Numerical study of the single fibre push-out test: Part III. Singularity of interface stresses

The singular behaviour at the free edges of the fibre-matrix interface is analysed for the fibre push-out test geometry based on the boundary element method. The fibre push-out test has been extensively used to measure the fibre-matrix interfacial properties in polymer, ceramic and metal matrix composites. There are two free edges in the fibre push-out specimen: one is at the loaded fibre end and the other at the supported fibre end. The singular stresses can be expressed as a function of singular exponent and singular stress intensity. It is shown that the singular exponents obtained at both fibre ends are characteristic of composite constituent properties, such as Young's moduli of fibre and matrix, and does not vary with specimen dimensions. The singular exponents are real and identical for the shear and radial stress components at fibre ends where the wedge angles are the same. The singular stress intensities are also implicit in material properties, and vary with specimen dimensions, such as fibre to matrix radius ratio, fibre aspect ratio and support hole size. An interfacial failure criterion is proposed here based on the average stress concept to determine the critical singular stress intensities in mode I and mode II loads.     

Interphase analysis of hierarchical composites via transmission electron microscopy

Observation and analysis of the interphase are essential for a detailed understanding of the global composite properties when nanofillers are incorporated as interfacial agents. Techniques such as atomic force microscopy and nano-indentation provide valuable information on interfacial properties associated with the viscoelastic behavior of each phase. However, when the morphology of this region is observed in detail, instrumental errors may regularly appear, decreasing the accuracy of measurements. In this work, the use of transmission electron microscopy (TEM) was explored to image the glass fiber-reinforced polymer GFRP interphase containing interfacial nanocellulose. TEM lamellas were prepared via a focused ion beam to observe the phases disposed within the composite arrangement. Energy dispersive X-ray spectroscopy was also performed to determine the elemental composition in each sample phase. Interphase sizes between 25 and 50 nm thick were found, highlighting the ability of this characterization route to give accurate interfacial measurements. This kind of measurement will open new routes for getting rich information on hierarchically structured composites containing a nanostructure as an interfacial agent.     

On the use of single fibre composites testing to characterise the interface in natural fibre composites

In recent years, natural fibre composites have received considerable attention as a serious contender to replace glass fibres in composite material applications. One of the key aspects in composite materials is the interface between the reinforcing fibres and the matrix and a critical assessment of the interfacial bond is needed for a successful design of the final component. Natural fibres possess many intriguing advantages over man-made fibres such as glass, but they also present serious difficulties, especially in terms of material heterogeneity and more specifically in terms of fibre diameter. In this sense, most of the traditional methods for interfacial characterisation are difficult to apply, since the required data reduction involves the use of stress analysis or fracture mechanics approaches in which the fibre diameter is a critical parameter. In the present study, interfacial characterisation is discussed for flax fibre/polypropylene composites and a sensitivity analysis is presented for the single fibre fragmentation test. The results indicate that traditional stress analysis fails to correctly assess the interface, whilst a statistical based data analysis can overcome the fibre heterogeneity problem.     

An appraisal of composite interface mechanics models and some challenging problems

A critical review of previous mechanics models proposed for the evaluation of interfacial properties from single fibre tests is presented with regard to their applicability and limitations. New results which include the effects of some important factors, such as pre-existing fibre flaws. thermal residual stresses and matrix cracks. are provided for a single fibre fragmentation test. By comparing the stress distributions of single fibre fragment and multi-fibre fragment, a basic method to study the multi-fibre composite is introduced in order to relate the interfacial parameters to the mechanical properties of the bulk composite. Some challenging problems on fibre-matrix interfaces are discussed for future research work.     

Mechanical properties of flat braided composite with flexible interphase

Textile composites have been used extensively as industrial materials because of the excellent mechanical properties resulting from the continuously oriented fiber bundle. In a study of the mechanical properties, it is important to consider the fiber/matrix interface property as for other composite materials. In a recent study, the fiber/matrix interface is regarded as an interphase that has its own material constants and thickness; consequently, the mechanical properties of a composite can be controlled by specifically designing the interphase. In this study, we applied this concept to braided composites with flexible resin as interphase for the purpose of designing the interphase. In a static tensile test, though there were no improvements in Noncut specimens (normal braided composites), but a Cut specimen (each side of the Noncut specimen was cut) with flexible interphase was improved in fracture load and displacement. The observation of the specimen edge was carried out and it was confirmed that the progress of debonding at the fiber bundle intersection was interrupted by a flexible interphase, and a matrix crack did not occur in the Cut specimen with flexible interphase. In a fiber bundle pull-out test, it was confirmed that debonding progressed not into the fiber/resin interface but into the flexible interphase in the specimen with flexible interphase, and the interfacial property at the fiber bundle intersection was improved.     

