Inhomogeneous Fiber Research Articles

On Oscillation of Inhomogeneous Fibres with Imperfect Interfaces

This work deals with an asymptotic model of oscillation of an inhomogeneous fibre containing a layer of imperfect interface (thin adhesive layer). We derive a lower-dimensional model and study propagation of waves associated with the displacement jump across the interface.

Calculation of spatially filtered signals produced by a motor unit comprising muscle fibres with non-uniform propagation.

Simulation of actual muscle potentials is necessary to understand processes that underlie changes in electromyographic signals. The work reported aims to analyse existing methods and suggest new ways of calculating precisely the signals (MUS) detected by a multielectrode from motor units (MUs) consisting of homogeneous or inhomogeneous (functionally and geometrically) fibres. Simulation (based on cable equations) of intracellular action potential (IAP) in a muscle fibre with a moderate geometrical inhomogeneity demonstrates that considerable changes in propagation velocity (more than 3.5 times) are accompanied by insignificant changes in the IAP amplitude (< 5%) and IAP shape in the temporal domain. MUS can therefore be considered as the output signal of a timeshift-invariant system whose input signal is the first temporal derivative of the IAP. As a result, calculation of MUS is reduced to a single convolution in the case of muscle composed of both homogeneous and inhomogeneous fibres. The suggested approach is valid for simulation of recordings obtained with points or rectangular plates leading off surfaces from muscles consisting of fibres that are parallel or inclined to the skin surface. The MUS terminal phases are prolonged because of fibre inhomogeneities. The presence of geometrical inhomogeneities results in additional positive-negative phases in MUS.

Modulation instability of the wave packet in a periodically inhomogeneous nonlinear fibre

The modulation instability conditions are studied for a wave packet consisting of two strongly coupled modes co-propagating in a two-mode fibre. The two modes are linearly coupled by the phase matching conditions, which take the longitudinal periodicity of the fibre into account. The nonlinear coupling of the modes is provided by the cross-modulation interaction. The influence of the initial conditions of the fibre excitation on the subsequent development of the modulation instability is analysed. It is shown that the modulation instability can exist in a region of normal material dispersion of the fibre.

Formation of microvoids during resin-transfer molding process

Voids in a composite part are deleterious because they degrade its strength and modulus. In resin-transfer molding (RTM), voids result mainly from inhomogeneous fiber architecture. Such inhomogeneity leads to non-uniform permeability of the fiber preform, which in turn causes the resin velocity to vary from point to point at a micro scale. The capillary pressure, which also prevails at this length scale, exacerbates the spatial variation of the resin velocity. The combined effect of pressure gradient and capillary pressure can be described by the capillary number. The resulting microscopic perturbations in the resin-flow front allow voids to form. The present paper proposes a mathematical model to describe the mechanisms of void formation. The existing data are used to validate the assumptions introduced. The model is then used to analyze new data from one-dimensional RTM experiments.

A screw dislocation interacting with a coated fiber

A close-form analytical solution is obtained for the stress field due to a screw dislocation near a coated fiber inhomogeneity in isotropic material. The forces on dislocations are derived. The equilibrium positions of the dislocation are discussed in detail for various material constants’ combinations. It is found that when the coating layer is thick, the elastic property of the fiber (inclusion) has no significant influence on the force of the dislocation, therefore the equilibrium and stability of the dislocation can be obtained similarly from the two-phase model adopted by Dunders (1967. Recent Advances in Engineering Science 2, 223–233). On the other hand when the coating layer is thin, if both the fiber and the coating layer are “softer” (i.e., have lower modulus) than the matrix, the dislocation is always attracted by the fiber, and if both the fiber and the coating are “harder” (i.e., have higher modulus) than the matrix, the dislocation is always repelled by the fiber. As a result, there are no equilibrium positions under these two conditions. While if the fiber is harder and the coating is softer than the matrix, there is at least one unstable equilibrium position near the coating–matrix interface, if the fiber is softer and the coating is harder than the matrix, there is at least one stable equilibrium position near the coating–matrix interface.

