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.     

Direct comparison of the loss of load transfer to “E” and “S” glass fibres manufactured by drawing into different environments

Accelerated water uptake tests have been used to compare the onsets of destruction of the ability to transfer shear stress at fibre/matrix interfaces in epoxy matrix glass reinforced plastic (GRP) manufactured with each of four different fibres. The ability to transfer shear stress has been monitored directly by measurement of stress birefringence through and adjacent to individual fibres. Full theoretical and practical details of the experimental method are given. S glass fibres, drawn into an atmosphere of ammonia in an attempt to promote the deposition of primary amines and/or secondary amines, rapidly lose their ability to receive shear stress from the matrix. This is attributed to neutralization of CO₂ by NH₃ within interfacial pockets of dissolved water, and the associated generation of osmotic pressure. Commercial samples of S and E glass fibres and E glass fibres drawn into an atmosphere of ammonia, all survive much larger water uptakes although, in the case of both kinds of E glass fibre, immersion in boiling water eventually gives rise to interfacial pressure pockets. These pressure pockets are also attributed to osmosis, with the role of dissolved solutes tentatively ascribed to the modifying agents present in E glass formulations.     

The mechanical behaviour of PVC short-fibre composites

Competitive deformation processes between interfacial debonding and matrix cracking at the fibre ends is shown for the short-fibre reinforced composites of polyvinyl chloride (PVC). The increase of interfacial shear strength by chemical coupling prevents early failure at the interface, thus increasing the tensile failure stress of short-fibre composites. The previously proposed general yield criterion for PVC and its short-fibre composites is also examined. No significant effect due to improved fibre-matrix adhesion on the upper shear yielding of short-fibre composites is observed. The matrix flow in the post-yield region is less restricted when debonding occurs.     

Single-fibre polymer composites

We have used Raman spectroscopy to measure the axial stress distribution along a fibre during a quasi-static single fibre pull-out test. The stress distribution at the debonding front during the progress of debonding gives the maximum interfacial shear strength _s directly. In addition, the stress distribution along the fibre after debonding can be used to evaluate the interfacial normal stress and the frictional coefficient. For the plasma treated high modulus polyethylene (PE) fibres used here, _s is found to be 28 MPa by this method, while the apparent mean interfacial shear strength _a obtained from the regular single fibre pull-out test varies from 3 to 15 MPa with the fibre embedded length I _e. Stress distributions derived from the shear-lag theory fit the experimental data for fully bonded fibres well, giving values for the shear-lag constant K and the stress transfer length 1/ [1]. According to the shear-lag theory, _s = l _eacoth(l _e). If can be found for a given system from Raman spectroscopy, _s can be evaluated from the pull-out test using this equation.The regular pull-out tests, corrected for residual stress and interfacial friction, give the same _s but not the same or pull-out load as the slower Raman test. The shear-lag constant K can be expressed as a function of the matrix shear modulus and geometric terms. One of these terms is the effective interfacial radius, r _e, the radius at which the strain in the matrix equals the average matrix strain. Raman measurements indicate that r _e is small, only four times the fibre radius. This result is supported by polarizing optical microscopy. The model of Greszczuk [2], which assumes a uniform shear within an effective interaction thickness b _i, gives a similar result. We find that b _i = 20 m, about twice the fibre radius. Using the pull-out test data, as for other fibre composites, b _i and r _e predicted by shear-lag theories do not agree with the results of microscopy to this extent. In these cases _s is much larger than the yield strength of the matrix and as neither treatment considers plastic deformation of the matrix agreement should not be expected.     

Steady state creep of a composite material with short fibres

The shear within a matrix volume is assumed to be an important process during the creep of composite material reinforced with short rigid fibres. The rate of elongation of such a composite with certain fibre distributions can be estimated. The agreement with a few experimental data is reasonably good.List of main symbols V _f volume fraction of fibres in composite - aspect ratio of a fibre - L length of a fibre - h transverse size of a fibre - h interfibre spacing - m, _m , _m constants for creep for a matrix material - n, _f, _f constants of creep for a fibre material _{f m} - v rate of relative motion of two fibres - _* ultimate strength of a fibre - ^* the first critical value of aspect ratio - ^** the second critical value of aspect ratio This work was carried out when the author was a guest worker at the National Physical Laboratory, Teddington, Middlesex, UK.     

