Hierarchical modelling of a polymer matrix composite

A hierarchical modelling scheme to predict the properties of a polymer matrix composite is introduced. The stress–strain curves of amine-cured tetraglycidyl 4,4′-diaminodiphenylmethane (TGDDM) cured have been predicted using group interaction modelling (GIM). The GIM method, originally applied primarily to linear polymers, has been significantly extended to give accurate, consistent results for TGDDM, a highly crosslinked two-component matrix. The model predicts a complete range of temperature-dependent properties, from fundamental energy contributions, through engineering moduli to full stress–strain curves through yield. The predicted properties compare very well with experiment. Using the GIM-predicted TGDDM stress–strain curve, a 3D finite element model is used to obtain strain concentration factors (SCF) of fibres adjacent to a fibre break in a unidirectional (UD) composite. The strain distribution among the intact neighbouring fibres is clearly affected by the yielding mechanism in the resin matrix. A Monte Carlo simulation is carried out to predict the tensile failure strain of a single composite layer with the thickness equal to the fibre ineffective length. The effect of matrix shear yielding is introduced to the model through the SCF of surviving fibres adjacent to the fibre-break. The tensile failure strain of the composite is then predicted using a statistical model of a chain of composite layers.     

Unidirectional carbon fibre reinforced polyamide-12 composites with enhanced strain to tensile failure by introducing fibre waviness

Unidirectional (UD) carbon fibre reinforced polymers offer high specific strength and stiffness but they fail in a catastrophic manner with little warning. Gas-texturing and non-constrained annealing were used to introduce fibre waviness into UD polyamide 12 composites produced by wet-impregnation hoping to produce composites with a more gradual failure mode and increased failure strain. Both methods increased the variation of fibre alignment angle compared to the control samples. The composites containing wavy fibres exhibited a stepwise, gradual failure mode under strain controlled uniaxial tension rather than a catastrophic failure, observed in control samples. Gas-texturing damaged the fibres resulting in a decrease of the tensile strength and strain to failure, which resulted in composites with lower tensile strength and ultimate failure strain than the control composites. Non-constrained annealing of carbon fibre/PA-12 produced wavy fibre composites with ultimate failure strain of 2%, significantly higher than 1.6% of the control composite.     

Modelling of strain rate effects on matrix dominated elastic and failure properties of unidirectional fibre-reinforced polymer–matrix composites

A phenomenological-based, strain rate dependent failure theory, which is suitable for the numerical modelling of unidirectional (UD) carbon fibre reinforced polymer composites (CFRPs), is presented. A phenomenological-based approach is also proposed for the three-dimensional (3D) modelling of strain rate induced material hardening in UD polymer composites. The proposed theory and approach are implemented in the Finite element (FE) code ABAQUS/Explicit for one integration point solid elements. Validation is presented against experimental data from dynamic compressive tests using results available in the published literature.     

Fracture mechanisms and failure analysis of carbon fibre/toughened epoxy composites subjected to compressive loading

This study investigates the failure mechanisms of unidirectional (UD) HTS40/977-2 toughened resin composites subjected to longitudinal compressive loading. A possible sequence of failure initiation and propagation was proposed based on SEM and optical microscopy observations of failed specimens. The micrographs revealed that the misaligned fibres failed in two points upon reaching maximum micro-bending deformation and two planes of fracture were created to form a kink band. Therefore, fibre microbuckling and fibre kinking models were implemented to predict the compressive strength of UD HTS40/977-2 composite laminate. The analysis identified several parameters that were responsible for the microbuckling and kinking failure mechanisms. The effects of these parameters on the compressive strength of the UD HTS40/977-2 composite systems were discussed. The predicted compressive strength using a newly developed combined modes model showed a very good agreement to the measured value.     

Establishing a new Forming Limit Curve for a flax fibre reinforced polypropylene composite through stretch forming experiments

In developing an understanding of the failure in natural fibre reinforced polymer composites, the failure limits of this class of the material system are required. It is found that the conventional Forming Limit Curve is not suitable to predict the failure initiated in the natural fibre composite as principal strains cannot differentiate the strain on the flax fibres and the polypropylene matrix. This study proposes a new Forming Limit Curve for the composite which expresses limiting fibre strain as a function of forming mode depicted by the ratio of minor strain to major strain. The new Forming Limit Curve, along with the Maximum Strain failure criterion have been successfully implemented in FEA simulations, and numerical simulations suggest that the former is more accurate. The current work provides an innovative method to predict the onset of failure in natural fibre composites, which can be applied in composite forming and structural design.     

