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.     

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.     

Modelling cyclic shear deformation of fibre/epoxy layers in fibre metal laminates

Relations for a theoretical model were derived describing the shear deformation of uni-directional fibre/epoxy layers in Fibre Metal Laminates. The shear deformation is induced by the cyclic shear stresses at the interface that result from the cyclic load transfer from aluminium to the bridging fibre/epoxy layers during fatigue loading of the laminate. With the presented relations the crack opening contribution as result of shear deformation can be calculated. As the shear deformation is hard to measure experimentally, the theoretical model has been validated by comparing the model with finite element analysis. A good correlation has been obtained between the presented theoretical model and the FE-model representing the complex reality.     

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.     

Evaluation of fibre bridging stress of short fatigue cracks in SCS-6/Ti-15-3 composite

Single‐edge notched specimens of a unidirectional SiC long fibre reinforced titanium alloy, were fatigued under four point bending. The propagation behaviour of short fatigue cracks from a notch was observed on the basis of the effects of fibre bridging. The branched fatigue cracks were initiated from the notch root. The fatigue cracks propagated only in the matrix and without fibre breakage. The crack propagation rate decreased with crack extension due to the crack bridging by reinforced fibres. After fatigue testing the loading and residual stresses in the reinforced fibres were measured for the arrested cracks by the X‐ray diffraction method. The longitudinal stresses in the reinforced fibres were measured using high spatial resolution synchrotron radiation. A stress map around the fatigue cracks was then successfully constructed. The longitudinal stress decreased linearly with increasing distance from a location adjacent to the wake of the matrix crack. This region of decreasing stress corresponded to the debonding area between the fibre and the matrix. The interfacial frictional stress between the matrix and the fibre could be determined from the fibre stresses. The bridging stress on the crack wake was also measured as a function of a distance from a notch root. The threshold stress intensity factor range, corrected on the basis of the shielding stress, was similar to the propagation behaviour of the monolithic matrix. Hence the main factor influencing the shielding effect in composites is fibre bridging.     

Effect of thermomechanical loads on the propagation of crack near the interface brittle/ductile

The purpose of this paper is to understand the combined effect of thermal and mechanical loading on the initiation and behaviour of sub-interface crack in the ceramic. In this study a 2D finite element model has been used to simulated mixed mode crack propagation near the bimaterial interface. The assembly ceramometalic is subjected simultaneously to thermomechanical stress field. The extent of a plastic zone deformation in the vicinity of the crack-tip has a significant influence on the rate of its propagation. The crack growth at the joint specimen under four-point bending (4PB) loading and the influence of residual stresses was also evaluated by the maximum tensile stress criterion. The J-integral at the crack tip is generally expressed by the thermomechanical local stresses. The results obtained show the effect of the temperature gradient ΔT, the size of the crack and the applied stresses on the J-integral.     

Micromechanical modelling of strain hardening and tension softening in cementitious composites

This paper will describe a procedure for modelling the complete macroscopic response (including strain hardening and tension softening) of two short fibre reinforced cementitious composites and show how their microstructural parameters influence this response. From a mathematical point of view it is necessary to examine how bridging forces imposed by the fibres alter the opening of multiple cracks in elastic solids under unidirectional tensile loading. The strain hardening is essentially due to elastic bridging forces which are proportional to crack opening displacements. After a certain critical crack opening displacement is reached, some fibres progressively debond from the elastic matrix and thereafter provide a residual bridging force by frictional pull-out, while others continue to provide full bridging. This results in a kind of elasto-plastic bridging law which governs the initial tension softening response of the composite. Besides the usual square-root singularity at crack tips, the elasto-plastic bridging law introduces a logarithmic singularity at the point of discontinuity in the bridging force. These singularities have been analytically isolated, so that only regular functions are subjected to numerical integration. Unbridged multiple crack problems have in the past been solved using double infinite series which have been found to be divergent. In this paper a superposition procedure will be described that eliminates the use of double infinite series and thus the problem of divergence. It is applicable to both unbridged and bridged multiple cracks. The paper will end by showing how the model of multiple bridged cracks can accurately predict the prolonged nonlinear strain hardening and the initial tension softening response of two cementitious composites.     

Numerical and experimental analysis of residual stresses for fatigue crack growth

In this paper computational and experimental results are presented concerning residual stress effects on fatigue crack growth in a Compact Tension Shear (CTS) specimen under cyclic mode I loading. For a crack of constant length it is found that hardly any compressive residual stresses or crack closure effects are generated along the crack surfaces behind the crack tip through the considered cyclic mode I loading with a load ratio of R=0.1. Only if fatigue crack growth is modelled during the simulation of the cyclic loading process these well-known effects are found. On the other hand it is shown that they have hardly any influence on the residual stresses ahead of the crack tip and thus on further fatigue crack growth. For all cases considered the computational finite element results agree well with the experimental findings obtained through X-ray diffraction techniques.     

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.     

