Axial compressive behaviour of reinforcing fibres and interphase in glass/epoxy composite materials

Axial compressive behaviour of reinforcing fibres and interphase in glass fibre/epoxy resin composites were examined. Axial compressive strengths of glass fibres were evaluated by the tensile recoil method. The effects of silane-based coupling surface treatment agent on the fibre compressive strengths were investigated. The glass fibres showed higher compressive strengths when coated by the surface treatment. Interphase behaviour was also investigated by means of the single-fibre embedded compressive test. The particular stress and strain distributions inside the specimen were examined by a three-dimensional finite element analysis. The parameter interfacial transmissibility instead of the conventional critical fibre length theory was introduced as an index of interfacial properties. This parameter was useful to estimate the interfacial properties at the elastic state apart from the complicated critical state. It was confirmed that the surface treatment improved the glass/epoxy interphase under axial compressive load.     

Effect of fibre misalignment on fracture behaviour of fibre-reinforced composites

When a matrix crack encounters a fibre that is inclined relative to the direction of crack opening, geometry requires that the fibre flex is bridging between the crack faces. Conversely, the degree of flexing is a function of the crack face separation, as well as of (1) the compliance of the supporting matrix, (2) the crossing angle, (3) the bundle size, and (4) the shear coupling of the fibre to the matrix. At some crack face separation the stress level in the fibre bundle will cause it to fail. Other bundles, differing in size and orientation, will fail at other values of the crack separation. Such bridging contributes significantly to the resistance of the composite to crack propagation and to ultimate failure. The stress on the composite needed to produce a given crack face separation is inferred by analysing the forces and displacements involved. The resulting model computes stress versus crack-opening behaviour, ultimate strengths, and works of failure. Although the crack is assumed to be planar and to extend indefinitely, the model should also be applicable to finite cracks.Glossary of Symbols a radius of fibre bundle - C 2 _f /aE _f - ^* critical failure strain of fibre bundle - _b bending strain in outer fibre of a bundle - _c background strain in composite - _f axial strain in fibre - _s strain in fibre bundle due to fibre stretching = _f - () strain in composite far from crack - E Young's modulus of fibre bundle - E _c Young's modulus of composite - E _f Young's modulus of fibre - E _m Young's modulus of matrix - f() number density per unit area of fibres crossing crack plane in interval to + d - F total force exerted by fibre bundle normal to crack plane - F _s component of fibre stretching force normal to crack plane - F _b component of bending force normal to crack plane - G _m shear modulus of matrix - h crack face opening relative to crack mid-point - h _m matrix contraction contribution to h - h _f fibre deformation contribution to h - h _max crack opening at which bridging stress is a maximum - I moment of inertia of fibre bundle - k fibre stress decay constant in non-slip region - k ₀ force constant characterizing an elastic foundation (see Equation 7) - L exposed length of bridging fibre bundle (see Equation 1a) - L _f half-length of a discontinuous fibre - m, n parameters characterizing degree of misalignment - N number of bundles intersecting a unit area of crack plane - P _b bending force normal to bundle axis at crack midpoint - P _s stretching force parallel to bundle axis in crack opening - Q() distribution function describing the degree of misalignment - s _f fibre axial tensile stress - s _f ^* fibre tensile failure stress - S stress supported by totality of bridging fibre bundles - S _max maximum value of bridging stress - v fibre displacement relative to matrix - v elongation of fibre in crack bridging region - u _coh non-slip contribution to fibre elongation - U fibre elongation due to crack bridging - v overall volume fraction of fibres - v _f volume fraction of bundles - v _m volume fraction matrix between bundles - w transverse deflection of bundle at the crack mid-point - x distance along fibre axis, origin defined by context - X distance between the end of discontinuous fibre and the crack face - X ^* threshold (minimum) value of X that results in fibre failure instead of complete fibre pullout - y displacement of fibre normal to its undeflected axis - Z() area fraction angular weighting function - tensile strain in fibre relative to applied background strain - ^* critical value of to cause fibre/matrix debonding - angle at which a fibre bundle crosses the crack plane - (k ₀/4EI)^1/4, a parameter in cantilever beam analysis - v_m Poisson's ratio of matrix - L (see Equation 9) - shear stress - _* interlaminar shear strength of bundle - _d fibre/matrix interfacial shear strength - _f frictional shear slippage stress at bundle/matrix interface - angular deviation of fibre bundle from mean orientation of all bundles - angle between symmetry axis and crack plane     

