Fatigue fracture mechanisms and fractography of short-glassfibre-reinforced polyamide 6

An adaptation to existing failure models for fatigue fracture of short-fibre-reinforced thermoplastics is presented. This was based on results using some new experimental methods. These results led to the conclusion that cracks in glassfibre-reinforced polyamide 6 (conditioned to equilibrium water content) remain bridged by plastically drawn matrix material and/or fibres until just prior to final fracture. In this article, emphasis will be on the fractographic evidence for the existence of this failure mechanism. Also some other phenomena in glassfibre-reinforced polyamide will be mentioned. Apart from the normal fractographic investigations, specimens were cryogenically fractured after fatigue, revealing the structure of damage, before failure. Both fracture surfaces were compared, showing that only a small fraction of the fibres is broken in fatigue; mostly the fibres are pulled out. The mechanism consists of the following steps: damage begins with void formation, mainly at fibre ends; these voids coalesce into small cracks. These cracks, however, do not grow into one full crack, but the crack walls remain connected at several points. This is contrary to the fracture mechanism for the dry as-moulded material. When the material is dry as moulded, the matrix material cracks, without showing much ductility, and no bridges are formed. This revised version was published online in November 2006 with corrections to the Cover Date.     

Crack growth in hybrid fibrous composites

A preliminary analysis is made of the energetics of transverse crack growth in a brittle elastic matrix bridged by elastic fibres fictionally bonded to the matrix. Studies made of the stability of a crack of finite length in a brittle polymeric material reinforced with steel wires are found to be in reasonable agreement with the predictions of the theory. It is proposed that the stability of transverse cracks in a very brittle matrix could be increased substantially by the inclusion of a second fibre component designed specifically to increase the work of fracture of the matrix. This has been shown to be possible using a very small volume fraction of glass fibres as a matrix toughening component and it has also been observed that stable transverse matrix crack growth can be achieved with composite systems of this type. This principle might have applications in the design of hybrid composites utilizing either a brittle polymeric or ceramic matrix.     

The stress-strain behaviour of a porous unidirectional ceramic matrix composite

The stress-strain behaviour of a porous unidirectional ceramic matrix composite is investigated. The fibres are SiC (Nicalon) and the matrix is an aluminium phosphate based system. Microscopic observations indicate that pores and microcracks break up the continuity of the matrix to create an irregular array of discontinuities or ‘matrix cracks’. Load/unload tensile test results indicate an increase in compliance, permanent strain and hysteresis as the peak stress is increased. These features are attributed to sliding at the fibre-matrix interface. In the model developed, the product of the crack spacing and interfacial sliding stress, l_cτ, completely defines the stress-strain response provided the constituent properties, residual stresses and initial crack spacing are known. For the material investigated, the product l_cτ maintains a value of about 1.0 mm MPa throughout the tensile test. This result is corroborated by optical measurements of the pore/microcrack spacing and push-out test results.     

Fatigue crack propagation in SiC continuous fibre-reinforced Ti-6Al-4V alloy metal-matrix composites

Fatigue crack growth from a through-thickness cut notch has been studied at ambient temperature in a Ti-6Al-4V alloy matrix reinforced with Sigma (SiC) fibres. All tests have been carried out in three-point bending, and localized dominant cracks have been produced in all cases. In these composites such dominant cracks often grow off-axis, and marked effects of stress ratio on crack growth rates have been measured. At low stress ratio, the composites exhibit outstanding crack growth resistance. It has been possible to observe fatigue striations within the matrix alloy and these observations allow local crack growth rates (and hence local effective stress intensity ranges) to be determined. The implications of such studies for defect tolerance and usable stress ranges for these composites have been considered.     

复合材料层合板基体裂纹的协同损伤演化模型

首先,为研究复合材料层合板在准静态载荷下的基体裂纹演化特征,提出了一个基于能量的协同损伤演化模型。然后,通过模型对损伤进行了多尺度分析:从微观角度,采用三维有限元方法求得裂纹表面位移;从宏观角度,结合裂纹表面位移,推导了萌生基体裂纹的能量释放率。最后,根据裂纹萌生准则对基体裂纹的演化过程进行预测。模型考虑了演化过程中损伤的相互影响、残余应力、基体材料非线性、材料初始损伤分布及损伤演化的不均匀性。根据演化分析流程计算了[±θ/904]s铺层玻璃纤维复合材料的基体裂纹演化过程。结果表明:这一模型能够准确地预测准静态载荷下复合材料层合板基体裂纹的损伤演化规律。     

