Micromechanics of multiple cracking Part II Statistical tensile behaviour

A computational model for fibre-reinforced brittle materials in tension is developed. The model includes multiple cracking and strain-hardening processes, as well as single fracture and strain softening. The composite behaviour is derived from a single-fibre analysis by integrating over all possible fibre locations and orientations. The single-fibre analysis is based on symmetry fibres satisfying the equilibrium condition. The result is a complete constitutive relation: stress–strain or stress–crack width curve, and a prediction of crack spacing. The model is an extension of the ACK theory by Aveston, Cooper and Kelly, as it can be used with discontinuous fibres with different distributions, as well as for analysing hybrid composites. Fibre orientation introduces additional phenomena, which are taken into account with simple models. It was seen that matrix spalling at the fibre exit point may have a considerable effect on the composite strain and the crack width. The effect of fibre aspect ratio on the failure mode was studied, and it was found that with an intermediate fibre diameter the composite fails by fibre pull-out in a multiple-cracking stage, resulting in a strain-hardening material with a high ductility. The proposed model was verified against experimental results of a strain-hardening material, called an engineered cementitious composite. The model can be used in tailoring new materials to meet certain requirements, or in studying the effects of micromechanical properties on the composite behaviour, including the crack width, crack spacing, post-cracking strength, ultimate strain, and ductility. The derived constitutive relationship can further be used in finite element analyses defining the behaviour perpendicular to the crack. © 1998 Kluwer Academic Publishers     

The longitudinal tensile strength of unidirectional fibrous composites

When a fibre-plastic composite in which the fibres are brittle, continuous, and unidirectional is subjected to longitudinal tension under essentially static loading conditions, there exists a range of possible composite strengths. This paper presents a model which may be used to predict that range of possible composite strengths. An important feature of the model is that it considers both static and dynamic stress concentration effects on intact fibres which result from a fibre failure. A computer simulation technique is used to generate a set of generalized scatter limits for the average fibre stress at composite failure from the model. The generalized scatter limits may be used to predict the range of strengths for a composite material. The model results are used to predict the ranges of strength for composite materials prepared from three types of carbon fibre and these are compared with experimental results.     

Fracture statistics of single-fibre composite specimens

The failure of unidirectional composite materials is subject to wide dispersion owing to the occurrence of flaws or imperfections in the fibres. Fracture modelling requires the use of statistical models to deal with this variability in stength. We are currently developing an original and general approach that combines random models of defects with mechanical models and tests on composite materials. The present study is devoted to the problem of the characterisation of single fibres.

The fragmentation test is used to study the flaw population along the fibre as a function of applied stress. Each fracture is to a flaw in the fibre with a critical stress, σ_c, less than the applied stress σ. We can means of a multifragmentation test. Various density estimate the flaw distribution as a function of stress by means of a multifragmentation test. Various density functions are proposed and tested and good agreement is found between the experimental data and theoretical results. Following the proposed model, which has been verified experimentally, numerical simulations were carried out to study the validity of the parameters of the model.     

Failure mechanisms and fracture energy of hybrid materials

A shear-lag model of hybrid materials is developed. The model represents an alternating arrangement of two types of aligned linear elastic fibres, embedded in a linear elastic matrix. Fibre and matrix elements are taken to fail deterministically when the axial and shear stresses in them reach their respective strengths. An efficient solution procedure for determining the stress state for arbitrary configurations of broken fibre and matrix elements is developed. Starting with a single fibre break, this procedure is used to simulate progressive fibre and matrix failure, up to composite fracture. The effect of (1) the ratio of fibre stiffnesses, and (2) the ratio of the fibre tensile strength to matrix shear strength, on the composite failure mechanism, fracture energy, and failure strain is characterised. Experimental observations, reported in the literature, of the fracture behaviour of two hybrid materials, viz., hybrid unidirectional composites, and double network hydrogels, are discussed in the framework of the present model.     

Failure modes of fibre reinforced composites: The effects of strain rate and fibre content

The many aspects of high speed response of fibre reinforced composite materials have received the attention of a large number of investigators. Nevertheless, the understanding of the mechanisms governing failure under high speed loadings remain largely unknown. The effect of rate and fibre content on failure mechanisms was investigated by viewing fractured surfaces of tensile specimens using a scanning electron microscope (SEM). Tensile tests were conducted on a woven glass/epoxy laminate at increasing rates of strain. A second laminate (with random continuous glass reinforcement) was tested in tension at varying fibre volume fractions in order to ascertain the relationship between fibre content and failure mechanisms. The results suggest a brittle tensile failure in fibres of the woven laminate. In addition, the matrix was observed to play a greater role in the failure process as speed was increased, resulting in increased matrix damage and bunch fibre pull-out. The results also indicated that increasing the fibre volume fraction increased the likelihood of a matrix dominated failure mode.     

