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     

The thermal expansion of carbon-fibre reinforced plastics

The thermal expansion characteristics of a series of carbon-fibre fabric reinforced plastic laminates over the approximate temperature range 90 K to 440 K have been determined. The reinforcements included Morganite Type II fibres in a plain weave and a two-by-two twill weave and Courtaulds Grafil E/XAS fibres in a two-by-two twill weave, a five-shaft satin weave and in an unwoven unidirectional disposition. The results show that the ratio of fibre tow densities in the principal fibre directions, the crimp in the reinforcing fibres and the laminate stacking sequence all influence the magnitudes and temperature dependences of the linear thermal expansion coefficients, as well as the detailed manner in which the dimensions respond to changes of temperature. Volume shrinkage effects resulting from temperature cycling are also reported. The linear thermal expansion coefficients of Courtaulds Grafil E/XAS carbon fibres in directions parallel, ^f , and perpendicular, _¶ ^f , to the fibre axis have been estimated as ^f =–2.6× 10^–7 K^–1 and ^f =2.6×10^–5 K^–1.     

Diffusion coefficients of tetrazolium blue in homogeneous and micellar solutions

Diffusion coefficients of the electron acceptor dye tetrazolium blue were measured by the Taylor dispersion method, with an accuracy better than 4%, in two solvents: (i) a homogeneous one-aqueous phosphate buffer, 0.1 M, pH=7.0 (medium I); and (ii) a heterogeneous one-nonionic micelles of Triton X-100, 2.0 mM (where M stands for mol·dm^–3), in the same aqueous phosphate buffer (medium II). The values obtained were D ₁₂ ^I =3.64×10^–10m²·s^–1 and D ₁₂ ^II =3.01×10^–10m²·s^–1·D ₁₂ ^II has the meaning of a macroscopird or average diffusion coefficient, in which the partition coefficient of tetrazolium blue between micelles and water, as well as the diffusion coefficients of this dye and of the micelles in the aqueous phase, are involved.     

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.     

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     

Zr-Hf interdiffusion in polycrystalline Y2O3-(Zr+Hf)O2

Lattice and grain-boundary interdiffusion coefficients were calculated from the concentration distributions determined for Zr-Hf interdiffusion in polycrystalline 16Y₂O₃·84(Zr_1–x Hf _x )O₂ withx=0.020 and 0.100. The lattice interdiffusion coefficients were described byD=0.031 exp [–391 (kJ mol^–1)/RT] cm² sec^–1 and the grain-boundary diffusion parameters byD=1.5×10^–6exp [–309(kJ mol^–1)/RT] cm³ sec^–1 in the temperature range 1584–2116° C. Comparison of the results with those for the systems CaO-(Zr+Hf)O₂ and MgO-(Zr+Hf)O₂ indicated that the Zr self-diffusion coefficient was insensitive to the dopants in the fluorite-cubic ZrO₂ solid solutions.     

Oxygen self-diffusion in a potassium strontium silicate glass using proton activation analysis

Oxygen self-diffusion coefficients were measured in a 20K₂O-20SrO-60SiO₂ (wt%) glass above and below the glass transition temperature using the single spectrum proton activation analysis of oxygen-18 using the nuclear reaction ¹⁸O(p, )¹⁵N. The -particle spectrum recorded during proton irradiation is used to determine the ¹⁸O concentration profile. The self-diffusion coefficients, D, determined for the three diffusion times of about 22 h, 3 1/2 and 7 1/2 days were in good agreement within experimental error, except for the two lowest temperatures of the short-time run possibly because of the shallow depths of diffusion and surface exchange. In the temperature range 600 to 1000 K, D values with the relations, above the glass transition temperature D=7.6×10¹⁴ exp(–119 kcal/RT) cm²sec^–1, and below the glass transition temperature D=1×10^–12 exp(–10 kcal/RT) cm²sec^–1, were obtained.     