Air-plasma treated polyethylene fibres: effect of time and temperature ageing on fibre surface properties and on fibre-matrix adhesion

The effect of a low energy air-plasma treatment of extended chain polyethylene (ECPE) fibres (Spectra®900) on the adhesion with a matrix of epoxy resin has been studied. Surface energies of fibre and matrix were calculated by contact angles, measured with a Wilhelmy microbalance in different liquids, and the adhesion between fibres and the matrix was evaluated through a pull-out test. The results showed an increase in fibre-matrix adhesion by a factor of ca. 1.5 calculated by surface energy measurements, and by a factor of ca. 4 measured by the pull-out tests. Time (up to six months) and temperature (in the range 20–120 °C for 2 h) ageing caused some decrease in adhesion with respect to the values evaluated just after the fibre plasma treatment. The plasma treatment did not affect the fibre's mechanical properties.On leave from Dept. of Chemistry, University of Naples Federico II, Italy.     

Mechanical properties of injection moulded styrene maleic anhydride (SMA) Part II Influence of short glass fibres and weldlines

The dependence of the various mechanical and fracture properties on the volume fraction ofshort glass fibres in the styrene maleic anhydride (SMA) polymer was investigated. Special attention has been given to describing the dependence of various mechanical properties on the volume fraction of the glass fibres, f by way of the rule of mixtures. It was found that, strength, elastic modulus and fracture toughness, all follow a simple rule-of-mixtures of the form Qc=Qff+Qm(1–f), where Qc is the measured quantity for the composite, Qm and Qf are the corresponding values for the matrix and the fibre, respectively, and is the overall efficiency of the fibres, taking into account the orientation and the length of the fibres in the composite. It was also found that, while the presence of the weldline had no significant effect upon elastic modulus, its presence significantly reduced tensile strength and the fracture toughness of SMA and its composites. © 1998 Kluwer Academic Publishers     

The strength of hybrid glass/carbon fibre composites

The tensile mechanical properties of hybrid composites fabricated from glass and carbon fibres in an epoxy matrix have been evaluated over a range of glass: carbon ratios and states of dispersion of the two phases. The failure strain of the carbon phase increased as the relative proportion of carbon fibre was decreased, and as the carbon fibre was more finely dispersed. This behaviour is commonly termed the hybrid effect, and failure strain enhancement of up to 50% has been measured. Only part of the effect may be attributed to internal compressive strains induced in the carbon phase by differential thermal contraction as the composite is cooled from its cure temperature. The laminae or ligaments of carbon fibre dispersed in the glass fibre phase show a multiple failure mode, and when the constitution is favourable catastrophic failure does not occur until a considerable number of ligament fractures have accumulated. Failure is thus progressive, and the material is effectively tougher than equivalent all-carbon fibre composites.     

Fatigue crack growth behaviour of tungsten carbide-cobalt hardmetals

Fatigue crack propagation studies have been carried out on a range of WC-Co hardmetals of varying cobalt content and grain size using a constant-stress intensity factor double torsion test specimen geometry. Results have confirmed the marked influence of mean stress (throughK _max), which is interpreted in terms of static modes of fracture occurring in conjunction with a true fatigue process, the existence of which can be rationalized through the absence of any frequency effect. Dramatic increases in fatigue crack growth rate are found asK _max approaches that value of stress intensity factor ( 0.9K_IC) for which static crack growth under monotonic load (or static fatigue) occurs in these materials. Lower crack growth rates, however, produce fractographic features indistinguishable from those resulting from fast fracture. These observations, and the important effect of increasing mean free path of the cobalt binder in reducing fatigue crack growth rate, can reasonably be explained through a consideration of the mechanism of fatigue crack advance through ligament rupture of the cobalt binder at the tip of a propagating crack.     

Mechanics of fibre fragmentation

A fragmentation specimen consists of a single fibre embedded along the axis of a long narrow resin block. When the fibre is broken by a tensile load, either a lateral crack runs outwards into the resin, initiated by the break, or a debond (or equivalently a cylindrical crack in the resin) propagates along the fibre. Debonding always occurs with thin fibres. Strain energy release rates have now been calculated, analytically for long debonds and by FEA for short ones. The force to propagate a debond is found to increase as the debond grows, reaching a final value, termed pull-out force, that is higher for softer fibres. If this force exceeds the strength of the fibre, then the fibre breaks again. This is the proposed mechanism of fibre fragmentation. For weakly-bonded, stiff fibres, the inferred minimum distance between breaks, i.e. the critical fragment length, is deduced to be of the order of the geometric mean of the radii of fibre and resin block, about 0.1–0.5 mm for typical fragmentation specimens, and it increases as the ratio of fibre stiffness to resin block stiffness increases, in agreement with observation.     

