix, with the interfaces between the different phases being fully bonded. The results indicate that the constituent material properties (two phase composite) and spatial distribution have a significant effect on the localised stress distributions around the primary crack tip. However, the strain energy release rate associated with crack propagation is predominantly influenced by the material composition. The three-phase hybrid composite exhibited an apparent intermediate fracture toughness value, compared to the all-glass and all-carbon models. Furthermore, the strain energy release rate for the macrocrack lowers as it enters a zone of localised damage (microcracking). The presence of microcracks relaxes the stress field, which can result in a significant reduction in the energetics of the primary crack.     

Stress distribution in discontinuous fibres in a model composite

In order to calculate stress distribution in unidirectional discontinuous fibres embedded in a metal matrix, a method based on the shear-lag analysis was proposed. Using this method, the influence of fibre length, interfacial bonding strength, distance between fibre ends in the longitudinal direction, and applied strain to composite on both stress distribution and average stress of fibres was estimated for a number of examples.     

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.     

Effective simulation of the mechanics of longitudinal tensile failure of unidirectional polymer composites

An efficient computational model to simulate tensile failure of both hybrid and non-hybrid composite materials is proposed. This model is based on the spring element model, which is extended to a random 2D fibre packing. The proposed model is used to study the local stress fields around a broken fibre as well as the failure process in composite materials. The influence of fibre strength distributions and matrix properties on this process is also analysed. A detailed analysis of the fracture process and cluster development is performed and the results are compared with experimental results from the literature.