Transverse Spin Diffusion in a Dilute Spin-Polarized Degenerate Fermi Gas

We re-examine the calculation of the transverse spin-diffusion coefficient in a dilute degenerate spin-polarized Fermi gas, for the case of s-wave scattering. The special feature of this limit is that the dependence of the spin diffusion coefficient on temperature and field can be calculated explicitly with no further approximations. This exact solution uncovers a novel intermediate behaviour between the high field spin-rotation dominated regime in which D H^–2 , D T^–2 , and the low-field isotropic, collision dominated regime with D = D T^–2 . In this intermediate regime, D_, T^–2 but D D. We emphasize that the low-field crossover cannot be described within the relaxation time approximation. We also present an analytical calculation of the self-energy in the s-wave approximation for a dilute spin-polarized Fermi gas, at zero temperature. This emphasizes the failure of the conventional Fermi-liquid phase space arguments for processes involving spin flips. We close by reviewing the evidence for the existence of the intermediate regime in experiments on weakly spin-polarized ³ He and ³ He– ⁴ He mixtures.     

Anomalous temperature dependence ofD andT 2 for dilute solutions of3He in solid4He

Results of measurements of the spin diffusion coefficientD and NMR relaxation timesT ₁,T ₂, and T_1p are presented for a range of fractional³He concentrations 1 × 10^–4x ₃2.5 × 10^–3 in solid⁴He at molar volumes 19.85V _m21.0 cm³ and temperatures 0.4<T<2 K in both hcp and bcc phases. We observe a minimumD(T) atx ₃=5×10^–4, which is interpreted in terms of a transition from coherent impuriton motion to thermally activated diffusion. ForT<0.8 K, (lnD)/(lnV _m)=60±8. TheT ₂ measurements show a minimum as a function of temperature forx ₃10^–3. TheT ₂ (T) andT ₁ (T) results yield values for activation energy and tunneling frequency of vacancies in these dilute solutions. Forx ₃=5×10^–4 andT 0.5 K,T ₂ (V _m) is anomalous.T ₁ measurements at the same concentration indicate there is an important contribution to the spectral density of dipole field fluctuations in the kHz region.Financial support provided for apparatus, materials, and a research studentship (ARA) by the Science Research Council.     

The surface diffusion coefficients of MgO and Al2O3

From the measurement of neck size and neck curvature during the sintering of two spheres the surface diffusion coefficients of MgO and Al₂O₃ were determined. The spheres of both materials were machined from single crystals. The following values of surface diffusion coefficients were found: for MgO,D _{s s} = 3.7 × 10^–4 exp (407.8 kJ mol^–1/RT m³ sec^–1; for Al₂O₃,D _{s s} = 1.5 × 10^–2 exp (518.7 kJ mol^–1/RT) m³ sec^–1.     

Fracture mechanics studies of crack healing and welding of polymers

Compact tension tests have been performed on re-healed and welded glassy polymers (PMMA-PMMA, SAN-SAN and PMMA-SAN). At temperatures above the glass transition temperature,T _g, it was observed that the facture toughness,K _Ii, in the interface increased with contact time,t, asK _Ii t ^1/4 as predicted by a diffusion model. The self-diffusion constantD(T _g + 15 K) of chains of molecular weight 1.2×10⁵ can be estimated as 1×10^–21sec^–1 with an activation energy of 274 kJ mol^–1. For full material resistance, the depth of interdiffusion, x ^21/2, was calculated to be between 2 and 3 nm. Vacuum drying of the specimens, as well as polishing the interfaces, decreases the speed of interdiffusion.On leave from Department of Mechanical Engineering, Imperial College of Science and Technology, Exhibition Road, London, UK.     

