Interfacial properties of fibrous composites

The processes for debonding and pull-out in parallel-sided as well as tapered fibre composites are described. Models which can predict and account for all the reported experimental debonding and pull-out behaviour are developed. The effect of the interfacial properties on the plot of maximum pull-out force against fibre embedded length is elucidated. Knowledge of the interfacial parameters of a composite allows proper characterization and leads to better prediction of the mechanical properties.     

Crack growth in hybrid fibrous composites

A preliminary analysis is made of the energetics of transverse crack growth in a brittle elastic matrix bridged by elastic fibres fictionally bonded to the matrix. Studies made of the stability of a crack of finite length in a brittle polymeric material reinforced with steel wires are found to be in reasonable agreement with the predictions of the theory. It is proposed that the stability of transverse cracks in a very brittle matrix could be increased substantially by the inclusion of a second fibre component designed specifically to increase the work of fracture of the matrix. This has been shown to be possible using a very small volume fraction of glass fibres as a matrix toughening component and it has also been observed that stable transverse matrix crack growth can be achieved with composite systems of this type. This principle might have applications in the design of hybrid composites utilizing either a brittle polymeric or ceramic matrix.     

Thermal stress development in fibrous composites

In this work, the thermal stress development in anisotropic fiber-reinforced polymer composites is investigated for temperatures below the glass transition temperature of the resin. By applying two independent experimental methodologies, it was found that the initial thermal (residual) strain in the reinforcing fibers is compressive of about − 0.04% at ambient temperatures. This is due to the mismatch of the thermal expansion coefficient between the polymer matrix and fiber, as the material is cooled down from the processing temperature. However, on reheating the composites the compressive stress in the fiber gradually diminishes and becomes zero at 50 °C. Further heating to 100 °C introduces tensile strains in the fiber of maximum of 0.13%. The conformity of these results to analytical models that relate the composite thermal strain to the thermal expansion coefficients of fiber and resin, as well as, the fiber volume fraction, is examined. Finally, the possibility of tailoring the sign (positive, negative or, even, zero) of the composite thermal expansion coefficient of certain advanced composites by simply varying the thermal expansion of the polymer matrix, is discussed.     

The interfacial properties of fibrous composites

The dependence of the magnitude of the interfacial parameters for a glass-fibre-reinforced polypropylene on the thickness of the applied silane layer on the glass-fibre surface was investigated. The interfacial parameters studied included the interfacial-shear strength, the interfacial coefficient of friction, the interfacial-frictional stress and the shrinkage pressure. These parameters were evaluated from pull-out data using a recent model. The results indicate that the maximum interfacial-shear strength is obtained at a critical thickness of the silane layer on the treated fibre. Both the interfacial-frictional stress and the interfacial coefficient of friction decreased with increased thickness of the silane coat.     

Debonding and pull-out processes in fibrous composites

The processes of debonding and pull-out in fibrous composites are described. Models predicting the debond length and the probability distribution of pull-out lengths of fibres and bundles are derived. These lengths are functions of the fibre, matrix and interface properties. Prediction is then compared with experiment and a simple relationship between pull-out and debond lengths is found. An understanding of the debonding and pull-out processes is important because they affect the fracture toughness of fibre composites.     

Reliability-based optimization of fibrous laminated composites

This paper is concerned with the optimum design of multiaxial fiber reinforced laminate systems under probabilistic conditions of loads and material properties. A multiaxially laminated composite is treated as a structural system with each ply contained in the composite as one element. The Tsai-Wu failure criterion is adopted as the limit state function of a unidirectional ply. It is assumed that the system failure occurs when any one of the plies in a laminate system fails. The multiple-check-point method is successfully applied to evaluate the system reliabilities of multiaxial laminates under probabilistic in-plane stresses. An optimization problem is defined to find the optimal number of fiber orientation axes, optimum orientation angles, and optimum ply ratios which yield the highest system reliability.     

Pyroelectric and pyromagnetic coefficients of functionally graded multilayered multiferroic composites

This paper presents a method for analyzing some product properties of functionally graded magneto-electro-thermoelastic (METE) multilayer composites. The method is based on an exact matrix formulation for the effective properties of multilayer composites with various coupled physical effects including piezoelectricity, piezomagnetism, and thermoelasticity. Analytical expressions are derived for the effective properties of a functionally graded transversely isotropic METE multilayer composite. The effects of functional gradation on the pyroelectric and pyromagnetic coefficients are numerically evaluated. It is shown that both the pyroelectric and pyromagnetic coefficients can be significantly enhanced (more than two times) by functional gradation, and the relative volume fractions at which these coefficients are maximized tend to extreme values. It is thus demonstrated that the present method can be used in the design of multilayered METE composites for the purpose of achieving a maximum energy conversion or transduction capability.     

