Microstress distribution in graphite fibre/epoxy composites containing an elastomeric interphase: response to uniaxial and biaxial loading conditions

A micromechanical model based upon the method of cells is introduced to characterize three-phase composites that contain a distinct and homogeneous interphase region. Initially, the performance characteristics of the model are shown to be quite consistent with those of a concentric cylinder model formulation. Subsequently, a parametric study is performed that examines the mechanical response of model graphite/epoxy composites as a function of selected interphase properties. The micromechanical model is utilized to establish an interdependence among the interphase Young's modulus, the interphase thickness and the average stresses within the fibre, interphase and matrix resulting from two external loading conditions: uniaxial longitudinal tension and biaxial transverse shear. Material combinations are considered wherein the interphase Young's modulus is systematically varied above and below the matrix Young's modulus. The simulation indicates that the selected interphase properties significantly influence the stress state within each of the three composite constituents. The manner in which the stress states are modified proves to be non-intuitive in many of the cases considered. In particular, there are material domains encountered where the model predicts that certain stress components in a constituent will exhibit (1) a maximum with respect to variations in the interphase Young's modulus and/or (2) a minimum with respect to variations in the interphase thickness.     

The effect of the interphase and material properties on load transfer in fibre composites

An interphase between a fibre and a matrix is modelled with its own mechanical properties to study the load transfer through this crucial region. The effect of material properties on the maximum shear stress during the load transfer is investigated. The results indicate an optimum point where the shear stress would be the lowest at the interphase. With the help of this model, the effect of crack initiation at the interphase on the stresses is illustrated. It is shown that cracks are likely to initiate at the fibre/interphase interface rather than at the interphase/matrix side.     

Interphase behaviour in graphite-thermoplastic monofilament composites

The role of the fibre-matrix interphase in transferring load from the matrix to the fibre in graphite-thermoplastic composites is not well understood. The goal of this work was to alter the interphase of graphite-thermoplastic monofilament composites in a controlled manner by treating the fibre surface, and then correlating fibre surface morphology, fibre surface energy, fibre strength, and matrix properties with interphase behaviour. A monofilament composite system was employed to study the fibre-matrix interphase because fibre-fibre interaction and processing variability are eliminated. A fragmentation method was used to observe the interphase behaviour of the monofilament composites indirectly by measuring the interphase shear stress, a parameter which governs the load transfer from the matrix to the fibre. It was found that the improvement in the ability of the interphase to transfer load from the matrix to the fibre increased with the severity of the treatment and was due primarily to increased micromechanical locking (increased surface roughness). Debonding at the interphase occurred along either the fibre-matrix interphase (in the composites with a tough matrix) or perpendicular to the fibre (in composites with a weaker matrix, and a strong interphase). Thus the matrix properties, by limiting the properties of the composite, strongly influenced the value of improving the interphase properties.     

Glass fibre sizing/matrix interphase formation in liquid composite moulding: effects on fibre/matrix adhesion and mechanical properties

The glass fibre sizing/matrix interactions in a liquid composite moulding environment have been investigated to develop an understanding of the effect of wetting between sized fibre surfaces and the reacting liquid matrix, the structure of the resulting interphase and its effect on fibre/matrix adhesion and composite properties. The overall research objectives in this programme are to develop an experimental protocol for measurement of the key wetting parameters of the fibre and matrix; to quantify the effect of wetting on the mechanical properties of the composites formed by liquid composite moulding; and to formulate a time-, temperature- and geometry-dependent model of the liquid composite moulding process which incorporates the surface properties of the fibre, its finish and the reactive polymer matrix.Results are presented for a series of sized glass fibres consisting of incompatible and compatible sizings, studied with a reacting vinyl ester matrix system. Surface free energy analysis was conducted to characterize the fibre surfaces. Axial and transverse wicking rates were measured to quantify the change in total surface free energy of the fibre/matrix systems. The sizing surface free energy and its solubility in the matrix strongly affected the fibre/matrix interphase formation and consequently the fibre/matrix adhesion and composite shear and flexural strengths.     

A micromechanical characterization of graphite-fiber/epoxy composites containing a heterogeneous interphase region

An improved micromechanical model based on the method of cells is introduced in order to describe three-phase, continuous-fiber composite materials containing a heterogeneous interphase region. The model's capability represents a significant improvement over that of the previous version (which is applicable to a homogeneous interphase) in that additional microstress information is obtained within the interphase region. A critical assessment of the model demonstrates that the predictions are consistent with data reproduced by using other micromechanical models. The study includes a parametric simulation in which the effective properties and the mechanical stresses associated with model graphite-fiber/epoxy composites are predicted as a function of the dimensions and Young's modulus of the interphase. Three different interphases are modeled such that the Young's modulus varies between that of the fiber and the matrix according to a generalized parabolic function of the radial coordinate. The parabolic functions are specified such that two of the model composites possess an interphase whose effective Young's modulus is above that of the matrix. The third interphase is specified such that its effective Young's modulus is below that of the matrix. The data indicate that the interphase dimensions and the functional form describing the interphase Young's modulus significantly influence the composite microstresses. These data may be used to help identify optimum material combinations during composite material synthesis.     

