Deformation micromechanics in high-modulus fibres and composites

It is demonstrated that Raman spectroscopy can be used to study the deformation micromechanics of aramid fibres and of the fibres in a model single-fibre composite with an epoxy resin matrix. It is shown that the peak position of the 1610cm⁻¹ aramid Raman band shifts to lower frequency under the action of stress or strain as a result of the macroscopic deformation leading to direct stretching of the aramid molecules. The strain-induced band shifts can be used to follow the deformation of the aramid fibres in a composite matrix. This allows the distribution of strain to be mapped along a fibre, and it is shown that the behaviour is consistent with that predicted by the classical shear-lag analysis. It is also demonstrated that the interfacial shear stress can be calculated from the distribution of strain along the fibre. Finally, the technique is extended to measure the strain in fibres in a single-fibre composite which are aligned at an angle to the tensile axis. In this case it is shown that the strain in the centre of the fibres is identical to that predicted by classical elasticity theory.     

Theory of multiple fracture of fibrous composites

The theoretical stress-strain behaviour of a composite with a brittle matrix in which the fibre-matrix bond remains intact after the matrix has cracked, is described. From a consideration of the maximum shear stress at the fibre-matrix interface, the extent of fibre debonding and the crack spacing in a partially debonded composite are derived. The energetics of cracking and the conditions leading to an enhanced matrix failure strain are then discussed and, finally, the crack spacing expected in composites containing fibres isotropically arranged in two or in three dimensions is derived for the case of very thin and hence very flexible fibres.     

Hierarchical modelling of a polymer matrix composite

A hierarchical modelling scheme to predict the properties of a polymer matrix composite is introduced. The stress–strain curves of amine-cured tetraglycidyl 4,4′-diaminodiphenylmethane (TGDDM) cured have been predicted using group interaction modelling (GIM). The GIM method, originally applied primarily to linear polymers, has been significantly extended to give accurate, consistent results for TGDDM, a highly crosslinked two-component matrix. The model predicts a complete range of temperature-dependent properties, from fundamental energy contributions, through engineering moduli to full stress–strain curves through yield. The predicted properties compare very well with experiment. Using the GIM-predicted TGDDM stress–strain curve, a 3D finite element model is used to obtain strain concentration factors (SCF) of fibres adjacent to a fibre break in a unidirectional (UD) composite. The strain distribution among the intact neighbouring fibres is clearly affected by the yielding mechanism in the resin matrix. A Monte Carlo simulation is carried out to predict the tensile failure strain of a single composite layer with the thickness equal to the fibre ineffective length. The effect of matrix shear yielding is introduced to the model through the SCF of surviving fibres adjacent to the fibre-break. The tensile failure strain of the composite is then predicted using a statistical model of a chain of composite layers.     

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.     

Experiments on shear deformation,debonding and local load transfer in a model graphite/glass/epoxy microcomposite

Recent statistical theories for the failure of polymer matrix composites depend heavily on details of the stress redistribution around fibre breaks. The magnitudes and length scales of fibre overloads as well as the extent of fibre/matrix debonding are key components in the development of longitudinal versus transverse crack propagation. While several theoretical studies have been conducted to investigate the roles of these mechanisms, little has been substantiated experimentally about the matrix constitutive behaviour and mechanisms of debonding at the length scale of a fibre break. In order to predict the growth of transverse and longitudinal cracks using the same micromechanical model, we microscopically observed the epoxy shear behaviour around a single fibre break in a three-fibre microcomposite tape. The planar specimens consisted of a single graphite fibre placed between two larger glass fibres in an epoxy matrix. The interfibre spacing was less than one fibre diameter (<6 m) in order to reflect the spacing between fibres found in typical composites. The epoxy constitutive behaviour was modelled using shear-lag theory where the epoxy had elastic, plastic, and debond zones. The criteria for debonding were modified from conventional shear-lag approaches to reflect the orientational hardening in the epoxy network structure. The epoxy, which is brittle in bulk, locally underwent a shear strain of about 60% prior to debonding from the fibre.     

