Data reduction methodologies for single fibre fragmentation test: Role of the interface and interphase

The single fibre fragmentation test (SFFT) is commonly used to characterise the fibre/matrix adhesion. In order to quantify the fibre/matrix adhesion the cumulative stress transfer function (CSTF) methodology was developed so that the elastoplasticity of the matrix could be included in the analysis through the plasticity-effect model [Tripathi D, Chen F, Jones FR. A comprehensive model to predict the stress fields in a single fibre composite. J Comp Mater 1996;30;1514–38., Tripathi D, Jones FR. Measurement of the load-bearing capability of the fibre/matrix interface by single fibre fragmentation. Comp Sci Technol 1997;57:925–35.] The limitations of this technique for the data reduction have been addressed by the use of the Plasticity Model to input the non-linearity of the matrix into methodology for fragmentation of a fibre in a matrix. An improved methodology, known as the revised cumulative stress transfer function (RCSTF) is described. The adhesion of a nanoscale plasma copolymer coated glass/epoxy system has been used to examine this approach to the fragmentation process. This methodology is also extended to account for the presence of an interphase. To validate the three phase model, carbon fibre coated with high and medium modulus epoxy resin were used to simulate fibre/interphase/matrix.     

State of Polarization in Open- and Closed-loop Helices of Single-mode Fibres

Abstract

The state of polarization in helically wound single-mode fibres is described in terms of coupled-mode equations and the Mueller matrix for an elliptically birefringent single-mode fibre in the quasi-monochromatic case. Possible depolarization has been accounted for by means of the mutual correlation function |γ| between eigenpolarization modes. The polarization state in closed-loop fibre-optic helices has been studied experimentally under single- and dual-mode operation. It has been shown that the closed-loop set-up can be used for the development of compact fibre-optic sensors.     

The effect of interfacial imperfections on the micromechanical stress and strain distribution in fibre reinforced composites

A mathematical model for the determination of micromechanical stress and strain distribution in a unidirectional fibre reinforced composite is developed. The model consists of three phases represented as concentric cylinders, including the existence of an interphase. Both fibre and matrix have well defined elastic properties, while the interphase properties follow an exponential law of variation. The effect of an abrupt variation of elastic properties at the fibre—interphase boundary on the micromechanical state of stress is also presented. The degree of adhesion between fibre and matrix is described by means of adhesion parameters introduced, and a parametric study is performed wherein the stress and strain distribution around the fibre are determined as a function of adhesion efficiency and fibre volume fraction. Analytical results were confirmed by means of a finite element technique introduced and applied to the model.     

Jones matrix treatment for polarization fourier optics

Abstract

In this work we introduce the use of a Jones matrix method to evaluate the far-field diffraction produced by spatially variant polarization elements. We extend the scalar Fourier optics theory to a vectorial theory by the use of the Jones matrix formalism. With this method it is possible to analyse the diffraction pattern and the local state of polarization in the Fraunhofer approximation by means of the usual Jones matrix calculus.     

Concise formula for tensile strength of knitted fabric reinforced composite

Abstract

A simple one-dimensional formula, as concise as Krenchel's model for stiffness calculation, is presented in this paper to calculate the ultimate tensile strength of a knitted fabric reinforced composite in the loading direction. Its deteriorated form can be used to determine the off axial strength of a unidirectional composite. The formula has been developed based on the understanding of internal stresses generated in the constituent fibre and matrix materials. These stresses are explicitly expressed as functions of the overall applied load, and only the stress components in the loading direction are retained. The ultimate strength of the composite is defined as the overall applied stress under which one of the constituent materials fails. The proposed formula has been applied to calculate the off axial strength of a unidirectional composite and the tensile strengths of two plain weft knitted glass fibre fabric reinforced epoxy matrix composites subjected to wale and course direction loads. All the calculated strengths are in reasonable agreement with experimental data.     

On the Gain of a Passive Linear Depolarizing System

Abstract

Transformation of a partially polarized light by a passive linear optical system must satisfy certain physical realizability constraints imposed on the elements of the Jones operator (matrix) characterizing the system. In this note we extend earlier work by Jones, Barakat, and Azzam and Bashara and derive a set of conditions on the elements of the Jones operator which depend explicitly on the input light degree of polarization. This is accomplished by a simple and novel approach based on the Cauchy-Schwartz—Bunyakowski inequality for coherency matrices.     

Conditions for the Physical Realizability of Polarization Matrices Characterizing Passive Systems

Abstract

We derive conditions for the physical realizability of polarization matrices characterizing passive systems or scattering media. By physically realizable, we mean that 0  g  1 where g ≡ (output intensity/input intensity). Using the singular-value decomposition of an arbitrary 2 × 2 complex-valued matrix, we prove that a Jones matrix T _J is physically realizable if 0  det T _J ⁺ T _J  1. Consequently singular Jones matrices (i.e. det T _J = 0) completely extinguish the output intensity irrespective of the input intensity because g ≡ 0. Corresponding results are obtained for Mueller-Jones matrices (the 4 × 4 real-valued matrices which are the four-dimensional representations of the two-dimensional 2 × 2 complex-valued Jones matrices). We also study the problem for general Mueller matrices; however because of their phenomenological character they do not admit of such criteria as do the Jones and Mueller-Jones matrices. This is because g now depends upon the matrix elements of the Mueller matrix and the input Stokes parameters; whereas for the Jones and Mueller-Jones matrices, g only depends upon the matrix elements. Finally we study the problem of relating the input and output mean randomness.     

