Fracture behaviour and pullout analysis in ceramic matrix composites using m0dified Rosen's model

Abstract

A modified Rosen's model is proposed to predict the ultimate tensile load and pullout in ceramic matrix composite materials. The model assumes a Weibull distribution for the fibre strength and that the matrix is already cracked. The solid is discretised in fibre segments between matrix cracks. After fracture of one fibre segment, the load is redistributed among the intact neighbouring segments. This in turn produces further fibre failures and subsequent load transfer. Then, the load is increased on the testpiece until new segments are fractured, and the procedure is iterated until one fracture path isfound. The model is applied to a silicon carbide fibre/calcium aluminium silicate (SiC_f/CAS) material and compared with experimental results. It is concluded that upper and lower bounds can be obtained using different load transfer assumptions.     

Silicon carbide (NicalonTM) fibre-reinforced borosilicate glass composites: mechanical properties

The objective of this study was to assess the applicability of an extrinsic carbon coating to tailor the interface in a unidirectional NicalonTM–borosilicate glass composite for maximum strength. Three unidirectional NicalonTM fibre-reinforced borosilicate glass composites were fabricated with different interfaces by using (1) uncoated (2) 25 nm thick carbon-coated and (3) 140 nm thick carbon coated Nicalon fibres. The tensile behaviours of the three systems differed significantly. Damage developments during tensile loading were recorded by a replica technique. Fibre–matrix interfacial frictional stresses were measured. A shear lag model was used to quantitatively relate the interfacial properties, damage and elastic modulus. Tensile specimen design was varied to obtain desirable failure mode. Tensile strengths of NicalonTM fibres in all three types of composites were measured by the fracture mirror method. Weibull analysis of the fibre strength data was performed. Fibre strength data obtained from the fracture mirror method were compared with strength data obtained by single fibre tensile testing of as-received fibres and fibres extracted from the composites. The fibre strength data were used in various composite strength models to predict strengths. Nicalon–borosilicate glass composites with ultimate tensile strength values as high as 585 MPa were produced using extrinsic carbon coatings on the fibres. Fibre strength measurements indicated fibre strength degradation during processing. Fracture mirror analysis gave higher fibre strengths than extracted single fibre tensile testing for all three types of composites. The fibre bundle model gave reasonable composite ultimate tensile strength predictions using fracture mirror based fibre strength data. Characterization and analysis suggest that the full reinforcing potential of the fibres was not realized and the composite strength can be further increased by optimizing the fibre coating thickness and processing parameters. The use of microcrack density measurements, indentation–frictional stress measurements and shear lag modelling have been demonstrated for assessing whether the full reinforcing and toughening potential of the fibres has been realized. This revised version was published online in November 2006 with corrections to the Cover Date.     

Influence of microstructure on the strength of Nicalon-reinforced aluminium metal-matrix composites

The microstructure and mechanical properties of two aluminium-based composites reinforced with Nicalon fibre are investigated. During composite processing, aluminium carbide forms at the interface as a result of a reaction between aluminium and free carbon in the fibre. Magnesium, when present in the aluminium matrix, diffuses into the outer (~ 200 nm) layer of the fibre where it reacts with the silicon oxycarbide constituent to form magnesium-containing oxide and also to free carbon for the production of more interfacial aluminium carbide. These chemical reactions affect to differing degrees the strength of a fibre, as measured after extraction from the two composites, and influence the respective fibre/matrix interfacial friction stress and composite strength. A simple rule-of-mixtures approach based upon the measured strength of extracted fibres gave some agreement with longitudinal properties of the composite, but treatment of the fibres as bundles, using a Weibull probability distribution of properties, provided more accurate predictions.     

The impact strength of fibre composites

Two models have been developed which predict the crack initiation energy, notched impact strength and unnotched impact strength of fibre composites. One is applicable to composites containing short fibres and the other to composites containing long fibres. Data obtained with randomly oriented short fibre composites were consistent with the one model. The other model has been verified using composites containing uniaxially oriented long fibres and long fibres oriented randomly in a plane. The success of the model demonstrates that the high notched impact strength with long fibres is due to the redistribution of stress away from the stress concentrating notch, the extra stress that can be held by the fibre relative to the matrix and the work required to pull fibres out of the matrix during crack propagation. The parameters which have been shown to control the fracture energy are composite modulus, fibre length, fibre volume fraction, effective fibre diameter, fibre tensile strength and the coefficient of friction during fibre pull-out from the matrix. The matrix toughness on the other hand usually has no effect at all for composites containing fibres randomly oriented in two dimensions and only a minor effect in exceptional cases. The shear strength of the fibre-matrix bond has only an indirect effect in that it controls the number of fibres which pull out rather than fracture.     

