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.     

Creep strength of discontinuous fibre composites

A unidirectional, discontinuous fibre composite is considered under conditions of steady state creep in the direction of reinforcement. The composite consists of noncreeping, discontinuous, perfectly aligned, uniformly distributed fibres which are perfectly bonded to a matrix obeying a power relation between stress and strain rate. Expressions for the interface stress, the creep velocity profile adjacent to the fibres and the creep strength of the composite are derived. Previous results for the creep strength,σ _c obtained for composites of the same type are briefly reviewed and compared with the present result. It is shown that all results reduce to the same general expression $$\sigma _c = \alpha V_{f^{\sigma _0 } } \left( {\frac{{\dot \in }}{{\dot \in _{0 } }}} \right)1/n_{\rho ^{1 + 1/n} }$$ in whichρ is the fibre aspect ratio, \(\dot \in\) is the composite creep rate,V _f is the fibre volume fraction,σ ₀,ε ₀ andn are the constants in the matrix creep law. The creep strength coefficient α is found to be very weakly dependent onV _f and practically independent ofn whenn is greater than about 6.     

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.     

Probabilistic strength analyses of interlaminated hybrid composites

This paper deals with the ultimate failure strength of four-layered hybrid laminated composites. A shear-lag model is first applied to obtain the stress redistributions after the breakage of layers. On the basis of the knowledge of these stress redistributions, the probabilistic ultimate failure strength is evaluated by applying the approach of Harlow and Phoenix. The effects on the ultimate strength of hybrid laminates, due to the scatter of lamina strengths, relative fiber volume fractions, composite size and laminate stacking sequence, are identified.     

Effective thermoelastic properties of short-fiber composites

Summary The effective elastic properties of short fiber composites are calculated in terms of tensors which are measures of the strain concentration and excess thermal strain in the fibers relative to to the average matrix strain. These tensors are estimated on the basis of the so-called equivalent inclusion method which utilizes the Eshelby's solution. A comparison of the results with the available bounds and limited experimental data suggests that the proposed estimates of effective properties may be quite reliable.With 6 Figures     

Tensile strength and failure mechanics of fibre composites

This paper is concerned with the prediction of the tensile strengths of fibre composites where the fibres are aligned in the direction of tensile loads, and are flawed to some extent. A theory is derived for predicting the strengths and failure mechanisms of such composites. The theory agrees reasonably well with experiments, and may be qualitatively applicable to composites containing randomly aligned fibres.     

Evaluation of single-fibre strength distribution from fibre bundle strength

A new modified Weibull distribution function has been suggested for analysing the strength of fibres used as reinforcements for advanced composites. The function provides an upper and a lower strength limit and is characterized by two shape and two location parameters. A method for determining the parameters of this distribution from the analysis of the tensile curves of fibre bundles has also been developed. Application of the method to the experimental results on Thornel-300 carbon fibres shows that the shape parameters become modified in the case of bundles.     

Some aspects of fracture in brittle fibre composites

This paper describes some observations on the propagation of cracks through a brittle matrix reinforced with strong, stiff, unidirectional fibres. By means of a model material, observations are made of the interaction of a matrix crack with an isolated fibre normal to the crack. The experiments were extended to cover interaction with a row of fibres. The results of these tests are then compared with the behaviour of a real composite. One interesting observation concerns a mechanism whereby a single initial crack can initiate a series of parallel cracks which enable the opening displacement of the main crack to be distributed among this series of secondary cracks as fracture proceeds through the material.     

Tensile strength of fibre-reinforced metal matrix composites with non-uniform fibre spacing

The influence of non-uniform fibre spacing on the strength of unidirectional fibre-reinforced metal matrix composites was studied by means of a Monte-Carlo computer simulation experiment. The influence of yield stress of the matrix and scatter of the fibre strength on the strength of composites were also studied for both uniform and non-uniform fibre spacings. It was demonstrated that (1) the strength of composites with non-uniform fibre spacing is lower than that with uniform spacing due to the high stress concentration arising from the breakage of fibres, and (2) the reduction in strength of composites due to the non-uniformity increases with increasing scatter of fibre strength. For both cases of uniform and non-uniform spacings, the following tendencies were observed : (a) the strength of composites increases but then decreases with increasing yield stress of matrix, (b) it is very sensitive to yield stress of the matrix when the scatter of fibre strength is large but not when it is small, and (c) it decreases but then increases with increasing scatter of fibre strength when the yield stress of the matrix is high, while it decreases monotonically with increasing scatter of fibre strength when the yield stress is low.     