Modelling the mean stress effect on fatigue life of fibre reinforced plastics

The mean stress influence on fatigue life of carbon and glass fibre reinforced plastics is investigated in detail. A new phenomenological approach is presented to model the mean stress effect in various material systems and fibre dominated stacking sequences. The model is calibrated to fatigue data via a developed fitting-routine that is based on least squares method. The calibration input data is one Woehler curve at R = 0.1 and the ultimate static strengths in tension and compression loading. The characterization effort is reduced by this significantly. Finally the method is verified successfully by fatigue data of several material systems.     

Interfacial separation of fibres in fibre reinforced composites

An analytical model is proposed to predict the ultimate tensile strength of fibre-reinforced composites when the failure is governed by fibre debonding.

The analytical analysis is based on the principle of the compliance method in fracture mechanics with the presence of an interfacial crack at the fibre/matrix interface. The model is developed on the basis of the assumption that both the matrix and the fibre behave elastically and the matrix strain at a zone far from the matrix-fibre interface is equal to the composite strain. Furthermore, it is assumed that a complete bond exists between the fibre and the matrix and that the crack faces are traction free.

It is shown that the separation strain energy release rate for fibre-reinforced composites can be obtained for cases with and without the existence of an interfacial crack. Numerical examples are presented and compared with results obtained in the literature by finite element analyses and from experimental tests. The comparison demonstrates the accuracy and the convergence of the model.     

琼斯矩阵在分布式光纤传感器偏振态分析中的应用

针对基于Sagnac原理的分布式光纤传感器中光波偏振态在双折射影响下所带来的干涉信号"偏振诱导衰落"问题,运用琼斯矩阵分析法,建立了传输光偏振态影响系统功率传输系数的数学模型;根据仿真分析的结果,发现使用反射镜作为反射元件,只能消除光纤圆双折射的影响,而不能消除线性双折射的影响.因此,提出了使用法拉第旋转镜提高系统抗偏振衰落能力的改进方法,仿真结果表明可以很好地消除传感光纤的线性双折射和圆双折射的影响.     

PROGRESSIVE MICROCRACKING IN UNIDIRECTIONAL BRITTLE MATRIX COMPOSITES

Abstract

In this work we investigate the initiation of microcracking in a unidirectional Nicalon^TMfibre, glass-ceramic (CAS) matrix composite under flexural loading. We find that damage develops and grows in these composites as a continual initiation of new transverse cracks in a more-or-less random manner, as well as growth of existing cracks, within the matrix. Initial cracks are usually of limited extent, being stopped when they encounter the nearest fibres, in a mode idealized by the so-called full-cell cracking model. Each new crack that initiates under increasing load yields another data point, provided the precracked state of stress and crack geometry at the initiation site can be determined. The latter conditions are satisfied since the zone of influence of each crack can be determined analytically and the full-cell cracking mode geometry receives at least partial validation. Analysis is accomplished by use of an axisymmetric micro mechanical model based on Reissner's variational principle in which variable fibre spacing can be recognized. In a semi-empirical failure model, the matrix axial stress just prior to crack initiation is computed and assumed to act on an unbounded matrix containing a penny-shaped crack having a radius dictated by the local fibre spacing, s. This model is geometrically appropriate for the case of large localized fibre spacings. Statistical information on s and the critical matrix mode I stress intensity factor is presented, and the average value seems to be consistent with expectation based upon measurements on monolithic samples of the matrix material. Application of the micromechanical model shows that, at least for the predominant range of s, sufficient energy is available to mobilize annular matrix cracks at stresses predicted by the semi-empirical model, and also that interfacial crack deflection is expected rather than fibre penetration. In accordance with this observation, very few fibre breaks were seen in the test programme. Finally, some comments regarding the practical consequences of this work are offered and the conventional view of a constant microcracking stress level in a steady-state model is dismissed, at least for the class of composites considered.     

In situ fibre strength determination in metal matrix composites

Single fibre fragmentation tests were performed at room temperature on SiC/Ti-6242 specimens in order to estimate the in situ fibre strength. Tensile specimens were instrumented with two acoustic emission transducers and an extensometer in order to monitor the strain at which fibre breaks occurred. Data analysis utilized Monte Carlo simulations of fibre fragmentation. The fibre/matrix stress transfer profile near a fibre break was derived using a finite element analysis. Cohesive zone model is used to describe damage of the interfacial zone. Thermally induced residual stresses and matrix plastic deformations were accounted for. The results presented in this paper show that the in situ Weibull parameters of the fibre are smaller than the reference obtained on as received fibres. Analysis of data raised questions about the validity of the Monte Carlo simulation method.     

