Relationship between strength variability and size effect in unidirectional carbon fibre/epoxy

Unidirectional carbon fibre/epoxy exhibits a size effect which is not necessarily consistent with the variability of specimen strengths predicted on the basis of classical Weibull theory. In some cases the variability is higher than expected and this may be due to other sources of variability in the tests apart from the material. However, in bending tests consistently lower variability than expected has been measured. This is explained qualitatively in terms of the splitting that occurs during failure which means that the composite behaves between the extremes of a brittle solid and a loose fibre bundle. This also implies that the size effect should be more strongly dependent on specimen length than indicated by Weibull theory. Three-point bending tests on specimens of different lengths but the same cross-section have been carried out which support this.     

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.     

Elastoplastic shear-lag analysis of single-fiber composites and strength prediction of unidirectional multi-fiber composites

A new procedure is proposed to predict the strength of multi-fiber composite based on the single fiber composite test. First, the flaw distribution in an embedded fiber is estimated with the statistical simulation. The stress distribution in the simulation is obtained by the elastoplastic shear-lag analysis considering the linear strain hardening effect of matrix. The simulated results are found to fit well with the experimental data, which shows the validity of the present simulation to estimate the statistical strength parameters for the embedded fiber. Then, the multi-fiber composite strength is predicted based on the obtained statistical fiber strength parameters. The stress profile in the multi-fiber composite is calculated with the elastoplastic three-dimensional (3D) shear-lag-analysis. The predicted strength via the weakest size scaling technique has a good agreement with our previous experimental data.     

Micromechanical analysis of the strength of unidirectional fiber composites

A micromechanical analysis is presented for the prediction of ultimate stresses of unidirectional fiber composites under complex loading systems. The method is based on micro-failure criteria applied to the fiber and matrix phases as well as to the fiber/matrix interfaces. The theory is implemented for the prediction of the off-axis strength of six types of laminae for which measured data are available, and good agreement is shown to exist in most cases. Several possible generalizations are discussed.     

Enhancing compressive strength of unidirectional polymeric composites using nanoclay

Morphology of nanoclay dispersed in resin and suspended in acetone was studied using scanning electron microscopy (SEM) and transmission electron microscopy (TEM). SEM and TEM images show intercalation of resin in the gallery spaces of nanoclay and regions of exfoliated clay with random orientation. A vacuum assisted wet lay-up (VAWL) process was used for the inclusion of nanoclay in conventional fiber reinforced composites. The VAWL specimen displayed improvement in off-axis compressive strength for nanoclay enhanced fiber composites. Addition of nanoclay produced a substantial increase in longitudinal compressive strengths (extracted from off-axis tests) of glass fiber reinforced composites. An elastic–plastic model was used to predict the compressive strength of fiber reinforced composites based on the matrix properties. The model predictions matched well with the experimental results.     

Compressive strength of unidirectional fiber composites with matrix non-linearity

A study has been made of the effect of fiber misalignment and non-linear behavior of the matrix on fiber microbuckling and the compressive strength of a unidirectional fiber composite. The initial fiber misalignment constituted the combined axial and shear stress state in the matrix, and the state of stress just prior to the buckling was considered to be the initial state of stress in bifurcation analysis. The expression for the critical microbuckling stress was found to be the same as that for the elastic shear-mode microbuckling stress except that the matrix elastic shear modulus was replaced by the matrix elastic-plastic shear modulus. Incremental theory of plasticity and deformation theory of plasticity were used to model the matrix non-linearity. The analysis results showed reasonable correlation with available experimental data for AS4/3501-6 and AS4/PEEK graphite composites with 2° to 4° range of initial fiber misalignment.     

Compressive strength of unidirectional and crossply carbon fibre/PEEK composites

The commonly accepted production methods of composite systems generally result in departure of the plies properties from transverse isotropy due to stresses acting during fibre—matrix bond formation. This anisotropy coupled with the composite structure affects compressive loading; the ultimate stresses as well as the direction, in- or out-of-plane, of kink propagation. A unidirectional and a crossply carbon fibre/PEEK composites were compression tested at ambient and elevated temperature as well as exposed to various chemical environments. Significant disruptions in fibre—matrix interface in the crossply composite were indicated. The compression tests showed that failure occurred through in-plane and out-of-plane fibre bucking and kinking in the unidirectional and crossply composites, respectively. Failure of the longitudinal plies in the crossply laminate occurred at significantly higher compression stress than for the unidirectional composite. Compressive failure mechanisms in unidirectional and multi-directional laminates are considered.     

