Fibers Of Circular Cross Section Research Articles

Averaging the electrical properties of fiber-reinforced metal composites

Using the regular structure model, we average the electrical properties of unidirectional fiber-reinforced metal composites and propose procedures for determination of the effective electrical conductivity tensor of these materials. For the general case of packing of fibers of arbitrary cross section, the problem is reduced to calculation of some functionals determined in solutions of the integral equation of the corresponding boundary current problem for the structure. In the special case of symmetric packing of fibers of circular cross section, the solution is written in the form of series in elliptic functions.

Transverse strength of metal matrix composites reinforced with strongly bonded continuous fibers in regular arrangements

The composite limit flow stress for transverse loading of metal matrix composites reinforced with a regular array of uniform continuous fibers is calculated using the finite element method. The effects of volume fraction and matrix work hardening are investigated for fibers of circular cross section distributed in both sqyare and hexagonal arrangements. The hexagonal arrangement is seen to behave isotropically with respect to the limit stress, whereas the square arrangement of fibers results in a composite which is much stronger when loaded in the direction of nearest neighbors and weak when loaded at 45° to this direction. The interference of fibers with flow planes is seen to play an important role in the strengthening mechanism. The influence of matrix hardening as a strengthening mechanism in these composites increases with volume fraction due to increasing fiber interaction. The results for a power law hardening matrix are also applicable to the steady state creep for these composites. The influence of volume fraction on failure parameters in these composites is addressed. Large increases in the maximum values of hydrostatic tension, equivalent plastic stain, and tensile stress normal to the fiber-matrix interface are seen to accompany large increases in composite strength.

A micromechanics model for the effective thermomechanical behaviour of multiphase composite media

A micromechanics model is presented for predicting the effective thermomechanical moduli of multiphase particulate and fibrous composites. Particulate composites containing spherical inclusions and fibrous composites consisting of long cylindrical fibers of circular cross-section are considered. Results are presented for three-phase media which show excellent agreement with experimental data and also fall within existing bounds.

Direct casting of continuous fibres and wires by in-rotating-liquid spinning

A newly designed facility for direct casting and rapid quenching of metallic fibres and wires by melt spinning into a rotating coolant was built up. To control the entire process over an extended time period the flow behaviour of the melt jet was theoretically and experimentally studied. The important process parameters were examined to optimize the quality of the fibres and wires. Different alloys were spun to continuous fibres of circular cross-section and constant diameter.

A bimodal lognormal model of the distribution of strength of carbon fibres: effects of electrodeposition of titanium di (dioctyl pyrophosphate) oxyacetate

The tensile strength distribution of Fortafil-3 carbon fibres of circular cross-section has been investigated at different gauge lengths. The unimodal Weibull, unimodal lognormal and bimodal lognormal models were tested. Estimating the model parameters by the method of maximum likelihood, and testing each model by the Kolmogorov-Smirnov goodness-of-fit statistic at prescribed levels of significance, it is found that the data for untreated unsized fibres fit a bimodal lognormal model best. The proportions of the low and high strength populations,p andq, respectively, did not show any well-defined trend with gauge length and had average values close to 0.5. But the lognormal mean for each population showed an increasing trend with decreasing gauge length. It is inferred thatp andq are, respectively, related to the presence of surface flaws and internal defects, both of which probably have the same structural origin. After electrodeposition of titanium di (dioctyl pyrophosphate) oxyacetate (TDPO), the fibre strength was still best approximated by a bimodal lognormal distribution. But the weighting factorp for the weak population was reduced markedly, with a corresponding increase ofq, indicating the healing of surface flaws during electrodeposition of a protective layer of TDPO. Furthermore, in contrast to the observations with untreated fibres, the lognormal means for both the low and high strength populations of the electrocoated fibres were essentially unchanged with gauge length. Changes were also indicated in the number and severity of surface flaws, caused by concurrent electrochemical processes.

Ultrahigh birefringent optical fibers

The modes of weakly guiding fibers, constructed from anisotropic material which exhibits ultrahigh birefringence, are investigated. These modes are plane polarized unless the fiber is virtually uniaxial, with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n_{x} = n_{y} \neq n_{z}</tex> . The modal intensity patterns are, in general, noncircular, even for fibers of circular cross section.

