Van der Pauw measurement of metal fibre orientation in a plastic-metal composite

Stainless steel fibres in ABS plastic form a composite with an anisotropic resistivity. Samples are rectangular shapes with uniform thickness. By assuming two principal resistivities and by using van der Pauw's technique, we find ² = _{x y} . For rectangular samples, field theory determines _y / _x and hence fibre direction. Results for three sample geometries agree with the theoretical predictions of the fibre patterns and with X-ray data. Samples formed by a centre-sprue feed are the best for fabricating large, uniform samples, while samples with a large length-to-width ratio have the most uniform metal density and fibre orientation. Resistivity was also measured by the more-common two-probe technique. Results correlate well to van der Pauw data, with 95% confidence.     

Microstructure and fracture behaviour of short and long fibre-reinforced polypropylene composites

Microstructure and fracture mechanical behaviour of injection-moulded, longer glass fibrereinforced polypropylene (Verton* aspect ratio 320) were studied as a function of fibre volume fraction and compared to that of shorter fibre-filled polypropylene (aspect ratio 70). Toughness was measured using instrumented notched lzod and falling weight impact tests, as well as compact tension specimens. It was found that the addition of longer fibres generally increased the toughness of the material, although more significant increases were seen in the impact tests than were seen in the compact tension test. For the latter results, a correlation between toughness improvement and microstructural details was performed on the basis of the microstructural efficiency concept, a semi-empirical approach of the formK _c,C = (a* +nR)K _c,M, where,K _c,C andK _c,M are the fracture toughnesses of the composite and the matrix, respectively,_a* is a matrix stress correction factor,n is a scaling parameter andR is a fibre reinforcement effectiveness factor. The latter corrects for differences in the composite microstructures, and incorporates effective fibre orientation factors, layering of injection moulded parts, and fibre volumes in the different layers.Nomenclature a crack length - a ^* matrix toughness correction factor - A cross-sectional area - B thickness of the sample plaques - C thickness of the composite core regions - E _peak energy adsorbed up to the maximum force in the impact load-displacement curve - E _t tensile modulus - F _max maximum force in impact force-displacement curves - f _p fibre orientation factor - f _pe effective orientation factor - f _pe,C effective orientation parameter, core region - f _{pe, s} effective orientation parameter, surface region - F critical load in the tensile test load-displacement curves - K _c critical stress intensity factor/fracture toughness - K _L fracture toughness of the composite materials - K _d dynamic fracture toughness - K _L fracture toughness of the matrix - L test with crack parallel to the mould filling direction - M microstructural efficiency factor - n scaling parameter for reinforcement effectiveness factor (energy absorbtion ratio) - R reinforcement effectiveness factor - S thickness of the composite surface regions - T test with crack perpendicular to the mould filling direction - V _f fibre volume fraction - V _m matrix volume fraction (= 1 —V _f) - W specimen width - W _f fibre weight fraction - W _m matrix weight fraction (= 1 —W _f) - X _n number average fibre length - X _v volume average fibre length - Y(a/ W) polynomial correction for compact tension specimens - variable in effective orientation factor formula - variable in effective orientation factor formula - _B strain to break - _c density of the composite - _f fibre density - _m matrix density - _F fracture strength - fibre angle with respect to a reference direction     

Effect of fibre concentration, strain rate and weldline on mechanical properties of injection-moulded short glass fibre reinforced thermoplastic polyurethane

The effect of fibre concentration, strain rate and weldline on tensile strength, tensile modulus and fracture toughness of injection-moulded thermoplastic polyurethane (TPU) reinforced with different concentration levels of short glass fibres was investigated. It was found that tensile strength, σ_c, of single-gated mouldings increased with increasing volume fraction of fibres, ϕ_f, according to a second order polynomial function of the form and increased linearly with natural logarithm of strain rate (). Tensile modulus and fracture toughness (at initiation) of single-gated mouldings increased linearly with increasing ϕ_f (rule-of-mixtures) and . A linear dependence was obtained between fibre efficiency parameter for composite modulus, η_E, and . The presence of weldline in double-gated mouldings reduced tensile strength, tensile modulus and fracture toughness of TPU composites but had no significant effect upon properties of the TPU matrix. All the aforementioned properties increased with increasing fibre concentration and showed a linear dependence with respect to . Weldline integrity factor for all three properties decreased with increasing fibre concentration showing no strain-rate effect of any significance. Results indicated that tensile strength was more affected by the presence of weldline than tensile modulus or fracture toughness. It was noted that composite properties in the presence of weldline were still much greater than those for the unweld matrix. Weldline integrity values close to unity indicated that measured properties for the matrix were not significantly affected by the weldline.     

