The deformation of hybrid-particulate composites

The deformation behaviour of a hybrid-particulate epoxy composite has been examined. The Young's modulusE and yield stress have been determined as a function of temperature and volume fraction of rigid glass spheres, for both a simple epoxy matrix and a two-phase epoxy toughened by the presence of rubber particles. In addition, the effect of improving the particle-matrix interface with a silane bonding agent has been studied. It is found that there is a steady increase in Young's modulus with the volume fraction of spheres for all systems. In contrast, the yield stress is only found to increase with the volume fraction of rigid particles when the epoxy matrix is not toughened with rubber. It is found that the yield stress is virtually independent of particle volume fraction when a rubber-modified epoxy matrix is employed. Finally, it is found that for all compositions tested the Young's modulus and yield stress increase with increasing temperature. The overall behaviour has been discussed in terms of existing theories concerning the deformation behaviour of amorphous polymers.     

Crack bridging and fibre pull-out in polyethylene fibre reinforced epoxy resins

An investigation has been undertaken of the stress distributions in high-performance polyethylene fibres bridging cracks in model epoxy composites. The axial fibre stress has been determined from stress-induced Raman band shifts and the effect of fibre surface treatment has been followed using untreated and plasma-treated polyethylene fibres. It is found that when the specimen is cracked, the fibres do not break and stress is transmitted from the matrix to the fibre across the fibre/matrix interface. A debond propagates along the fibre/matrix interface accompanied by friction along the debonded interface. The axial stress distributions in the fibres can be analysed using a partial-debonding model based upon shear-lag theory and it is found that the maximum interfacial shear stress at the bond/debond transition is a function of the debond length. The debonding process has been modelled successfully in terms of the interfacial fracture energy-based criterion developed by Hsueh for the propagation of a debond along a fibre/matrix interface accompanied by constant friction along the interface.     

Fragmentation analysis of glass fibres in model composites through the use of Raman spectroscopy

Raman spectroscopy has been used to monitor deformation micromechanics in a model discontinuous fibre composite comprising a single glass fibre in an epoxy resin. The glass fibre was coated with a diacetylene-containing urethane copolymer that was subsequently cross-polymerised thermally. During composite deformation, the stress-induced Raman band shifts of the polydiacetylene sequences in the cross-polymerised coating were used to map the distributions of strain along glass fibres inside the epoxy resin matrix. The fragmentation of the fibre has been followed in detail and the behaviour analysed using classical shear-lag analysis. Values of the interfacial shear stress along fibre fragments were determined from the measured fibre strain distributions and were shown to be limited by the shear yield stress of the matrix. The effect of adhesion between the coating and the fibre upon the strain distributions has been investigated in detail. The fibre strain distributions can only be determined accurately when the adhesion is good. However, in the case of poor adhesion, although the strain distribution in the coating follows that of the matrix, the fragmentation process can still be monitored.     

Three-dimensional elastoplastic finite element modelling of deformation and fracture behaviour of rubber-modified polycarbonates at different triaxiality

A periodic face-centred cuboidal cell model is provided to account for inter-particle interaction, and a particle-crack tip interaction model is developed to study the interaction between a blunting model I crack tip and the closest array of initially spherical rubber particles in an effective medium. Three-dimensional elastoplastic finite element analysis has been preformed to study the deformation and fracture behaviour of rubber-modified polycarbonates. The effective elastoplastic constitutive relation is derived by the method of homogenisation and local stress and strain distributions are obtained to explore the role of rubber cavitation in the toughening process at different stress triaxiality. 3D elastoplastic finite element results are compatible with experimental observations, that is, rubber particles can act as stress concentrators to initiate crazing or shear yielding in the matrix but they behave differently from voids at high triaxiality. Rubber cavitation plays an important role in the toughening process under high tensile triaxial stresses.     

Fragmentation in alumina fibre reinforced epoxy model composites monitored using fluorescence spectroscopy

It has been found that well-defined fluorescence R₁ and R₂ lines can be obtained from PRD-166 alumina-zirconia fibres and that the fluorescence R lines shift with applied stress. They are found to shift to higher wavenumber when subjected to tensile deformation and to lower wavenumber in compression. The stress-sensitive fluorescence R₂ line has been used to map the distribution of stress along PRD-166 fibres embedded in an epoxy resin matrix cured under different conditions. It has been shown that the distributions of stress along the PRD-166 fibres at different levels of matrix strain are consistent with those predicted by conventional shear-lag analysis. The interfacial shear stress has been derived from the point-to-point variation of stress along the fibre. The fluorescence technique has also been used to map the stress distribution along a PRD-166 fragment in an epoxy matrix during a single-fibre fragmentation test where it is found that debonded regions propagate along the fibre fragments during loading, after initial fragmentation has occurred.     