A numerical technique for solving the scalar wave equation for Gaussian and smoothed-out profiles

A numerical technique, based on transforming the scalar wave equation to a finite interval before discretization is applied, is proposed for the solution of the scalar wave equation defining the modal fields and propagation constants of optical fibres. It is used to compute the propagation constants and modal fields of weakly guiding fibres of circular cross-section when the refractive index profile has a Gaussian or smoothed-out form. The smoothed-out profiles are studied because they vary continuously from the Gaussian to the step profile. Results are compared with and shown to be accurately approximated by simply explicit functions, dependent only on the fibre parameter.

Light scattering from unclad fibers: approximate ray theory of backscattered light

Formulas have been derived allowing the determination of the parameter ka (k = 2pi/lambda, a is the fiber radius) based on the approximate geometric theory for dielectric nonabsorbing unclad fibers of circular cross section from the course backscattered light intensity. The application of the method is restricted to fibers with the refractive indices within the interval ( radical2,2) and for ka > 100. In this region the method yields results with an accuracy of about 5%.

Analysis of Longitudinal ThicknessrShear Stiffness of a Monolayer Filamentary Composite

The longitudinal thickness-shear behavior of a rectangular cross-section prism containing circular cross-section fibers embedded in a matrix is analyzed. The problem is formulated as a Saint-Venant flexure problem modeled by a tip-loaded cantilever composite beam and solution is obtained by the boundary-point least-squares method. It is shown that the longitudinal thickness-shear modulus is much greater than the in-plane shear modulus for a monofilament composite and therefore an independent analysis is necessary to predict the longitudinal thickness-shear behavior of the composite. Numerical results are presented in graphical form for various values of fiber volume fraction and material parameters typical of modern advanced composites.

Analysis of Twisting Stiffness for a Multifiber Composite Layer

The twisting stiffness of a rectangular cross section consisting of a single row of solid circular cross-section fibers embedded in a matrix is analyzed. The problem is formulated as a Dirichlet torsion problem of a multielement region and solved by the boundary-point least-squares method. Numerical results for a single-fiber square cross section compare favorably with previous relaxation-method results. New numerical results for three and five-fiber composites suggest that the torsional rigidity of a multifiber composite can be approximated from the torsional rigidities of single and three-fiber models.

Isotropic fiber coarsening in unidirectionally solidified eutectic alloys

A theory of coarsening has been developed for the case of fibers of circular cross section in unidirectionally solidified eutectic alloys. The fibers are assumed to be randomly distributed throughout the unoccupied space in the matrix (uniformly distributed), and diffusion of solute is assumed to occur under steady-state conditions with cylindrical symmetry. The theory predicts that the cube of the average fiber radius increases linearly with time for all fiber volume fractions. As the volume fraction increases, the coarsening rate increases and the theoretical distribution of fiber radii becomes broader. It is shown that isotropic fiber coarsening occurs at approximately half the rate at which the same phase would coarsen if it were in the form of spherical precipitates for volume fractions up to 0.6. It is also demonstrated that the fibers will coarsen at a faster rate when they are uniformly distributed than when they are arranged on an hexagonal lattice.

Transmission Properties of Optical Fibers*†

Equations which describe the flux transmitted and the angular distribution of the emergent light from straight cylindrical fibers of circular cross section have been derived and numerically evaluated. Loss of light due to imperfect reflections, bulk absorption, and Fresnel reflections, are included in the formulation. All skew rays in the fiber have been considered in these calculations.Measurements of the attenuation and angular distribution of the emitted light from plastic scintillating fibers have been made. From the theoretical equations it has been deduced that these fibers are characterized by an internal reflectivity of 0.993±0.002 and an absorption coefficient of 0.015±0.003 cm−1.Measurements of the light transmitted by single-clad glass fibers indicate that these fibers are characterized by an internal reflectivity of 0.9993±0.0002 and an absorption coefficient of the order of 10−4 cm−1. Some experimental data on glass fiber bundles also are included.

11—Effect of Penetration on Reflectance of Dyed Textile Fibres

The absorption and scatter coefficients, K and S, used by Atherton to define the reflectance of dyed textile materials have been determined on the assumption that fibres of circular cross-section represent the absorbing and scattering elements through which the principal paths of light can be traced. It is shown that the ratio K/S is a function of fibre diameter, dye concentration and extinction coefficient, and the predicted relation is compared with that determined experimentally. The agreement is found to be such as to justify the extension of the theoretical model to a study of the effect of fibre penetration on reflectance of dyed fibres, and the predicted dependence on penetration is found to agree closely with that found in practice. An increase in penetration from 10 per cent to 100 per cent is shown to have the same effect on reflectance as a 33 per cent increase in dye concentration.The effect of fibre refractive index on the reflectance of undyed fibres has has also been estimated.