Transverse properties of a Ti-6-4 matrix/SiC fibre-reinforced composite under monotonic and cyclic loading

The transverse response of a Ti-6-4/SM1140+ fibre-reinforced composite to both monotonic and cyclic loading has been investigated. Five distinct regions were found in the monotonic stress versus strain curve: (I) elastic deformation of the composite, (II) failure of the fibre/matrix interfaces, (III) elastic deformation of the remaining matrix ligaments, (IV) yielding of the matrix ligaments, and (V) gross plastic deformation, which ultimately leads to specimen failure. The stresses at which interface debonding, matrix yield and final failure occurred rose with increased displacement rate. Stressing to levels above the interface failure stress caused significant damage and limited (0.025%) plastic deformation. A non-linear stress-strain response was observed on unloading/reloading, because the presence within the specimen of constrained holes (containing debonded fibres) resulted in non-homogeneous elastic straining of the matrix. The transverse low-cycle fatigue lives of Ti-6-4/SM1140+composite specimens were strongly dependent on maximum stress for values up to the interfacial failure stress, but less so for maximum stresses greater than 260–265 MPa, where full fibre/matrix debonding had occurred. Fatigue life was also dependent on the uniformity of fibre spacings within the composite.     

Effects of the process conditions during dry-defibration on the properties of cellulosic networks

The influence of structural changes caused by dry-defibration of the pulp on the mechanical properties of dry-formed cellulosic networks has been investigated. The effects of fibre length, fibre curl and content of fine material on these properties are discussed. The fluff pulps used were one CTMP-grade and two kraft pulps. The primary parameters used to describe the networks were the storage modulus, G0 (measured at low strain amplitudes), and the critical strain, c (at which the network yields), obtained from dynamic-mechanical measurements, and the maximum force, Fmax, sustained by the network and the maximum strain, max (at Fmax), measured with a specially constructed shear tester. It was noted that the storage shear modulus, G0, and maximum force, Fmax, were affected in the same manner by the defibration conditions. To improve the deformability of the cellulosic network before rupturing, the ideal dry-defibration process should provide a greater number of free fibres per unit volume without producing fine material, at the same time as the curl index of the fibres should increase. Long and curled fibres are thus to be preferred. © 1998 Chapman & Hall     

Fibre orientation effects on the fracture of short fibre polymer composites: on the existence of a critical fibre orientation on varying internal material variables

The dependence of fracture toughness on fibre orientation, in short fibre reinforced polymers, was investigated using materials with different polymer matrix (polyamide 6.6, polyarylamide and polyoxymethylene), fibre sizing, fibre content, mean fibre length and fibre length distribution.To assess the dependence on fibre orientation, plates with unidirectionally oriented fibres were prepared and cut at various angles with respect to the direction of the aligned fibres. The fracture behaviour was investigated by single-edge notch three-point bending tests. In addition the stress-strain behaviour was examined by performing uniaxial tension and compression tests.Both the critical stress intensity factor K _C and the fracture energy G _C measured at fracture initiation were found to present a bi-linear relationship to the factor characterizing fibre orientation, with different slopes over different ranges of the orientation factor. This suggested the occurrence of a transition between different failure mechanisms with varying fibre orientation, namely matrix fracture and fibre debonding at low values of the fibre orientation factor, fibre breakage and pull-out at high values of the fibre orientation factor. This interpretation is supported by the observation of the crack growth direction (which varies with varying fibre orientation) and the analysis of the fracture surfaces. The slopes of the two linear branches of the toughness vs. fibre-orientation-factor plot and the critical fibre orientation angle depend on all internal variables investigated: constituent polymer matrix, degree of fibre-matrix adhesion, fibre content, mean fibre length and fibre length distribution.     