Finite element micromechanical modelling of a unidirectional composite subjected to axial shear loading

A micromechanical model is presented which predicts the behaviour of a unidirectional composite subjected to axial shear load using standard finite elements. Only a three-dimensional model can handle the necessary shear loading boundary conditions when using such elements. These boundary conditions give shear stress components but no direct stress components within the composite. A parametric study is carried out on unidirectional carbon fibre/epoxy within the linear elastic regime of both constituents. The study reveals that the most critical parameters controlling the axial shear modulus of the composite are matrix modulus and fibre volume fraction whilst the stress state in the composite is mainly controlled by geometrical features of the composite, i.e., fibre volume fraction and fibre spacing. Comparison between the predicted axial shear modulus based on the concentric cylinder model and the current finite element model shows good agreement for low and intermediate fibre volume fractions. Both predictions lie within the Hashin bounds and the finite element prediction tends to be closer to the upper Hashin bound for fibre volume fractions greater than 60%. The initial tangent shear modulus predicted with the finite element model and that measured differ by less than 2.5%. The non-linear shear stress/strain response of the composite material is also predicted and agreement with the experimental results is good.     

Characterisation of interphase nanoscale property variations in glass fibre reinforced polypropylene and epoxy resin composites

The local microstructure can be altered significantly by various fibre surface modifications, causing property differences between the interphase region and the bulk matrix. By using tapping mode phase imaging and nanoindentation tests based on the atomic force microscope (AFM), a comparative study of the sized fibre surface topography and modulus as well as the local mechanical property variation in the interphase of E-glass fibre reinforced epoxy resin and E-glass fibre reinforced modified polypropylene (PPm) matrix composites was conducted. The phase imaging AFM was found a highly useful tool for probing the interphase with much detailed information. Nanoindentation experiments indicated the chemical interaction during processing caused by a gradient profile in the modulus across the interphase region of γ-aminopropyltriethoxy silane (γ-APS) and polyurethane (PU)-sized glass fibre reinforced epoxy composite. The interphase with γ-APS/PU sizing is much softer than the PPm matrix, while the interphase with the γ-APS/PP sizing is apparently harder than the matrix, in which the modulus was constant and independent of distance away from the fibre surface. The interphase thickness varied between less than 100 and ≈300 nm depending on the type of sizing and matrix materials. Based on a careful analysis of ‘boundary effect’, nanoindentation with sufficient small indentation force was found to enable measuring of actual interphase properties within 100 nm region close to the fibre surface. Special emphasis is placed on the effects of interphase modulus on mechanical properties and fracture behaviour. The interphase with higher modulus and transcrystalline microstructure provided simultaneous increase in the tensile strength and the impact toughness of the composites.     

The influence of fibre surface treatment on the formation of an interphase in CFRP

In the scheme of a EURAM programme the influence of a wet oxidative surface treatment on the formation of an interphase, on the fibre-matrix bond strength and on the mechanical properties is investigated. The fibre CG 43–750 was supplied by Courtaulds treated to four different surface treatment levels (designated STL=0% or untreated, 10, 50 and 100%) sized (1% by weight) and impregnated with the resin HG 9106. This resin consists of di-, tri- and tetrafunctional epoxies with the hardener 3.3 DDS and also contains polyethersulphone. During the cure this resin separates in a continuous (thermoset-rich) phase which completely covers the fibres and a discontinuous (thermoplastic-rich) phase with a roughly globular structure. From water uptake experiments and matrix (interphase) sensitive composite properties (shear modulus G ₁₂, transverse modulus E ₂₂) it was concluded that the activated carbon fibre surface gives rise to a more fully crosslinked interphase, resulting in a reduction of the modulus of this interphase.     

Micro-Mechanical Behavior of a Unidirectional Composite Subjected to Transverse Shear Loading

The effects of interphase between fibers and matrix on the micro-and macro-mechanical behaviors of fiber-reinforced composite lamina subjected to transverse shear load at remote distance have been studied. The interphase has been modeled by the compliant spring-layers that are linearly related to the normal and tangential tractions. Numerical analyses on composite basic cells have been carried out using the boundary element method. For undamaged composites the micro-level stresses at the matrix side of the interphase and effective shear modulus have been calculated as a function of the fiber volume fraction and the interphase stiffness. Results are presented for various interphase stiffnesses from perfect bonding to total debonding. For a square array composite results show that for a high interphase stiffness k > 10, an increase in a fiber volume fraction results in a higher effective transverse shear modulus. For a relatively low interphase stiffness k < 1, it is shown that an increase in the fiber volume fraction causes a decrease in the effective transverse shear modulus. For perfect bonding, the effective shear modulus for a hexagonal array composite is slightly larger than that for a square array composite. Also for the damaged composite with partially debonded interphase, local stress fields and effective shear moduli are calculated and a decrease in the effective shear modulus has been observed.     