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     

Effect of fibre concentration and strain rate on mechanical properties of single-gated and double-gated injection-moulded short glass fibre-reinforced polypropylene copolymer composites

The effect of fibre concentration, strain rate and weldline on tensile strength, tensile modulus and fracture toughness of injection-moulded polypropylene copolymer (PPC) reinforced with 10, 20, 30 and 40% by weight short glass fibre was studied. It was found that tensile modulus of single- and double-gated mouldings increased with increasing volume fraction of fibres, ϕ_f, according to additive rule-of-mixtures, and increased linearly with natural logarithm of strain rate . The presence of weldlines in double-gated mouldings led to reduction in tensile modulus which for composite containing 40% by weight short fibres was as much as 30%. A linear dependence was obtained between fibre efficiency parameter for composite modulus and for both single- and double-gated moulding. Tensile strength of single-gated mouldings, σ _c, increased with increasing ϕ_f in a nonlinear manner. However, for ϕ_f in the range 0–12% a simple additive rule-of-mixtures adequately described the variation of σ _c with ϕ_f. A linear dependence was obtained between fibre efficiency parameter for tensile strength and The presence of weldlines in double-gated mouldings reduced tensile strength by as much as 70%. Tensile strength of both single- and double-gated mouldings increased linearly with Fracture toughness of single-gated mouldings increased linearly with increasing ϕ_f. The presence of weldlines in double-gated mouldings reduced fracture toughness by as much as 60% for composite containing 40% by weight short glass fibres.     

Interfacial debonding and fibre pull-out stresses

Two current theories [11, 17] of interfacial debonding and fibre pull-out, which have been developed on the basis of fracture mechanics and shear strength criteria, respectively, are critically compared with experimental results of several composite systems. From the plots of partial debond stress, _d ^p , as a function of debond length, three different cases of the interfacial debond process can be identified, i.e. totally unstable, partially stable and totally stable. The stability of the debond process is governed not only by elastic constants, relative volume of fibre and matrix but more importantly by the nature of bonding at the interface and embedded fibre length,L. It is found that for the epoxy-based matrix composite systems, Gaoet al.'s model [17] predicts the trend of maximum debond stress, _d ^* , very well for longL, but it always overestimates _d ^* for very shortL. In contrast, Hsueh's model [11] has the capability to predict _d ^* for shortL, but it often needs significant adjustment to the bond shear strength for a better fit of the experimental results for longL. For a ceramic-based matrix composite, _d ^* predicted by the two models agree exceptionally well with experiment over almost the whole range ofL, a reflection that the assumed stable debond process in theory is actually achieved in practice. With respect to the initial frictional pull-out stress, _f, the agreement between the two theories and experiments is excellent for all range ofL and all composite systems, suggesting that the solutions for _f proposed by the two models are essentially identical. Although Gaoet al.'s model has the advantage to determine accurately the important interfacial properties such as residual clamping stress,q _o, and coefficient of friction, , it needs some modifications if accurate predictions of _d ^* are sought for very shortL. These include varying interfacial fracture toughness,G _ic with debond crack growth, unstable debonding for very shortL and inclusion of shear deformation in the matrix for the evaluation ofG _ic and fibre stress distribution. Hsueh's model may also be improved to obtain a better solution by including the effect of matrix axial stress existing at the debonded region on the frictionless debond stress, _o.     

The stiffness and strength of a polyamide thermoplastic reinforced with glass and carbon fibres

It has been established that the optimum degree of mechanical property enhancement by fibre reinforcement of a typical thermoplastic material (polyamide 6.6) is achieved if comparatively long fibres are used, the fibre length required being determined by the properties of the interface between the fibre and the thermoplastic matrix. The extent of stiffness improvement at low strains is described by simple modifications to the law of mixtures to allow for fibre orientation and length. The strength enhancement is limited by an embrittlement effect which reduces the strain to fracture as the stiffness of the composite is improved. The cause of this effect has been identified as matrix crack formation at the ends of the reinforcing fibres. At strains of between 0.5% and 1.0%, according to fibre type, length andV _f, cracks form at the tips of the longest fibres aligned in the straining direction. Subsequently as the strain is increased more cracks form progressively at the ends of shorter and/or more misaligned fibres. It has been shown that initially this cracking can be accommodated by load transfer to adjacent fibres which bridge the cracked region. Final failure occurs when the extent of cracking across the weakest section reaches a critical level when the surrounding fibres and matrix can no longer support the increasing load.     