Influence of temperature on fracture initiation in PET and PA66 fibres under cyclic loading

The fatigue of single thermoplastic fibres has been well documented to occur in a reproducible manner when they are subjected to certain cyclic loading conditions. The fatigue fracture morphologies of these fibres are very distinctive and differ markedly from other types of failure. This type of behaviour, which is clearly seen with the unambiguous tests on single fibres, must reflect behaviour of fibres in more complex structures which are subjected to cyclic loading. Only limited numbers of reports have, however, shown similar fracture morphologies with fibres extracted from fibre bundles embedded in a matrix material such as rubber. Usually the fractured ends of fibres taken from structures are seen to be shorter than those obtained in single fibre tests and also they show more complex and confused crack growth. The present study reveals that the low thermal conductivity of the fibres, exacerbated when they are embedded in a rubber matrix, leads to very high temperature rises, which is not the case in single fibre tests and under these conditions, crack initiation occurs across the fibre section instead of being restricted to the near surface region. Tests on single fibres at temperatures up to and beyond the glass transition temperature have shown how the fracture morphologies become modified. The fatigue process has been seen to become generalised throughout the fibre and failure occurs due to the coalescence of several cracks, some of which are initiated in the core of the fibre. In all cases, the cracks can be seen to have been initiated by solid inclusions in the fibres.     

Prediction of failure modes in unidirectional short-fibre composites

In short-fibre reinforced composites, penny-shaped cracks often initiate from fibre-ends and propagate into the matrix until they are arrested by the neighbouring fibres. A theoretical study on the prediction of failure modes after the arrest, that is, either the penetration of the crack into the fibres or the debonding of the matrix-fibre interface, is performed. The analytical method used in this study is the extension of the two-dimensional model of Kendall to the three-dimensional crack problem. Strain energy release rates for the initiation of the cracks of the penetration and debonding types are calculated. Also computed are the total potential energy required for a complete penetration of the crack through the fibre diameter and a complete debonding of the matrix-fibre interface. Based on these computations, the failure modes of the crack arrested by the neighbouring fibres are discussed.This research was supported by the National Science Foundation under Grant No. CME-7918249.On leave from Department of Mechanical Engineering, University of Electro-Communications, Tokyo, Japan.     

The effect of the interaction of cracks in orthotropic layered materials under compressive loading

The non-classical problem of fracture mechanics of composites compressed along the layers with interfacial cracks is analysed. The statement of the problem is based on the model of piecewise homogeneous medium, the most accurate within the framework of the mechanics of deformable bodies as applied to composites. The condition of plane strain state is examined. The layers are modelled by a transversally isotropic material (a matrix reinforced by continuous parallel fibres). The frictionless Hertzian contact of the crack faces is considered. The complex fracture mechanics problem is solved using the finite-element analysis. The shear mode of stability loss is studied. The results are obtained for the typical dispositions of cracks. It was found that the interacting crack faces, the crack length and the mutual position of cracks influence the critical strain in the composite.     

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.     

Modelluntersuchungen zur Faserverstärkung keramischer Werkstoffe

Model Investigation of the Fibre Reinforcement of Ceramic Materials A mechanism for fibre reinforcement of high-modulus brittle materials, in particular ceramics, is investigated both experimentally and theoretically. A simple mathematical formalism representing crack extension in a brittle matrix reinforced by ductile fibres is derived, and characteristic property values, adapted to composite structures, are introduced. Alumina with unidirectional reinforcement by thin 80Ni20Cr wires is used as a model material. The mechanism presented allows to reduce the high sensivity of ceramic materials to cracks. It is necessary for the fibres to bridge matrix cracks under load. For this purpose, the fibres must not be bound too tightly to the matrix, and while a high ductility is certainly of value, it is not a necessity. The efficiency of the mechanism depends on

• – interface energy and friction at the matrix-fibre interface,
• – deformation and fracture behavior of the fibre material,
• – radius of the fibres,
• – volume fraction of the fibres,
• – critical stress intensity factor of the matrix,
• – size of the largest crack.

Among these, the fibre radius appears to be the most suitable one for variation with the goal of optimizing material quality.     