Designing and upgrading model of pre-denitrification systems

This paper reports a three-substrate steady-state integrated model, whose unknowns are expressed in explicit terms once concentrations of nitrogen compounds in the effluent flow are fixed. The model can be applied both to design and to upgrade wastewater treatment plants. The model is also able to evaluate the flexibility of existing wastewater treatment plants, which represents the capacity of the system to operate under different working conditions caused by increases in influent load or reductions in effluent quality standards. In this case the admissible variation of influent load or effluent concentration can be measured using suitable dimensionless flexibility indexes.List of symbols Q influent flow [L³ T^–1] - R₁ sludge recycle flow ratio - R₂ aerated mixed liquor recycle flow ratio - V_D denitrification reactor volume [L³] - V_N nitrification reactor volume [L³] - S biodegradable organic substrate concentration [M L^–3] - N-NH₄ ammonia nitrogen concentration [M L^–3] - N-NO₃ nitrate nitrogen concentration [M L^–3] - N_tot total nitrogen concentration [M L^–3] - O₂ oxygen concentration in the nitrification reactor [M L^–3] - X_H heterotrophic biomass concentration [M L^–3] - X_AUT autotrophic biomass concentration [M L^–3] - maximum removal rate of biodegradable organic substrate for an assigned value of temperature [T^–1] - maximum removal rate of nitrate for an assigned value of temperature [T^–1] - maximum removal rate of ammonia nitrogen for assigned values of pH and temperature [T^–1] - _S removal rate of biodegradable organic substrate [T^–1] - _D removal rate of nitrate [T^–1] - _N removal rate of ammonia nitrogen [T^–1] - K_S saturation coefficient for biodegradable organic substrate [M L^–3] - K_D saturation coefficient for nitrate [M L^–3] - K_SD saturation coefficient for organic substrate in the denitrification kinetic [M L^–3] - K_N saturation coefficient for ammonia nitrogen [M L^–3] - saturation coefficient for oxygen [M L^–3] - Y_H yield coefficient for heterotrophic microorganisms in the biodegradable organic substrate removal process - Y_D yield coefficient for heterotrophic microorganisms in the nitrate nitrogen removal process - Y_AUT yield coefficient for autotrophic microorganisms in the ammonia nitrogen removal process - (X_H)_r heterotrophic biomass concentration in the recycle sludge [M L^–3] - (X_AUT)_r autotrophic biomass concentration in the recycle sludge [M L^–3] - biodegradable organic mass consumption for unitary nitrate nitrogen mass reduction in the denitrification reactor - nitrogen consumption in the biodegradable organic oxidation process by mean of heterotrophic biomass     

Simulation of the diffusion of silicon in gallium arsenide. 4. DPSU program and results of numerical calculations

A program is developed for simulating the diffusion of silicon in gallium arsenide, and numerical calculations are performed for the process of high-concentration doping of gallium arsenide during thermal diffusion of silicon from a source with a constant concentration of the impurity near the surface of the semiconductor.Notation n _i concentration of intrinsic charge carriers - D _i intrinsic coefficient of silicone diffusion in gallium arsenide - V _Ga ^r– gallium vacancy in the charged state - V _As ^r+ arsenic vacancy in the charged stater _As ⁺ - × sign of the neutral charged state - and concentrations of gallium and arsenic vacancies reduced to thermally equilibrium values in the neutral charged state - C andC ^A concentrations of atoms at the nodes of the gallium and arsenic sublattices, respectively - C ^T total concentration of silicon atoms - N concentration of ionized atoms of a different impurity with the opposite type of conductivity - T temperature - t time of heat treatment - D(, T) effective coefficient of silicon diffusion in gallium arsenide - reduced concentration of electrons - C _S ^T total concentration of impurity atoms near the semiconductor surface - L _Ga ^V andL _As ^V diffusional mean free paths of gallium and arsenic vacancies, respectively Belarusian State University; Belarusian State University of Informatics and Radioelectronics, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 6, pp. 725–728, June, 1994.     

AlGaN/GaN HEMTS: material, processing, and characterization

The growth of AlGaN/GaN high electron mobility transistor (HEMT) structures on sapphire by metal organic vapor phase epitaxy (MOVPE) is described, with special emphasis on procedures to reduce dislocation density. All the processing steps involved in the fabrication of nitride-based HEMTs have been optimized, including dry etching by ion beam milling, evaporation of Pt/Ti/Au gate contacts, and SiN _x surface passivation. Devices with several gate lengths and different geometries have been fabricated by standard photo- and e-beam lithography. d.c. drain current and transconductance increase when gate length is reduced, up to 950 mA mm^–1 and 230 mS mm^–1, respectively, at V _GS=0 V, in HEMTs with a gate length L _G=0.2 m. A maximum output power higher than 5 W mm^–1 is estimated. Finally, small-signal measurements yield f _T=12 GHz and f _max=25 GHz for HEMTs with L _G=0.5 m, which increase up to 20 and 35 GHz for L _G=0.2 m, respectively. Limitation of high-frequency performance by parasitics is discussed.     