Interphase sizing temperature effect of LaRC PETI-5 on the dynamic mechanical thermal properties of carbon fiber/BMI composites

The dynamic mechanical thermal properties of carbon fiber-reinforced bismaleimide (BMI) composites processed using polyacrylonitrile(PAN)-based carbon fibers unsized and sized with LaRC PETI-5 amic acid oligomer as interphase material at 150°C, 250°C, and 350°C were investigated by means of dynamic mechanical thermal analysis. It was found that the storage modulus, loss modulus, tan δ and the peak temperature significantly depend on the sizing temperature as well as on the presence and absence of LaRC PETI-5 sizing interphase. The result showed that the carbon fiber/BMI composite sized at 150°C had the highest storage modulus at a measuring temperature of 250°C. The storage modulus decreased with increasing sizing temperature from 150°C to 350°C, being influenced by interdiffusion and co-reaction between the LaRC PETI-5 interphase and the BMI matrix resin. The present result is quite consistent with the interfacial result reported earlier in term of interfacial shear strength and interlaminar shear strength of carbon fiber/BMI composites. It is addressed that in the present composite system the sizing temperature of LaRC PETI-5 interphase critically influences not only the interfacial properties but also the dynamic mechanical thermal properties and its control is also important.     

Thermal stresses around a circular inclusion with functionally graded interphase in a finite matrix

Based on the theory of the complex variable functions, the analysis of non-axisymmetric thermal stresses in a finite matrix containing a circular inclusion with functionally graded interphase is presented by means of the least square boundary collocation technique. The distribution of thermal stress for the functionally graded interphase layer with arbitrary radial material parameters is derived by using the method of piece-wise homogeneous layers when the finite matrix is subjected to uniform heat flow. The effects of matrix size, interphase thickness and compositional gradient on the interfacial thermal stress are discussed in detail. Numerical results show that the magnitude and distribution of interfacial thermal stress in the inclusion and matrix can be designed properly by controlling these parameters.     

Interphase characterization in epoxy resin/carbon fibre composites

In this paper, interphase properties of carbon fibre/epoxy resin single-fibre model and unidirectional (UD) composites are reported. To study the contribution of the carbon fibre surface chemistry and morphology and of the resin itself to the overall properties of the composites, untreated, oxidized and sized fibres are used with bi- and tetrafunctional, diglycidylether of Bisphenol A, DGEBA and tetraglycidyl 4,4'-diaminodiphenylmethane, TGDDM-based resins, cured with amine and anhydride hardeners. Adsorption measurements and single fibre contact angle experiments, as well as the pull-out test were applied to characterize the surface of carbon fibre and the interfacial shear strength with different matrices. It was shown that the presence of the size on the surface can drastically affect the wettability as well as the starting rate of the cure reaction of epoxide in the vicinity of the fibre surface, as revealed by FTIR microscopy. Different elastic-plastic behavior of model composites before debonding is found for untreated, oxidized and sized fibres, due to the various interphase structures formed. Both micro-and macromechanical properties of the composites are found to be significantly affected by the matrix properties. The role of the surface treatment of fibers becomes especially important in high performance resin systems.     

Effect of Geometry,Loading and Elastic Moduli on Critical Parameters in a Nanoindentation Test in Polymeric Matrix Composites with a Nonhomogeneous Interphase

Fiber nanoindentation models are developed for polymeric matrix composites with nonhomogeneous interphases. Using design of experiments, the effects of geometry, loading and material parameters on the critical parameters of the indentation test such as the load–displacement curve, the maximum interfacial shear and normal stresses are studied. The sensitivity analysis shows that the initial load–displacement curve is dependent only on the indenter type, and not on parameters such as fiber volume fraction, interphase type, thickness of interphase, and boundary conditions. The interfacial tensile radial stresses are not sensitive to indenter type, or to type and thickness of interphase, while the interfacial compressive radial stresses are sensitive mainly to boundary conditions and thickness of interphase; however, the influence of these factors on the interfacial radial stresses can be large. In contrast, the interfacial shear stress is sensitive to all factors, but the influence of the factors is relatively small.     