Simulation of the Process of Water Freezing in a Round Pipe

The problem of freezing of pure water in a round pipe is treated with due regard for convection under asymmetric thermal boundary conditions in the absence of motion along the pipe. The problem is solved numerically using the control volume approach, SIMPLER algorithm, and the enthalpy method. Results are obtained for three Grashof (Gr) and six Biot (Bi) numbers: Gr = 1.55 × 10⁶, Bi = 0.305 (0 < ), Bi = 0.044 ( < 2); Gr = 1.24 × 10⁷, Bi = 0.610 (0 < ), Bi = 0.087 ( < 2); Gr = 9.89 × 10⁷, Bi = 1.220 (0 < ), Bi = 0.174 ( < 2). The correctness of calculation of the problem disregarding free-convection flows is analyzed.     

Chemical stress cracking of acrylic fibres

The generation of periodic microscopic transverse cracks in oriented acrylic fibres immersed in hot alkaline hypochlorite solution is described in detail and shown to be a variety of chemical stress cracking. It is greatly accelerated by external tensile stress, high fibre permeability, moderate fibre orientation, and water-plasticization. The proposed mechanism for bond cleavage involves cyclization of nitrile groups (similar to the prefatory reaction in pyrolysis of acrylic fibres), followed immediately by N-chlorination and chain scission. Mechanical retractile forces (internal or external) then cause chain retraction and crack growth. Despite the remarkable regularity of the crack pattern, which typically resembles a series of stacked lamellae, the process is independent of any such underlying fibre morphology. The cracking process does, however, appear to be a sensitive indicator of residual latent strain in the fibre, which may persist even after high-temperature annealing.     

Copper coating on carbon fibres and their composites with aluminium matrix

A uniform and continuous coating of copper was given to carbon fibres by cementation or electroless techniques. In both cases, when coating thicknesses were less than 0.2 m, copper deposition was discontinuous over the fibres, and above 0.2 m, coatings were continuous. In electroless coating, about 75% of the continuously coated fibres had a coating thickness range 0.2–0.5 m and above this showed isolated dendrite deposits of copper. In the cementation process, about 75% of the continuously coated fibres had a coating thickness range 0.2–0.6 m, and above this thickness, fine crystallite-type copper deposition was found over smoothly coated copper. The ultimate tensile strength of continuously electroless-coated fibres were nearer to the uncoated fibres, suggesting defect-free coating, while fibres coated by the cementation process exhibited lower ultimate tensile strength values. The tensile fracture of both electroless- and cementation-coated fibres showed delamination of the coating, suggesting poor bonding between coating and the fibre. In composites, prepared by dispersing the coated chopped fibres in a pure aluminium matrix, uniform and random distribution of the fibres were observed without appreciable fibre-metal interaction. The CuAl₂ intermetallics were largely found in the matrix and only very small amounts were observed at fibre/matrix interfaces. Additions of about 2 wt% Mg to the matrix prior to the fibre dispersion did not appreciably change the distribution pattern of the fibres, but in addition to CuAl₂ phase, Mg₂Si phases were observed in the matrix as well as at the interface.     

Fibre formation in the hydrostatic extrusion of linear polyethylene — sodium lignosulphonate blends

A blend consisting of equal amounts (by weight) of linear polyethylene and a technical grade of sodium lignosulphonate (a water soluble substance), was processed using hydrostatic extrusion with extrusion ratios varying from 5 to 20. The resulting extrudate contained thin (2 to 5m) fibres of the linear polyethylene in a matrix of the lignosulphonate. The fibres were basically continuous throughout the extrudate. Their stiffness was of the same order as that observed for pure hydrostatically extruded polyethylene. The fibre phase was easily isolated by dissolving the matrix material in water.     

Interfacial debonding and fibre pull-out stresses

Based on a theoretical model developed previously by the authors in Part II of this series for a single fibre pull-out test, a methodology for the evaluation of interfacial properties of fibre-matrix composites is presented to determine the interfacial fracture toughness G _c, the friction coefficient , the radial residual clamping stress q _o and the critical bonded fibre length z _max. An important parameter, the stress drop , which is defined as the difference between the maximum debond stress _d ^* and the initial frictional pull-out stress _fr, is introduced to characterize the interfacial debonding and fibre pull-out behaviour. The maximum logarithmic stress drop, In(), is obtained when the embedded fibre length L is equal to the critical bonded fibre length z _max. The slope of the In()-L curve for L bigger than z _max is found to be a constant that is related to the interfacial friction coefficient . The effect of fibre anisotropy on fibre debonding and fibre pull-out is also included in this analysis. Published experimental data for several fibre-matrix composites are chosen to evaluate their interfacial properties by using the present methodology.On leave at the Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong.     