Tensile behaviour of squeeze cast and forged short alumina fibre reinforced AA 6061

Abstract

The tensile properties of a composite consisting of 20 vol.-% short δ alumina fibres in an aluminium matrix (AA 6061) prepared by squeeze casting have been investigated, before and after 30% reduction by forging. By annealing the composite before forging, a 30% forging reduction could be achieved at room temperature, without crack formation. A reduction in mean fibre length from about 65 to 15 μm was observed but most fibre breaks were filled by matrix. By heat treating the composites after forging, their elongation to fracture was increased to about twice that of a similarly heat treated unforged composite of comparable strength. The improvement of ductility is attributed to break-up of the fibre skeleton structure inherited from the fibre preform. A model is presented that predicts that for these fibres an optimum effective reinforcement is achieved at fibre lengths of about 100 μm, which explains why the reduction in fibre length caused by forging does not result in significant strength loss.

MST/1720     

Torsion of a fiber reinforced hyperelastic cylinder for which the fibers can undergo dissolution and reassembly

In previous work, the authors have developed a theory for treating microstructural changes in fiber reinforced hyperelastic materials. In this theory, fibers undergo dissolution as a result of increasing elongation and then reassemble in a direction defined as part of the model. Processes in which the fibers reassemble in the direction of maximum principal stretch of the matrix were specifically considered. This model was previously illustrated for various cases of homogeneous deformation. The present work studies the implications of the model during the non-homogeneous deformation of axial stretch and torsion of a circular solid cylinder composed of an isotropic matrix and families of helically wound fibers. It is shown that the process of fiber dissolution and reassembly produces complex morphological changes in the fibrous structure and hence, in the response of the cylinder. Such events can give rise to an outer layer of material in which the fibers have undergone dissolution and reassembly. The interface between this region and the as yet unaltered core material can then move radially inward as axial stretch and/or twist increase. Gradual reassembly of the fibers with increasing stretch and twist changes their contributions to the torque and axial force and their helical orientation. Different sequences of axial stretch and twist result in different morphologies in the fibrous structure.     

Light propagation in a planar dielectric waveguide with a gyrotropic layer

The nature of the magneto-optic Kerr effect in a planar dielectric waveguide geometry has been investigated by calculation of the Jones matrix for a planar waveguide structure with a gyrotropic magnetic material as one wall. The intensity of the component of the field that is in the polarization state orthogonal to the input was calculated as a function of length of the gyrotropic material and input polarization state. The degree of polarization rotation depends on the relative orientation of the magnetization in the magnetic material and the direction of propagation. It is found that there exists an optimal waveguide length and input polarization at which the output signal is maximized and that a significant enhancement in polarization rotation is available with respect to free-space reflection. These results indicate that a magnetic-film-bounded planar waveguide can be used for device applications such as magnetic field sensors or magneto-optic modulators.     

Effective Lennard–Jones potential for cubic metals in the frame of embedded atom model

Generalized Lennard–Jones potentials are proposed in the frame of the embedded-atom method (EAM) of Daw and Baskes for homonuclear cubic metals. The basic functions of the model (the pair interaction potential, electron density function and embedding energy function) are presented in analytical forms. It is shown that N-body Finnis–Sinclair potentials and Daw–Baskes embedded atom potentials are mathematically equivalent. The developed potentials suit very well most of the fcc metals and alkali metals, and they are convenient for computer simulations.     

A theoretical model on piezoelectric fibre pullout with electric input

A theoretical model of a single piezoelectric fibre pullout from an elastic matrix was developed to study the effect of an input electric field. The stress distributions in the fibre under both mechanical and electric loads are obtained. The relationships between pullout force, induced electric potential and deformation are evaluated by computer simulation. The effects of electric input, piezoelectric parameters and fibre volume fraction on the load- displacement curve for fibre pullout are discussed. Numerical results obtained in this study indicate that the pullout force can be adjusted by changing the value or the direction of the applied electric field. Also, the results show that piezoelectric parameters and fibre volume fraction play important roles on the pullout force in the piezoelectric fibre.     

Numerical simulation of thermal conductivity of MMCs: effect of thermal interface resistance

Abstract

The thermal conductivity of metal matrix composites is investigated by computational simulations, in which the effect of a thermal barrier resistance between the constituent phases is explicitly taken into account. A numerical unit cell approach, which is based on the finite element method, an analytical mean field method of the Mori–Tanaka type and bounding techniques are employed. To predict the effective conductivities of fibre composites two different types of unit cell are utilised for the numerical studies. Two dimensional unit cells are developed which allow for investigations of aligned, continuous fibre reinforced composites while three dimensional unit cells are employed to study a large variety of different arrangements of non-staggered and staggered aligned short fibres. In the case of short fibres the thermal barrier resistances of the end faces and of the cylindrical surfaces are modelled independently, which allows one to study both their individual and their combined influences on the overall behaviour. Results are presented for carbon fibre/copper composites and their overall thermal conductivities are investigated in terms of interfacial thermal barriers and microtopologies.