Analysis of the impedance spectra of short conductive fiber-reinforced composites

The presence of small amounts of short conductive fibers in a composite of finite matrix conductivity results in the subdivision of the one matrix impedance arc into two separate low and high frequency arcs in the complex impedance plane. These features are attributable to a frequency-switchable interfacial impedance on the fiber surfaces, rendering them insulating at DC and low AC frequencies, but conducting at intermediate frequencies. A combination of physical simulations (single wires in tap water) and pixel-based computer modeling was employed to investigate the roles of fiber pull-out, debonding, and orientation on the impedance response of fiber-reinforced composites. The ratio of the low frequency arc size to the overall DC resistance (-parameter) is sensitive to pull-out and/or debonding, especially when a fiber just barely makes contact with the matrix. The -parameter is also quite sensitive to fiber orientation with respect to the direction of the applied field. Ramifications for the characterization of cement, ceramic, and polymer matrix composites are discussed.     

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     

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.     

Polypropylene nucleation on a glass fibre after melt shearing

Thermoplastic composites may exhibit a wide range of crystalline morphologies in the neighbourhood of fibres. It was found that glass fibre shearing of a molten polypropylene at high temperature modifies the subsequent isothermal crystallization (T _c=122°C) under static conditions. The crystallization results have been analysed as a function of the previous high temperature, shear, , shear rate, , and shear stress, . The mechanical parameters at high temperature, , , , have been calculated for two shearing temperatures (T=170, 210°C) and two fibre displacements. An -phase nucleation process took place at the fibre surface after shearing at the higher temperature (T=210°C). The nucleation increased with shear but did not appear for static conditions. A strong nucleation process in phase appeared on the fibre surface after shearing of the polymer at the lower temperature (T=170°C). These strong morphological modifications with shearing temperature have been analysed as a function of mechanical and thermodynamical parameters.     

Fractography of unidirectional graphite-epoxy as a function of moisture,temperature and specimen quality

The tensile failure surfaces of (0°)₈ T300/5208 graphite-epoxy specimens were examined using both optical and scanning electron microscopy. Fractography was used to determine how moisture content and temperature as well as specimen preparation technique, prepreg batch and cure condition affected the failure mode. A distinctive low-energy failure morphology was found in defective specimens and also in those whose edges were poorly prepared. This morphology was predominant in failures at elevated temperature or moisture content for specimens which had been made from one suspect batch of prepreg. This finding combined with unusual end-tab failures from such specimens indicated that this batch was indeed defective, but that such defective batches could in the future be identified by tests under hot, wet conditions. For specimens made from good prepreg, temperature or moisture appeared to decrease flaw sensitivity and thus increase strength, even though moisture also seemed to increase interfacial debonding between filament and matrix. When combined, moisture and temperature appeared to degrade performance by increasing interfacial debonding and making the epoxy matrix more prone to fracture.     

The wear and friction of short glass-fibre-reinforced polymer composites in unlubricated rolling-sliding contact

The wear and friction behaviour of short glass-fibre-reinforced polyamide 66 composites running against each other, unlubricated, in non-conformal, rolling-sliding contact has been investigated. Both a wide range of loads and slip ratios and a range of samples with different fibre concentration and different crystallinity have been examined. Short glass-fibre reinforcement makes the polyamide 66 exhibit unique tribological behaviour. There is a high resistance to wear and friction which results from a significant self-lubricating property. A thin film layer exists on the contacting surfaces when two discs run against each other within the range of the test conditions. It is this thin film that plays a dominant role in the self-lubricating property of the composite. The formation of the thin film and the life of the composite depend on a complex of interactions between structure, strength and fibre concentration, and the specific conditions of load and slip ratio imposed. Under identical loading conditions, either lower fibre concentration or lower crystallinity cause the thin film to form continuously during the wear process so that the life of the composite may reach 6×10⁶–10⁷ cycles. It is suggested that the self-lubricating property may be used in the working period of engineering components rather than only during the temporary running-in period of machine elements.     