An evaluation of acoustic emission from fibre-reinforced composites

An analysis of acoustic emission(AE) from epoxy matrices of different amounts of hardener and model composites containing a glass bead, carbon and glass fibres has been carried out to identify the sources of emission. A few AE events generated by microcracking were observed for epoxy matrix near the final fracture strain. From microscopic and emission observations it was found that the emission was generated by interfacial debonding at the pole for the model composite containing a single particle of the glass bead, and that the source of AE bursts for a continuous single carbon fibre/epoxy composite was succeeding fibre fractures along fibre length. The high AE activity due to fibre fracture was observed for a composite consisting of a bundle of glass fibres. The total of AE events was in agreement with the number of fibre fracture counted with the aid of a microscope in a carbon/epoxy composite. The shear strength at the carbon/epoxy interface was evaluated by a critical length of the fractured fibres using the AE results.     

Tensile strength of discontinuous fibre-reinforced composites

A stochastic Monte-Carlo approach, based on Eyring's chemical activation rate theory, is used to study the factors controlling the tensile strength of discontinuous fibre-reinforced composites. The model explicitly takes into account the local distribution of stress near fibre ends. Both the fibre and the matrix are allowed to break during fracture of the composite. The stress-strain curves and the modes of failure of the composite are found to be strongly dependent on the volume fraction and aspect ratio of the fibres. The importance of adhesion at the fibre/matrix interface is also studied. The results are compared with available experimental data.     

Interface and fracture of carbon fibre reinforced Al-7 wt% Si alloy

The interface structure in an aluminium-7 wt% silicon alloy reinforced with carbon fibres has been investigated using analytical electron microscopy. Crystals of aluminium carbide (Al₄C₃) have been identified in interface regions and their structure and growth are discussed. Mechanical properties of the composite have been measured and fracture behaviour studied using acoustic emission analysis in parallel with microstructural examination. The results indicated that the aluminium carbide interfacial reaction had produced a strong fibre matrix bond, but reduced the fibre strength and embrittled the matrix. Consequently, whole fibre bundles failed in a brittle manner in the longitudinal direction with limited pull-out of individual fibres. The findings are discussed in relation to the method used to manufacture the composite.     

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     

Statistical fracture of E-glass fibres using a bundle tensile test and acoustic emission monitoring

Mechanical strength studies have been carried out on fibre bundles used in composite manufacturing. The variability in mechanical properties of glass fibres has been studied using bundles of about 2000 filaments. The fibre strength distributions were analysed using the survival probability-applied strain (S–ε) curve, in relation with various experimental conditions. We also examine the effect of lubricant’s viscosity on the fracture behaviour of E-glass fibre bundles. Acoustic emission (AE) was monitored during the bundle tensile tests in order to verify that individual filament failures are statistically independent. On tensile tests with lubricated bundles of E-glass fibres, it is shown that each individual fibre break can be detected using AE. Hence, AE monitoring of a lubricated bundle of E-glass fibres provides a convenient and relatively quick method to obtain the Weibull parameters of strength distribution.     

Plasma surface modification of advanced organic fibres

The interlaminar shear strength, interlaminar fracture energy, flexural strength and modulus of extended-chain polyethylene/epoxy composites are improved substantially when the fibres are pretreated in an ammonia plasma to introduce amine groups on to the fibre surface. These property changes are examined in terms of the microscopic properties of the fibre/matrix interface. Fracture surface micrographs show clean interfacial tensile and shear fracture in composites made from untreated fibres, indicative of a weak interfacial bond. In contrast, fracture surfaces of composites made from ammonia plasma-treated fibres exhibit fibre fibrillation and internal shear failure as well as matrix cracking, suggesting stronger fibre/matrix bonding, in accord with the observed increase in interlaminar fracture energy and shear strength. Failure of flexural test specimens occurs exclusively in compression, and the enhanced flexural strength and modulus of composites containing plasma-treated fibres result mainly from reduced compressive fibre buckling and debonding due to stronger interfacial bonding. Fibre treatment by ammonia plasma also causes an appreciable loss in the transverse ballistic impact properties of the composite, in accord with a higher fibre/matrix interfacial bond strength.     