Micromechanics of multiple cracking Part I Fibre analysis

Fibre-reinforced brittle materials exhibiting a strain-hardening tensile behaviour undergo a multiple cracking process. A micromechanical analysis of a straight smooth fibre, bridging one or several cracks in a multiply-cracked composite is introduced, taking into account the full or elastic bond, gradual debonding, and frictional sliding of the fibre. Equilibrium is satisfied by means of a two-fibre system introducing a symmetry fibre within the segment. Equations for different debonding cases are derived. The fibre ends are analysed using a simplified approach, the validity of which is discussed. The system equations are derived from the compatibility condition of equal crack widths. Two examples are analysed to study the effects of crack spacing. ©1998 Kluwer Academic Publishers     

The embedded single-fibre dynamic load test — a new non-destructive interphase investigation tool

Embedded single-fibre tests are commonly used to investigate fibre/matrix adhesion. However, unstable crack propagation renders these destructive tests hard to interpret. Most of the relevant theories apply an energy or a strength criterion to indirectly deduce interphase properties from the obtained results. A new method, the embedded single-fibre dynamic load (SFD) test, was developed to measure interphasial viscoelastic properties directly in a non-destructive way. Using different fibres in combination with poly(phenylene sulfide) in a comparative study, it is shown that results from the SFD test correlate well with those from single-fibre pull-out (SFP) tests. The morphology is established as a key link for an understanding of the fracture behaviour as well as the dynamic-mechanical behaviour of the interphase in fibre-reinforced composites.     

Evaluation of toughness of textile concrete

High Performance Fibre Reinforced Cementitious Composites (HPFRCC) are characterized by a stress–strain response in tension that exhibits strain-hardening behaviour accompanied by propagation of multiple cracks. This process is often referred to as pseudo-ductility due to multiple cracking with relatively large energy absorption capacity. The cracking characteristics are dependent on matrix strength, fibre/matrix bond, fibre volume fraction and the aspect ratio of the fibre used in the composite. The matrix cracking strength and interfacial bond vary with the degree of hydration of cement in the matrix, which is time and environment dependent. This study analyses the multiple cracking patterns formed in weathered Textile Concrete (TC) samples due to direct tensile testing, and links the cracking patterns to the tensile behaviour. The specimens used for the study were thin laminates which were produced by casting six layers of specially made polypropylene (PP) textile in fine-grained mortar. The samples were cured under controlled laboratory conditions for 28 days, and thereafter exposed to different weathering regimes for different periods. The weathered samples were tested in direct tension in a Universal Testing Machine (UTM) over a range of stresses. For all the samples tested, it was observed that the tensile behaviour was characterised by strain hardening and multiple cracking, which gave high tensile strains in excess of 20% at final failure. It was further found that the cracking patterns varied mainly with age, weathering history and stress levels. Other factors that contributed to the cracking characteristics were moisture state of the specimen and the fibre/matrix bonding strength. A strong bond and dense matrix resulted in wide crack spacings compared with samples with a weaker bond which developed closely spaced cracks. A general trend of increasing crack widths and crack spacings with ageing was observed which was accredited to increased hydration accompanied by an increase in fibre/matrix bond strength.     

Research on production,performance and fibre dispersion of PVA engineering cementitious composites

Abstract

Polyvinyl alcohol (PVA) fibre is considered as one of the most suitable polymeric fibres to be used as the reinforcement of engineered cementitious composites (ECCs). Research and application have shown that PVA–ECC can significantly counteract the deficiency of ordinary concrete. In the present paper, micromechanics based design theory and fracture mechanics formulation leading to energy and strength criteria to achieve strain hardening and multiple cracking are described. Engineered cementitious composites showing pseudo strain hardening behaviour with over 6% of strain capacity under tension is produced. Uniaxial tensile tests of PVA–ECC are conducted and the results support the validity of the proposed theory. Also viscosity modifying agent plays an important role in the dispersion of the fibres in the matrix. It is shown that a uniform distribution of fibres throughout the bulk of the composite material is crucial to its excellent workability, tight crack width and reduction in the autogenous and drying shrinkage strains.     

