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.     

Numerical analysis of debond propagation in the single fibre fragmentation test

A numerical analysis, using the Boundary Element Method, of the stress state within the specimen in the single fibre fragmentation test is presented first. Thermal residual stresses and fibre–matrix interfacial friction along the debonding crack faces have been considered in the study. Special attention has been paid to the axial stresses along the fibre and the interfacial tractions and relative displacements in the neighbourhood closest to the debonding crack tips. In order to analyse the debond propagation, the associated Energy Release Rate has been evaluated from the near-tip elastic solution. Numerical results show that both the effects of thermal residual stresses and of fibre–matrix interfacial friction are opposed to the debond propagation. Additionally, the effect of the debond propagation on the load transfer through the interface has been studied, showing that fibre–matrix interfacial friction has a weak influence on the distance needed to re-establish the nominal axial load within the fragment.     

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.     

A low cycle fatigue model of a short-fibre reinforced 6061 aluminium alloy metal matrix composite

A low cycle fatigue model has been developed to predict the fatigue life of both the unreinforced aluminium alloy and the short-fibre reinforced aluminium alloy metal-matrix composites based solely on crack propagation from microstructural features. In this approach a crack is assumed to initiate and grow from a microstructural feature on the first cycle. The model assumes that there is a fatigue-damaged zone ahead of the crack tip within which the actual degradation of the material takes place. The low-cycle fatigue crack growth and the condition for failure are controlled by the amount of cyclic plasticity generated within the fatigue-damaged zone ahead of the crack tip and by the ability of the short fibres to constrain this cyclic plasticity. The fatigue crack growth rate is directly correlated to the range of crack-tip opening displacement. The empirical Coffin–Manson and Basquin laws have been derived theoretically and applied to compare with total-strain controlled low-cycle fatigue life data obtained on the unreinforced 6061 aluminium alloy at 25 °C and on the aluminium alloy AA6061 matrix reinforced with Al₂O₃ Saffil short-fibres of a volume fraction of 20 vol.% and test temperatures from −100 to 150 °C. The proposed model can give predicted fatigue lives in good agreement with the experimental total-strain controlled fatigue data at both high strain low-cycle fatigue and low strain high-cycle fatigue regime. It is remarkable that the addition of high-strength Al₂O₃ fibres in the 6061 aluminium alloy matrix will not only strengthen the microstructure of the 6061 aluminium alloy, but also channel deformation at the tip of a crack into the matrix regions between the fibres and therefore constrain the plastic deformation in the matrix. The overall expected effect is therefore the reduction of the fatigue ductility.     

Finite element modelling of interfacial failure in model carbon fibre-epoxy composites

Finite element analysis has been used to model a single unsized carbon fibre embedded in an epoxy matrix subjected to tensile loading. The predicted fibre strain distribution is compared with experimental data, obtained using the technique of laser Raman spectroscopy, for a number of incremental applied strain levels. Good correlation is obtained on the assumption that the prevailing mode of interfacial failure in the composite involves a conical matrix crack initiating at the fibre end. The geometry of the matrix crack is estimated on the assumption that the crack propagates in a self-similar manner.     

The mechanics of matrix cracking in fiber reinforced ceramic composites containing a viscous interface

A detailed fracture mechanics analysis of matrix cracking in a fiber reinforced ceramic composite is presented for the case where the fiber—matrix interface exhibits viscous flow as can be the case when ceramic composites containing amorphous interfacial layers are subjected to loads at elevated temperatures. The analysis considers the case where matrix cracks are fully bridged by fibers, and the role of the viscous interface is to introduce a time dependence into the stress-intensity formulations. Such time-dependence arises because the bridging fibers are able to pull out of the matrix by viscous interfacial flow, with the result that the crack opening, as well as the actual (or shielded) matrix crack-tip stress-intensity factor, increase with time under the action of a constant externally applied load to the composite. The differential equation governing the mechanics of the fiber pull-out is derived. This is then applied to obtain expressions for the time-dependence of the crack opening and the effective crack-tip stress-intensity factor in terms of material and microstructural factors. These expressions predict that the matrix crack will exhibit stable crack growth, with the crack growth rate being essentially crack length (and time) independent and a function only of the applied stress and of material and microstructural factors. It is also shown that the composite lifetime is independent of the sizes of pre-existing cracks and is dependent only on a critical microstructure dependent flaw size, applied stress and microstructural factors.     