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     

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.     

Self-diffusion and the isotope-mass-effect in stearic acid single crystals

Self-diffusion parallel to the molecular axis in melt-grown crystals of the monoclinic c form of stearic acid has been examined in the temperature range 320 to 340 K using the radiotracer serial-sectioning technique. The results are best described by an expression of the form D=4×10³³ exp (–314±4 kJ mol^–1/RT) m²sec^–1. The value of the preexponential factor and activation energy are similar, relatively, to those obtained previously for other organic solids and are consistent with self-diffusion by a vacancy mechanism. Isotope-mass-effect measurements yielded mass factors E _ab=fK=0.3±0.04. For vacancy migration in a simple monoclinic lattice f _v0.6, thus K0.5. This is not an unreasonable value of K. It is argued however that values of f for vacancy diffusion in such anisotropic lattices as stearic acid could be significantly lower than expected.     

Carbon self-diffusion in tungsten carbide

Dense, hot pressed tungsten carbide specimens were used to study the self-diffusion of ¹⁴C into WC in the temperature range 2238 to 2643 ° K. The necessity for extended diffusion anneal times was eliminated by using a submicron sectioning technique, and the diffusion penetration depth was determined by spectrophotometric W^V thiocyanate analysis of the sample sections. The existence of two clearly delineated diffusion mechanisms was demonstrated from the shape of the activity versus penetration curves. The first obeyed a bulk diffusion law, originated at the specimen surface, demonstrated anomalously low diffusion coefficients, dominated to a depth of about 0.5 m, and could be represented by the expression: D _vol=1.90×10^–6 exp–(88,000/RT).Autoradiography demonstrated that the second mechanism was grain-boundary diffusion which dominated at depths greater than 1 m. The Fisher grain-boundary diffusion analysis and the Suzuoka analysis gave apparent grain-boundary diffusion activation energies of 74 Kcal/mole and 71 Kcal/mole respectively. By using an estimated value of the bulk diffusion coefficient, the Suzuoka analysis permitted direct calculation of the grainboundary diffusion coefficient, and can be represented by: D _g.b.=4.57×10² exp–(71,000/RT).     

Fabrication of C/SiC composites by an electrodeposition/sintering method and the control of the properties

Carbon fibre reinforced SiC matrix composites (C/SiC composites) were fabricated using an electrodeposition/sintering method and the control of properties such as flexural strength. Young's modulus and thermal expansion coefficient was investigated in order to fabricate C/SiC-based functionally gradient materials. By means of choosing the condition of electrodeposition and sintering, C/SiC composites with volume fraction of fibre (V _f) ranging from 45 to 78% were fabricated. Maximum flexural strength and Young's modulus were 185 MPa and 47.5 GPa with V _f of 75%, but both properties decreased with the decrease in V _f. Conversely, the thermal expansion coefficient increased with the decrease in V _f; the value varied from 0.2 to 2.75 × 10^–6K^–1.     

Mass and spin diffusion near the λ line in dilute3He-4He mixtures

We examine the possibility of using NMR and other measurements on very weak solutions of ³ He in liquid ⁴ He to investigate the superfluid phase transition. It is found that even for these very weak solutions the mass (D _m) and spin (D _s) diffusion coefficients associated with the ³ He behave in radically different ways:D _m is predicted to diverge asT approaches T from above as (T–T) ^–1/3 , while the behavior ofD _s depends on the type of experiment, and for the ordinary spin-echo type has no particular singularity.Based on a D.Phil. thesis submitted to the University of Sussex by M. A. Eggington.