The stacked lamellar texture on the fracture surfaces of fibre composites

A fracture surface texture, which has been variously termed as lacerations, hackles or serrations, is often observed on the matrix surface of fibre composites, most often in resin-rich regions. This texture, referred to here as a stacked lamellar texture to emphasize its plate-like nature, was studied in an E-glass/epoxy composite. Scanning electron fractographs of these materials suggest that the stacked lamellar texture arises from crack fingers due to a meniscus instability mechanism interacting with a reorienting stress field.     

The frictional behaviour of LiF single crystals

A study has been made of the influence of initial surface roughness, renewable and non-renewable surface contaminants, and irradiation hardening on the coefficient of friction for one LiF single crystal (A) sliding on another (B) in {100}_A<010>_A{100}_B 010_B orientation at 295 K. The normal load was 1 N, the nominal contact pressure 0.1 MPa, the sliding velocity 0.2 to 0.6 mm sec^–1, and the amplitude of the (reciprocate) motion a few millimetres. Any influence of non-renewable contaminants persisted only for cumulative relative displacements 0.1 m, and that of micrometre-scale initial surface roughness only for a few metres. At steady state in the presence of renewable contaminants the coefficient of friction varied only from a high of 0.45 in ultra-high vacuum ( 7.5 × 10^–8 Pa) and dry nitrogen-rich air ( 10⁵ Pa, relative humidity 15%) to a low of 0.38 in moist nitrogen-rich air ( 10⁵ Pa, relative humidity 50%). Irradiation hardening had no effect on the coefficient of friction at steady state. The worn surfaces created by steady-state sliding always exhibited a grooved topography partly obscured by more-or-less adherent layers of variously consolidated equiaxed debris particles 100 nm in size. Owing to the action of image forces, these particles contained no dislocations. It is suggested that the coefficient of friction was determined at steady state by the stress needed to shear these tiny particles past one another as near-rigid bodies.     

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.     

Thermodynamic and structural factors determining the wear resistance of aluminum cast irons

When the carbon content in aluminum cast iron containing about 2.5% Al is reduced (to about 2.5%),. carbon is concentrated near the dendritic branches where a specific variety of pearlite (containing a finely dispersed carbon-rich -phase) is formed, the interdendritic regions remaining ferritic. Modifying cast irons of this kind with cerium leads not only to spherodization of graphite but also to the formation of -phase dendrites with a corresponding reduction in the carbon content in the ferritic matrix surrounding -phase dendrites and pearlite. This has a beneficial effect on the wear resistance of cast iron.     

The tensile strength and ductility of continuous fibre composites

The plastic instability approach has been applied to the tensile behaviour of a continuous fibre composite. It is shown that the combination of two components with different strengths and degrees of work-hardening produces a new material with a new degree of work-hardening, which may be determined by the present analysis. Expressions for the elongation at rupture and the strength of a composite have been obtained and the results of the calculation are compared with some experimental data.List of symbols V _f volume fraction of fibres in composite - , , true strain of fibre, matrix and composite - s true stress - , , nominal stress on fibre, matrix and composite - _*, _*, _* critical stress of fibre, matrix and composite (ultimate tensile strength) - _*, _* critical strain of separate fibre and matrix - _* critical strain of composite - Q external load - A cross-sectional area - A ₀ initial value of area     

Interlaminar Fracture Toughness of CF/PEI and GF/PEI Composites at Elevated Temperatures