Micromechanical modeling of load transfer in fibrous composites

A unified analytical treatment is presented for the study of micromechanical stress distribution in unidirectional fibrous composites loaded with various thermal and mechanical loads. Two models are considered to represent the composite. Both use a concentric cylindrical system with the difference that one requires laterally free while the other requires laterally constrained outer boundaries, broadly describing situations of plane stress and plane strain, respectively. The present work has been motivated by the recent work of McCartney (McCartney, Proc. Roy. Soc. London, Ser. A 425 (1989) 215–244) who analyzed the laterally free system, and by our previous work (Nayfeh, Fibre Sci. Technol. 10 (1977)) in which we analyzed the laterally constrained one. For axisymmetric loading, and upon adopting some appropriate restrictions on the radial behavior of some field quantities, an elasticity-based procedure reduces the two-dimensional field equations, which hold in both the fiber and matrix components, together with the appropriate interface and boundary conditions, to a quasi-one-dimensional system. The resulting system is capable of identifying the stress distribution in each component as influenced by the other component via the readily identifiable interaction (transfer) terms. The model is general and applicable to a large variety of situations. These include situations of matrix cracking, fiber break and even regions of slip at the fiber–matrix interface. As a by-product, the model was capable of obtaining the classical Lamé solutions (the iso-strain case) as a degenerate case. Confidence in the modeling was gained when it identically reproduced all of the numerical examples presented by McCartney. Numerical results that parallel some of the ones presented by McCartney are included in the form of comparisons between results obtained based upon the laterally constrained and the laterally free systems.     

Carrier-mediated magnetoelectricity in complex oxide heterostructures

Increasing demands for high-density, stable nanoscale memory elements, as well as fundamental discoveries in the field of spintronics, have led to renewed interest in exploring the coupling between magnetism and electric fields. Although conventional magnetoelectric routes often result in weak responses, there is considerable current research activity focused on identifying new mechanisms for magnetoelectric coupling. Here we demonstrate a linear magnetoelectric effect that arises from a carrier-mediated mechanism, and is a universal feature of the interface between a dielectric and a spin-polarized metal. Using first-principles density functional calculations, we illustrate this effect at the SrRuO3/SrTiO3 interface and describe its origin. To formally quantify the magnetic response of such an interface to an applied electric field, we introduce and define the concept of spin capacitance. In addition to its magnetoelectric and spin capacitive behaviour, the interface displays a spatial coexistence of magnetism and dielectric polarization, suggesting a route to a new type of interfacial multiferroic.     

Brittle coating studies on fibrous composites

A brittle coating stress analysis technique applicable to orthotropic materials has been developed. The technique has been applied to a unidirectional glass fibre reinforced epoxy. Its behaviour has been studied under uniaxial and biaxial stress fields using cantilever beam specimens and circular disc specimens under diametral compression. Fibre orientation in the specimens has been varied. In each case it has been observed that the cracks represent the direction of principal strains in the specimen material and not the direction of principal stresses. Application of brittle coating techniques has been suggested to establish the direction and magnitude of principal stresses and strains at every point in a problem with unknown stresses and strains.     

Theory of multiple fracture of fibrous composites

The theoretical stress-strain behaviour of a composite with a brittle matrix in which the fibre-matrix bond remains intact after the matrix has cracked, is described. From a consideration of the maximum shear stress at the fibre-matrix interface, the extent of fibre debonding and the crack spacing in a partially debonded composite are derived. The energetics of cracking and the conditions leading to an enhanced matrix failure strain are then discussed and, finally, the crack spacing expected in composites containing fibres isotropically arranged in two or in three dimensions is derived for the case of very thin and hence very flexible fibres.     

Longitudinal tensile failure of unidirectional fibrous composites

This paper presents a theoretical treatment of the tensile strength of a unidirectional fibrous composite, subjected to a tensile load in the fibre direction. The fibres are treated as having a statistical strength distribution which results in fibre failure prior to composite failure. The failure geometry of the model is similar to the observed geometry of fractured glass/epoxy and glass/polyester composites. Failure criterion is established and the strength is shown to decrease as the length of the specimen is increased. This size effect is very small.     

Asymmetric behaviour of fibrous metal matrix composites

Abstract

Experimental investigations have illustrated that unidirectional metal matrix composites (MMCs) show asymmetric behaviour under uniaxial tensile and compressive loading. This asymmetry occurs when the material is loaded along the fibre direction and also when loaded in the transverse direction. In this paper, results from finite element micromechanical models are presented. The models were used to study the asymmetric behaviour of unidirectional fibre reinforced MMCs subjected to longitudinal and transverse loading. The effects of the thermal residual stresses arising from the manufacturing process were included in the study. Also, the influence of the degree of bonding of fibre to matrix was examined, from perfectly bonded to completely debonded. Results reveal that thermal residual stresses are responsible for the asymmetric behaviour of the MMCs in the longitudinal direction. In transverse loading, both the degree of interface bonding and residual stresses account for the asymmetric behaviour. The predicted stress–strain response of the MMC shows good agreement with the available experimental data for both tènsile and compressive loading. Results also suggest that in order to predict accurately the yielding behaviour of MMCs, the current symmetric yield criteria require modification.     

