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.     

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

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

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.     

Implications of interface friction for crack growth in fibre-reinforced metal matrix composites by three-dimensional finite element modelling

A three-dimensional finite element model of a compact tension specimen consisting of a Ti-6Al-4V matrix reinforced with unidirectional, continuous SiC fibres under monotonic and cyclic loading has been developed. This has enabled true Coulomb frictional interface sliding resulting from thermal residual stresses to be modelled. The results, which include the action of individual bridging fibres close to the crack-tip, are compared to results from a two-dimensional weight function method which uses fibre-induced bridging tractions on the crack face based on a constant interface strength. Reasonable agreement was found between the two methods used. An investigation of the fibre stresses showed that together with normal crack bridging tractions a strong bending component is present in the fibres which also affects crack opening and could affect the mode of fibre failure. The influence of processing induced thermal residual stresses and friction at the fibre-matrix interface on the crack growth behaviour during monotonic and cyclic loading has been assessed. It was found that the bridging fibres strongly reduce the crack-tip stress intensity factor. The thermal residual stresses produce a crack-tip opening load in the absence of an external load and have an influence on the crack-tip load ratio. The effect of the crack-tip load ratio on the fatigue threshold has a significant impact on the likelihood of crack arrest.     

Shear capacity of steel and polymer fibre reinforced concrete beams

This paper deals with the application of a plasticity model for shear strength estimation of fibre reinforced concrete beams without stirrups. When using plastic theory to shear problems in structural concrete, the so-called effective strengths are introduced, usually determined by calibrating the plastic solutions with tests. This approach is, however, problematic when dealing with fibre reinforced concrete (FRC), as the effective strengths depend also on the type and the amount of fibres. In this paper, it is suggested that the effective tensile strength of FRC can be determined on the basis of the tensile stress-crack opening relationship found from wedge splitting tests. To determine the effective compressive strength of FRC, it is proposed to adopt the formula used for conventional concrete and modify it by introducing a fibre enhancement factor to describe the effect of fibres on the compressive softening behaviour of FRC. The enhancement factor is determined as the ratio of the areas below the stress–strain curves for FRC and for conventional concrete. The outlined approach has been verified by shear testing of beams containing no fibres, 0.5% steel fibre volume and 0.5% polymer fibre volume. The tests results are compared with estimations and show satisfactory agreements, indicating that the proposed approach can be used.     

A new data reduction scheme for the fragmentation testing of polymer composites

A new reduction scheme of fragmentation data for the derivation of interfacial mechanical properties in polymer composites is proposed. The scheme is based on a theoretical model that accounts for elastic load transfer and friction at the interface, as well as for the statistical nature of fibre strength. Interface mechanical behaviour is characterized by two independent parameters, namely the interface bond strength and interface frictional resistance. Derived values of the two interface properties are computed, such that they yield the best possible agreement between experimental and theoretical results for the evolution of fibre fragment aspect ratio and debonding ratio as a function of applied strain. Results are reported for carbon fibres embedded in an epoxy matrix, with different levels of fibre surface treatment.     

The influence of fibre sizing on the strength and fracture toughness of glass fibre composites

The influence of the fibre/matrix interface strength on fibre cross-over bridging in a crack along fibres is investigated. Four different composite systems (commercial glass fibre with two different sizings and two matrix resins) resulting in strong and weak interfaces were manufactured. Their crack growth resistance during crack propagation with fibre bridging in a double cantilever beam specimen loaded with end moments was measured. Bridging laws were derived from the experimental results and correlated with the chemical interface characteristics and a micromechanical model. It was found that a strong interface provided higher transverse strength and crack initiation loads, while the weak interface exhibited higher toughness due to enhanced fibre bridging. Composites with different matrix resins showed large variations in bridging behaviour even if their transverse strength was similar.     

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.     

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.     

Interfacial failure in poly(p-phenylene benzobisoxazole) (PBO)/epoxy single fibre pull-out specimens

The pull-out behaviour of poly(p-phenylene benzobisoxazole) fibres from an epoxy resin has been shown to follow that predicted by the elastic stress transfer shear-lag model at low applied strains, but at higher matrix strains a partial debonding model was more suitable. Debonding of the fibre/matrix interface led to interfacial failure where only friction resisted fibre extraction. Raman spectroscopy was able to quantify this level of friction and together with in situ optical microscopy proved an excellent method for the close monitoring of the frictional pull-out process. The effect of fibre surface treatment was also studied. The interfacial shear stress values from the heat-treated and corona-treated fibres showed only small differences. The failure processes were examined further using scanning electron microscopy and clean fibre pull-out was observed with the heat-treated fibre whereas fracture of the free fibre occurred with the corona-treated fibre.     