Fracture energy maps for fibre composites

Analytical expressions are presented which predict the debonding and pull-out lengths observed in brittle-fibre composites. The characteristic lengths are combined with models of four toughening mechanisms to calculate the work of fracture of a composite. The results are presented as maps showing not only contours of toughness but also the dominant toughening micromechanism. The toughness is largely determined by six material parameters, and each map demonstrates the combined effect of changing two of these simultaneously. Maps are presented for glass fibres in epoxy and carbon fibres in epoxy. Their use is demonstrated by showing the effects of hygrothermal aging on the toughness of the composites.Nomenclature A value ofP just less than one - B value ofP just greater than zero - d fibre diameter - E _f tensile modulus of fibre - g(l) general probability distribution ofl - G _II critical strain energy release rate per Mode 2 fibre-matrix bond failure - G ₂ G _II divided by geometry factor - G _m shear modulus of matrix - l _d total debonded length of fibre - l _n maximum pull-out length - ¯l _p mean pull-out length - ¯l average value of a distributed length,l - m Weibull modulus - P cumulative probability of failure - S cumulative probability of survival - W _e elastic work (per fibre) - W _i surface energy of fibre-matrix interface (per fibre) - W _p pull-out work (per fibre) - W _pdf post-debond friction work (per fibre) - x general distance from debond crack - x _c value ofx which only a fractionB of pull-out lengths can exceed - geometry factor from integration of stress field around fibre - constant, but exact value depends on author - surface energy of the composite - _m surface energy of the matrix - _f failure strain of fibre - _m failure strain of matrix - parameter dependent only on the Weibull modulus - ₁, ₂ stresses at which fractions,A, B of fibres have broken - _d debond stress - _f average fibre strength - ₀ characteristic strength of fibre - ₀ shear strength of fibre-matrix adhesive bond - _f frictional shear stress     

On the tension test as a means of characterizing fibre composite failure mode

A model of composite tensile failure, which has been utilized previously in analysing modes of composite fracture [1], is extended to describe fracture in systems not considered previously. This model, based on tensile testing with a stiff, elongation rate controlled machine, predicts a strain concentration in the vicinity of a fibre break during such testing. The magnitude of the stress increase associated with this strain concentration is analytically predicted and compared with experimental data. The existence of this strain concentration can lead to phenomenologically different modes of composite failure. The type of failure observed depends upon the properties of the composite constituents as well as the composite parameters, fibre volume fraction (V _f), number of fibres in the composite (N) and ratio of specimen length to fibre ineffective length (L).     

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     

A theory for the free shrinkage of steel fibre reinforced cement matrices

The paper presents a theoretical model to predict the free shrinkage of cement matrices reinforced with randomly oriented discrete steel fibres. The model is based on the consideration that the equivalent aligned length of a random fibre is responsible for restraining the shrinkage of a thick matrix cylinder of diameter equal to the fibre spacing, through the fibre-matrix interfacial bond strength. The validity of the model is established by means of extensive experimental data for different types of steel fibres in cement, mortar or concrete matrices. The theoretical model is also used to determine the values of coefficient of friction,, and the average bond strength,, of the fibre-matrix interface. It is shown that is a basic property of the matrix and fibre interface, which is affected by the surface roughness and mechanical deformation of the fibres., however, is greatly influenced by the shrinkage of the matrix and volume fraction of fibres. Finally, an empirical expression is derived to determine the shrinkage of steel fibre reinforced cement matrices based on the shrinkage of unreinforced matrices and fibre properties.     

