Carbon fibre-reinforced cement

This review describes fabrication processes for aligned fibre and random fibre carbonreinforced cement and links important process parameters with composite theory. The way in which the material fits into the general framework of crack constraint and matrix cracking theories is discussed. A broad survey is made of the mechanical properties, durability and dimensional stability of a variety of carbon-reinforced cement composites, and economic constraints on potential applications are considered.List of symbols b breadth of three-point bend specimen - d depth of three-point bend specimen - E _c composite Young's modulus - E _f fibre Young's modulus - E _m matrix Young's modulus - l fibre length - l _c fibre critical transfer length - l _s specimen span in three-point bend test - m Weibull modulus - r fibre radius - P applied load - V _f fibre volume fraction - V _m matrix volume fraction - x length of fibre needed to transfer load _mu V _m - x _d crack spacing in a composite with short, aligned fibres - _fu fibre ultimate strain - _mu matrix ultimate strain - _fu fibre ultimate strength - _mu matrix ultimate strength - _cu composite ultimate strength - _MOR modulus of rupture - _T tensile strength - interlaminar shear strength - _i interfacial shear strength - _m matrix work of fracture - _F work of fracture     

Brittle matrices reinforced with polyalkene films of varying elastic moduli

The inclusion of polyalkene films of different moduli in a cement-based matrix has shown the benefits to be gained, in terms of increased stress at a given strain, from the use of films of high elastic modulus. Further, the concept of load-bearing cracks is used to explain the transition region between the limit of proportionality and the bend-over point on the tensile stress-strain curve, which is found to exist with high film modulus composites. This transition region could be an important factor affecting the choice of film to be used in a commercial composite.Nomenclature E _c uncracked composite modulus - E _m matrix modulus - E _f film modulus - V _m matrix volume-fraction - V _t film volume-fraction - V _f(crit) (E _{c mu})/ _fu - A _c cross-sectional area of composite - (E _m V _m/E _fV_f) - _m matrix strain - _mu matrix cracking strain - _mu average matrix cracking strain, (#x03C3;_co)/E _c - _mc strain at end of multiple cracking - _fu ultimate fibre stress - _cu ultimate composite stress - _co average composite cracking stress (assumed at a strain of _mc/2) - S4 81 draw ratio polypropylene film - S8 181 draw ratio polypropylene film - E3H polyethylene film - LOP limit of proportionality (stress at first crack, assumed to be a departure from linearity of the tensile stress-strain curve of a perfectly straight and uniform test specimen. However, this point cannot be reliably determined from the stress-strain curve because of the clamping strains induced in warped specimens) - BOP bend-over point (stress at which the approximately horizontal portion of multiple cracking region commences. The BOP is generally higher than the LOP and is a much more reliable point to determine experimentally than the LOP)     

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.     

The compression strength of composites with kinked,misaligned and poorly adhering fibres

Experiments carried out on pultruded fibre reinforced polyester resins show that, at moderate fibre volume fractions, the compressive strength of aligned fibre composites depends linearly on the volume fraction. The strength falls off when the fibre volume fraction,V _f=0.4 with Kevlar and high strength carbon fibres. The effective fibre strength atV _f<0.4 is much less than the tensile strength but it is close to the tensile strength with E-glass fibres and high modulus carbon fibres. Poor adhesion between fibres and matrix reduces the compressive strength, as does kinking the fibres when the fibre radius of curvature is reduced to below 5 mm. Misalignment of the fibres reduces the compressive strength when the average angle of misalignment exceeds about 10° for glass and carbon fibres. However, with Kevlar no such reduction is observed because the compression strength of Kevlar reinforced resin is only a very little better than that of the unreinforced resin.     

