Interfacial separation of fibres in fibre reinforced composites

An analytical model is proposed to predict the ultimate tensile strength of fibre-reinforced composites when the failure is governed by fibre debonding.

The analytical analysis is based on the principle of the compliance method in fracture mechanics with the presence of an interfacial crack at the fibre/matrix interface. The model is developed on the basis of the assumption that both the matrix and the fibre behave elastically and the matrix strain at a zone far from the matrix-fibre interface is equal to the composite strain. Furthermore, it is assumed that a complete bond exists between the fibre and the matrix and that the crack faces are traction free.

It is shown that the separation strain energy release rate for fibre-reinforced composites can be obtained for cases with and without the existence of an interfacial crack. Numerical examples are presented and compared with results obtained in the literature by finite element analyses and from experimental tests. The comparison demonstrates the accuracy and the convergence of the model.     

Stress transfer in the fibre fragmentation test

An improved micromechanics model has been developed of the stress transfer for a single fibre embedded in a matrix subjected to uniaxial loading. Debond crack growth is analysed based on the shear strength criterion such that when the interfacial shear stress reaches the shear bond strength, debonding occurs; and the average strength concept based on Weibull statistics is considered for fibre fragmentation. The influences of the interfacial shear bond strength and the fibre strength on the stress distributions in the composite constituents are evaluated. Depending on the relative magnitudes of these two strength parameters and given the elastic constants and geometric factors, three distinct conditions of the fibre-matrix interface are properly identified which include full bonding, partial debonding and full frictional bonding. Also quantified are the necessary criteria which must be satisfied in order for each interface condition to be valid. Finally, the mean fibre fragment length is predicted as a function of applied strain using a model composite of carbon fibre-epoxy matrix. The parametric study suggests that the critical transfer length predicted when the applied strain (or stress) required for further fibre fragmentation approaches infinity, can be regarded as a material constant, which is the sum of the bonded and the debonded lengths for the model composite.     

The influence of thermal treatments on interfacial properties and fatigue crack growth resistance in SCS-6/Ti β21s composites

The mechanical properties of fibre-reinforced composites are dependent on the properties of the fibres, the matrix and the fibre/matrix interface. The latter two were investigated in a metastable β Ti matrix (Ti β21s) reinforced with silicon carbide (SCS-6) fibres by heat treatment for 2 and 6 h at 910°C (solution treatment) and 8 h at 540°C (ageing). Characterization of the microstructure using scanning and transmission electron microscopies revealed that the interfacial reaction layer had become thicker in the solution-treated specimens. This variation did not result in any significant change in interfacial shear strength, determined by a fibre push-out technique, nor in the fatigue crack growth resistance in three-point bending. Conversely, ageing at 540°C resulted in the precipitation of 34% volume fraction of α plates with negligible change to the fibre/matrix reaction layer thickness. This resulted in a large increase in both the interfacial debonding and frictional shear strength, which was consistent with local volume changes in the matrix on precipitation of α. The fatigue crack growth resistance of the peak-aged composite was also reduced under some testing conditions employed. In particular, the number of cycles to failure was decreased markedly after ageing.     

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.     

A non-local fracture model for composite laminates and numerical simulations by using the FFT method

In this paper, we present a fracture model for composite laminates and its numerical solution by using the Fast Fourier Transforms (FFTs). The FFT-based formulation initially proposed for seeking the average behaviour of linear and non-linear composites by means of the homogenisation procedures [1], [2] was adapted to evaluate the damage growth in brittle materials. A non-local damage model based on the maximal principal stress criterion was proposed to assess the failure in the matrix and the fibres. This non-local model was then connected to the Griffith–Irwin criterion in the aim of predicting crack growth. In order to assess the matrix/fibre interface delamination, we have adapted the cohesive model developed by Li [3] for accounting the mixed-mode dependent interface failure. To this end, the interfaces between the matrix and the fibres are replaced by a thin layer of interphase with the purpose of facilitating the FFT simulations. By using the proposed model, we carried out several numerical simulations on fracture process in different specimens. From these studies, we can conclude that the present FFT-based analysis is capable to deal with crack initiation and crack growth in composite laminates with high accuracy and efficiency, especially in the cases of matrix/fibre interface debonding and of multi-crack growth.     

Mechanical Characterisation of Interface for Steel/Polymer Composite Using Pull-out Test： Shear-Lag and Frictional Analysis

Fibre-matrix interface is known to have contribution to the mechanical performance of fibre-reinforced composite by its potential for load transfer between the fibre and the matrix. Such load transfer is of great importance in dentistry when a post is used for fixing a ceramic crown on the tooth. In this study, a pull-out test was carried out to analyse the interfacial properties of a steel fibre embedded in a polyester and epoxy matrices. It was found that the fibre-matrix interface is debonded on the whole embedded length when the fibre stress reached the debonding stress. Then, the fibre stress fell down to the initial extraction stress required to pulling out the debonded fibre from the matrix. Both debonding stress and initial extraction stress initiated a linear increase with the implantation length after the debonding stress reached horizontal asymptotes. To analyse the fibre-matrix load transfer before debonding, an analytical shear-lag model was adopted to in this test conditions. Fitting the experimental results with the analytical model provided the interfacial shear strength. By considering the Coulomb friction at the fibre-matrix interface during the fibre extraction process, an analytical model which considers Poisson＇s effects on both fibre and matrix, was developed. In this model, knowledge of the initial extraction stress of the fibre provides the residual normal stress at the fibre-matrix interface.     