Prediction of mode I fracture toughness of unidirectional fibre composites with arbitrary crack fibre orientation from its lowest or matrix fracture tougness

Corrigendum

Prediction of mode I fracture toughness of unidirectional fibre composites with arbitrary crack fibre orientation from its lowest or matrix fracture tougnessby P.K. Sarkar and S.K. Maiti     

Interfacial debonding and fibre pull-out stresses

Following the development of an improved theoretical analysis of fibre pull-out on the basis of the concept of fracture mechanics in Part II of this paper, the theory has been successfully used to characterize the debonding and frictional pull-out behaviour in cement mortar matrix composites reinforced with steel and glass fibres. It is shown from the plots of partial debond stress, _d ^p , versus debond length, , that these composites are typical of mechanical bonds at the interface. For the steel fibre-cement matrix composites, the theory overestimates the post-debond frictional pull-out stress, _fr, particularly for long embedded fibre length, L, otherwise the prediction agrees well with the experiments for the maximum debond stress, _d ^* . This seems to be a direct result of decay of frictional bonds at the interface region after debonding due mainly to compaction of the porous cement mortar surrounding the fibre, effectively reducing the residual clamping stress, q ₀, arising from shrinkage of the cement matrix. Therefore, a correct theoretical prediction is made for _fr using a lower value of q ₀ while other parameters are kept constant, which gives good agreement with experimental results. For glass fibre-cement matrix composites, an accelerated cure condition promotes rapid hydration of cement and densification of the matrix. This effectively improves the chemical as well as mechanical bonds at the fibre-matrix interface through the formation of CH crystals and large fibre-solid matrix contact area of the interface, and consequently ameliorating the interfacial properties, interfacial fracture toughness, G _ic and q _o in particular. Predictions of _d ^* and _fr taking into account these changes due to cure condition, results in good agreement with experimental results.     

Compression strength of carbon,glass and Kevlar-49 fibre reinforced polyester resins

The compression behaviour of a series of polyester resins of various compositions and in different states of cure has been investigated. Their mechanical characteristics having been established, the same range of resins was then used as a matrix material for a series of composites reinforced with carbon, glass and aromatic polyamide fibres. The composites were unidirectionally reinforced, having been manufactured by pultrusion, and were compression tested in the fibre direction after a series of experiments to assess the validity of a simple testing procedure. Rule of Mixtures behaviour occurred in glass-polyester composites up to limiting volume fractions (V _f) of 0.31 for strength and 0.46 for elastic modulus, the compression modulus being equal to the tensile modulus, and the apparent fibre strength being in the range 1.3 to 1.6 GPa at this limiting V _f. At a V _f of 0.31 the strengths of reinforced polyesters were proportional to the matrix yield strength, _my, and their moduli were an inverse exponential function of _my. For the same matrix yield strength a composite with an epoxy resin matrix was stronger than polyester based composites. At V _f=0.30, Kevlar fibre composites behaved as though their compression modulus and strength were much smaller than their tensile modulus and strength, while carbon fibre composites were only slightly less stiff and weaker in compression than in tension. The compression strengths of the polyester resins were found to be proportional to their elastic moduli.     

Stress distributions along a short fibre in fibre reinforced plastics

This paper develops an analysis for predicting the normal stress and interfacial shearing stress distribution along a single reinforcing fibre of a randomly oriented chopped-fibre composite, such as sheet moulding compound (SMC), from a knowledge of the constituent properties and the length-to-diameter ratio of the fibres. The analysis is useful in analysing the tensile strength of SMC, and as a guide to increasing the tensile strength by altering the elastic characteristics. The model is based on a generalized shear-lag analysis. Numerical values of the normal stress and interfacial shearing stress are presented as functions of various parameters. It is observed that the maximum normal stress occurs at the middle of the fibre and the maximum shear stress occurs at the end. The analysis is restricted to loading which does not result in buckling of the fibre; i.e., axial loads on the fibre can be at most only slightly compressive.List of symbols a _f Ratio of the fibre length to diameter (aspect ratio, l _f/d _f) - E _a Young's modulus of the composite (defined in Equation 21) - E _f Young's modulus of the fibre material - E _m Young's modulus of the matrix material - G _f Shear modulus of the fibre material - G _m Shear modulus of the matrix material - l Half the length of the matrix sheath which surrounds the fibre - l _f Half of the length of the fibre - Q Defined in Equation 14. - R Ratio of the length of the fibre to the matrix in a representative volume element; a parameter 0R[(1/V _f–1) ] - r _a Radius of the composite body (we assume r _ar _m, r _f) - r _f Radius of the fibre - r _m Radius of the matrix sheath which surrounds the fibre - u _a Displacement of the composite along the fibre direction - u _f Displacement of the fibre along the fibre direction - V _f Fibre volume fraction - (XYZ) Co-ordinate system with Z-axis parallel to the direction of the applied load (Fig. 1a) - (xyz) Co-ordinate system which is rotated by about the X-axis (Fig. 1a) - (¯x¯y¯z) Co-ordinate system which is rotated by about the z-axis (Fig. 1b) - Fibre orientation angle measured from the Z-axis - _m Engineering shear strain in the matrix - Defined in Equation 8 - Polar angle measured from the x–z plane - Defined in Equation 9 - Applied normal stress - _a Normal stress in the composite along the fibre axis - _f Normal stress in the fibre along the fibre axis - _m Normal stress in the matrix along the fibre axis - Shear stress on the fibre—matrix interface     