合成纤维复合夹层屏蔽结构改性及其电磁特性研究

提出具有复合介质夹层屏蔽结构模型的设想,利用铜箔-聚四氟乙烯为原材料,设计了单层屏蔽结构与复合夹层屏蔽结构的对比实验,测试了复合夹层屏蔽结构的电磁屏蔽效能增量,并用Ватолцн多层电磁屏蔽理论公式进行了验证。具有复合夹层屏蔽结构材料的电磁屏蔽效能明显优于单层屏蔽结构材料的电磁屏蔽效能。继而以涤纶无纺布、锦纶合成纤维为研究对象,采用电化学改性的方法,制备了具有复合夹层屏蔽结构的柔性电磁屏蔽材料。结果表明,通过对研究对象的选择和优化电化学改性的工艺,可以制备出1 MHz~1000 MHz入射电磁波频段范围内,满足不同要求的合成纤维复合夹层屏蔽结构改性材料,其SE值最高可达98 dB。     

A non-local fracture model for composite laminates and numerical simulations by using the FFT method

In this paper, we present a fracture model for composite laminates and its numerical solution by using the Fast Fourier Transforms (FFTs). The FFT-based formulation initially proposed for seeking the average behaviour of linear and non-linear composites by means of the homogenisation procedures [1], [2] was adapted to evaluate the damage growth in brittle materials. A non-local damage model based on the maximal principal stress criterion was proposed to assess the failure in the matrix and the fibres. This non-local model was then connected to the Griffith–Irwin criterion in the aim of predicting crack growth. In order to assess the matrix/fibre interface delamination, we have adapted the cohesive model developed by Li [3] for accounting the mixed-mode dependent interface failure. To this end, the interfaces between the matrix and the fibres are replaced by a thin layer of interphase with the purpose of facilitating the FFT simulations. By using the proposed model, we carried out several numerical simulations on fracture process in different specimens. From these studies, we can conclude that the present FFT-based analysis is capable to deal with crack initiation and crack growth in composite laminates with high accuracy and efficiency, especially in the cases of matrix/fibre interface debonding and of multi-crack growth.     

Deformation micromechanics of a thermoplastic-thermoset interphase of epoxy composites reinforced with poliethylene fiber

The polyethylene fibre is one of the strongest man-made materials; its strength is based on its high crystalinity order. Nevertheless, due to the Polyethylene chemical nature, it shows a low reactivity, which limits its use for composite materials, especially with thermoset matrices like the Epoxy resin. The present work uses Raman Spectroscopy to monitor the loading and failure of a thermoplastic-thermoset interface. Pull-out specimens were prepared with Spectra 1000 Polyethylene fibre embedded in a epoxy resin block; the fibre extraction was performed in a stepwise fashion and with the aid of a micro-Raman, spectra were taken along the interface through out the whole process. The technique allowed to measure the interface strength and to monitor the propagation of the debonding front up to total failure. Some results correspond to specimens were the interface was improved by changing the surface chemistry of the thermoplastic fibre to make it more compatible to the thermoset matrix.     

Some matrix failure peculiarities of unidirectional fibre-reinforced plastics and layers in laminated composites

An analysis has been conducted of debonding effects on the matrix failure process of unidirectional composites and layers in laminates with complicated structure. These materials have different residual microstresses resulting in a tendency for debonding. For modelling, a transverse layer of a composite is assumed to consist of cells, each simulating the fibre and its matrix sheath; the debonding strain of separate cells follows a normal probability distribution function. The proposed statistical model enables explanations of the unexpectedly low value of ultimate transverse tensile strain of unidirectional composites (less than 1%), even if matrix failure strain is greater than 50%, and the more significant influence of matrix flexibility on first cracking strain of complex structure laminates.     

An evaluation of failure criteria for matrix induced failure in composite materials

This paper reports on work being undertaken in the Cooperative Research Centre for Advanced Composite Structures Ltd. (CRC-ACS) to develop improved techniques for predicting the failure of composite materials. The procedures being investigated include a maximum strain criterion for fibre failure. For failure of the resin a new approach, which includes determination of the residual stresses due to manufacturing, is being trialed. This work closely parallels the new criteria proposed by Gosse and Hart-Smith [AIAA/CRC-ACS text on composite materials, submitted for publication] and we have subsequently replaced a simple stress criterion for matrix failure with their proposals based on strain invariants. The new procedures are applied to the failure of laminates in bolted joints with complex steered fibre patterns. Thermal residual stress was included to predict the matrix failure of T-section laminates under loads that open the angle between the flanges and the web. Here a transverse tension stress criterion was used.     