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.     

Microstructure and tensile properties of BN/SiC coated Hi-Nicalon, and Sylramic SiC fiber preforms

Batch to batch and within batch variations, and the influence of fiber architecture on room temperature physical and tensile properties of BN/SiC coated Hi-Nicalon and Sylramic SiC fiber preform specimens were determined. The three fiber architectures studied were plain weave (PW), 5-harness satin (5HS), and 8-harness satin (8HS). Results indicate that the physical properties vary up to 10 percent within a batch, and up to 20 percent between batches of preforms. Load-reload (Hysteresis) and acoustic emission methods were used to analyze damage accumulation occurring during tensile loading. Early acoustic emission activity, before observable hysteretic behavior, indicates that the damage starts with the formation of nonbridged tunnel cracks. These cracks then propagate and intersect the load bearing 0° fibers giving rise to hysteretic behavior. For the Hi-Nicalon preform specimens, the onset of ° bundle cracking stress and strain appeared to be independent of the fiber architecture. Also, the 0° fiber bundle cracking strain remained nearly the same for the preform specimens of both fiber types. TEM analysis indicates that the CVI BN interface coating is mostly amorphous and contains carbon and oxygen impurities, and the CVI SiC coating is crystalline. No reaction exists between the CVI BN and SiC coating.     

Deformation of a carbon-epoxy composite under hydrostatic pressure

This paper describes the behaviour of a carbon-fibre reinforced epoxy composite when deformed in compression under high hydrostatic confining pressures. The composite consisted of 36% by volume of continuous fibres of Modmur Type II embedded in Epikote 828 epoxy resin. When deformed under pressures of less than 100 MPa the composite failed by longitudinal splitting, but splitting was suppressed at higher pressures (up to 500 MPa) and failure was by kinking. The failure strength of the composite increased rapidly with increasing confining pressure, though the elastic modulus remained constant. This suggests that the pressure effects were introduced by fracture processes. Microscopical examination of the kinked structures showed that the carbon fibres in the kink bands were broken into many fairly uniform short lengths. A model for kinking in the composite is suggested which involves the buckling and fracture of the carbon fibres.List of symbols d diameter of fibre - E _f elastic modulus of fibre - E _m elastic modulus of epoxy - G _m shear modulus of epoxy - k radius of gyration of fibre section - l length of buckle in fibre - P confining pressure (= ₂ = ₃) - R radius of bent fibre - V _f volume fraction of fibres in composite - _t, _c bending strains in fibres - angle between the plane of fracture and ₁ - ₁ principal stress - ₃ confining pressure - _c strength of composite - _f strength of fibre in buckling mode - _n normal stress on a fracture plane - _m strength of epoxy matrix - shear stress - tangent slope of Mohr envelope - slope of pressure versus strength curves in Figs. 3 and 4.     

Finite element analysis of a polymer composite subjected to a sliding steel asperity Part I Normal fibre orientation

FE micro-models have been developed in order to determine contact, stress and strain conditions produced by a steel asperity sliding on the surface of a normally oriented fibre-reinforced polymer composite. A displacement coupling technique was introduced to model a micro-environment as part of a macro-environment and to get more realistic simulation results about the failure conditions in the composite structure, in comparison to the so far widely applied anisotropic analytical or numerical macro-models. On the basis of the results, conclusions may be drawn for the possible wear mechanisms of the fibre-reinforced polymer composite. Stress results in the vicinity of the fibers in the contact area show high shear loading of the matrix leading to the formation of stretched-out matrix wear debris. In addition, high repeated compression-tension stresses at the fibre/matrix interface near the surface can lead to fibre debonding phenomena. Considering the fibre ends in the contact region, high compression stresses at their rear edges can produce fibre cracking features. To study the wear mechanisms experimentally, a single asperity scratch test was also performed showing shear failure events of the polymer matrix, fibre/matrix debonding and fibre cracking effects, as expected from the modelling studies.     

The strength of pitch-based carbon fibre at high temperature

The strengths of some high modulus pitch-based carbon fibres have been determined up to 1300 °C in both air and nitrogen atmospheres. The fibres possessed Young's moduli of 700 GPa and were 10 m in diameter. The strength of the fibres was seen to be gauge length dependent but to a lesser extent than is usual with PAN-based carbon fibres. The fibre strength was observed to increase with temperature as did the Weibull modulus.