Tensile rupture of short fibre filled thermoplastic elastomer

Tensile rupture in short silk fibre filled thermoplastic elastomer blends from low-density polyethylene and natural rubber (NR) containing pre-cuts of different lengths has been studied. _b, the tensile strength of the blends, was found to decrease with increase in the cut length in accordance with the Griffith's theory of fracture. However, unlike in the case of vulcanized NR, no critical cut length (at which the strength drops abruptly) was found in the case of both blends and unvulcanized NR. The energy to fracture per unit volume,W _b, also varied inversely with the length of the pre-cut. Values of inherent flaw size,I _O, of the composites, determined by extrapolation ofW _b to the value obtained when no initial pre-cut was present, were found to increase with fibre loading. Blends with longitudinally oriented fibres showed higherI _O values than those with transversely oriented fibres.     

Compression fracture of organic fibre reinforced plastics

To measure the fibre strength _f a new method was used and the value _f=450±70 MPa was obtained. The compression strength dependence of unidirectional organic fibre reinforced plastics on the fibre volume fraction may be described by the well known mixture law. The compression strength of polyparaphenilenterephtalamid and polyparaamidobenzimidazol fibres practically coincide in spite of differences in chemical structures, tensile strengths and Young moduli. Epoxy matrix constrains the plastic fibre yield in composite and the fibre yield limit in composite is greater than the isolated fibre strength. The higher the matrix content the greater the effect. The fracture process begins with the appearance of a net of fine shear microlines, only after that do shear macrolines (so-called kinks) appear. At elevated temperatures the formation of yield macrolines is also observed but the fibre bend in the lines is symmetrical due to the symmetrical mode of fibre stability loss. The strength of organic fibre reinforced plastics is insensitive to the stress concentration effect and to the test method due to the plasticity of the composite.     

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.     

The impact toughness of discontinuous boron-reinforced epoxy composites

Previous theories for the impact strength of discontinuously-reinforced composites predict that the toughness is a maximum when critical transfer length fibres are used. Experiments utilizing mini-Charpy specimens of unidirectional boron-fibre-reinforced epoxy composites have been conducted which corroborate this prediction. However, calculations of the fracture energy, based on a uniform interfacial shear stress during fibre pull-out, proved inadequate for the reinforced epoxy composites. Revisions to existing theories are presented to take into account the non-uniformity of the interfacial shear stress distribution along the fibre length and catastrophic failure of the interfacial bond.Nomenclature A _f fibre cross-sectional area - E _f fibre Young's modulus - G _m matrix shear modulus - l fibre length - L fibre pull-out length - l _c fibre critical length - r fibre radius - R half fibre centre-to-centre spacing - V _f fibre volume fraction - W mean work of fracture per unit area of specimen cross-section - x distance from fibre end - y dummy variable of integration - surface energy - strain in composite - tensile stress on fibre - _f fibre fracture strength - interfacial shear stress     

Fracture mechanism in short fibre reinforced thermoplastic resin composites

The properties of two types of short carbon fibre (CF) reinforced thermoplastic resin composites (CF-PPS and CF-PES-C), such as strength (_y). Young's modulus (E) and fracture toughness (K _1c), have been determined for various volume fractions (V _f) of CF. The results show that the Young's modulus increases linearly with increasingV _f with a Krenchel efficiency factor of 0.05, whereas _y andK _1c increase at first and then peak at a volume fraction of about 0.25. The experimental results are explained using the characteristics of fibre-matrix adhesion deduced from the load-displacement curves and fractography. By using a crack pinning model, the effective crack tensions (T) have been calculated for both composites and they are 57 kJ m^–1 for CF-PPS and 4.2 kJ m^–1 for CF-PES-C. The results indicate that the main contribution to the crack extension originates from localized plastic deformation of the matrix adjacent to the fibre-matrix interface.