Statistics for the strength and lifetime in creep-rupture of model carbon/epoxy composites

A theoretical model and experimental data are presented for the strength and lifetime in creep-rupture of unidirectional, carbon fiber/epoxy matrix microcomposites at ambient conditions. The model ‘microcomposites’ consisted of seven parallel carbon fibers (Hercules IM-6) embedded in an epoxy matrix (Dow DER 331 epoxy/No. 26 hardener) and forming an approximately hexagonal array. The results are interpreted by means of the model which involves Weibull distributions for fiber strength, micromechanical stress-redistribution, and power-law, matrix creep around noncatastrophic fiber breaks from which the creep-rupture originates. For the microcomposites, the model yields approximate Weibull strength and lifetime distributions with parameters depending on the various model parameters. Also obtained is a power-law relationship between stress level and lifetime whose exponent depends on the Weibull shape parameter for fiber strength, the creep exponent for the matrix, and the critical cluster size for failed fibers in the microcomposite. The experimental results agree quite well with theoretical predictions though time-dependent debonding appeared to be part of the failure process; this debonding was observed in independent experiments.     

Stress transfer in the fibre fragmentation test: Part III Effect of matrix cracking and interface debonding

A theoretical stress analysis has been developed for the fibre fragmentation test in the presence of matrix cracks at sites of fibre breaks. The strain energy release rates for both matrix cracking and interface debonding are calculated for a carbon fibre/epoxy matrix composite. By comparing these strain energy release rates with the corresponding specific fracture resistances, the competition between matrix crack growth and interface debonding has been studied. The distributions of fibre axial stress and interfacial shear stress obtained from the present analysis show that the matrix crack substantially reduces the efficiency of stress transfer from the matrix to the fibre. This revised version was published online in November 2006 with corrections to the Cover Date.     

The importance of constraint relief caused by rubber cavitation in the toughening of epoxy

Many rubber-toughened epoxies are thought to derive the bulk of their toughness through the processes of rubber cavitation and plastic shear-yielding in the epoxy matrix. Constraint relief has been considered to be a key mechanism which allows extra plastic shear deformation to occur. The present work attempts to provide direct experimental evidence of the constraint relief effect by combining testing geometries that vary the degree of constraint with microscopic observations. The results show that the success of a rubber as a toughening agent for epoxies is closely related to its ability to cavitate. Evidence for local constraint relief is presented. Upon cavitation of the rubber, the stress state in a specimen with initial constraint is found to change to a plane stress state. The constraint relief circumvents or delays the crack initiation in the matrix, which allows more plastic deformation to occur.     

Ultimate properties of rubber and core-shell modified epoxy matrices with different chain flexibilities

Preformed polystyrene-co-butylacrylate (PScoBu) core-shell particles and polystyrene microspheres as well as amine-terminated butadiene nitrile (ATBN) rubber have been used for modification of both rigid and more flexible crosslinked DGEBA-based epoxy networks having significantly different crosslink densities. Some variations in cure kinetics have been shown by both thermal and rheological measurements. Independently of the crosslink density of the neat epoxy matrix, function of the cycloaliphatic or aliphatic hardener used, the toughening effect via core-shell modification has been found as good as that for rubber modification but with a better retention of thermal properties. Results are investigated as a function of the morphologies obtained by scanning electron microscopy (SEM) but also by atomic force microscopy (AFM). Larger fracture toughness was obtained for every-unmodified and modified- epoxy matrices cured with the aliphatic hardener as a consequence of the lower crosslink density of the corresponding mixtures.     

Shear ductility and toughenability study of highly cross-linked epoxy/polyethersulphone

The objective of the present study was to determine whether the ductility and toughenability of a highly cross-linked epoxy resin, which has a high glass transition temperature, T _g, can be enhanced by the incorporation of a ductile thermoplastic resin. Diglycidyl ether of bisphenol-A (DGEBA) cured by diamino diphenyl sulphone (DDS) was used as the base resin. Polyethersulphone (PES) was used as the thermoplastic modifier. Fracture toughness and shear ductility tests were performed to characterize the materials. The fracture toughness of the DDS-cured epoxy was not enhanced by simply adding PES. However, in the presence of rubber particles as a third component, the toughness of the PES–rubber-modified epoxy was found to improve with increasing PES content. The toughening mechanisms were determined to be rubber cavitation, followed by plastic deformation of the matrix resin. It was also determined, through uniaxial compression tests, that the shear ductility of the DDS-cured epoxy was enhanced by the incorporation of PES. These results imply that the intrinsic ductility, which had been enhanced by the PES addition, was only activated under the stress state change due to the cavitation of the rubber particles. The availability of increasing matrix ductility seems to be responsible for the increase in toughness. This revised version was published online in November 2006 with corrections to the Cover Date.     