Probabilistic aspects of strength of unidirectional fibre-reinforced composites with matrix failure

In the previous paper [1], the stress distribution and the expected number of successive fibre breakages around broken fibres were calculated. It showed the following results. The fracture process that the crack originates from one isolated broken fibre and propagates due to the stress redistribution following the fibre breakage is unlikely to occur in the real unidirectional fibre-reinforced composite material. The matrix-failure is considered to play an important role in the fracture process of real composite materials. In the present paper, the stress (or strain) distribution and the expected number of successive fibre breakages around broken fibres are calculated when the matrix-damaged regions exist. The stress (or strain) distribution is obtained based on the three-dimensional hexagonalarray shear-lag model. Uniform shear force is assumed to occur in the matrix-damaged region. The expected number of the successive fibre breakages is calculated on the assumption that the flaws in the fibre follow a Poisson process.     

A non-destructive X-ray microtomography approach for measuring fibre length in short-fibre composites

An improved method based on X-ray microtomography is developed for estimating fibre length distribution of short-fibre composite materials. In particular, a new method is proposed for correcting the biasing effects caused by the finite sample size as defined by the limited field of view of the tomographic devices. The method is first tested for computer generated fibre data and then applied in analyzing the fibre length distribution in three different types of wood fibre reinforced composite materials. The results were compared with those obtained by an independent method based on manual registration of fibres in images from a light microscope. The method can be applied in quality control and in verifying the effects of processing parameters on the fibre length and on the relevant mechanical properties of short fibre composite materials, e.g. stiffness, strength and fracture toughness.     

Microdamage analysis of fibrous composite monolayers under tensile stress

The quasi-static deformation and fracture modes of several types of fibrous composite materials are studied from a fundamental viewpoint using a new experimental approach. Microcomposite monolayers, consisting of single fibres accurately positioned into a thin poly-meric matrix, were manufactured using a specially developed technique, and tested for strength by means of a custom-made miniature tensile testing machine. The materials used were E-glass, and Kevlar 29, Kevlar 49 and Kevlar 149 para-aramid fibres, and a room-temperature curing epoxy resin. The tensile testing machine was fitted to the stage of a polarized light stereozoom microscope and the fracture process was recorded both via a standard 35 mm camera and a colour video camera. The fibre content of the first generation of micro-composite monolayers used in this work was low (<0.025) but definite effects on the modulus and strength were obtained as the experimental data followed the rule-of-mixtures quite accurately in most cases. The failure process was different in each type of composite and current statistical models for strength are unable to account for the modes of failure observed in some of the systems studied. The experimental approach proposed is potentially useful in the study of the effects of interface chemistry modifications, fibre-fibre interactions, matrix toughness modification, misalignment effects, and more, on the deformation and failure micromechanics of composites.Incumbent of the Jacob and Alphonse Laniado Career Development Chair.     

The influence of powder packing on the rheology of fibre-loaded pastes

The effects of fibre addition on the extrusion rheology of ceramic particulate pastes has been investigated using model pastes containing chopped glass fibre and alumina powders. In these pastes where the fibre diameter was much larger than the alumina particle diameter, there was a decrease in the pressure required to extrude the paste as the powder component was replaced by fibre, up to a ratio of 0.4 powder to 0.6 fibre by volume. When the pastes were characterized using physically based models this behaviour was reflected in lower values of the derived rheological parameters. It is shown that this behaviour can largely be attributed to the packing behaviour of the fibre and powder-phase components. The results also suggest that the presence of fibres increases the die entry pressure drop relative to the die land pressure drop. It is shown that while the models proposed by Milewski in combination with the rheological models can be used to illustrate the expected behaviour of composite pastes, the observed behaviour was better predicted by using modified models proposed by Karlsson and Spring. At high fibre loadings (>60 vol%), extrudable materials could not be formed; this was attributed to packing and mixing problems leading to increased fibre-fibre interaction preventing flow. This is highlighted by materials in which the ratio of powder to fibre was 1 to 4 by volume, where the paste-like body was compressible and exhibited some elastic springback. For pastes where the solid phase contains <50 vol% fibre the rheological behaviour is predictable if the packing behaviour of the fibre and the rheological behaviour of the pastes containing only the powder are known. This can be used as a tool to aid the design of composite pastes and for the development of suitable process equipment.     