The influence of brittle boundary layers on the strength of fibrous metallic composites

The brittle boundary layers often caused during the production of composites or by their treatment at higher temperatures, may change the mechanical properties. On the steel wire/aluminium system the growth of the intermetallic boundary phase and its influence on the strength of the composite were investigated. Hence followed a maximum strength at small layer thicknesses. By means of fracture investigations new models were developed which allow the calculation of the dependence of strength behaviour on layer thickness.List of symbols E _f Young's modulus of fibre - E _b Young's modulus of boundary layer - _c external load - _f tensile stress in the fibre - _m tensile stress in the matrix - _b tensile stress in the boundary layer - _uc,f,b ultimate strength of the composite, the fibre or the boundary layer, respectively - averaged stress in the fibre - _bf shear stress in the boundary layer-fibre interface - ₀ shear strength of the boundary layer-fibre-interface - _uf ultimate strain of the fibre - fraction of the layer which has grown into the matrix - Weibull parameter - ^–1 characteristic length of stress transfer between fibre and boundary layer - d diameter of the boundary layer - 2l length of the boundary layer segments - r _f fibre radius - u(x) displacement field - v _{f, b,m} volume fraction of fibres, boundary layer or matrix respectively.     

Compressive strength of coated rigid-rod polymer fibres

One limitation to the use of high-strength/high-modulus rigid-rod polymer fibres like poly-(p-phenylene benzobisthiazole) (PBZT) and poly-(p-phenylene benzobisoxazole) (PBZO) in composite structures is their low compressive strength. Various theories have been developed to predict compressive strength of rigid-rod fibres. In this study the critical buckling stress for rigid-rod fibres with stiff external coatings has been theoretically modelled assuming that the failure mode in compression is the microbuckling of the fibrils in shear. Our model predicts that significant improvement in fibre compressive strength will occur only when relatively thick coatings, with thickness to diameter (t/D) ratios in excess of > 0.05, are used. Experimentally measured compressive strength of aluminium coated PBZT fibres shows values in good agreement to the theory at t/D ratios of 0.006 and below. Factors related to the selection of suitable coating materials and problems associated with establishing coating performance are identified.Nomenclature P axial compressive load - P _f axial compressive load on the fibre - P _c axial compressive load on the coating - P _cr ⁱ critical buckling load in the ith case - _cr critical buckling stress - _co compressive strength of the uncoated fibre - _c compressive strength of the coated fibre - v(x) lateral deflection of a buckled fibril or coating - V _m amplitude of the lateral deflection in the mth mode - m number of half-sine waves in the deflection mode - x coordinate distance along axial direction - y coordinate distance along radial direction - coordinate distance along circumferential direction - l length of the buckling unit - N number of fibrils in the fibre - D fibre diameter - d fibril diameter - t coating thickness - I _f moment of inertia of the fibril - A _f cross-sectional area of the fibril - E _f tensile modulus of the fibre - E _c tensile modulus of the coating material - E tensile modulus of the coated fibre - G torsional shear modulus of the fibre - v_c Poisson's ratio of the coating material - _f density of the fibre - _c density of the coating material - density of the coated fibre - U _f strain-energy change in the fibre - U _c strain-energy change in the coating - T _f external work done on the fibre - T _c external work done on the coating - d/D - t/D     

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     

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.     

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     

Internal material damping of polymer matrix composites under off-axis loading

The objective of this paper is to determine theoretically the material damping of short fibre-reinforced polymer matrix composites. The major damping mechanism in such composites is the viscoelastic behaviour of the polymer matrix. The analysis was carried out by developing a finite-element program which is capable of evaluating the stress and strain distribution of short fibre composites under axial loading (see Fig. 1a). Using the concept of balance of force we can express the modulusE _x along the loading direction as a function of the mechanical properties of the fibre and matrix materials, fibre aspect ratio,l/d, loading angle,, and fibre volume fraction,V _f. Then we apply the elastic-viscoelastic correspondence principle to replace all the mechanical properties of the composite, fibre and matrix materials such asE _x,E _f,E _m,G _m, by the corresponding complex moduli such asE _x +iE _x , andE _f +iE _f . After separation of the real and imaginary parts, we can expressE _' ^x/t' andE _x ^t" as functions of the fibre aspect ratio,l/d, loading angle,, stiffness ratio,E _f/E _m, fibre volume fraction,V _f, and damping properties of the fibre and matrix materials such as _f and _m. Numerical results of the composite storage modulus,E _x , loss modulus,E _x , and loss factor (damping), _C, are plotted as functions of parameters such asl/d,,V _f, and are discussed in terms of variations ofl/d,, andE _f/E _m, in detail. It is observed that for a given composite, there exist optimum values ofl/d and at whichE _x and _c are maximized. The results of this paper can be used to optimize the performance of composite structures.Nomenclature A _c,A _f,A _m cross-sectional area of composite, fibre and matrix, respectively - d fibre diameter - E _L longitudinal modulus of composite (along the fibre direction) (see Fig. 1a) - E _T transverse modulus of composite (see Fig. 1a) - E _x modulus of composite along thex-direction (see Fig. 1b) - E _f tensile modulus of fibre - E _m tensile modulus of matrix - G _m shear modulus of matrix - G _LT in-plane shear modulus of composite (see Fig. 1a) - l fibre length - m tip to tip distance between fibres - i (–1)^1/2 - R one-half of centre-to-centre fibre spacing - V _f fibre volume fraction - x distance along fibre from end of fibre - defined in Equation 22 - defined in Equation 3 - ^* defined in Equation 19 - _L extensional (longitudinal strain) of composite - _f, _m extensional (longitudinal strain) of fibre and matrix, respectively - _c, _f, _m extensional loss factor of composite, fibre and matrix respectively - G _m shear loss factor of matrix - angle between fibre and thex-direction - ¯ _c, ¯ _f, ¯ _m average longitudinal stress in composite, fibre and matrix, respectively - longitudinal stress in fibre - shear stress at fibre-matrix interface - defined in Equation 23     