Electrostatic tractions at crack faces and their influence on the fracture mechanics of piezoelectrics

The influence of electrostatic tractions acting upon crack faces on the fracture mechanical quantities in piezoelectric materials under electromechanical loading is investigated. The physical background are the mechanical and dielectric equilibria at an interface between two dielectric domains and related mechanical stresses. The model is applied to a crack problem, where a dielectric interface exists between the solid material and the insulating crack medium. The analytical solution for a crack in an infinite piezoelectric body accounting for intrinsic charges and electrostatic stresses on the crack faces gives insight into the influence of crack boundary conditions on the field intensity factors. Varying loading conditions and the dielectric permittivity of the flaw yields a parameter range in which induced crack surface tractions are relevant. Then, the calculation of the J-integral for thermodynamically consistent crack boundary conditions is discussed. The line integral along the crack faces is replaced by a simple jump term. This approach comes out to be exact only for a simplified model of the electrostatic tractions.     

Fatigue behaviour of carbon fibre-reinforced aluminium laminates

A new hybrid composite (CARALL), consisting of thin layers of carbon fibre/ epoxy prepreg sandwiched between aluminium sheets, has been developed. It is shown that this class of materials offers higher modulus, higher tensile strength and lower density than 2024-T3 alloy in the longitudinal direction. Under tension-tension fatigue loading, the hybrid laminates showed superior fatigue crack propagation resistance in the longitudinal direction, which may be attributed to the bridging effect imposed by the intact fibres in the crack wake. It has also been shown that the effectiveness of fatigue crack growth reduction increases with the thickness of the carbon fibre/epoxy layer. The resistance to fatigue crack propagation can be further improved by introducing compressive residual stresses in the aluminium layer by postcure stretching the laminate in the plastic region of the aluminium alloy.     

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.     

Interactions of fatigue cracks with elastic obstacles

To quantify the growth behaviour of fatigue cracks growing towards microstructural barriers or elastic obstacles, parametric solutions are obtained for crack-tip opening displacement and plasticity-induced crack closure of a mode I fatigue crack growing towards elastic obstacles. Three common bi-material systems are analysed using the finite element method, in which both constituent materials have identical elastic properties but only the phase that contains the crack can deform plastically. It has been found that under monotonic loading the crack-tip opening displacement decreases as the crack-tip approaches the interface boundary, but reaching a non-zero value when the crack-tip terminates at the boundary. For a fatigue crack growing under constant amplitude loading, the crack-closure stress has been found to increase as the crack grows towards the barrier. Based on these results a mechanistic model is proposed to quantify the influence of stress level on the fatigue threshold of microstructurally small fatigue cracks, with predictions being in close agreement with experimental data.     

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.     

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.     

Fatigue and Damage Tolerance of Glare

Methods have been developed to describe the fatigue initiation and propagation mechanisms in flat panels as well as mechanically fastened joints and to determine the residual strength of large flat panels. Glare shows excellent crack growth characteristics due to the mechanism of delamination and fibre bridging. The fatigue insensitive fibres restrain the crack opening and transfer load over the crack in the metal layers. During the initiation phase fibre bridging does not occur and the behaviour is dominated by the metal initiation properties. Mechanically fastened joints introduce additional effects such as secondary bending, load transfer and aspects related to the fastener installation. The residual strength of Glare is dependent on the amount of broken fibres and the delamination size and can be described with the R-curve approach.The impact resistance of Glare is related to the aluminium and glass/epoxy properties and is significantly higher than the impact resistance of monolithic aluminium. The same has been proven for fire resistance. Depending on the Glare grade and thickness, the outer aluminium layer will melt away, whereas the other layers will remain intact due to carbonisation of the glass/epoxy layers and delamination of the laminate. The air in the delaminations will act as insulation, keeping the temperatures at the non-exposed side relatively low.     

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.     

Finite element analysis of the stress distribution in a thermally and transversely loaded Ti–6Al–4V/SiC fibre composite

The load transfer between fibre and matrix in a metal matrix composite (MMC) depends on the properties and conditions of the fibre/matrix interfacial region. The objective of this investigation is to gain a better understanding of the stresses generated within a continuously reinforced MMC, particularly at this interface. Finite element analysis is used to investigate the effect of thermal and transverse mechanical loading on the SiC/Ti–6Al–4V composite system. The effect on the stress field of a carbon coating on the SiC fibres is also investigated. The results indicate that the interfacial region affects the stress distribution, with the presence of the carbon coating significantly altering the stress profiles generated. It is also found that the residual stresses generated as a result of cooling down the composite from processing temperature, has a marked effect on the stress profile and the behaviour of the composite when subsequent mechanical loading is applied.     

Response of fibre reinforced aluminium–lithium laminates to different fatigue conditions

Under fatigue conditions fibre reinforced aluminium–lithium laminates do not respond in the same manner as monolithic aluminium alloys. The variation of fatigue crack growth rates with initial loading condition has been examined for both carbon and glass fibre reinforced laminates, and compared with the behaviour of unreinforced 8090 aluminium–lithium alloy for a range of conditions (different initial nominal stress intensity factor range, load range and reversed loading). During fatigue, cracks grow in the metal layers of these laminates whilst the fibres in the crack wake remain intact, bridging the crack faces. The fibre bridging mechanism, inherent in this laminate system, reduces the fatigue crack growth rate. The magnitude of the bridging effect appears to be inversely related to the applied load range. This relationship can account for the behaviour observed in the performed experiments. This revised version was published online in November 2006 with corrections to the Cover Date.