Polymeric composite materials incorporating an elastomeric interphase: A mathematical assessment

A mathematical model based upon the method of cells is extended in order to describe three-phase composite materials containing an interphase. A parametric study is performed wherein the effective properties of the composites are determined as a function of interphase material properties, interphase thickness and fiber volume fraction. The simulation is designed in particular towards describing the behavior of model composites which incorporate elastomeric polymers as an interphase to bond carbon fibers chemically to a polymeric matrix. Two hypothetical interphases are considered: one whose properties are representative of elastomers (Young's modulus less than fiber and matrix) and one whose properties are intermediate with respect to the fiber and matrix. The two cases provide a broad assessment of how the interphase properties influence the effective composite properties.     

The effect of interfacial conditions on the elastic-longitudinal modulus of fibre reinforced composites

A model study is conducted on the prediction of the elastic longitudinal modulusE _CL of a unidirectional fibre reinforced composite. It is assumed in our model that the fibres are aligned in the uniaxial loading direction and that the representative volume element (RVE) consists of three coaxial cylinders, namely the fibre, the interphase and the bulk matrix. The interphase represents the third phase developed between the constituent phases of the composite and it is characterized by mechanical imperfections, physicochemical interactions and limited mobility of macromolecules due to their absorption on the filler surface. Thus the interphase properties are varied within this third phase in an unknown way. In the present study it is supposed that the elastic modulus of the interphase materialE _i is varied along the thickness following an exponential law of variation. Moreover, the interphase thickness is determined according to existing theory which is based on thermal capacity measurements. PredictedE _CL values agree well with respective experimental results. In addition the effect of an abrupt variation of the elastic modulus at the fibre surface onE _CL is considered. Results showed that this type of variation is of minor importance in predictingE _CL.     

Experimental measurement and predictive modelling of bending behaviour for viscous unidirectional composite materials

It is widely accepted that the key deformation mechanisms during forming of viscous textile composite (prepreg) sheets are in-plane shear and out-of-plane bending. This paper focuses on the bending deformation mechanism, including experimental characterisation and theoretical modelling of bending behaviour during viscous composite forming. Experimental measurements are obtained by means of a large-displacement buckling test at a variety of displacement rates and temperatures. Some important aspects, such as viscoelastic behaviour, are also investigated. A bending model based on elastic theory combined with uniaxial continuum theory for ideal fibre-reinforced fluids for viscous shear deformation has been developed, using material parameters obtained from industrial manufacturers as input data, such as composite geometry, fibre properties, fibre volume fraction and matrix rheology. Model predictions demonstrate that the model can capture the main characteristics of material properties, such as rate dependence. This bending model can be used in formability analysis for viscous unidirectional composite materials, and might be applied in a finite element forming simulation to account for the bending stiffness.     

Large deformation response of a hyperelastic fibre reinforced composite: Theoretical model and numerical validation

The mechanical behaviour of an incompressible neo-Hookean material directionally reinforced with a generalised neo-Hookean fibre is examined in the finite deformation regime. To consider the interaction between the fibre and the matrix, we use a composite model for this transversely isotropic material based on a multiplicative decomposition of deformation, which decouples the uniaxial deformation along the fibre direction from the remaining shear deformation. The model is then verified numerically by a unit cell model with periodic boundary conditions. The strain energy stored in the unit cell is compared with the energy predicted by the proposed theoretical model and excellent agreement is reported.     

Formation of the interphase in organic-matrix composites

This paper addresses attempts made to determine the mechanical and chemical properties of material within a micrometre of the surface of a single carbon fibre in an epoxy/amine matrix. Work reported earlier has shown that deformation data near a fibre can be interpreted as showing that the modulus of this material could be lower than that of the bulk matrix for a distance of about 0.5 μm from the fibre. Spectral evidence suggests that the material in this region is chemically different from material remote from the interface. Analysis of the variation of fibre debond forces in a composite as a function of the fibre content also suggests that the matrix is softer near the fibre. The present paper addresses studies done to determine a mechanism for the variation of mechanical and chemical properties over such a distance. Possibilities considered include modification of resin stoichiometry in the region by preferential absorption of active species, formation of a zone of incomplete polymerization caused by entropic effects related to the two-dimensional nature of the interface, and modification of the resin solidification mechanism in the region of the fibre.     