The Role of Interfacial Interactions in the Toughening of Precipitated Calcium Carbonate–Polypropylene Nanocomposites

This paper investigates the effect of the interphase properties and the interfacial interactions between matrix and filler on mechanical properties of precipitated calcium carbonate (PCC)–polypropylene nanocomposites. PCC particles were coated with stearic acid (SA). The weight ratio of SA on the particles (w _SA) ranged from 0 to 0.135 g SA/g PCC. The introduction of PCC particles resulted in an increase in stiffness and yield stress compared with the pristine polymeric matrix and, at the same time, it increased the impact resistance. The maximum improvement in the impact behaviour was achieved for the composites with w _SA =0.045 corresponding to the theoretical monolayer ratio. A decrease in interfacial interactions between monolayer coated PCCs and the matrix with respect to the uncoated particles was observed by using a semi-empirical equation developed by Pukànszky. The low degree of interfacial interactions between particulate filler and matrix allows a matrix–particle debonding phenomenon, as shown by scanning electron microscopy analysis. Extensive plastic deformations were evident as well, promoting an improvement in toughness. The thickness of the interphase between particles and matrix was evaluated by using the Shen–Li model which is based on the hypothesis of a non-homogeneous interphase. It results that the thickness increased in the order uncoated < monolayer coated < 3% SA coated ? 13.5% SA coated particles. The thinner and stronger interphase found for the composite with uncoated particles can be explained with the high interaction between matrix and filler and the consequent low mobility of the polymeric chains.     

The microdroplet test: experimental and finite element analysis of the dependance of failure mode on droplet shape

The microdroplet technique is usually designed as a fibre embedded in a drop of resin and subsequently pulled out while the drop is being supported by two knife edges, resulting in either debonding of the droplets from the fibres, or breakage of the fibres before debonding can occur. In this study, the microdroplet technique was performed using a platinum ring with a 40 μm hole instead of the usual two knife edges, giving an axisymmetric geometry, load and stress distribution. Glass/phenolic and glass/polyester composite systems were tested experimentally and subsequent finite element modelling studies were performed to assess the variation of droplet size, and contact angle between the droplet and fibre. It was found that contact angle is of major influence in the proposed failure model. This study characterizes the influence of the contact angle between the droplet and the fibre on the subsequent stress distribution in the microdroplet specimen.     

Physico-chemical characterization of the fibre/matrix interaction in polyethylene fibre/epoxy matrix composites

The interphase in polyethylene fibre/epoxy matrix composites is studied with FT-IR microspectroscopy using a set-up to investigate the matrix as close to the fibre as a few μm or less. It is shown that moisture present on the fibre surface is able to influence the polymerization reaction of the epoxy/anhydride matrix in an irreversible manner. This effect is enhanced for composites from the more hydrophilic polyvinylalcohol fibre. The fibre/matrix interaction in these thermoplastic fibre composites is also studied with DSC through the characterization of the fibre melting. A decreased 'DSC interaction parameter' is found if the composition of the interphase is changed by moisture. For a composite with an epoxy/amine matrix, on the other hand, the DSC interaction parameter is unaffected by moisture from the fibre surface.     

Interphase formation and fiber matrix adhesion in carbon fiber reinforced epoxy resin: influence of carbon fiber surface chemistry

The chemistry and morphology of the carbon fiber surface are important parameters which govern the properties of the interfacial region and the adhesion between carbon fibers and polymeric matrix in carbon fiber reinforced polymers. In the presented paper the surface chemistry of the fibers is varied while the surface morphology is left unchanged. We analyze chemical functionality and morphology of carbon fiber surfaces showing different degrees of activation, together with the adhesion of these fibers to an epoxy matrix and the width of the interfacial region between fiber and matrix. An increase of the oxygen and nitrogen concentration of the fiber surface, in particular in form of carboxyl functional groups, results in a significant increase of interfacial shear strength. Also the width of the interphase, as determined by scanning force microscopy in nanomechanical mode, depends on the activation degree of the carbon fibers. However, no direct correlation between interphase width, surface chemistry and fiber matrix adhesion is found, suggesting no direct influence of interphase width on adhesion properties.     