Rainbow Scattering by an Inhomogeneous Cylinder with an Off-Axis Gaussian Beam Incidence at Normal

The problem of an off-axis Gaussian beam incident perpendicular on an infinitely long multi-layered cylinder is investigated. The efficient and accurate recursive algorithm for computing the scattering field is discussed. The stability of the numerical scheme allows us to extend the feasible range of computations, both in size parameter and in number of layers for a given size. Particular attention is paid to rainbow scattering of homogeneous and inhomogeneous fibers.

Increase in the correlation length of nonmonochromatic radiation during propagation in a single-mode optical fiber containing random inhomogeneities and the influence of this increase on the operation of a fiber ring interferometer

An analysis is made of the conditions under which the coupling of orthogonal polarization modes at random inhomogeneities in single-mode optical fibers leads to an increase in the correlation length of a source of nonmonochromatic radiation. It is shown that when long-base fiber ring interferometers with a single-mode fiber ring system possessing weak linear birefringence are used, the correlation length of the nonmonochromatic radiation at the interferometer exit is increased, which means that the interference pattern can have satisfactory visibility even when there is an appreciable difference between the interferometer arms as a result of the Sagnac effect due to the Earth’s rotation. The calculations were made by mathematical modeling of random inhomogeneities in the fiber.

Effect of Cylindrically Orthotropic Carbon Fibers with Transversely Isotropic Core on Effective Thermal Conductivity of Unidirectional Composites

Carbon fibers can be considered cylindrically orthotropic. Depending on the arrangement of basal planes, predominant configurations are circumferential and radial, but in the core of the fiber, the alignment is undetectable, and consequently it is considered as transversely isotropic. In composites reinforced with these types of fibers, the effective thermal conductivity transverse to the fiber direction will be affected by the core and by the thermal resistance between the fiber and the matrix. The analytical models available are not adequate because they assume that the fiber is totally homogeneous. In this paper, a model of finite elements is presented, which allows combination of the effects of core with the cylindrical orthotropic of the fiber and the thermal contact resistance between the fiber and the matrix. The effective conductivity of composites with orthotropic and inhomogeneous fibers are compared to those with orthotropic and homogeneous fibers. This allows evaluation of the effect for the different morphology of the fibers. The model reveals a significant effect for radially orthotropic fibers (pitch-based). The model also contributes to a better understanding of the heat flux paths in cylindrically orthotropic and inhomogeneous fibers. Finally, this numerical simulation can be of interest first, in the microstructural studies focused on the relationship between the transverse thermal conductivity of carbon fibers and some microstructural parameters, and secondly, in the studies designed to estimate the interfacial contact resistance.

Transverse behavior of a unidirectional composite (glass fibre reinforced unsaturated polyester). Part II. Influence of shrinkage strains

A micromechanical investigation of the transverse creep behavior of unidirectionally reinforced glass fibre composites with an unsaturated polyester matrix is presented. More specifically the influence of initial strains induced by polymerization shrinkage of the unsaturated polyester is studied. A previously established nonlinear viscoelastic model of the deformational behavior of the unsaturated polyester matrix is used in the numerical calculations. The matrix model includes effects of physical ageing of the resin and, in its general 3D-formulation, is able to describe time-dependent lateral contraction (Zhang, Ernst and Brouwer, 1997. Mech. Mater. 26, 141–166, 167–195). It has been shown that this uniaxially characterized 3D model can be used to describe three-dimensional loading situations successfully. In another paper (Zhang, Ernst and Brouwer, 1998. Mech. Mater. 27 (1998) 13–36), the theory has been further applied to model the transverse creep of the composites. New fibre packing geometries have thereto been presented. These packing geometries overcome the shortcomings of the traditional rectangular and hexagonal geometries, as in some sense they take into account the inhomogeneous fibre distribution in the transverse plane. In this paper, the initial strains induced by curing shrinkage of the unsaturated polyester during the manufacturing process of the composite are introduced. The model calculations show that the stresses caused by the initial strains gradually relax in the composite even without external loading. Complete relaxation of these stresses however takes a very long time and may never be realized in practice. It is further shown that, although the global creep behavior is relatively insensitive to the presence of initial strains, the local stress distribution is completely distorted. This result suggests that polymerization shrinkage significantly influences the onset of crack initiation in composites.