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     

Fully plastic crack-tip fields for plane strain shallow-cracked specimens under pure bending

Detailed finite element (PE) analyses are performed to study the effect of crack depth on crack-tip constraint at full yielding for pure bending of plane strain single-edge-cracked specimens. Analyses are based on small-strain formulations and perfect plasticity. The crack depth a/W ranges from 0.1 to 0.7, and the deformation is applied up to the limiting state of full plasticity where crack-tip stresses reach steady-state limiting values.At load levels smaller than the limit load (contained yielding), the crack-tip constraint (stress triaxiality) gradually decreases as a/W decreases, but, at load levels close to the limit load (or at the limit load), it decreases very sharply. In terms of a/W, tractable closed-form approximations for fully plastic crack-tip stress and strain fields are proposed, and fully plastic values of crack-tip stresses are re-phrased in terms of the Q-parameter [1, 2]. The role of crack-tip strains on fracture of shallow-cracked bending specimens is briefly discussed.     

CRACK CLOSURE AND THE FATIGUE-CRACK PROPAGATION THRESHOLD AS A FUNCTION OF LOAD RATIO

The phenomenon of crack closure, which involves the premature closing of fatigue cracks during the unloading portion of a fatigue cycle resulting in the development of crack-tip shielding due to crack wedging, has become widely accepted as a critical mechanism influencing many aspects of the behaviour of fatigue cracks in metallic materials; these include effects of load ratio, variable-amplitude loading, crack size, microstructure, environment and the magnitude of the fatigue threshold. Recently, however, the significance of crack closure has been questioned and alternative suggestions made for many of these phenomena, e.g. the effect of the load ratio (i.e. the ratio R of the minimum to maximum loads) on threshold behaviour. In the light of this, the present paper provides evidence to rebut the assertion that crack closure is an insignificant process. Particular attention is given to the effect of crack closure on the threshold level as a function of load ratio.     

Influence of local fracture energy distribution on maximum fracture load of three-point-bending notched concrete beams

The maximum fracture load of a notched concrete beam has been related to the local fracture energy at the cohesive crack tip region analytically in this paper, and then the correlation between the size effects on the maximum fracture loads and the RILEM specific fracture energy is established. Two extreme conditions have been established, namely zero crack-tip bridging with zero local fracture energy and maximum crack-tip bridging with the maximum size-independent fracture energy. It is concluded that the local fracture energy at the crack tip region indeed varies with the initial crack length and the size of specimen. The tri-linear model for the local fracture energy distribution is confirmed by using the proposed simple analytical solution.     

Creep crack growth in fiber reinforced composites with rate-dependent bridging - Role of a viscous fiber matrix interface

A model is developed for creep crack growth in continuous fiber reinforced composites wherein a growing matrix crack is subjected to rate-dependent bridging by unbroken fibers. The rate-dependence in this model arises as a result of the presence of a viscous fiber/matrix interfacial layer. Under load this layer undergoes shear flow causing time-dependent pull-out of bridging fibers from the crack surfaces. The mechanics of time-dependent bridging is combined with a failure criterion based on secondary failure in a crack-tip creep process zone. The dependence of the matrix creep crack growth rates on flaw size and crack wake parameters as well as on composite microstructure is derived. It is shown that the crack wake plays a predominant role in influencing not only the magnitude of creep crack growth rates but also the relationship of growth rates to the crack sizes. A closed form expression is derived for the dependence of crack growth rates on loading, creep and bridging parameters in the regime wherein crack growth rates are independent of crack size.     