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 anisotropic diffusion of water in Kevlar-epoxy composites

The diffusion of water into unidirectional Kevlar fibre reinforced epoxy resins was studied as a function of fibre orientation and, for unidirectional (0°) composites, as a function of volume fraction (V_f). As the angle increased from 0 to 90°, the diffusivity increased dramatically; i.e. as more and more fibre-ends were exposed to the shorter diffusion path, the diffusivity increased. The equilibrium weight gain of water (M) in the composites increased with theV _f of the fibre. M of Kevlar fibre was calculated to be 4.9%. At a constantV _f, specimens of the same thickness and width but different lengths were used to determineD ₂₂, the diffusion coefficient of the composite along the fibre, andD ₂₂, the diffusion coefficient transverse to the fibre. The initial data for the percentage weight gain against the square root of time were non-linear, which was attributed to the anisotropy of the diffusion process. The anisotropy arises from the much higher value ofD ₁₁ as compared toD ₂₂. AsV _f increased from 0.37 to 0.59,D ₁₁ increased from about 0.83 to about 4.2 × 10^–12m² sec^–1, whereasD ₂₂ decreased from 0.21 to 0.033 × 10^–12 m2 sec^–1. Thus, the ratioD ₁₁/D ₂₂ increased from 3 to over 100 as U increased. The experimental sorption data could be fitted satisfactorily with these diffusion coefficients.     

Fractographic analysis of vitreous calcia-alumina eutectic fibres produced by inviscid melt spinning (IMS)

The mechanical properties of inviscid melt spun (IMS) CaO-Al₂O₃ (46.5 wt % CaO-53.5 wt % Al₂O₃) eutectic fibres were examined by fractographic analysis as well as four-point bending and micro-indentation. The averaged fracture strength and elastic modulus values of the IMS Calcia-Alumina (CA) fibre were determined to be 460 MPa and 99.8 GPa, respectively by using four-point bending tests. The inner mirror constant (M) was determined to be 2.39 MPa·m^1/2 by using the plot of the fracture strength (_f) obtained from the bending tests as a function of r ^–1/2, where r is the inner mirror radius measured from scanning electron microscopy (SEM) on the fractured CA fibres. The flaw-to-mirror ratio (c/r) for the CA fibre was calculated to be 111.24. Also, the critical flaw size (c) of the CA fibre was estimated to be 2.35 m. The averaged elastic modulus value from Knoop micro-indentation was determined to be 102.5 GPa which is in good agreement with that from the four-point bending tests.     

Sunhemp fibre-reinforced polyester

This paper describes the tensile and impact behaviour of polyester composites reinforced with continuous unidirectional sunhemp fibres of plant origin. The tensile strength and Young's modulus of sunhemp fibre were found to be 389 MPa and 35.4 GPa, respectively. Tensile strength of composites containing up to 0.4 fibre volume fraction (V _f) were found to increase linearly with (V _f) and the results showed good agreement with the rule of mixtures. The work of fracture, as determined by Izod impact test, was also found to increase linearly with (V _f) and the work of fracture for 0.24 (V _f) composite was found to be approximately 21 kJ m^–2. The analysis of various energy absorbing mechanisms during impact fracture showed that fibre pull out and interface fracture were the major contributions towards the high toughness of these composites. The results of this study indicate that sunhemp fibres have potential as reinforcing fillers in plastics in order to produce inexpensive materials with a high toughness.     