Predicting the flexural load–deflection response of steel fibre reinforced concrete from strain, crack-width, fibre pull-out and distribution data

A semi-analytical model is presented, based on conventional principles of mechanics, to predict the flexure behaviour of steel fibre reinforced concrete. The model uses a stress-block approach to represent the stresses that develop at a cracked section by three discrete stress zones: (a) a compressive zone; (b) an uncracked tensile zone; and (c) a cracked tensile zone. It is further shown that the stress-block, and hence flexural behaviour, is a function of five principal parameters: compressive stress–strain relation; tensile stress–strain relation; fibre pull-out behaviour; the number and distribution of fibres across the cracked section in terms of their positions, orientations and embedment lengths; and the strain/crack-width profile in relation to the deflection of the beam. An experimental investigation was undertaken on both cast and sprayed specimens to obtain relationships for use in the model. The results of the study showed a reasonable agreement between the model predictions and experimental results. However, the accuracy of the model is probably unacceptable for it to be currently used in design. A subsequent analysis highlighted the single fibre pull-out test and the sensitivity of the strain analysis tests as being the main cause of the discrepancies.     

Tensile behaviour of thermally bonded nonwoven structures: model description

Nonwovens are complex three-dimensional anisotropic structures and consisting of fibres orientated in certain directions, which are bonded by thermal, chemical, mechanical entanglement or a combination of these techniques. Thermally bonded are further classified in two categories, i.e. through-air and calendared nonwoven structures. In this study, a modified micromechanical model describing the tensile behaviour of thermally bonded nonwovens is proposed by incorporating the effect of fibre re-orientation during the deformation. The anisotropic behaviour of through-air bonded structures is demonstrated through theoretical stress–strain curves and the relationship between the fibre re-orientation and fabric strain is also analysed. Furthermore, the failure criterion of thermally bonded nonwovens is analysed using pull-out behaviour of fibres in the system. A parametric study revealing the dependencies of various structural and geometrical characteristics of fibres on pull-out behaviour of fibres in thermally bonded nonwovens is also discussed.     

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.     

Analysis of interfacial micromechanics of model composites using synchrotron microfocus X-ray diffraction

The deformation micromechanics of single-fibre embedded model composites of poly(p-phenylene benzobisoxazole) (PBO) and poly(p-phenylene terephthalamide) (PPTA) fibres, embedded in an epoxy resin have been examined using synchrotron microfocus X-ray diffraction. Single fibres (in air) were deformed and the c-spacing monitored to establish a calibration of crystal strain against applied stress. Subsequently, the variation in crystal strain along fibres, embedded in the resin matrix was mapped using synchrotron microfocus X-ray diffraction. Raman spectroscopy was then used to map molecular deformation on the same samples (recorded as shifts in the Raman band wavenumber) in order to provide a complementary stress data. A shear-lag analysis was conducted on the axial fibre stress data in order to calculate interfacial shear stress and identify different stress-transfer modes at fibre/resin interfaces. The results establish that the axial fibre stress distributions measured by synchrotron microfocus X-ray diffraction correlate well with those obtained using Raman spectroscopy. The interfacial shear stress data derived from the stress-transfer profiles also show a good degree of correlation.     

The full-cell cracking mode in unidirectional brittle-matrix composites

In this work we consider the issues associated with predicting the initiation of matrix cracking within a unidirectional brittle-matrix composite (BMC). The analysis is accomplished as a case study for a restrictive, though important, class of composites consisting of silicon carbide fibres and a glass-ceramic matrix. A newly-derived axisymmetric variational model is employed to predict the stress field and energy release rates in a composite having a single damaged cell (or randomly located non-interacting cells) in which an annular matrix crack is introduced. Propagation of this crack to the fibre/matrix interface generates what we call the full-cell cracking mode. Strength and toughness properties of the matrix material are assumed to infer the potential for growth of the annular crack as well as its influence on the interface stresses and plausible scenarios governing the behaviour of secondary flaws. In turn, the synergistic influence of the latter flaws on the original annular crack is predicted. Since fibre spacing seems to be of paramount importance in real composites, a model of a composite having a non-uniform fibre distribution is also developed. The work includes a study of crack deflection at the fibre/matrix interface and comments are made regarding the perceived need for poor bonding in these materials. Also noted are the key parameters that need to be determined by experiment to quantify the failure prediction.     

An advanced equipment for single-fibre pull-out test designed to monitor the fracture process

A newly designed single-fibre pull-out machine with optimized stiffness in all components was developed, in order to obtain stable crack propagation during the fibre pull-out. On the basis of a mathematical model, which simulates the debonding process during a single-fibre pull-out experiment, calculations of the stress distribution, the force-displacement traces and the fracture propagation were made. Some of these results are compared with pull-out measurements using glass fibres embedded in thermoplastic matrices. The agreement between simulation and test results is good, and shows that stable crack propagation is achievable. Because friction has an important influence on pull-out forces, the interpretation of single-fibre test results has to be revised.     