Constitutive modelling of fibre-reinforced composites with unidirectional plies using a plasticity-based approach

This paper presents the development of a constitutive model able to accurately represent the full non-linear mechanical response of polymer-matrix fibre-reinforced composites with unidirectional (UD) plies under quasi-static loading. This is achieved by utilising an elasto-plastic modelling framework. The model captures key features that are often neglected in constitutive modelling of UD composites, such as the effect of hydrostatic pressure on both the elastic and non-elastic material response, the effect of multiaxial loading and dependence of the yield stress on the applied pressure.The constitutive model includes a novel yield function which accurately represents the yielding of the matrix within a unidirectional fibre-reinforced composite by removing the dependence on the stress in the fibre direction. A non-associative flow rule is used to capture the pressure sensitivity of the material. The experimentally observed translation of subsequent yield surfaces is modelled using a non-linear kinematic hardening rule. Furthermore, evolution laws are proposed for the non-linear hardening that relate to the applied hydrostatic pressure.Multiaxial test data is used to show that the model is able to predict the non-linear response under complex loading combinations, given only the experimental response from two uniaxial tests.     

The effect of fibre dispersion on initial failure strain and cluster development in unidirectional carbon/glass hybrid composites

By adding glass fibres to carbon fibre composites, the apparent failure strain of the carbon fibres can be increased. A strength model for unidirectional hybrid composites was developed under very local load sharing assumptions to study this hybrid effect. Firstly, it was shown that adding more glass fibres leads to higher hybrid effects. The hybrid effect was up to 32% for a hybrid composite with a 10/90 ratio of carbon/glass fibres. The development of clusters of broken fibres helped to explain differences in the performance of these hybrid composites. For 50/50 carbon/glass hybrids, a fine bundle-by-bundle dispersion led to a slightly smaller hybrid effect than for randomly dispersed hybrids. The highest hybrid effect for a 50/50 ratio, however, was 16% and was achieved in a composite with alternating single fibre layers. The results demonstrate that thin ply hybrids may have more potential for improved mechanical properties than comingled hybrids.     

On longitudinal compressive failure of carbon-fibre-reinforced polymer: from unidirectional to woven, and from virgin to recycled

Modelling the longitudinal compressive failure of carbon-fibre-reinforced composites has been attempted for decades. Despite many developments, no single model has surfaced to provide simultaneously a definitive explanation for the micromechanics of failure as well as validated predictions for a generic stress state. This paper explores the reasons for this, by presenting experimental data (including scanning electron microscopic observations of loaded kink bands during propagation, and brittle shear fracture at 45° to the fibres) and reviewing previously proposed micromechanical analytical and numerical models. The paper focuses mainly on virgin unidirectional (UD) composites, but studies for woven and recycled composites are also presented, highlighting similarities and differences between these cases. It is found that, while kink-band formation (also referred to in the literature as microbuckling) is predominant in UD composites under longitudinal compression, another failure mode related to the failure of the fibres can be observed experimentally. It is also shown that the micromechanics of the failure process observed in UD composites is similar to that in other fibre architectures, hence encouraging the adaptation and application of models developed for the former to the latter.     

Strain-sensitive Raman spectroscopy and electrical resistance of carbon nanotube-coated glass fibre sensors

This paper presents the development of glass fibres coated with nanocomposites consisting of carbon nanotubes (CNTs) and epoxy. Single glass fibres with different CNT content coating are embedded in a polymer matrix as a strain sensor for composite structures. Raman spectroscopy and electrical response of glass fibres under mechanical load are coupled for in situ sensing of deformation in composites. The results show that the fibres with nanocomposite coating exhibit efficient stress transfer across the fibre/matrix interface, and these with a higher CNT content are more prone to fibre fragmentation at the same matrix strain. A relationship between the fibre stress and the change in electrical resistance against the fibre strain is established. The major finding of this study has a practical implication in that the fibres with nanocomposite coating can serve as a sensor to monitor the deformation and damage process in composites.     