Size effect in fracture of unidirectional composite plates

Fracture of notched, unidirectionally reinforced composite plates with well-bonded ductile matrices is typically preceded by the formation of long, discrete plastic shear zones aligned in the fiber direction. Onset of fracture is associated with a critical tension stress in a certain small process zone ahead of the notch tip; the critical stress is often equal to the tensile strength of the unnotched composite plate. Length of the shear zones can be estimated by plastic limit-analysis, and the local tension stress ahead of the notch found by superposition of the stress caused by remotely applied loads with the stress induced by the shear tractions in the plastic zone, which is shown to be dominated by a logarithmic singularity. In as-fabricated boron-aluminum composites, this fracture mechanism was analyzed and confirmed by numerous experiments (G.J. Dvorak, J. Zarzour and Y. Benveniste, Engineering Fracture Mechanics 42, 501–517, 1992). Since the notch tip field is not described by a stress intensity factor, experimental notched strength data cannot be interpreted in terms of a single material property, such as toughness. An alternative scaling procedure is outlined for prediction of notched strength of wide plates on the basis of data obtained from small size specimens. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Size effect on compression strength of fiber composites failing by kink band propagation

The effect of structure size on the nominal strength of unidirectional fiber-polymer composites, failing by propagation of a kink band with fiber microbuckling, is analyzed experimentally and theoretically. Tests of novel geometrically similar carbon–PEEK specimens, with notches slanted so as to lead to a pure kink band (not accompanied by shear or splitting cracks), are conducted. They confirm the possibility of stable growth of long kind bands before the peak load, and reveal the existence of a strong (deterministic, non-statistical) size effect. The bi-logarithmic plot of the nominal strength (load divided by size and thickness) versus the characteristic size agrees with the approximate size effect law proposed for quasibrittle failures in 1983 by Bažant. The plot exhibits a gradual transition from a horizontal asymptote, representing the case of no size effect (characteristic of plasticity or strength criteria), to an asymptote of slope -1/2 (characteristic of linear elastic fracture mechanics, LEFM). A new derivation of this law by approximate (asymptotically correct) J-integral analysis of the energy release, as well as by the recently proposed nonlocal fracture mechanics, is given. The size effect law is further generalized to notch-free specimens attaining the maximum load after a stable growth of a kink band transmitting a uniform residual stress, and the generalized law is verified by Soutis, Curtis and Fleck's recent compression tests of specimens with holes of different diameters. The nominal strength of specimens failing at the initiation of a kink band from a smooth surface is predicted to also exhibit a (deterministic) size effect if there is a nonzero stress gradient at the surface. A different size effect law is derived for this case by analyzing the stress redistribution. The size effect law for notched specimens permits the fracture energy of the kink band and the length of the fracture process zone at the front of the band to be identified solely from the measurements of maximum loads. The results indicate that the current design practice, which relies on the strength criteria or plasticity and thus inevitably misses the size effect, is acceptable only for small structural parts and, in the interest of safety, should be revised in the case of large structural parts. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analysis of the strength and fracture behaviour of unidirectional and angle-ply graphite-aluminium composites

The tensile behaviour of unidirectional and [±]_s angle-ply P100 graphite-reinforced 6061-Al composites was determined as a function of the angle () between the fibre and the applied load. The experimentally determined values of the elastic modulus and tensile strength of the composites are compared with those predicted from classical laminate theory. The measured elastic modulus values agreed with theoretical values, but the strength of the [\+-\gq]_s angle-ply composites was substantially greater than predicted. The discrepancy between experiment and theory is attributed to the stress required to fail the fibre ply/separator foil interface present in the angle-ply composites. The composite failure modes are also documented, and it is shown that the separator foils of the angle-ply composites shift the transition from tensile to shear failure to greater values of\gq relative to the off-axis unidirectional composites.     

Monte-Carlo simulation on notched strength of unidirectional boron—aluminium composites

A Monte-Carlo simulation was carried out on the fracture behaviour of centre-notched unidirectional boron-aluminium composites assuming quasi self-similar notch extension. The main results obtained in this work are summarized as follows: (i) the experimental results for notched strength of Awerbuch and Hahn and those of Poe and Sova could be described well by the present simulation method; (ii) the notched strength decreased with increasing notch size for a fixed width of specimen and with increasing width of specimen for a fixed relative notch size; (iii) the semi-empirical failure criteria proposed by Waddoups, Eisenman and Kaminski, Whitney and Nuismer, and Mar and Lin could approximately describe the notched strength obtained by the present simulation method under limited conditions, despite the difference in basic concept between these models and the present method; and (iv) the characteristic lengths in the models of Waddoups, Eisenman and Kaminski, and Whitney and Nuismer, which were originally assumed to be material constants, were dependent on notch size and width of specimen. It was demonstrated that these characteristic lengths have a strong positive correlation with damage zone size.     

Study of the interlaminar shear strength of unidirectional high-modulus polyethylene fibre composites

The interlaminar shear strength of a unidirectional high-modulus polyethylene fibre-epoxy resin composite, measured using a short-beam bend test, increases when the fibre has been plasma treated but decreases with increasing fibre content or increasing filament diameter. Attempts have been made to explain these observations. From observation of the sample failure and the bending load/deflection curves, it was found that there are two possible failure modes dependent on fibre type, fibre volume fraction and fibre plasma treatment. These are (1) brittle failure of the resin and (2) failure at the fibre/resin surface. The present results appear to be consistent with the interlaminar shear strength data obtained from high-modulus polyethylene fibre samples made by the hot compaction process developed at Leeds.     