Effective anti-plane properties of piezoelectric fibrous composites

Anti-plane shear of piezoelectric fibrous composites is theoretically investigated. The geometry of composites is described by the 2-dimensional geometry in a section perpendicular to the unidirectional fibers. The previous constructive results obtained for scalar conductivity problems are extended to piezoelectric anti-plane problems. First, the piezoelectric problem is written in the form of the vector-matrix ${\mathbb{R}}$ -linear problem in a class of double periodic functions. In particular, application of the zeroth-order solution to the ${\mathbb{R}}$ -linear problem yields a vector-matrix extension of the famous Clausius–Mossotti approximation. The vector-matrix problem is decomposed into two scalar ${\mathbb{R}}$ -linear problems. This reduction allows us to directly apply all the known exact and approximate analytical results for scalar problems to establish high-order formulae for the effective piezoelectric constants. Special attention is paid to non-overlapping disks embedded in a two-dimensional background.     

Recent progress in multiferroic magnetoelectric composites: from bulk to thin films

Multiferroic magnetoelectric composite systems such as ferromagnetic-ferroelectric heterostructures have recently attracted an ever-increasing interest and provoked a great number of research activities, driven by profound physics from coupling between ferroelectric and magnetic orders, as well as potential applications in novel multifunctional devices, such as sensors, transducers, memories, and spintronics. In this Review, we try to summarize what remarkable progress in multiferroic magnetoelectric composite systems has been achieved in most recent few years, with emphasis on thin films; and to describe unsolved issues and new device applications which can be controlled both electrically and magnetically.     

Statistical issues in the fracture of brittle-matrix fibrous composites

This paper reviews recent work and presents new results on statistical aspects of the failure of composites consisting of brittle fibers aligned in a brittle matrix. The failure process involves quasi-periodic matrix cracking in planes perpendicular to the fiber, frictional sliding of the fibers in fiber break zones, and fiber bridging of cracks in a load-sharing framework that may vary from global to fairly local. First, we review the overall statistical features of the failure process, and identify certain issues in terms of critical geometric, statistical and mechanical parameters. This leads to two interesting cases, one where the spacing of matrix cracks is small relative to the length scale of load transfer in the fibers, and one where it is larger. Next we consider ‘characteristic’ bundles in the composite which capture essential features of the statistics of the failure process, and develop their distributions for strength in terms of certain characteristic stress and length scales. We then model the composite as a chain arrangement of such bundles both longitudinally and laterally, as the scale of load transfer among fibers in a bundle may be smaller than the full composite cross-section. This scale, though not precisely quantified, depends on such things as the stiffness of the matrix relative to the fibers, the volume fraction of the matrix and the spacing of periodic cracks. We then consider the strength distribution for the composite on the basis of the failure of the weakest characteristic bundle. We also consider issues related to fiber pull-out and the work of fracture as well as the possibility of severe strain localization especially within the bundle triggering overall failure. Substantial reductions in strength are predicted for smaller bundle sizes, but composite reliability is typically very high and the size effect very mild. Finally, we mention limited comparisons with Monte Carlo simulations and experimental results.     

The development of compression damage zones in fibrous composites

Recent experimental work (Narayanan S, Schadler LS. Mechanisms of kink band formation in graphite/epoxy compsites: a micromechanical experimental study. Comp Sci Technol 1999; 59:2201-13) suggests that kink bands in unidirectional continuous carbon fiber reinforced polymer composites initiate from damage zones formed under axial compressive loads. A damage zone consists of a cluster of locally crushed fibers and broken fibers, that are often fractured at an angle, θ > 0°, normal to the fiber axis. Typically, under compressive loads, fiber breaks in damage zones form roughly along a plane at an angle φ, normal to the fiber axis. These damage zones produce stress concentrations which can lead to instabilities in the nearby fiber and matrix and initiate microbuckling and kink bands. This paper extends a micromechanical influence function technique based on earlier shear lag fiber composite models. Our modified technique calculates the fiber axial and matrix shear stress concentrations due to multiple angled and crushed fibers in arbitrary configurations. Modeling reveals that angled or ‘shear’ breaks (θ > 0°) can lead to higher shear stress concentrations in the matrix than transverse breaks (θ=0°). Also we find that the damage zone is more likely to form at an angle φ, which is greater than that of its individual fiber breaks, θ. When φ is slightly greater than θ, the shear stress in the surrounding matrix regions within the damage zone achieves a maximum, potentially weakening the matrix and interface and consequently leading to kink band formation. Monte Carlo simulations incorporating this stress analysis predict that the initiation and propagation of crushed and angled breaks progress roughly along an angle, φ ≈ 17° in a linear elastic system. When possible, our model results are compared to strain measurements of fiber composites under compression obtained by Narayanan and Schadler using micro-Raman spectroscopy (MRS).