Constitutive modelling of arteries considering fibre recruitment and three-dimensional fibre distribution

Structurally motivated material models may provide increased insights into the underlying mechanics and physics of arteries under physiological loading conditions. We propose a multiscale model for arterial tissue capturing three different scales (i) a single collagen fibre; (ii) bundle of collagen fibres; and (iii) collagen network within the tissue. The waviness of collagen fibres is introduced by a probability density function for the recruitment stretch at which the fibre starts to bear load. The three-dimensional distribution of the collagen fibres is described by an orientation distribution function using the bivariate von Mises distribution, and fitted to experimental data. The strain energy for the tissue is decomposed additively into a part related to the matrix material and a part for the collagen fibres. Volume fractions account for the matrix/fibre constituents. The proposed model only uses two parameters namely a shear modulus of the matrix material and a (stiffness) parameter related to a single collagen fibre. A fit of the multiscale model to representative experimental data obtained from the individual layers of a human thoracic aorta shows that the proposed model is able to adequately capture the nonlinear and anisotropic behaviour of the aortic layers.     

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.     

Testing E-glass fibre bundles using acoustic emission

In tensile tests on lubricated bundles of a few hundred parallel E-glass fibres it is shown that individual fibre breaks, to the last fibre in the bundle, can be detected using acoustic emission (AE). By this means the single-fibre strength distribution is deduced. Relationships are obtained between some AE signal parameters and the fibre fracture stress which are consistent with theoretical expectations. Studies are made of the distribution of fibre break locations, the occurrences of multiple (stimulated) fibre breaks and the attenuation of the AE signals.     

Weibull statistical analysis of tensile strength data of short mullite fibre reinforced aluminium alloy composite

Abstract

A statistical evaluation by means of Weibull statistics was carried out on the tensile strength data of a short mullite fibre reinforced aluminium alloy composite, which was prepared by squeeze casting. The results show that the material has a high and reliable tensile strength. The area fractions of the fibres on the cut surface and on the fracture surface of specimens have been statistically analysed. The fibre distribution shows heterogeneity in the microsturcture. On the cut surface the average area fraction of fibres which make large angles with the normal of the cut surface (denoted as A _fl ) is slightly less than that of those fibres which make a small angle with the normal of the cut surface (denoted as A _fs ). However, on the fracture surface of the composite, A _fl is much bigger than A _fs , and the lower the tensile strength of the specimen, the bigger is A _fl on the fracture surface. Debonding of the interface between the large angle fibres and the matrix is an important cause of failure of the composite, and the non-uniform distribution of the large angle fibres is one of the main causes of the large scatter in the data.     

Influence of Fabric Parameters on Microstructure,Mechanical Properties and Failure Mechanisms in Carbon-Fibre Reinforced Composites

The effects of fibre/matrix bonding, fabric density, fibre volume fraction and bundle size on microstructure, mechanical properties and failure mechanisms in carbon fibre reinforced composites （plastic and carbon matrix） have been investigated. The microstructure of unloaded and cracked samples was studied by optical microscopy and scanning electron microscopy （SEM）, respectively whereas the mechanical behaviour was examined by 3- point bending experiments. Exclusively one type of experimental resole type phenolic resin was applied. A strong fibre/matrix bonding, which is needed for high strength of carbon fibre reinforced plastic （CFRP） materials leads to severe composite damages during the pyrolysis resulting in low strength, brittle failure and a very low utilisation of the fibres strain to failure in C/C composites. Inherent fabric parameters such as an increasing fabric density or bundle size or a reduced fibre volume fraction introduce inhomogenities to the CFRP＇s microstructure. Results are lower strength and stiffness whereas the strain to failure increases or remains unchanged. Toughness is almost not affected. In C/C composites inhomogenities due to a reduced bundle size reduce strain to failure, strength, stiffness and toughness. Vice versa a declining fibre volume fraction leads to exactly the opposite behaviour. Increasing the fabric density （weight per unit area） causes similar effects as in CFRPs.     