Mode II interfacial toughening through discontinuous interleaves for damage suppression and control

An investigation is described concerning the interaction of propagating inter-laminar cracks with embedded strips of interleaved materials in E-glass fibre reinforced epoxy composite. The approach deploys inter-ply strips of thermoplastic film, chopped aramid fibres, pre-impregnated fibre reinforced tape and thermosetting adhesive film, ahead of the crack path on the mid-plane of end loaded split (ELS) specimens promoting energy absorbing mechanisms, at low strain rates, through interfacial toughening ahead of the propagating crack.Following experimental mode II tests, the features were observed to imbue an apparent increase in the toughness of the parent material and suppression of crack growth. The mechanism behind the energy absorption and the behaviour of the crack interaction at the boundary of the interleave edge on ingress and egress were analysed using fractographic processes.     

Relationships between microstructures and fracture energies in carbon fibre/PEEK composites

The aim of this investigation was to characterize the fracture surfaces of a series of similar composites, and to relate the features observed to the fracture modes. The materials used in this study were based on the ICI material APC-2, being uniaxially aligned composites of carbon fibre in a matrix of poly-ether-ether-ketone, peek. The fracture method chosen for this comparative study was to propagate cracks in the weakest plane of the materials, so that the samples split under the wedging action of a blade driven into the material. The fracture surfaces are thus representative of cracks propagating parallel to the fibres and normal to the prepreg layers. Fracture energies were obtained from analysis of the geometry of the crack without the need for any load measurements using a specially developed technique, the razor blade test^1,2. The fracture surfaces were prepared from the slivers of material split off in the test, and were examined in the scanning electron microscope (sem). They were thus taken from the same region of material which yielded the data on fracture energy. The principal microstructural factors identified as being significant were the matrix ductility and the fibre/matrix adhesion.     

Effects of inter-fibre spacing and matrix cracks on stress amplification factors in carbon-fibre/epoxy matrix composites. Part I: planar array of fibres

When the loading on a composite is sufficient to cause fracture of an individual fibre, the resulting stress amplification in the adjacent intact fibres may be large enough to cause failure of these fibres. In this work, 3D elasto-plastic finite element analysis was used to investigate the effect of inter-fibre spacing on the stress amplification factor in a composite comprising a planar array of fibres. A Progressional Approach was used in the FE analysis to simulate the constituent non-linear processes associated with the generation of thermal residual stresses from fabrication, the fibre fracture event and the subsequent initiation and propagation of conical matrix cracks induced with incremental tensile loading. As the inter-fibre spacing increases, the effect of fibre fracture on the stress distribution in the neighbouring intact fibres is reduced, whereas the effect on the matrix material is increased, thereby inducing localised yielding. The presence of a conical-shaped matrix crack was found to increase both the stress amplification factor and the positively affected length in neighbouring fibres. For a large inter-fibre spacing, a longer matrix crack is required to obtain good agreement with LRS measurements of fibre stress.     

X-ray tomographic observations of microcracking patterns in fibre-reinforced mortar during tension stiffening tests

For the last decades, new reparation or fabrication processes have been studied to replace traditional rebar by roving of different mineral or organic fibres to avoid corrosion issues. Such materials refer to the family of cementitious composite. Their tensile strength would directly depend on the proportion of reinforcement and strongly on the interfacial mechanical properties between fibres and cementitious matrix. From now, evaluation of interfacial properties was mostly limited to the use of force–displacement curves obtained from mechanical experiments. This work presents a new methodology using micromechanical tension stiffening tests combined with X-ray computed tomography (XRCT) observations, performed at the Anatomix beamline at Synchrotron SOLEIL, and specific image processing procedures. Multi-XRCT acquisitions with suitable scanning strategy are used to image the whole fibre-matrix interface along centimetric samples at four to five different levels of loading magnitude. Intensive image processing is then performed on tomographic images including digital volume correlation (DVC), image subtraction and Hessian-based filtering. This experiment allows to study damage mechanisms at small scale. The proposed methodology shows great potential to provide both qualitative and quantitative elements on interfacial mechanical behaviour such as crack growth and crack orientation. The interface between mortar and sufficiently small multi-fibre yarn used in this paper is shown to behave in certain condition as traditional rebar interface producing conical cracks in the surrounding matrix rather than debonding in mode 2, permitting a much higher energy dissipation during debonding. According to this study, conical cracks repartition and geometry are mostly influenced by the cementitious matrix. The spacing between cracks goes from 50 to 100 μm, and the angle between crack normal vector and yarn orientation goes from 35° to 50°.     