基体局部软化对纤维/环氧树脂复合材料力学行为影响的数值分析

聚合物基体的变形局部化在复合材料破坏过程中起着重要作用。采用有限元分析方法, 借助用户材料子程序(UMAT), 描述了具有应变软化特点的高聚物弹塑性的本构关系, 研究了纤维/环氧树脂复合材料在拉伸破坏过程中基体局部变形的演化规律, 分析了基体的局部应变软化对纤维/环氧树脂复合材料应力的影响。结果表明: 纤维的应力分布及基体的塑性变形具有不均匀性; 基体局部变形降低了邻近断点的完好纤维的应力集中程度; 随着纤维间距的增加, 邻近断点的完好纤维的应力集中区域变宽, 而且应力集中程度降低。     

Numerical and experimental studies on the fracture behavior of rubber-toughened epoxy in bulk specimen and laminated composites

To study the toughening mechanisms of liquid rubber (LR) and core-shell rubber (CSR) in bulk epoxy and composite laminate, experimental and numerical investigations were carried out on compact tension (CT) and double-cantilever-beam (DCB) specimens under mode-I loading. The matrix materials were pure epoxy (DGEBA), 15% LR (CTBN) and 15% CSR modified epoxies. Experimental results and numerical analyses showed that both liquid rubber (LR) and core-shell rubber (CSR) could improve significantly the fracture toughness of pure epoxy (DGEBA). However, the high toughness of these toughened epoxies could not be completely transferred to the interlaminar fracture toughness of the unidirectional carbon fibre reinforced laminate. The main toughening mechanism of CSR in bulk epoxy was the extensive particle cavitation, which greatly released the crack-tip triaxiality and promoted matrix shear plasticity. The poor toughness behavior of CSR in the carbon fibre laminate was thought to be caused by the high constraint imposed by the stiff fibre layers. No particle cavitation had been observed in LR modified epoxy and the main toughening mechanism was merely the large plastic deformation near the crack-tip due to the rubber domains in the matrix which results in a lower yield strength but a higher elongation-to-break.     

Effect of cross-linking density on the toughening mechanisms of rubber-modified thermosets

Solid rubbers have been incorporated into thermosets using the compositional quenching process. Electron micrographs reveal that rubber particles a few micrometres or less in size have been dispersed in the matrix. Two model systems were studied: an epoxy resin cured with primary amines which represents a tight network structure, and a phenoxy resin cross-linked with methylene diisocyanate which represents a loose network. The present study indicates that a small amount of a cross-linking agent can reduce the degree of matrix yielding with a resultant drop in impact strength. SEM fractography provides complementary information on the transition from ductile fracture to brittle fracture.     

Low-temperature behaviour of epoxy-rubber particulate composites

Toughness and mechanical property data are presented for a carboxyl-terminated acrylonitrile butadiene (CTBN) rubber-modified epoxy resin in the temperature range 20 to – 110° C. A toughening model based on ultimate strain capability and tear energy dissipation of the rubber, present as dispersed microscopic particles in an epoxy matrix, is used to explain the suppression of composite toughness (G _Ic ) below – 20° C. The toughness loss is attributed to a glass transition in the rubber particles, and to a secondary transition in the epoxy resin, both occurring in the range – 40 to – 80° C. Strain-tofailure and modulus measurements on bulk rubber-epoxy compounds, formulated to simulate rubber particle compositions, confirm a decrease in rubber ductility coincident with the onset of composite toughness loss. An increase in rubber tear energy associated with its transition to a rigid state can explain the observation that even at low temperatures composite toughness generally remains significantly higher than that of pure epoxy. Although the low-temperature epoxy transition reduces molecular mobility in the matrix phase, residual ductility in, and energy dissipation by, the rubber particles determine the extent of composite toughness suppression. The low-temperature data bear out the particle stretching-tearing model for toughening.     

Evaluation of interface fracture energy for single-fibre composites

Raman and luminescence spectroscopy have been used for the first time to determine the interface fracture energy for single-fibre composites. By using the measured fibre stress distributions in single-fibre fragmentation composite specimens and a simple energy-balance scheme, the energy for the initiation of interfacial debonding has been estimated for carbon (T50) and α-alumina (PRD-166 and Nextel 610) fibres embedded in epoxy resins. It has been found that the interface fracture energy shows good sensitivity to changes in the level of fibre/matrix adhesion due to surface treatment and sizing of the fibres. It is also found that the values of interface fracture energy correlate well with measured values of interfacial shear strength determined for the same fibre/matrix systems.     