Effective thermoelastic constants of short-fiber composites

This paper studies the effective thermal stress and thermal expansion coefficients of unidirectional short-fiber composites. The thermoelastic constants in the form of infinite series are obtained based upon the known local elastic field solution derived by the perturbation expansion of the Green's tensor function. Approximations of the series expansions are presented for multi-phase short-fiber composites such as hybrids. The results are further reduced to binary systems and the upper and lower bound predictions of effective thermoelastic constants are given.     

Determination of single fibre strength distribution from fibre bundle testings

The strength of fibres used as reinforcement materials for advanced composites is often assumed to follow the two-parameter Weibull distribution function. However, the experimental process widely used for obtaining the two parameters is tedious and prone to error. In this paper, two simple methods for determining the parameters of the Weibull distribution function are developed based upon the analysis of the tensile curves of fibre bundles. The first method focuses on the relation between the shape of a fibre bundle tensile curve and the survivability of fibres; the second method makes use of the relation between the maximum load point of a fibre bundle tensile curve and the shape parameter of the Weibull distribution of fibre strength. These two methods, in particular the second one, have greatly simplified the fibre testing process. Experimental results on Thornel-300 carbon fibres further demonstrate the validity of these techniques.On leave from Northwestern Polytechnical University, Xian, Shaanxi, China.On leave from Yantze Valley Planning Office, Wuhan, China.     

The strength of hybrid glass/carbon fibre composites

The tensile mechanical properties of hybrid composites fabricated from glass and carbon fibres in an epoxy matrix have been evaluated over a range of glass: carbon ratios and states of dispersion of the two phases. The failure strain of the carbon phase increased as the relative proportion of carbon fibre was decreased, and as the carbon fibre was more finely dispersed. This behaviour is commonly termed the hybrid effect, and failure strain enhancement of up to 50% has been measured. Only part of the effect may be attributed to internal compressive strains induced in the carbon phase by differential thermal contraction as the composite is cooled from its cure temperature. The laminae or ligaments of carbon fibre dispersed in the glass fibre phase show a multiple failure mode, and when the constitution is favourable catastrophic failure does not occur until a considerable number of ligament fractures have accumulated. Failure is thus progressive, and the material is effectively tougher than equivalent all-carbon fibre composites.     

The tensile strength and ductility of continuous fibre composites

The plastic instability approach has been applied to the tensile behaviour of a continuous fibre composite. It is shown that the combination of two components with different strengths and degrees of work-hardening produces a new material with a new degree of work-hardening, which may be determined by the present analysis. Expressions for the elongation at rupture and the strength of a composite have been obtained and the results of the calculation are compared with some experimental data.List of symbols V _f volume fraction of fibres in composite - , , true strain of fibre, matrix and composite - s true stress - , , nominal stress on fibre, matrix and composite - _*, _*, _* critical stress of fibre, matrix and composite (ultimate tensile strength) - _*, _* critical strain of separate fibre and matrix - _* critical strain of composite - Q external load - A cross-sectional area - A ₀ initial value of area     

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.     

Effects of fibre length on tensile strength of carbon/glass fibre hybrid composites

The tensile strength of epoxy resin reinforced with random-planar orientation of short carbon and glass fibres increased as the length of the reinforcing fibres increased, and the increase in tensile strength remained almost unchanged after the fibre length reached a certain level. The tensile strength of composites at any fibre length could be estimated by taking the strain rate and temperature dependence of both the yield shear strength at the fibre-matrix interphase and the mean critical fibre length into consideration. The tensile strength of the hybrid composite could be estimated by the additive rule of hybrid mixtures, using the tensile strength of both composites.     

A probabilistic theory for the strength of short fibre composites

This paper presents a probabilistic theory for predicting the strength of unidirectional short fibre composites. It is assumed that the failure of the composite occurs due to the inability of the short fibres bridging a critical zone to carry the load. The stress concentrations on the fibres bridging a fibre end gap are evaluated as a function of the number of fibre ends forming the gap. The sizes of the gaps are predicted from a probabilistic approach. The short fibre composite strength is then estimated from the gap size and the corresponding stress concentration factor. Comparisons of the present work with existing theories and experiments have been made.On leave from the Institute of Space and Aeronautical Science, University of Tokyo, Japan.