Inhomogeneities and segregation behavior in strontium—barium niobate fibers grown by laser-heated pedestal growth technique. Part II

Inhomogeneities in Ce-doped and undoped fibers grown by laser-heated pedestal growth (LHPG) along the c- or a- axis were investigated by two-dimensional scanning electron microprobe analysis (SEPMA). SEPMA data indicated that these cores are primarily connected with the source rod compositions utilized and the convection characteristics of the LHPG technique. Ba enrichment and Sr decrease were primarily detected in the cores and qualitatively described in terms of the composition-control mechanism of LHPG, the complex-segregation and a modified Burton—Prim—Slichter (BPS) equation. Certain aspects of defect structure as a complex congruency related phenomenon are also discussed in the paper giving a more complete interpretation of the origin of cores in SBN fibers.

Investigation of Interlaminar Defects and their Influence on Interlaminar Strength

In this paper, we directed our attention to the interlaminar defects and their influence on the interlaminar strengths. With the aid of a S-570 scanning electron microscope, the morphology and distribution of interlaminar defects were inspected and documented. According to their shape, size and cause of formation, the defects were classified into five types: flakiness void, irregular shaped debond, local imperfectly cured resin, debond in two multi-directional plies, and inhomogeneous fibers and the large scale debond by these fibers. The cause of defects formation was discussed by analyzing the manufacturing process of composites. The influence of defects on the interlaminar strength and its mechanism was analyzed experimentally and theoretically. The results indicate that these defects, with different effects, decrease the interlaminar strength because they form interlaminar cracks, and the interlaminar shear strength is less affected than interlaminar tensile strength, which is measured according to GB4944 test method. To comprehend defects distribution effect, a four-point-bending test method was introduced to measure the interlaminar peel strength, and a discussion was made on the correlation between the interlaminar tensile strength, interlaminar peel strength and in-plane transverse tensile strength. Finally the concept of interlaminar defect coefficient, which can be used to characterize the defects, was set up and the formula to calculate it was proposed.

Effect of cellular inhomogeneity on cardiac tissue mechanics based on intracellular control mechanisms.

Our earlier description of the intracellular control (IC) of contraction of a single cell, based on coupling calcium kinetics with cross-bridge cycling, is extended here to study the performance of a multicellular inhomogeneous tissue common in pathophysiological situations. Inhomogeneity in calcium affinity or in cross-bridge kinetics is first simulated by analyzing two fiber segments connected as parallel or serial duplexes. The calculated characteristics of the parallel duplex are tested against our experimental data with two parallel nonuniform rat papillary fibers. The predicted serial duplex behavior is compared with reported experimental data of the effects of segmental hypoxia along a papillary fiber. Fiber inhomogeneity leads to polyphasic contraction of the fiber segments, reduces muscle length shortening, and affects the control of relaxation. We next investigated the force generated by a nonuniform tissue containing small areas of necrosis, evident in subendocardial infarction. Theoretical analysis suggests that the IC mechanism decreases the extension of cell necrosis by lowering the energy consumption of the viable cells in the ischemic zone. The study emphasizes the importance of IC in determining the global and local function of the inhomogeneous myocardium.

Elastic waves in a composite containing inhomogeneous fibers

We consider the problem of elastic wave propagation in a composite with multiple-coated fibers. The fibers are assumed to be composed of N concentric layers of homogeneous isotropic or transversely isotropic materials and randomly distributed in the matrix medium. We use a homogenization technique which combines the Generalized Self Consistent model (GSCM) and a statistical averaging procedure to calculate the frequency dependent phase velocity and attenuation of the average waves. In the case of a fiber containing a single interface layer, the influence of the thickness, density, and shear modulus of the interface on the phase velocity and attenuation of the average waves is investigated through a parameter study. The results show that changes in the thickness and density of the interface have no significant effect on the phase velocity of the average waves but the shear modulus has a stronger influence. The feasibility of nondestructively characterizing the interface properties through the inversion of low frequency phase velocity data is discussed.

Analysis of modal cutoffs of radially inhomogeneous two-core optical fibers by circular harmonics expansion method

A scalar theory based on generalization of the circular harmonics expansion method combined with the finite element method is formulated to determine cutoff values for higher order normal modes on the two-core fiber with radially inhomogeneous core index profiles under the weakly guiding approximation. The validity of the field expansion expression in the derived generalized circular harmonics expansion method is proved rigorously by expanding the Green's function for the Laplace equation in a surface integral equation into generalized circular harmonics. Numerical examples are given for the two identical-core cases with power-law core index profiles. Our method is shown to be able to provide exact cutoff values for the touching-core case.