Effect of interphase on fibre-bridging toughness of a unidirectional FRP composite thin plate

A parametric analysis of the toughening mechanisms in a uniaxially fibre reinforced polymer (FRP) thin plate with a power-law hardening shear interphase is presented. An interfacial shear-lag model is used to analyse the relationship between the crack surface traction exerted by the intact fibres and the crack opening displacement (COD). Numerical solutions of the equations governing bridge-toughening are given. Two special kinds of interphase, i.e. linearly elastic and perfect plastic, are discussed. The results demonstrate that the toughening ratio of the composite thin plate is sensitive to several parameters, e.g. the thickness of the interphase between fibre and matrix, the hardening parameter of the interphase, the interfacial shear properties (stiffness and strength), the fibre radius and the far-field load. The results of this investigation will be beneficial to the selection of constitutive materials, the improvement of mechanical behaviour and the fabrication process of FRP composites.     

Cooling rate influences in carbon fibre/PEEK composites. Part 1. Crystallinity and interface adhesion

The effect of cooling rate on the fibre–matrix interface adhesion for a carbon fibre/semicrystalline polyetheretherketone (PEEK) composite was characterised based on the fibre fragmentation, fibre pullout and short beam shear tests. The interface adhesion was correlated to the degree of crystallinity and the crystalline morphology, as well as the bulk mechanical properties of neat PEEK resin, all of which were in turn controlled by cooling rate. It was shown that the interface bond strength decreased with increasing cooling rate; the tensile strength and elastic modulus of PEEK resin decreased, while the ductility increased with increasing cooling rate through its dominant effect on crystallinity and spherullite size. The improvement of crystalline perfection and flattened lamella chains with high crystallinity at the interphase region were mainly responsible for the strong interface bond in composites processed at a low cooling rate. The interphase failure was characterised by brittle debonding in slow-cooled composites, whereas the amorphous PEEK-rich interphase introduced in fast cooled specimens failed in a ductile manner with extensive plastic yielding.     

The transverse coefficient of thermal expansion of a unidirectional composite

Various analytical models of the effective thermal expansion coefficients of unidirectional fibre-reinforced composite materials predict for certain fibre-matrix combinations an increase in the transverse coefficient of thermal expansion over that of its constituents at low fibre volume content. This effect is especially noticeable if the composite is fabricated with fibres of high modulus and low thermal expansion coefficient in matrices of low modulus and high thermal expansion coefficient. An experimental investigation was therefore conducted to study this behaviour in Textron fibre (SCS-6)-reinforced Hercules 3501 -6 epoxy matrix. Numerical calculations for this material system have shown that increases of the order of 20% over the matrix expansion coefficient is possible for fibre volume fraction in the range 3%–4%. Experimental measurements of the effective thermal expansion coefficients are seen to be in favourable agreement with the theoretical predictions. A parametric study is also undertaken to examine the influence of constituent properties on the effective composite behaviour. It is shown that the axial restraint of the fibre is responsible for a peak in the behaviour of the transverse expansion coefficient.     

On the influence of pre-stress on the mechanical properties of a unidirectional GRE composite

The effect of composite pre-stress on the mechanical properties of E-glass fibre in an epoxy resin has been investigated theoretically and experimentally. Experimental results have been obtained for pre-stresses (0, 25, 50, 75, 100, 200 MPa) at each of three fibre volume fractions (0.35, 0.45, 0.6). A theoretical model has been developed to predict the effect of composite pre-stress on the pre-load strain in fibre and matrix, tensile strength and elastic modulus of the composite. The results show that pre-tensioning of the fibre during fabrication increases the tensile strength and elastic modulus of the composite. This increase has been found to be a function of composite pre-stress and fibre volume fraction. Good agreement has been obtained between the theoretical results and experimental measurements.     

含孔隙混凝土复合材料有效力学性能研究

混凝土、岩石等工程材料是典型的多孔介质材料,孔隙或微裂纹的存在对材料的弹性模量及强度等力学参数产生很大影响。该文基于三相球模型确定了含孔隙复合材料的有效体积模量,提出采用空心圆柱形杆模型推导得到了含孔隙复合材料有效剪切模量的理论公式,并在各向同性材料的假设条件下确定了材料的有效弹性模量及泊松比;推导并得到了含孔隙材料的有效抗拉、抗压强度及有效抗剪强度与孔隙率之间的定量关系公式,并进一步得到了含孔基质在达到有效强度时的临界应变与孔隙率之间的定量关系。结果表明该文方法能较好的预测含孔混凝土材料的有效力学性能,且公式简单,易于应用。