复合材料连续损伤力学模型在螺栓接头渐进失效预测中的应用

提出考虑层合板面内(纤维和基体失效)和层间失效的复合材料连续损伤力学模型,对螺栓接头的渐进失效行为进行预测。基于Tsai-Wu强度准则,发展可以判定复合材料面内和层间失效的强度准则。采用幂指数衰减材料退化模型模拟复合材料的损伤扩展过程。建立连续损伤力学模型用以研究0°铺层比例和螺栓直径对复合材料螺栓接头挤压性能的影响,预测结果与实验结果吻合。结果表明:0°铺层比例过高,接头发生剪切破坏,降低连接结构承载能力;增大螺栓直径,层合板损伤受到抑制,可提高复合材料螺栓接头的挤压强度。      

Analysis of the vacuum infusion moulding process: I. Analytical formulation

The present work is primarily concerned with the analytical formulation of governing equations for flow of incompressible fluids through compacting porous media and their application to vacuum infusion (VI) of composite materials. The literature on VI and the effects of compacting media on permeability and flow is reviewed. A complete development of the proposed governing equation is shown along with a suggested numerical solution. The proposed model is subsequently used to quantify the effect of process parameters such as inlet and outlet pressures, fibre architecture and lay-up. Implications for industrial production are discussed.     

Shear behaviour of steel fibre reinforced self-consolidating concrete beams based on the modified compression field theory

A series of steel fibre reinforced self-consolidating concrete (SFRSCC) beams have been tested to investigate the influence of steel fibres and the combined effect of fibres and stirrups on the deflection and cracking, ultimate loads and failure pattern. The experiment indicates that the shear strength increases clearly with the increasing of fibre content. The combination of steel fibres and stirrups demonstrates a positive composite effect on the ultimate load, ductility and failure pattern of concrete beam. This study also examines the feasibility of applying the modified compression field theory (MCFT) for the suitable assessment of shear resistance in fibre and steel rebar reinforced self-consolidating concrete beams. For fibre reinforced concrete member, a theoretical method is proposed based on the MCFT. The proposed ultimate shear capacity model was verified by the comparison with different test results.     

Numerical and Experimental Investigation of the Hydrostatic Performance of Fibre Reinforced Tubes

The increasing demands in subsea industry such as oil and gas, led to a rapidly growing need for the use of advanced, high performance, lightweight materials such as composite materials. E-glass fibre laminated pre-preg, filament wound and braided tubes were tested to destruction under hydrostatic external pressure in order to study their buckling and crushing behaviour. Different fibre architectures and wind angles were tested at a range of wall thicknesses highlighting the advantage that hoop reinforcement offers. The experimental results were compared with theoretical predictions obtained from classic laminate theory and finite element analysis (ABAQUS) based on the principal that the predominant failure mode was buckling. SEM analysis was further performed to investigate the resulting failure mechanisms, indicating that the failure mechanisms can be more complex with a variety of observed modes taking place such as fibre fracture, delamination and fibre-matrix interface failure.     

A simple material model for unidirectionally aligned fibre reinforced composites

A material model for the nonlinear behaviour of composite materials is proposed. The model combines the linear elastic fibre properties with the nonlinear behaviour of the matrix in order to obtain the average properties of the composite. The interaction between the fibre and the matrix is considered using stress partitioning factors, which are based on the experimental behaviour of the material.     

On the failure of unidirectional carbon-epoxy composites Part I:The effect of fibre sizing upon filament fracture and damage evolution

It has been demonstrated that – in certain cases – the sizing of carbon fibres can have a dramatic effect upon the mode of failure of unidirectional fibre-reinforced composites. The sizing appears to reduce the strength of composite tows by confining the failure process to a very small area that exhibits high stress concentration. In this paper, the effect of fibre sizing upon the two-dimensional fibre break density and break cluster populations is investigated as a function of applied strain prior to composite failure. It is shown that the size of the damage sites, their spatial distribution in the composite and the alignment between the individual breaks in the cluster are affected by the interface properties. Fractographic analysis has shown that groups of adjacent fibre fractures of greater than three were observed for the sized composite tows, whereas for the unsized samples a higher proportion of single and double breaks were seen to exist at a particular stress level. As a result, the overall filament damage was seen to be more widespread in the case of the unsized composite tows. Two possible mechanisms of fracture nucleation based on changes in fibre break density and in cluster populations are proposed: (a) failure due to growth of a critical cluster of fibre fractures and/or (b) linking up of several smaller cluster to form a critical cluster.