Damage assessment and lifing of continuous fibre-reinforced metal-matrix composites

The fatigue response of a continuous silicon carbide (SCS-6) fibre-reinforced Ti-6Al-4V metal-matrix composite in the presence of a sharp precrack has been studied in single-edge notched test-pieces in bending. Crack growth rates have been measured for different values of span-to-width ratio (s/W) at ambient temperature and at a test temperature of 550°C in air by the use of a direct current potential difference technique. It was found that in most cases the observed crack growth rates initially decreased with increasing crack length (and hence increasing nominal applied stress intensity range). Effects of frequency on fatigue crack growth rates at 550°C in air have also been identified. In general, crack growth rates are increased at 550°C only at low frequencies, relative to the crack growth rates measured at ambient temperature. Based on observations to date it has been shown that fatigue cracks grown at a large span-to-width ratio propagate to failure more rapidly than cracks grown at small span-to-width ratios for equivalent initial nominal stress intensity ranges. Metallographic sections through the composite indicate that the improved fatigue life observed at low values of s/W ratio may be attributable to debonding at the fibre/matrix interface, which is deduced to delay the onset of fibre failure.     

The role of interfaces and matrix void nucleation mechanism on the ductile fracture process of discontinuous fibre-reinforced composites

The role of fibre morphology, interface failure and void nucleation mechanisms within the matrix on the deformation and fracture behaviour of discontinuous fibre-reinforced composites was numerically investigated. The matrix was modelled using a constitutive relationship that accounts for strength degradation resulting from the nucleation and growth of voids. For the matrix, two materials exhibiting identical strength and ductility but having different void-nucleation mechanisms (stress-controlled and strain-controlled) were considered and fibres were assumed to be elastic. The debonding behaviour at the fibre interfaces was simulated in terms of a cohesive zone model which describes the decohesion by both normal and tangential separation. The results indicate that in the absence of interface failure, for a given fibre morphology the void nucleation in the matrix is the key controlling parameter of the composite strength and ductility, hence, of the fracture toughness. The weak interfacial behaviour between the fibres and the matrix can significantly increase the ductility without sacrificing strength for certain fibre morphology and for certain matrix void-nucleation mechanisms.     

Fracture mechanics of single-fibre pull-out test

Pull-out of an elastic fibre from an elastic matrix was investigated. A simple pull-out mechanics has been developed, based on the fracture energy criterion, to describe the debonding process, including friction. Experiments were carried out using polytetrafluoroethylene (PTFE) fibres embedded in a polypropylene (PP) matrix. It was found that growth of an interfacial crack was stable after the initiation of a debond at the loaded fibre end. At first, the debonding force increased linearly with the crack length due to friction in the debonded region. However, the crack accelerated after reaching a critical length, dependent on the embedded fibre length. At this point, the force required to propagate the debond levelled off. Thus, further increase in the debonding force was not necessary to further complete the debonding process. The debonding force was found to be in good agreement with that predicted by the present theory. Techniques for determining the interfacial properties, including adhesive fracture energy, compressive residual stress and coefficient of friction, were considered. In addition, a simple criterion has been derived to predict which fibre end, either embedded end or loaded end, will debond first when the specimen is subjected to an axial load.     

复合材料随机渐进失效分析与声发射监测

结合随机渐进失效分析方法和声发射监测对复合材料单向拉伸试件进行损伤分析。结果表明: 随机渐进失效方法能很好地反映复合材料失效的随机性和渐进性特征。受载初期, 复合材料失效的随机性特征明显, 在整个试件内均有失效产生。随着载荷的增加, 损伤不断累积, "随机临界核"形成, 复合材料很快失效, 且一旦有失效产生, 纤维断裂数的增加与声发射事件数的累积具有很好的一致性。比较基体开裂和界面脱粘对复合材料拉伸性能的影响: 界面脱粘比基体开裂更容易导致复合材料拉伸性能的下降, 当不存在基体开裂和界面脱粘时, 纤维断裂呈现"集簇"特征, 复合材料断裂的脆性特征较为明显。      

Micromechanics characterization of sublaminate damage

A micromechanics analytical model is developed for characterizing the fracture behaviour of a fibre reinforced composite laminate containing a transverse matrix crack and longitudinal debonding along 0/90 interface. Both the matrix and the fibres are considered as linear elastic. A consistent shear lag theory is used to represent the stress-displacement relations. The governing equations, a set of differential-difference equations, are solved satisfying the boundary conditions appropriate to the damage configuration by making use of an eigenvalue technique. The properties of the constituents appear in the model explicitly. Displacements and stresses in the fibres and the matrix are obtained, and the growth of damage is investigated by using the point stress criterion. The investigation includes fibre stress distribution in zero degree plies, transverse crack and debonding intitiation as functions of laminate geometry, and the effect of fibre breaks in the zero degree ply on damage growth. The predicted damage growth patterns and the corresponding critical strains agree with the finite element and experimental results.     