Load carrying characteristics of short fiber composites containing a heterogeneous interphase region

A micromechanics finite element model has been developed for the stress transfer in short fiber composites, incorporating a heterogeneous interphase region. The specimen consists of a single fiber under stress embedded in an epoxy matrix. Considering a heterogeneous and compliant interphase, a generalized computational procedure has been developed that enables imperfect adhesion or loss of interphasial strength simulations. Varying the global variables of the problem, parametric studies were performed to study the influence of the model parameters on the load transfer characteristics from the fiber to matrix. Numerical results of the stress distribution have been determined as a function of geometric and material variables. The effect of both the imperfect adhesion between the fiber and the matrix, and the loss of interphase compliance on stress state were demonstrated and discussed. The results showed that the interphase plays a significant role in stress transfer characteristics of fibrous composites, and extension of the load transfer zone is restricted very close to the loaded fiber end.     

Viscoelastic micromechanical modeling of free edge and time effects in glass fiber/epoxy cross-ply laminates

A viscoelastic finite element analysis has been carried out to investigate the free edge and time effects in a [0/90]_ns glass fiber/epoxy cross-ply laminate, subjected to mechanical loads. The analysis is based on a three-dimensional micromechanical model that predicts the stress/strain field at the fiber and matrix levels near the free edge surface of the cross-ply laminate. The epoxy matrix is represented by a nonlinear viscoelastic constitutive model. In addition, two different damage criteria for the matrix cracking and interface debonding have been introduced into the model, which were incorporated into the finite element analysis program, adina, through the user-defined subroutine. Damage initiation as well as damage growth in the cross-ply laminate is predicted by the present model. It is found that the edge effect is more dominant in the damage initiation process and its influence on the global properties of cross-ply laminate, is not significant. Under a constant load, it is possible for the damage to grow further due to the viscosity of the matrix and the stress/strain redistribution in the cross-ply laminate.     

Effect of rubber interlayers on the fracture of glass bead/epoxy composites

The effectiveness of rubber interlayers between inorganic particles and polymer matrix for toughening has been a controversial subject. In this research, a series of rubber-encapsulated glass beads and its epoxy composites were prepared, and underlying mechanisms which can connect material parameters related with rubber interlayers with energy dissipation mechanisms, were investigated. The critical stress intensity factor (K _IC) and critical strain energy release rate (G _IC) of rubber-encapsulated glass bead filled epoxies were found to insignificantly depend on the existence and thickness of rubber interlayers. Microscopy studies on fracture process identified four different micro-mechanical deformations which can dissipate fracture energy: step formation, micro-shear banding, debonding of glass beads, and diffuse matrix shear yielding. It was found that the first two became less extensive and the others became more extensive as the thickness of rubber interlayers increases. This offsetting effect of micro-mechanical deformations seems to be the reason for the absence of significant toughening effect of rubber interlayers.     

Data reduction methodologies for single fibre fragmentation test: Role of the interface and interphase

The single fibre fragmentation test (SFFT) is commonly used to characterise the fibre/matrix adhesion. In order to quantify the fibre/matrix adhesion the cumulative stress transfer function (CSTF) methodology was developed so that the elastoplasticity of the matrix could be included in the analysis through the plasticity-effect model [Tripathi D, Chen F, Jones FR. A comprehensive model to predict the stress fields in a single fibre composite. J Comp Mater 1996;30;1514–38., Tripathi D, Jones FR. Measurement of the load-bearing capability of the fibre/matrix interface by single fibre fragmentation. Comp Sci Technol 1997;57:925–35.] The limitations of this technique for the data reduction have been addressed by the use of the Plasticity Model to input the non-linearity of the matrix into methodology for fragmentation of a fibre in a matrix. An improved methodology, known as the revised cumulative stress transfer function (RCSTF) is described. The adhesion of a nanoscale plasma copolymer coated glass/epoxy system has been used to examine this approach to the fragmentation process. This methodology is also extended to account for the presence of an interphase. To validate the three phase model, carbon fibre coated with high and medium modulus epoxy resin were used to simulate fibre/interphase/matrix.     

The stress transfer efficiency of a single-walled carbon nanotube in epoxy matrix

This paper investigates the effects of tube length and diameter on the distributions of tensile stress and interfacial shear stress of a single-walled carbon nanotube in epoxy matrix. It was shown that a smaller tube diameter has a more effective reinforcement and there exists an optimal tube length at which reinforcement is maximized. It was also found that a carbon nanotube has a greater stress transfer efficiency than a solid fibre, providing flexibility for toughness and tensile strength optimization.