The fibre pull-out energy of misaligned short fibre composites

A theoretical study on the fibre pull-out energy has been carried out for short fibre-reinforced composites. Two probability density functions were introduced for modelling the fibre-length distribution and the fibre-orientation distribution. By taking into account the effect of snubbing friction between fibres and matrix at the fibre exit point during fibre pull-out, and that of the fracture stress of fibres obliquely crossing the fracture plane (i.e. the inclined strength of fibres), the fibre pull-out energy of composites has been derived as a function of fibre-length distribution and fibre-orientation distribution, as well as interfacial properties. The previously existing fibre pull-out energy theories can be deduced from the present model. The effects of fibre-length distribution, fibre-orientation distribution, interfacial properties, snubbing-friction coefficient and parameter A for determining the inclined strength of fibres on the fibre pull-out energy, have been studied in detail. The present study provides the necessary information as to which fibre-length distribution, fibre-orientation distribution and interfacial property are required to achieve a desired fibre pull-out energy and hence a desired composite toughness. High-strength fibres, a large fibre-volume fraction and a large fibre diameter for a comparatively large mean fibre length, are shown to be favourable for achieving a high fibre pull-out energy. This revised version was published online in November 2006 with corrections to the Cover Date.     

Studies on carbon fibre reinforced aluminium composite processed using pre-treated carbon fibres

Carbon fibre reinforced Al-12% Si alloy composite has been fabricated by pre-treating the fibres with K₂ZrF₆ followed by molten alloy infiltration and subsequent hot pressing of the preforms. The infiltration conditions were arrived at based on the measurement of tensile strength of the fibres extracted from the preforms. The fibre volume per cent of 20 was found to result in composite tensile strength of about 240 MPa as compared to tensile strength of 100 MPa for the unreinforced matrix. Characterization of the interface revealed the formation of ZrSi₂ and diffusion of potassium and aluminium into the fibre. The interfacial bonding was strong as is evinced by the absence of fibre pull-out on to the fracture surface.     

Plasma surface modification of advanced organic fibres

A marked improvement in the interlaminar shear strength and flexural strength of aramid/ epoxy composites is observed when the fibres are pretreated in an ammonia or ammonia/ nitrogen gaseous discharge (plasma) to introduce amine groups on to the fibre surface. Scanning electron and optical microscopic observations are used to examine the microscopic basis for these results. Scanning electron micrographs of shear fracture surfaces show clean fibre/matrix separation in composites made from untreated fibres, indicative of weak interfacial bonding. In contrast, shear fracture surfaces of composites containing plasma-treated fibres exhibit clear evidence of fibre fibrillation and matrix cracking, suggesting stronger interfacial bonding. Optical microscopic examination of flexure specimens shows that enhanced strength results mainly from reduced compressive fibre buckling and debonding, due to an increase in fibre/matrix interfacial bond strength. This increase is not accompanied by any significant change in the interlaminar fracture energy or flexural modulus of the composites, but there is an appreciable loss in transverse ballistic impact properties. These results are also examined in terms of the observed increase in fibre/matrix interfacial strength.     

Probabilistic aspects of strength of short-fiber composites with planar fibre distribution

The study of the fracture of short-fibre composites must involve statistics as an integral part. Two components of composite strength, each with probabilistic aspects, are described in this paper: fibre crossover reinforcement, and fibre gap bridging before fracture. The fibre crossover density is proposed as a measure of mutual fibre strengthening. and simulations are performed to estimate this density. Several different fibre orientations are proposed which have identical elastic properties but different crossover densities, indicating that more information is required for strength prediction than for elastic property prediction. The crossover density is a random variable whose average increases roughly as a fibre length squared function, and whose coefficient of variation decreases with increasing fibre length. The phenomenon of fibres bridging microcrocks is also examined as a fracture mechanism for fibres whose length well exceeds their critical length. General probabilistic expressions are derived which give the distribution of the number of fibres bridging a gap perpendicular to the applied load. These formulae are applied to the distribution of strength of an aligned fibre system.     

The fracture toughness of composites reinforced with weakened fibres

Fibre fractures which occur near, but not at, the plane of matrix failure in a composite, lead to fibre pull-out during fracture. Energy absorbed in this process contributes directly to the work of fracture and hence to the toughness of the composite.Factors which determine the mean length of fibre pulled out during fracture are discussed for the case of composites reinforced with continuous fibres having variously spaced points of weakness. The presence of such weak points also affects the strength of the composite, but not all composites of the same strength have the same toughness. The greatest toughness for a given strength is always found in composites reinforced with discontinuous fibres.