The physics and mechanics of fibre-reinforced brittle matrix composites

This review compiles knowledge about the mechanical and structural performance of brittle matrix composites. The overall philosophy recognizes the need for models that allow efficient interpolation between experimental results, as the constituents and the fibre architecture are varied. This approach is necessary because empirical methods are prohibitively expensive. Moreover, the field is not yet mature, though evolving rapidly. Consequently, an attempt is made to provide a framework into which models could be inserted, and then validated by means of an efficient experimental matrix. The most comprehensive available models and the status of experimental assessments are reviewed. The phenomena given emphasis include: the stress/strain behaviour in tension and shear, the ultimate tensile strength and notch sensitivity, fatigue, stress corrosion and creep.Nomenclature a _i Parameters found in the paper by Hutchinson and Jensen [33], Table IV - a _o Length of unbridged matrix crack - a _m Fracture mirror radius - a _N Notch size - a _t Transition flaw size - b Plate dimension - b _i Parameters found in the paper by Hutchinson and Jensen [33], Table IV - c _i Parameters found in the paper by Hutchinson and Jensen [33], Table IV - d Matrix crack spacing - d _s Saturation crack spacing - f Fibre volume fraction - f _l Fibre volume fraction in the loading direction - g Function related to cracking of 90 ° plies - h Fibre pull-out length - l Sliding length - l _i Debond length - l _s Shear band length - m Shape parameter for fibre strength distribution - m _m Shape parameter for matrix flaw-size distribution - n Creep exponent - n _m Creep exponent for matrix - n _f Creep exponent for fibre - q Residual stress in matrix in axial orientation - s _ij Deviatoric stress - t Time - t _p Ply thickness - t _b Beam thickness - u Crack opening displacement (COD) - u _a COD due to applied stress - u _b COD due to bridging - v Sliding displacement - w Beam width - B Creep rheology parameter _o/ _o ⁿ - C _v Specific heat at constant strain - E Young's modulus for composite - E _o Plane strain Young's modulus for composites - Unloading modulus - E _* Young's modulus of material with matrix cracks - E _f Young's modulus of fibre - E _m Young's modulus of matrix - E _L Ply modulus in longitudinal orientation - E _T Ply modulus in transverse orientation - E _t Tangent modulus - E _s Secant modulus - G Shear modulus - G Energy release rate (ERR) - G _tip Tip ERR - G _tip ^o Tip ERR at lower bound - K Stress intensity factor (SIF) - K _b SIF caused by bridging - K _m Critical SIF for matrix - K _R Crack growth resistance - K _tip SIF at crack tip - I _o Moment of inertia - L Crack spacing in 90 ° plies - L _f Fragment length - L _g Gauge length - L _o Reference length for fibres - N Number of fatigue cycles - N _s Number of cycles at which sliding stress reaches steady-state - R Fibre radius - R R-ratio for fatigue (_max/_min) - R _c Radius of curvature - S Tensile strength of fibre - S _b Dry bundle strength of fibres - S _c Characteristic fibre strength - S _g UTS subject to global load sharing - S _o Scale factor for fibre strength - S _p Pull-out strength - S _th Threshold stress for fatigue - S _u Ultimate tensile strength (UTS) - S _* UTS in the presence of a flaw - T Temperature - T Change in temperature - t Traction function for thermomechanical fatigue (TMF) - t _b Bridging function for TMF - Linear thermal coefficient of expansion (TCE) - _f TCE of fibre - _m TCE of matrix - Shear strain - _c Shear ductility - _c Characteristic length - Hysteresis loop width - Strain - _* Strain caused by relief of residual stress upon matrix cracking - _e Elastic strain - _o Permanent strain - _o Reference strain rate for creep - Transient creep strain - _s Sliding strain - Pull-out parameter - Friction coefficient - Fatigue exponent (of order 0.1) - Beam curvature - Poisson's ratio - Orientation of interlaminar cracks - Density - Stress - _b Bridging stress - ¯_b Peak, reference stress - _e Effective stress = [(3/2)s _ijs_ij]^1/2 - _f Stress in fibre - _i Debond stress - _m Stress in matrix - _mc Matrix cracking stress - ^o Stress on 0 ° plies - _o Creep reference stress - _rr Radial stress - ^R Residual stress - _s Saturation stress - _s ^* Peak stress for traction law - Lower bound stress for tunnel cracking - ^T Misfit stress - Interface sliding stress - _f Value of sliding stress after fatigue - _o Constant component of interface sliding stress - _s In-plane shear strength - ¯_c Critical stress for interlaminar crack growth - _ss Steady-state value of after fatigue - ^R Displacement caused by matrix removal - _p Unloading strain differential - _o Reloading strain differential - Fracture energy - _i Interface debond energy - _f Fibre fracture energy - _m Matrix fracture energy - _R Fracture resistance - _s Steady-state fracture resistance - _T Transverse fracture energy - Misfit strain - _o Misfit strain at ambient temperature     