Analysis of the single-fibre pull-out test by means of Raman spectroscopy: Part II. Micromechanics of deformation for an aramid/epoxy system

The single-fibre pull-out test has been analysed for Kevlar-49 fibres in a cold-cured epoxy resin by using both a conventional pull-out experiment and Raman spectroscopy. The interfacial shear strength (ISS) has been estimated from the pull-out force for fibres with a range of embedded lengths. Raman spectroscopy has been used to analyse the distribution of fibre strain in the pull-out test by mapping the variation of strain along an aramid fibre undergoing pull-out from the epoxy resin matrix. At low strains the behaviour follows elastic shear-lag analysis but, as the fibre strain is increased, debonding takes place at the fibre/matrix interface. It is found that this debond propagates along the interface until the entire fibre is debonded. The fibre is then pulled out of the resin matrix by a frictional pull-out process. It is shown that the conventional pull-out experiment produces only an apparent value of ISS and that through a partial-debonding model it is possible to use the interfacial parameters obtained from the Raman analysis to predict the data from the conventional test.     

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.     

Constitutive behaviour of confined fibre reinforced concrete under axial compression

Steel fibre reinforced concrete is finding extensive use in field applications. The mechanism of delaying and arresting crack propagation by the fibres can be made use in passive confinement of concrete. Such concrete was termed as confined fiber reinforced concrete (CFRC). This paper presents an analytical model for predicting the stress–strain behaviour of CFRC based on the experimental results. A total of ninety prisms of size 150×150×300 mm were cast and tested under strain control rate of loading. The increase in strength and strain of CFRC were used in formulating the constitutive relation.     

A design concept with the use of RUHTCC beam to improve crack control and durability of concrete structures

Aiming at design issues of strictly anti-cracking structures or aseismic design in crucial locations of structures when using ultra high toughness cementitious composite (UHTCC), investigations on flexural behavior of reinforced ultra high toughness cementitious composite (RUHTCC) members are carried out due to excellent crack dispersion and strain energy absorption abilities of UHTCC. According to elastic theory, a calculation model of strain-hardening composites flexural members including theoretical calculation of moment, deflection and curvature, as well as critical reinforcement ratio is proposed in detail. Then experiment on RUHTCC beams without web reinforcement is performed to verify theoretical equations. For RUHTCC beams, there is a good agreement between test results and theoretical calculation. The safe calculated ductility indices can be used to predict ductility of structures. Compared with reinforced concrete beams, UHTCC delays yielding of reinforcements and improves load bearing capacity and ductility of structures, then steel reinforcement is saved; low reinforcement ratio is propitious to exert advantages of UHTCC. Under service load conditions, crack width in RUHTCC beams is limited to 0.05 mm and can be considered without negative influence on durability. Durability of structures will be significantly improved by using UHTCC instead of concrete.     

Meso-scale deformation and damage in thermally bonded nonwovens

Thermal bonding is the fastest and the cheapest technique for manufacturing nonwovens. Understanding mechanical behaviour of these materials, especially related to damage, can aid in design of products containing nonwoven parts. A finite element (FE) model incorporating mechanical properties related to damage such as maximum stress and strain at failure of fabric’s fibres would be a powerful design and optimisation tool. In this study, polypropylene-based thermally bonded nonwovens manufactured at optimal processing conditions were used as a model system. A damage behaviour of the nonwoven fabric is governed by its single-fibre properties, which are obtained by conducting tensile tests over a wide range of strain rates. The fibres for the tests were extracted from the nonwoven fabric in a way that a single bond point was attached at both ends of each fibre. Additionally, similar tests were performed on unprocessed fibres, which form the nonwoven. Those experiments not only provided insight into damage mechanisms of fibres in thermally bonded nonwovens but also demonstrated a significant drop in magnitudes of failure stress and respective strain in fibres due to the bonding process. A novel technique was introduced in this study to develop damage criteria based on the deformation and fracture behaviour of a single fibre in a thermally bonded nonwoven fabric. The damage behaviour of a fibrous network within the thermally bonded fabric was simulated with a FE model consisting of a number of fibres attached to two neighbouring bond points. Additionally, various arrangements of fibres’ orientation and material properties were implemented in the model to analyse the respective effects.