On the interaction between a screw dislocation and a circular coated inclusion with interfacial cracks

Summary The problem of the elastic interaction between a screw dislocation, which is located at an arbitrary point inside either the matrix or the inclusion, and a circular coated inclusion with interfacial cracks is dealt with. An efficient and concise method for a complex multiply connected region is developed, in terms of which the general solutions to the problem are derived. As an illustrative example, explicit series form solutions for complex potentials are presented in the case of one interfacial crack. Based on the complex potentials, image forces on the screw dislocation are then calculated using the Peach-Koehler formula. The equilibrium position of the dislocation is discussed in detail for various crack geometries, coating layer thicknesses and material constant combinations. It is shown that the influence of interfacial cracks on the motion of the dislocation near the coated inclusion is significant. The present solutions contain a number of previously known results as special cases.     

不同裂纹分布的孔隙材料渗透系数

含裂纹孔隙材料渗透性由裂纹的微观结构决定,其研究对工程实践意义重大。该文假设含裂纹孔隙材料是由孔隙基体和裂纹组成的二相复合材料,基于细观均匀化理论给出了四种不同裂纹分布的渗透张量稀疏解、相互作用直推（IDD）解和修正的IDD解。基于单元嵌入技术和弹性比拟的数值模拟方法,采用不连通的离散裂纹模型,研究了裂纹数目对有效渗透系数数值解收敛性的影响及不同裂纹分布的孔隙材料渗透性,并将得到的数值解和理论解对比分析,结果表明:随着裂纹数目的增加,有效渗透系数的变化范围逐渐减小,并最终趋于稳定,而且选择合适的裂纹数目,能同时保证计算的随机收敛性和合理的计算效率;对于所研究的四种分布的裂纹,相比稀疏解,IDD解更接近数值解,但随着裂纹密度的增加,裂纹间的相互作用增强,IDD解会逐渐偏离数值解;修正的IDD解充分考虑了裂纹间的相互作用和边界效应,能更好地估计含裂纹孔隙材料的渗透性。     

Mode I interfacial toughening through discontinuous interleaves for damage suppression and control

An investigation is described concerning the interaction of propagating interlaminar cracks with embedded strips of interleaved materials in E-glass fibre reinforced epoxy composites. The approach deploys interlayer strips of a thermoplastic film, thermoplastic particles, chopped fibres, glass/epoxy prepreg, thermoset adhesive film and thermoset adhesive particles ahead of the crack path on mid-plane of Double Cantilever Beam (DCB) specimens. During these mode I tests, the interlayers were observed to confer an apparent increase in the toughness of the host material. The crack arrest performance of individual inclusion types are discussed and the underlying mechanisms for energy absorption and the behaviour of the crack at the interaction point of the interleave edge were analysed using scanning electron microscopy.     

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.     

Effect of microcracking on the micromechanics of fatigue crack growth in austempered ductile iron

The effect of microcracking on the mechanics of fatigue crack growth in austempered ductile iron is studied in this paper. The mechanism of fatigue crack growth is modelled using the boundary element method, customized for the accurate evaluation of the interaction effects between cracks and microcracks emanating from graphite nodules. The effects of nodule size and distribution and crack closure are considered, with deviation bounds of computed results estimated through weight-function analyses. A continuum approach is employed as a means of quantifying the shielding effect of microcracking on the dominant propagating crack, due to the reduction of stiffness of the material in the neighbourhood of the crack tip. Although the results obtained may not yield actual numbers for real cases, they are in accordance with experimental observations and demonstrate how the main factors affect the crack growth of the macrocrack.     

The mechanical properties of carbon fibre reinforced Pyrex glass

The mechanical properties of carbon fibre reinforced Pyrex glass are discussed in terms of the volume fraction of fibre, the orientation of the fibres, fibre damage during fabrication, matrix porosity, matrix critical strain, interface properties and the mode of failure in bend tests. The stress at which matrix cracking occurs increases with fibre concentration indicating that the critical strain of the matrix increases as the fibre separation decreases. The ultimate strength of the composite is considerably greater than the stress at which the matrix begins to crack. Preliminary stress cycling experiments at stresses above that at which matrix cracks are formed suggest that propagation of these cracks is inhibited by the fibres.