Single fibre and multifibre unit cell analysis of strength and cracking of unidirectional composites

Numerical simulations of damage evolution in composites reinforced with single and multifibre are presented. Several types of unit cell models are considered: single fibre unit cell, multiple fibre unit cell with one and several damageable sections per fibres, unit cells with homogeneous and inhomogeneous interfaces, etc. Two numerical damage models, cohesive elements, and damageable layers are employed for the simulation of the damage evolution in single fibre and multifibre unit cells. The two modelling approaches were compared and lead to the very close results. Competition among the different damageable parts in composites (matrix cracks, fibre/matrix interface damage and fibre fracture) was observed in the simulations. The strength of interface begins to influence the deformation behaviour of the cell only after the fibre is broken. In this case, the higher interface layer strength leads to the higher stiffness of the damaged material. The damage in the composites begins by fibre breakage, which causes the interface damage, followed by matrix cracking.     

Influences of interfacial bonding strength and scatter of fibre strength on tensile behaviour of unidirectional metal matrix composites

The influences of interfacial bonding strength and scatter of strength of fibres on tensile behaviour of unidirectional metal matrix composites, whose matrix has low yield stress in comparison to the strength of fibres, were studied using the Monte-Carlo simulation technique using two-dimensional model composites. The following results were found. The strength of composites increases with increasing bonding strength, especially when the bonding strength exceeds the shear yield stress of the matrix and then remains nearly constant. The strength of composites is very sensitive to bonding strength when the scatter of fibre strength is large, but not when it is small. The fracture mode varies from non-cumulative to cumulative with increasing scatter of fibre strength for both cases of weak and strong interfacial bondings. The fracture surface becomes irregular when bonding strength becomes low and scatter of fibre strength becomes large. The applicability of the Rosen and Zweben models and the rule of mixtures to predict the strength of composites was examined.     

基于单胞解析模型的单向复合材料强度预报方法

基于单胞解析模型,建立一种从复合材料细观组分到宏观单向板的强度预报方法。根据连续介质力学和均匀化方法构建细-宏观关联矩阵,通过该关联矩阵将细观组分材料的弹性和损伤性能传递到宏观单向板中。考虑复合材料细观损伤状态,当纤维和基体满足各自强度准则时失效,并通过失效因子折算成刚度的衰减。在此基础上,结合有限元分析,实现复合材料单向板纵横向拉伸模拟,从而预报单向板的拉伸强度。结果表明:该方法预报的模量和强度与实验值基本一致,验证了该方法的有效性与高效性。     

The role of interfacial debonding in increasing the strength and reliability of unidirectional fibrous composites

A Monte-Carlo simulation technique based on a finite-element method has been developed in order to clarify the effect of interfacial shear strength on the tensile strength and reliability of fibrous composites. In the simulation a boron/epoxy monolayer composite was modelled, and five hundred simulations were carried out for various interfacial shear strengths. The interfacial shear strength value which raised the average strength of the composite corresponded approximately to the value which reduced the coefficient of variation. This implies the existence of an optimum value of interfacial shear strength which can increase the strength and reliability. The simulated strength and reliability were closely related to the degree and type of damage around a fiber break. That is to say, large-scale debonding caused by a weak interfacial bond and matrix cracking caused by a strong bond reduced the number of fiber breaks accumulated up to the maximum stress, and decreased the strength and reliability. On the other hand, small-scale debonding promoted comparatively the cumulative effect of fiber breaks and played a key role in increasing the composite strength and reliability.     

Influence of microstructure on axial strength of unidirectional continuous fibre reinforced aluminium matrix composites

Abstract

Systematic empirical investigations on the relationship between microstructural features and mechanical performance of unidirectionally reinforced continuous fibre Al matrix composites (CFAMCs) carried out by the present authors in recent years are summarised. The employment of a high strength matrix alloy and the development of a strong fibre/matrix interface are beneficial to maximise the strengthening effect of the fibre reinforcement. Processing defects, such as second brittle phases in the matrix, non-infiltration defects, matrix solidification shrinkage voids, excessive interfacial reactions, the presence of reaction products on the interface, weak interfacial binding, and excessively high fibre volume fraction reduce composite strength to different extents via a number of different mechanisms. Criteria for the microstructure design of CFAMCs for optimum fibre strengthening efficiency are proposed.     

Creep behavior of unidirectional composites

The creep behavior of the continuous fiber reinforced unidirectional composites due to the viscoelasticity of the resin matrix is investigated assuming that the constituent matrix obeys the nonlinear creep law and the fiber is the linear elastic materials. Utilizing a quasi three-dimensional finite element method, the macroscopic creep behavior of the composites with regular fiber packing is obtained, giving the orthotropic creep law for the composites. Then, the creep of the composites with random fiber packing is estimated applying the random model proposed by Kondo and Saito in which the neat matrix cylinders are embedded in the regular array composites. The theoretical predictions for the creep behavior are compared with the experimental results.