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.     

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     

Analysis of the strength and fracture behaviour of unidirectional and angle-ply graphite-aluminium composites

The tensile behaviour of unidirectional and [±]_s angle-ply P100 graphite-reinforced 6061-Al composites was determined as a function of the angle () between the fibre and the applied load. The experimentally determined values of the elastic modulus and tensile strength of the composites are compared with those predicted from classical laminate theory. The measured elastic modulus values agreed with theoretical values, but the strength of the [\+-\gq]_s angle-ply composites was substantially greater than predicted. The discrepancy between experiment and theory is attributed to the stress required to fail the fibre ply/separator foil interface present in the angle-ply composites. The composite failure modes are also documented, and it is shown that the separator foils of the angle-ply composites shift the transition from tensile to shear failure to greater values of\gq relative to the off-axis unidirectional composites.     

The second phases in a burn resistant stable beta titanium alloy—Ti40

The second phases in Ti40 (Ti25V-15Cr-0.2Si) burn resistant titanium alloy are studied. The higher solution temperature, the more second phases in Ti40 alloy. There are not second phases if the solution temperature is below 850°C, while there are rod-like and little Ti₅Si₃ phases if temperature is over 850°C. , Ti₅Si₃ and oblique phases emerge after Ti40 solution at 910°C followed by aging at 600°C, while only Ti₅Si₃ phases emerge after solution at 860°C followed by aging at 600°C. The effect of the second phases on properties at RT are not obvious. There are different shapes of and Ti₅Si₃ precipitates after Ti40 alloy exposure at 540°C for 100 h, which decreases the thermal stability.     

Fragmentation of aramid fibres in single-fibre model composites

Raman spectroscopy has been used to monitor the state of axial stress along fragmented, high-modulus Kevlar 149 aramid fibres in an epoxy resin matrix by monitoring the peak position of the strain-sensitive 1610 cm^–1 aramid Raman band along individual fragments. It is shown that the interfacial shear stress along each fragment, derived from the strain distribution profiles, is not constant as assumed by conventional fragmentation analysis. The fragmentation process of as-received Kevlar 149 fibres is compared to that of irradiated Kevlar 149 fibres exposed to ultraviolet light where the tensile strength and modulus of the fibres have been reduced. It is found that the derived interfacial shear stress and interfacial shear strength values are higher for those fibres exposed to ultraviolet light compared with the as-received fibres. It is also clearly demonstrated that the values of interfacial shear strength calculated at high matrix strains from conventional fragmentation analysis are considerably lower than the maximum value of interfacial shear stress prior to fibre fracture that was found to be close to the shear yield stress of the resin matrix. Hence the determination of the interfacial shear strength following the saturation of the fragmentation process may give rise to misleading results.Nomenclature e _f Fibre strain - e _m Matrix strain - e _f ^max Maximum strain along each fragment - e _f ^* Failure strain of the fibre - E _f Fibre tensile modulus - l _c Critical fragment length - l _c Mean critical fragment length - l _f Fragment length - r Fibre radius - x Distance along the fibre - _f ^max Maximum stress along each fragment - _f ^* Fibre tensile strength - Interfacial shear stress - _s Interfacial shear strength