Wedge splitting test for a steel-concrete interface

This paper presents a test method designated for the determination of the stress-crack opening relationship of a steel-concrete interface. The method is based on the well known wedge splitting test (WST), and it is illustrated how to obtain the stress-crack opening relationship through an inverse analysis. This inversion method utilizes the cracked hinge model, modified such that it describes the problem at hand. In this paper, pure concrete and steel-concrete composite specimens are tested and compared. It turns out that interfacial cracking of a bimaterial specimen usually behaves as one of the parent materials, in this case concrete. The stress-crack opening relationship of both the concrete and bimaterial specimens are obtained through the proposed inverse analysis. The results show, that interfacial cracking is dominated by the so-called wall-effect and its behavior can be described as quasi-brittle. However, due to the wall-effect, interfacial cracking is more brittle than for the pure concrete.     

Probabilistic aspects of strength of short-fiber composites with planar fibre distribution

The study of the fracture of short-fibre composites must involve statistics as an integral part. Two components of composite strength, each with probabilistic aspects, are described in this paper: fibre crossover reinforcement, and fibre gap bridging before fracture. The fibre crossover density is proposed as a measure of mutual fibre strengthening. and simulations are performed to estimate this density. Several different fibre orientations are proposed which have identical elastic properties but different crossover densities, indicating that more information is required for strength prediction than for elastic property prediction. The crossover density is a random variable whose average increases roughly as a fibre length squared function, and whose coefficient of variation decreases with increasing fibre length. The phenomenon of fibres bridging microcrocks is also examined as a fracture mechanism for fibres whose length well exceeds their critical length. General probabilistic expressions are derived which give the distribution of the number of fibres bridging a gap perpendicular to the applied load. These formulae are applied to the distribution of strength of an aligned fibre system.     

Influence of spatial correlations on crack bridging by frictional fibres

The effect of fibre interaction on matrix cracking in a unidirectional fibre-reinforced composite is analyzed. It is assumed that the matrix material contains a crack in a plane perpendicular to the fibres. Fibres, remaining intact, debond from the matrix and then act as bridging ligaments in the crack wake. The debonding process is accompanied by frictional sliding governed by a Coulomb friction law. Fibres are considered to be randomly located in the transverse plane. The fibre axial stress and longitudinal displacement are expressed in terms of the solution to a model problem for a single fibre in an ambient stress field due to all other fibres and applied load. The stress field produced by the other fibres is described using an ensemble averaging procedure. The radial distribution function g(r) that provides a quantitative measure of the correlations between the positions of different fibres is evaluated numerically from the Percus-Yevick equation for hard disks. The dependence of the fibre axial stress on the relative fibre-matrix displacement is examined for different values of the volume fraction of fibres. The resulting stress-displacement law is compared with results for other choices of the function g(r) and with a law given by a concentric cylinder model.     

Fatigue crack growth in hybrid boron/glass/aluminium fibre metal laminates

The crack growth behaviour of hybrid boron/glass/aluminium fibre metal laminates (FMLs) under constant‐amplitude fatigue loading was investigated. The hybrid FMLs consist of Al 2024‐T3 alloy as the metal layers and a mixture of boron fibres and glass fibres as the fibre layers. Two types of boron/glass/aluminium laminates were fabricated and tested. In the first type, the glass fibre/prepreg and the boron fibre/prepreg were used separately in the fibre layers, and in the second type, the boron fibres and the glass fibres were uniformly mingled together to form a hybrid boron fibre/glass fibre prepreg. An analytical model was also proposed to predict the fatigue crack growth behaviour of hybrid boron/glass/aluminium FMLs. The effective stress intensity factor at a crack tip was formulated as a function of the remote stress intensity factor, crack opening stress intensity factor, and the bridging stress intensity factor. The bridging stress acting on the delamination boundary along the crack length was also calculated based on the crack opening relations. Then, the empirical Paris‐type fatigue crack growth law was used for predicting the crack growth rates. A good correlation between the predicted and experimental crack growth rates has been obtained.     

Effects of fibre content on mechanical properties and fracture behaviour of short carbon fibre reinforced geopolymer matrix composites

Geopolymer matrix composites reinforced with different volume fractions of short carbon fibres (C_f/geopolymer composites) were prepared and the mechanical properties, fracture behaviour and microstructure of as-prepared composites were studied and correlated with fibre content. The results show that short carbon fibres have a great strengthening and toughening effect at low volume percentages of fibres (3·5 and 4·5 vol.%). With the increase of fibre content, the strengthening and toughening effect of short carbon fibres reduce, possibly due to fibre damage, formation of high shear stresses at intersect between fibres and strong interface cohesion of fibre/matrix under higher forming pressure. The property improvements are primarily based on the network structure of short carbon fibre preform and the predominant strengthening and toughening mechanisms are attributed to the apparent fibre bridging and pulling-out effect.     