Modelling of composite sheet forming: a review

The use of composite materials in sheet forming applications is gaining popularity with the rise of consumer demands and specific mechanical properties. In addition to unidirectional (UD) fibres, the use of textile reinforcements such as woven fabric and knitted fabric has been shown to be feasible in recent years. This paper gives a survey on the modelling of composite sheet forming for both UD fibre and textile composites. Two broad approaches are reviewed here—the mapping approach and the mechanics approach. Mapping approaches for UD fibre composites, woven fabric composites and knitted fabric composites are elucidated on the basis of their fibre geometry. For the mechanics approach both the viscous fluid models and elastic solid models, as a means of describing the constitutive properties, are reviewed. Various updating methods for modelling large deformation found in sheet forming are then described. Finally, a guideline for the choice of modelling techniques for various types of fibre/fabric reinforcements and suggestions for future work are given.     

Growth of carbon nanotubes on carbon fibre substrates to produce hybrid/phenolic composites with improved mechanical properties

Carbon nanotubes were grown by chemical vapor deposition (CVD) on different carbon fibre substrates namely, unidirectional (UD) carbon fibre tows, bi-directional (2D) carbon fibre cloth and three dimensional (3D) carbon fibre felt. These substrates were used as the reinforcement in phenolic resin matrix to develop hybrid CF–CNT composites. The growth morphology and other characteristics of the as grown tubes were analyzed by scanning electron microscopy (SEM), transmission electron microscopy (TEM) and thermal gravimetry (TGA) which confirmed a copious growth of multiwalled carbon nanotubes (MWNTs) on these substrates. The mechanical properties of the hybrid composites was found to increase with the increasing amount of deposited carbon nanotubes. The flexural strength (FS) improved by 20% for UD, 75% for 2D and 66% for 3D hybrid composites as compared to that prepared by neat reinforcements (without CNT growth) under identical conditions. Flexural modulus (FM) of these composites also improved by 28%, 54% and 46%, respectively.     

Computational micromechanics evaluation of the effect of fibre shape on the transverse strength of unidirectional composites: An approach to virtual materials design

Computational micromechanics of composites is an emerging tool required for virtual materials design (VMD) to address the effect of different variables involved before materials are manufactured. This strategy will avoid unnecessary costs, reducing trial-and-error campaigns leading to fast material developments for tailored properties. In this work, the effect of the fibre cross section on the transverse behaviour of unidirectional fibre composites has been evaluated by means of computational micromechanics. To this end, periodic representative volume elements containing uniform and random dispersions of 50% of parallel non-circular fibres with lobular, polygonal and elliptical shapes were generated. Fibre/matrix interface failure as well as matrix plasticity/damage were considered as the fundamental failure mechanisms operating at the microscale under transverse loading. Circular fibres showed the best averaged behaviour although lobular fibres exhibited superior performance in transverse compression mainly due to the higher tensile thermal residual stresses generated during cooling at the fibre/matrix interface.     

Development of a new constitutive model considering the shearing effect for anisotropic progressive damage in fiber-reinforced composites

A corrected Linde's criterion considering the shearing effect for anisotropic progressive damage is developed to describe the elastic-brittle behavior of fiber-reinforced composites. Based on this criterion, a new three-dimensional (3D) nonlinear finite element model for static damage of unidirectional fiber-reinforced composites is proposed within a framework of continuum mechanics. The model is validated by taking 3D braided composites as example to study the relationship between the damage of materials and the effective elastic properties. The impregnated unidirectional composites are treated as homogeneous and transversely isotropic materials, whose properties are calculated by the Chamis' equations. The more accurate failure mechanisms of composites are revealed in the simulation process, and the effects of braided parameters on the uniaxial tensile behavior of 3D braided composites are investigated. Comparison of numerical results and experimental data is also carried out, which shows a better agreement than that of former study using the 3D Hashin's criterion.     

Ductile unidirectional continuous rayon fibre-reinforced hierarchical composites

Endless rayon fibres (Cordenka®) were used to reinforce polyhydroxybutyrate (PHB) nanocomposites containing 2.5 wt.% nanofibrillated cellulose (NFC) to create truly green hierarchical composites. Unidirectional (UD) composites with 50–55% fibre volume fraction were produced using a solvent-free continuous wet powder impregnation method. The composites exhibit ductile failure behaviour with a strain-to-failure of more than 10% albeit using a very brittle matrix. Improvements at a model composite level were translated into higher mechanical properties of UD hierarchical composites. The Young’s moduli of rayon fibre-reinforced (NFC-reinforced) PHB composites were about 15 GPa. The tensile and flexural strength of hierarchical PHB composites increased by 15% and 33% as compared to the rayon fibre-reinforced neat PHB composites. This suggests that incorporation of NFC into the PHB matrix binds the rayon fibres, which does affect the load transfer between the constituents resulting in composites with better mechanical properties.     