Fatigue life prediction of fiber reinforced concrete under flexural load

This paper presents a semi-analytical method to predict fatigue behavior in flexure of fiber reinforced concrete (FRC) based on the equilibrium of force in the critical cracked section. The model relies on the cyclic bridging law, the so-called stress–crack width relationship under cyclic tensile load as the fundamental constitutive relationship in tension. The numerical results in terms of fatigue crack length and crack mouth opening displacement as a function of load cycles are obtained for given maximum and minimum flexure load levels. Good correlation between experiments and the model predictions is found. Furthermore, the minimum load effect on the fatigue life of beams under bending load, which has been studied experimentally in the past, is simulated and a mechanism-based explanation is provided in theory. This basic analysis leads to the conclusion that the fatigue performance in flexure of FRC materials is strongly influenced by the cyclic stress–crack width relationship within the fracture zone. The optimum fatigue behavior of FRC structures in bending can be achieved by optimising the bond properties of aggregate–matrix and fiber–matrix interfaces.     

Cyclic fatigue in monolithic alumina: mechanisms for crack advance promoted by frictional wear of grain bridges

The microstructural basis of cyclic fatigue-crack propagation in monolithic alumina has been investigated experimentally and theoretically. A true cyclic fatigue effect has been verified, distinct from environmentally assisted slow crack growth (static fatigue). Microstructures with smaller grain sizes were found to promote faster crack-growth rates; growth rates were also increased at higher load ratios (i.e. ratio of minimum to maximum applied loads). Using in situ crack-path analysis performed on a tensile loading stage mounted in the scanning electron microscope, grain bridging was observed to be the primary source of toughening by crack-tip shielding. In fact, crack advance under cyclic fatigue appeared to result from a decrease in the shielding capacity of these bridges commensurate with oscillatory loading. It is proposed that the primary source of this degradation is frictional wear at the boundaries of the bridging grains, consistent with recently proposed bridging/degradation models, and as seen via fractographic and in situ analyses; specifically, load versus crack-openingdisplacement hysteresis loops can be measured and related to the irreversible energy losses corresponding to this phenomenon.     

Microbuckling elastic modelling approach of a single carbon fibre embedded in an epoxy matrix

Carbon fibre alignment defect inside of an epoxy matrix is examined by the use of microscopy and video recording. The initiation and the growth of a fibre waviness defect was monitored during the cure of the matrix. The observations established that fibre defect appears during the hot stage of the epoxy matrix thermosetting reaction. The objective is to evaluate the possibility of a fibre microbuckling mechanism to explain the observations. A first elastic microbuckling model is proposed. Analytical expressions of the necessary elastic load for the appearance of a fibre buckling instability and its associated wavelength are established. The compressive load applied onto the fibre has been evaluated by using finite elements calculations based on mechanical characteristics of the materials. Comparison between the critical microbuckling load and the applied load onto the carbon fibre during the cure is in coherence with the observations. The associated wavelength is discussed.     

Fully plastic analyses of plane strain single-edge-cracked specimens subject to combined tension and bending

Accurate yield surfaces of plane strain single-edge-cracked specimens having shallow as well as deep cracks are developed using finite element limit analyses and monotonic interpolation functions. Fully plastic shallow crack configurations are classified based on certain aspects of the yield surfaces. Relationships between incremental plastic crack tip and crack mouth opening displacements and incremental load point displacement/rotation are obtained for a wide range of relative crack depths and loading ratios. Fully plastic crack-tip fields for a sufficiently deep crack in a single-edge cracked specimen are examined to provide the stress triaxiality and the angular orientation of flow line at the crack tip in terms of the remotely applied tension-to-bending ratio. Evidence for fully plastic crack-tip stress fields consisting of an incomplete Prandtl fan and a crack plane constant state region is discussed.     

A unified fatigue failure criterion for unidirectional laminates

A unified fatigue failure criterion using micromechanics related to the fracture plane has been developed to predict fatigue lives of unidirectional fibre reinforced polymer composites subjected to cyclic off-axis tension–tension loading. Since the failure criterion incorporates both stresses and strains it may be characterized as energy based. Accounting for the fibre load angle as well as the stress ratio is the novelty of this fatigue failure criterion. The criterion only requires the stress ratio to be known from the experimental procedure. The relation between the applied load and the micro-stress and micro-strain field can be determined from a numerical method. The fatigue failure criterion has been verified by applying it to different sets of experimental data. Several fibre load angles, different fibre/matrix combinations as well as stress ratios are covered. The predicted fatigue lives are in good agreement with the experimental results for both different fibre load angles and stress ratios.     