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

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

Micromechanics of multiple cracking Part II Statistical tensile behaviour

A computational model for fibre-reinforced brittle materials in tension is developed. The model includes multiple cracking and strain-hardening processes, as well as single fracture and strain softening. The composite behaviour is derived from a single-fibre analysis by integrating over all possible fibre locations and orientations. The single-fibre analysis is based on symmetry fibres satisfying the equilibrium condition. The result is a complete constitutive relation: stress–strain or stress–crack width curve, and a prediction of crack spacing. The model is an extension of the ACK theory by Aveston, Cooper and Kelly, as it can be used with discontinuous fibres with different distributions, as well as for analysing hybrid composites. Fibre orientation introduces additional phenomena, which are taken into account with simple models. It was seen that matrix spalling at the fibre exit point may have a considerable effect on the composite strain and the crack width. The effect of fibre aspect ratio on the failure mode was studied, and it was found that with an intermediate fibre diameter the composite fails by fibre pull-out in a multiple-cracking stage, resulting in a strain-hardening material with a high ductility. The proposed model was verified against experimental results of a strain-hardening material, called an engineered cementitious composite. The model can be used in tailoring new materials to meet certain requirements, or in studying the effects of micromechanical properties on the composite behaviour, including the crack width, crack spacing, post-cracking strength, ultimate strain, and ductility. The derived constitutive relationship can further be used in finite element analyses defining the behaviour perpendicular to the crack. © 1998 Kluwer Academic Publishers     

Loosely woven fabric model with viscoelastic crimped fibres for ballistic impact simulations

A computational micro‐mechanical material model of loosely woven fabric for non‐linear finite element impact simulations is presented in this work. The model is a mechanism incorporating the crimping of the fibres as well as the trellizing. The equilibrium of the mechanism allows the straightening of the fibres depending on the fibre tension. The contact force at the fibre crossover point determines the rotational friction dissipating a part of the impact energy. The stress–strain relationship is viscoelastic based on a three‐element model. The failure of the fibres is strain rate dependent. The model is implemented as user defined subroutine in the transient finite element code LS‐DYNA. The ballistic impact simulations with the model are in good agreement with the experimental results. Copyright © 2004 John Wiley & Sons, Ltd.     

Friction and wear of friction composites reinforced by natural fibres

In the present work, friction material composites were proposed to be used as automotive friction materials. The composites were reinforced by agricultural fibres of corn, palm, and sugar bars. The conventional friction materials based on asbestos cause serious lung diseases and being cancerous potential. The aim of the present work is to replace them by the proposed composites because they are environmentally friendly friction material for brake lining and clutch facings. Agricultural wastes of sugar bars, corn and palms fibres were prepared to obtain fibres of length less than 5 mm. The fibre materials were mixed by carbon, barium sulfate, silica, metallic powders and phenol formaldehyde. The proposed composites were pressed in the die at 105°C temperature. The produced specimens were subjected to machining processes to obtain the cylindrical form of 8 mm diameter. Experiments were carried out using test rig designed and manufactured to measure both friction and wear. It consists of a rotating hollow flat disc made of carbon steel, with an outside diameter of 250 mm and 16 mm thickness. The experiments investigated the effect of agriculture fibre wastes (corn, sugar bars, and palms fibres) on friction coefficient and wear. Wear mechanisms of the proposed composites were characterized by scanning electronic microscopy. The tribological properties of the proposed composites materials were compared to three commercial brake linings. Based on the experimental results it was found that, addition of agriculture fibre wastes (corn, sugar bars, and palms fibres) to composites materials increased friction coefficient and decreased wear. Friction coefficient slightly increased, while wear drastically decreased with increasing fibres content. The maximum friction value (0.58) was obtained by composites containing 30 wt.% iron and 25 wt.% sugar bar fibres. The corn fibres were more compatible with aluminum powder where it gave the highest friction coefficient and relatively lower wear compared to other composites. Wear resistance of the tested composites containing bunches and aluminum represented the lowest values among composites containing corn and bunches fibres. The lowest wear values were observed for composites containing 25 wt.% corn fibres and 30 wt.% aluminum and composites containing 20–25 wt.% sugar bar fibres.     

Prediction of steel fibre reinforced concrete under flexure from an inferred fibre pull-out response

Steel fibre-reinforced concrete (SFRC) is being used in a variety of structural applications, yet there is still considerable debate how to express and evaluate flexural toughness for design purposes. This is holding back the material's development as a permanent structural material. Existing beam and slab test methods have problems with variability or their application in structural design. Furthermore, existing models of SFRC flexural behaviour do not fully capture what happens at the cracked section in terms of the fibre-matrix interactions. Typical of these approaches is the modelling of the tension zone from single fibre pull-out tests, which is problematic in measurement of the load-displacement relationship, the interaction of groups of fibres and the extensive testing required to cover all permutations of fibre geometry. An alternative approach is proposed where the average pull-out response of the fibres bridging the cracked zone is inferred from flexural beam tests. The characteristic load versus crack-mouth opening displacement behaviour for a particular fibre concrete then forms part of the stress and strain/displacement profile in a flexural analysis to predict moment capacity in a design calculation. The model is explained together with its validation by comparing the predicted load-displacement response for a range of fibre volumes in sprayed and cast SFRC. It is concluded that the analysis of beam load/deflection curves to infer the fibre pull-out response is a viable approach. It offers a promising solution to the need for a flexural design model combined with a practical method of characterizing the tensile contribution of steel fibres.