The potential of harakeke fibre as reinforcement in polymer matrix composites including modelling of long harakeke fibre composite strength

Mechanical properties of aligned long harakeke fibre reinforced epoxy with different fibre contents were evaluated. Addition of fibre was found to enhance tensile properties of epoxy; tensile strength and Young’s modulus increased with increasing content of harakeke fibre up to 223 MPa at a fibre content of 55 wt% and 17 GPa at a fibre content of 63 wt%, respectively. The flexural strength and flexural modulus increased to a maximum of 223 MPa and 14 GPa, respectively, as the fibre content increased up to 49 wt% with no further increase with increased fibre content. The Rule of Mixtures based model for estimating tensile strength of aligned long fibre composites was also developed assuming composite failure occurred as a consequence of the fracture of the lowest failure strain fibres taking account porosity of composites. The model was shown to have good accuracy for predicting the strength of aligned long natural fibre composites.     

An experimental study on the in situ strength of SiC fibre in unidirectional SiC/Al composites

In order to investigate the effect of strain rate and high temperature exposure on the mechanical properties of the fibre in the unidirectional fibre reinforced metal-matrix composite, in situ SiC fibre bundles are extracted from two kinds of SiC/Al composite wires, which are heat-treated at two different temperatures (exposed in the air at 400 and 600 °C for 40 min after composition). Tensile tests for these two fibre bundles are performed at different strain rates (quasi-static test: 0.001 s⁻¹, dynamic test: 200, 700, and 1200 s⁻¹) and the stress–strain curves are obtained. The experimental results show that their mechanical properties are rate-dependent, the modulus E, strength σ_b and unstable strain _b (the strain corresponding to σ_b) all increase with increasing strain rate. Compared with the mechanical properties of the original SiC fibre, those of the two in situ fibres degrade to some extent, the degradation of the in situ fibre extracted from the composite wire exposed at 600 °C (hereafter referred to as in situ fibre 2) is more serious than that of the in situ fibre extracted from the composite wire exposed at 400 °C (hereafter referred to as in situ fibre 1). The mechanism of the degradation is investigated. A bi-modal Weibull statistical constitutive equation is established to describe the stress–strain relationship of the two in situ fibre bundles. The simulated stress–strain curves agree well with the experimental results.     

Numerical simulation of strain-rate dependent transition of transverse tensile failure mode in fiber-reinforced composites

This study numerically simulates strain-rate dependent transverse tensile failure of unidirectional composites. The authors’ previous study reported that the failure mode depends on the strain rate, with an interface-failure-dominant mode at a relatively high strain rate and a matrix-failure-dominant mode at relatively low strain rate. The present study aims to demonstrate this failure-mode transition by a periodic unit-cell simulation containing 20 fibers located randomly in the matrix. An elasto-viscoplastic constitutive equation that involves continuum damage mechanics regarding yielding and cavitation-induced brittle failure is used for the matrix. A cohesive zone model is employed for the fiber–matrix interface, considering mixed-mode interfacial failure. For the results, the relationship between failure modes and the strain rate is consistent with the authors’ previous studies.     

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.     

Film stacking impregnation model for a novel net shape thermoplastic composite preforming process

An impregnation model has been developed to evaluate the infiltration phenomena that occur during a novel near net shape preforming method. This process comprises automated deposition of thermoplastic resin and unidirectional (UD) carbon fibres to a pre-programmed stacking sequence, thereby forming tailored preforms for subsequent stamp-forming. Infiltration kinetics have been simulated to study the effect of different stacking scenarios, materials, and pre-consolidation routes on the novel preforming process. Isothermal infiltration of a liquid thermoplastic polymer into a compressed UD fibre bed has been examined and the experimental results have been used to validate an infiltration model based on local fluid flow in compressible porous media. This enables simulation of infiltration in alternating matrix film and fibre layers, relating pressure, time, and temperature with the local fibre volume fraction, pressure, and liquid and solid velocities in the stacked material. For a given set of processing conditions, the model fibre volume fraction distribution prediction enables the optimum matrix stacking layer thicknesses to be determined. It was shown that infiltration is inhibited above a limiting pressure which leads to increased fibre bed compaction and hence decreased permeability.