Fracture mechanisms in glass-reinforced plastics

Model glass fibre/polyester resin composites have been made in the form of double cantilever beams and the effect of a small number of fibres on quasi-static crack propagation has been studied by simultaneous plotting of load/deflection curves, measurements of crack length, and observation of the progress of fibre/resin debonding and fibre pull-out. By varying the condition of the fibre surface and the arrangement of the fibres to a limited extent and carrying out subsidiary experiments on single-fibre samples of identical character it has been possible to make direct measurements of all of the important parameters required for an analysis of the macroscopic behaviour in terms of established models of fibre/matrix interaction. Agreement between experimental and calculated fracture energies for these model composites is not highly satisfactory, but it seems clear that the fracture energy of grp is likely to be determined very largely by work done against friction between fibres and matrix after the debonding process has occurred. This conclusion opposes the currently-held view which attributes the largeγ _F values of grp to the fibre/resin debonding mechanism.     

Numerical simulation of fatigue crack growth behavior by crack-tip blunting

In ductile metals one of basic mechanisms for fatigue crack growth is that based on crack-tip blunting under the maximum load and re-sharpening of the crack-tip under minimum load. In this paper, simulations of fatigue crack growth by crack-tip blunting using ANSYS finite element code are presented. This investigation focuses solely on simulation of fatigue crack growth due to crack-tip plasticity only. As such, any material damage and its fracture is not considered. Due to high plastic deformation the present simulations utilize a remeshing technique which allows applying a number of load cycles without terminating the simulation due to the error caused by excessive mesh distortion. The simulations were conducted using a center cracked specimen under various loading conditions including different load ranges and load ratios R = −1, 0 and 0.333. It is shown that fatigue crack growth (FCG) slows down with number of cycles towards a steady state value. The simulated FCG data for constant amplitude loading follow the Paris power law relationship and also indicate a typical R-ratio dependence. It can be noted that for all load cases with load ratios R > 0 no crack closure in the vicinity of the crack-tip wake was observed.     

Interaction of welding residual stresses and warm pre-stressing on brittle fracture of a pipe containing an internal semi-elliptical crack

Residual stresses (RS) due to welding process, may change the load bearing capacity of cracked components. These stresses can also affect the benefit of warm pre-stressing (WPS) cycles which are used for improving structure behaviour. RS are obtained from a two-passes welding simulation of a pipe and verified by experiments. A semi-elliptical internal crack at the weld line is considered. Redistribution of RS field after introducing the crack shows a significant tensile RS are remained at the crack tip. Two common WPS cycles, load-cool-fracture (LCF) and load–unload-cool-fracture (LUCF), are applied using the model at room and low temperature subjected to axial loading. Using local approach to fracture shows that welding RS dramatically raise the fracture probability. LCF has more influence on reducing the fracture probability in comparison with LUCF. The interaction of welding RS and WPS cycles still improves the fracture properties, however, welding RS cause to decrease the benefit of WPS. Comparing RS distributions on crack-tip shows that applying WPS cause to release a significant amount of welding RS and therefore, WPS can be very useful for welded structures. The near crack-tip opening stresses at a same fracture load are further studied for all cases.     

Fracture toughness of the fibre-matrix interface in glass-epoxy composites

The failure process arising at a broken fibre end in polymer matrix composite materials has been studied experimentally and analytically using the finite element method. A series of experiments were carried out using S-glass and E-glass single filaments, with different sizings and/or coupling agents, embedded in epoxy matrices with different moduli. A finite element analysis was used to simulate the experiments and calculate the change in strain energy accompanying the observed fracture mode. The strain energy release rate upon arrest of the crack, G _arrest, was then calculated. The measured interface debonding energies varied from G _arrest=57–342 J m^–2, depending primarily on the nature of the fibre sizing and the ratio of moduli of the fibre and matrix. Transverse and shear matrix cracks were characterized by G _arrest values of 58–103 J m^–2. Subtle changes in the constituent properties or fibre surface treatment resulted in a change in the fracture mode. This measurement and analysis technique may suggest reasons for the variability of previous measurements of interfacial adhesion, and provide a standard method for characterizing fracture modes at broken fibre ends.