A modified rule-of-mixtures for prediction of tensile strengths of unidirectional fibre-reinforced composite materials

Measured ultimate tensile strengths in unidirectional fibre-reinforced composite materials have been observed to deviate from the linear predictions of the classical rule-of-mixtures relationship. The physical factors responsible are fibre-fibre interaction, inhomogeneous fibre distribution in the matrix and fibre misorientation to the loading direction. A recent modification to the classic rule-of-mixtures to account for fibre-fibre interaction has already resulted in good agreement between measured and predicted values of ultimate tensile strengths at high fibre volume fractions for Kevlar/epoxy composites. Additional modifications to the rule of mixtures to incorporate both fibre misorientation and inhomogeneous spread have been presented here. These modifications result in greater agreement between measured and predicted ultimate tensile strengths at low fibre volume fractions while retaining the accuracy of prediction at higher fibre volume fractions. Good agreement between measured and predicted values of inhomogeneous fibre spread were obtained at high fibre volume fractions. Furthermore, these additions to the classic rule-of-mixtures can be used to gauge the extent of each of the physical factors responsible for ultimate tensile strength reduction in unidirectional composite materials.

Interaction of stored, cooled proton beams with fiber targets

The use of thin fibers as internal targets for nuclear physics experiments in storage rings is discussed. We have measured the lifetime and the energy spread of stored, electron-cooled beams in the presence of an internal carbon fiber target. Measurements have been carried out in the Indiana Cooler with proton beams between 100 MeV and 300 MeV. The effect of the inhomogeneous fiber target on the beam is the same as that of a homogeneous gas target of equivalent thickness within the accuracy of the measurement. The measurements are compared with a Monte Carlo simulation of the stored beam. It is demonstrated that charging of the fiber target can significantly affect the lifetime and energy spread of the stored beam.

Numerical method for a model of inhomogeneous muscle fibers

AbstractThe numerical solution of a nonlinear and nonlocal system of integro‐differential equations that models the contraction of a single heterogeneous muscle fiber is studied. The method proposed is a form of the finite difference method of characteristics. Optimal error bounds are established for the resulting approximation. © 1993 John Wiley &amp; Sons, Inc.

On the solution of mixed problems for a fiber with a vertical circular cylindrical cavity

A method of solving paired integral equations that appear in considerations of mixed problems of elasticity and thermoelasticity theory is given, with the help of generalized integral Weber transforms. The paired equations are reduced to an integral Fredholm equation of the second kind on the semiaxis, which have a discontinuous kernel, or to Fredholm equations of the second kind on a finite interval and infinite systems of linear algebraic equations, which are normal in the sense of Poincare-Koch. As an example, contact problems for an inhomogeneous fiber with a cavity are considered. If the fiber is bonded with the elastic half-space, then a second appproach is realized, which is based on a reduction to an equation with a self-adjoint operator, for which some method of sequential iteractions and the Bubnov-Galerkin method are justified.

Defects in squeeze-cast Al 2O 3/Al alloy composites and their effects on mechanical properties

The microstructure and defects in squeeze-cast, random shortfibre Al0·6Mg and Al5Si3CuMg composites were examined by optical microscopy, electron microscopy and tomography. The effects of the defects on tensile and fatigue properties were studied. Fibre breakage, porosity, inclusions, preform cracking and inhomogeneous fibre orientation and weak interface bonding in the composites are the main defects, and these are the principal causes of the property data scatter and the poor tensile strengths and fatigue lives.

Investigation of structure of planar inhomogeneous filter media from glass fibers

Using known methods for measuring local sheet thickness and area mass, investigations of inhomogeneous glass fiber filter materials were carried out. Special attention was given to the determination of the size of inhomogeneities using methods prevalent in time series analysis. For commercially manufactured papers the characteristic sizes of inhomogeneities were proved to be dependent on the direction of measurement, thus demonstrating a preferred fiber deposition direction in the production process.