On steady-state fibre pull-outII Computer simulation

On the basis of Part I of this paper (Zhang X, Liu, H-Y, Mai Y-W, Diaox X. On steady-state fibre pull-out Part I: stress field. Composites Science and Technology, 1999;59:2179–89) we present an extended analysis for the single-fibre pull-out process. The solutions of fibre axial stress, fibre displacement, and applied pull-out stress versus fibre displacement are obtained for the whole pull-out process. As distinct from previous work (Gao Y-C, Mai Y-W, Cottrell B. Fracture of fibre-reinforced materials. ZAMP 1988;39:550–72; Hutchinson JW, Jensen HN. Model of fibre debonding and pull-out in brittle composites with friction. Mechanics of Materials 1990;9:139–63; Hsueh C-H. Interfacial debonding and fibre pull-out stresses of fibre-reinforced composites. Materials Science and Engineering 1990;A123:1–11), a local shear strain criterion, in which the critical shear strain depends on the pull-out rate, is adopted as a more realistic interface debonding criterion. Load/displacement curves of the fibre pull-out process, which includes elastic deformation with a fully bonded interface, elastic deformation with a partially debonded interface and elastic deformation plus frictional sliding with a fully debonded interface, are obtained by computer simulations. The effects of fibre pull-out rate, thermal residual stress, friction coefficient and fibre volume fraction are also discussed.     

Mikromechanisches stochastisches Versagensmodell uniaxial faserverstärkter Verbundwerkstoffe

Micromechanical stochastic failure model of uniaxial fibre-reinforced composites A theoretical model of stress transfer between a transversal isotropic fibre and the surrounding matrix material in a uniaxially fibre-reinforced composite near a single matrix flaw is discussed including friction controlled fibre-matrix interface debonding. The rise of fracture toughness due to frictional fibre sliding is studied accounting for Weibull strength distribution of fibres. The total dissipative work may be used as figure of merit regarding the damage tolerance. A critical evaluation is presented concerning some previous models of local failure probabilities. Numerical results are demonstrated. Conditions for an optimized C/Al-composite are presented.     

Matrix cracking with frictional bridging fibres in continuous fibre ceramic composites

Interfacial debonding and matrix cracking due to residual axial stresses have been analysed for unidirectional fibre-reinforced ceramic composites. The analytical solutions for the crack-opening displacement, the axial displacement of the composite due to interfacial debonding, and the critical residual axial stress for matrix cracking have been obtained. The solutions were then compared with those for tensile loading in the fibre direction. Three issues related to Part I, i.e. the effective fracture toughness of the composite, the critical loading stress for matrix cracking in the presence of residual stresses, and the debonded fibre length due to loading, were also addressed in the present study.     

Optimising the crack arrest ability of unidirectional metal matrix composites

Optimisation of the fatigue crack arrest ability of unidirectional continuous fibre reinforced metal matrix composites is investigated by considering the damaging processes of interfacial debonding and fibre bridging. A sensitivity analysis of the parameters affecting these damage mechanisms is presented. It is suggested that fibre interface debonding is the principal controlling factor in determining the crack arrest ability of these materials. The Fatigue Damage Map was used to estimate the values of interfacial shear strength needed to optimise the crack arrest condition.     

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.     

Micro-mechanical theory of macroscopic stress-corrosion cracking in unidirectional GFRP

A micro-mechanical theory of macroscopic stress-corrosion cracking in a unidirectional glass fibre-reinforced polymer composite is proposed. It is based on the premise that under tensile loading, the time-dependent failure of the composite is controlled by the initiation and growth of a crack from a pre-existing inherent surface flaw in a glass fibre. A physical model is constructed and an equation is derived for the macroscopic crack growth rate as a function of the apparent crack tip stress intensity factor for mode I. Emphasis is placed on the significance of the size of inherent surface flaw and the existence of matrix crack bridging in the crack wake. There exists a threshold value of the stress intensity factor below which matrix cracking does not occur. For the limiting case, where the glass fibre is free of inherent surface flaws and matrix crack bridging is negligible, the relationship between the macroscopic crack growth rate and the apparent crack tip stress intensity factor is given by a simple power law to the power of two.     

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.     

Fracture mechanics approach for a partially debonded cylindrical fibre

The mechanical behaviour of the fibre-reinforced composites depends on the properties of the matrix, the fibres and their reciprocal bonding. Degrading effects occurring in such materials under service – such as matrix–fibre detaching (debonding), fibre breaking, matrix cracking – must be taken into account in the safety assessments. In the present paper, the fibre–matrix debonding phenomenon at the fibre–matrix interface is examined through fracture mechanics concepts, since a geometric discontinuity arises at the edge of the debonded zone (between two dissimilar materials) producing a stress singularity. The mixed mode stress-intensity factors are determined, and the effects of the geometrical and mechanical parameters related to matrix and fibres are discussed.