An experimental study has been conducted to assess temperature effects on mode-I and mode-II interlaminar fracture toughness of carbon fibre/polyetherimide (CF/PEI) and glass fibre/polyetherimide (GF/PEI) thermoplastic composites. Mode-I double cantilever beam (DCB) and mode-II end notched flexure (ENF) tests were carried out in a temperature range from 25 to 130°C. For both composite systems, the initiation toughness, G _IC,ini and G _IIC,ini, of mode-I and mode-II interlaminar fracture decreased with an increase in temperature, while the propagation toughness, G _IC,prop and G _IIC,prop, displayed a reverse trend. Three main mechanisms were identified to contribute to the interlaminar fracture toughness, namely matrix deformation, fibre/matrix interfacial failure and fibre bridging during the delamination process. At delamination initiation, the weakened fibre/matrix interface at elevated temperatures plays an overriding role with the delamination growth initiating at the fibre/matrix interface, rather than from a blunt crack tip introduced by the insert film, leading to low values of G _IC,ini and G _IIC,ini. On the other hand, during delamination propagation, enhanced matrix deformation at elevated temperatures and fibre bridging promoted by weakened fibre/matrix interface result in greater G _IC,prop values. Meanwhile enhanced matrix toughness and ductility at elevated temperatures also increase the stability of mode-II crack growth.     

Effect of temperature on interfacial shear strengths of SiC-glass interfaces

The in situ temperature dependencies of both the debonding, _d, and frictional, _f, shear stresses of a C-coated 140 m SiC monofilament (Textron SCS-6 SiC fibre) were measured using the single fibre pullout-test. Two matrices, a borosilicate (7740 Corning Glass) and a soda-lime (Thomas Scientific) with different thermal expansion coefficients, were tested. At lower temperatures both _d and _f were found to decrease linearly with increasing temperature as a result of the relaxation of the residual stresses developed during processing, which were compressive in both cases. The stress free debonding shear stress for the borosilicate matrix was found to be 3.5 ± 1 M Pa and the friction coefficient between that matrix and the fibres was calculated to be 0.18. Fibre oxidation are believed to be responsible for enhanced bonding between the fibres and the borosilicate matrix at higher temperatures which results in an increase in both _d and _f. The large thermal expansion mismatch between the soda-lime matrix and the SiC fibres resulted in radial cracking of the former during processing. A technique is described where the whole temperature dependence of the interfacial shear stresses can be measured by a single specimen.     

Theoretical estimation of fracture toughness of fibrous composites

A method of estimating the fracture surface energy of fibre-reinforced materials is discussed. The surface work is shown to increase with increasing fibre content, strength and diameter, and decrease with increasing fibre modulus and matrix flow stress (or hardness).Relatively short fibres should be used if high toughness is required, and the maximum toughness that can be achieved is limited by the amount of crack opening that can be permitted. Under certain conditions, incorporation of fibres into a material can lead to embrittlement.Symbols used c half length of crack - d fibre diameter - D average separation of nearest neighbour fibres - E Young's modulus - G shear modulus of matrix - K fracture toughness - L length of fibre on either side of crack - n number of fibres per unit area - P force on fibre - R pressure exerted by matrix on fibres - u displacement - U work - x distance Greek symbols 8 G/d ² E _fr log(2/p 3) - surface energy or work - tensile strain - _fm E _mr/E_fr R - tensile stress - shear stress - coefficient of friction - Poisson's ratio Suffixes c composite - e elastic - f fibre - m matrix     

The energy of crack propagation in carbon fibre-reinforced resin systems

The energy expended during controlled crack propagation in unidirectionally reinforced composites of carbon fibre in a brittle resin matrix has been evaluated in terms of the energy dissipated during fibre-snapping, matrix-cracking and fibre pull-out. The work of fracture, _F, is found to depend principally on the frictional shear stress at the fibre/resin interface opposing pulling out of broken fibres. Differences in _F for carbon fibre/resin composites exhibiting a range of interfacial shear strengths and void contents have been explained with reference to variations in fracture surface topography of the fibrous composites. The effect of environment on properties of the interface and work of fracture was also investigated. The energy required to propagate a crack has been compared with the energy for fracture initiation, _I, using a linear elastic fracture mechanics approach. It was found that fibre pull-out energy is the principal contribution to _F, and _I is similar to the elastic strain energy release rate at the initiation of fracture of a brittle, orthotropic solid. For crack propagation parallel to fibres, _F and _I are similar and not unlike the fracture surface energy of the resin alone. The strength of the interface is important only in so far as it affects the value of _I.