Fibre-matrix interphases and interfaces in ceramic matrix composites processed by CVI

The fibre-matrix (FM) interfacial zone plays a key role in the mechanical behaviour of Si-C(O)/SiC inverse composites fabricated by chemical vapour infiltration (CVI) from ex-polycarbosilane Si-C(O) fibres precoated with pyrocarbon or boron nitride. It consists not only of the C (or BN) main interphase, but also of very thin secondary interphases (i.e. carbon and silica) resulting from the decomposition of the metastable Si-C(O) fibres thought to occur during the fabrication of the fibres and/or the composites. The FM interfacial zone may play two complementary roles: (i) it provides low-energy microcrack propagation paths parallel to the fibre axis, and (ii) it may act as a compliant buffer for the relaxation of the residual thermal compression stresses on the interface. The FM bond strength is low or moderate when a quasi-continuous thin layer of anisotropic carbon is present between the fibre and the main interphase and when the fibre surface remains smooth. The mechanical behaviour in tension is non-brittle with a wide non-linear stress-strain domain when the FM bonding is low or moderate, and tends to become brittle when the bonding is too strong. Finally, the thickness (and presumably the microtexture) of the carbon main interphase plays an important role in the oxidation resistance of the material, a self-healing behaviour being observed at high temperatures with a thin interphase. Replacing carbon by BN and adding an external coating of SiC (or Si₃N₄) to the composite improves its oxidation resistance.     

An energy criterion for the initiation of interface failure ahead of a matrix crack in brittle matrix composites

The mechanism of interfacial failure occurring as a consequence of the stress concentration induced by a matrix crack located in the vicinity of the interface is analysed. For this purpose, an asymptotic analysis is carried out to assess the competition between the propagation of the matrix crack towards the interface and the nucleation of an interfacial debond. An energetic approach provides a necessary condition comparing the ratio of the interfacial toughness over the matrix toughness to a critical value depending on the elastic mismatch between the fibre and the matrix and the ratio of the interfacial nucleation length over the width of the matrix ligament. Presented results show that the interfacial debonding is enhanced if the matrix is softer than the fibre. Further, a modified condition which does not involve the crack increment ratio is established if the matrix crack lies in the stiffest material.     

Influence of Fibre Taper on the Interfacial Shear Stress in Fibre-Reinforced Composite Materials during Elastic Stress Transfer

The paper is concerned with finite element (FE) analysis of stress transfer from an elastic matrix to an elastic fibre, which need not be a uniform cylinder, in a fibre-reinforced composite material. Axisymmetric models of fibres embedded in co-axial cylindrical matrices were investigated by the FE method. Fibre shapes investigated were cylindrical, ellipsoidal, paraboloidal taper and conical taper. The effects of varying the fibre aspect ratio, q (ranging 200 to 3500) and Young's modulus (relative to that of the matrix), E _f /E _m (ranging 10³ to 10⁶) were investigated. The results show that ellipsoidal and parabolic tapers lead to a similar distribution of interfacial shear stress (τ) to that observed for a uniform cylindrical fibre, except that the magnitude of the stress is higher. For a conical taper (except for q = 200, E _f /E _m = 10⁶), the interfacial stress increases to a maximum between the centre and the end of the fibre and then decreases towards the fibre ends. The effect of fibre taper on the distribution of τvalues is reflected in the axial tensile stress, σ_z , distribution induced in a fibre. For example, for a fibre with a conical taper, the distribution of τ values can lead to an even distribution of σ_z along the length of a fibre.     

A study of damping in fiber-reinforced composites

Damping contributions from the viscoelastic matrix, interphase and the dissipation resulting from damage sites are considered to evaluate composite material damping coefficients in various loading modes. The paper presents the results of the FEM/Strain energy investigations carried out to predict anisotropic-damping matrix comprising of loss factors η₁₁, η₂₂, η₁₂ and η₂₃ considering the dissipation of energy due to fiber and matrix (two phase) and correlate the same with various micromechanical theories. Damping in three phase (i.e., fiber-interphase-matrix) composite is also calculated as an attempt to understand the effect of interphase. The contribution of energy dissipation due to sliding at the fiber-matrix interface is incorporated to evaluate its effect on η₁₁, η₂₂, η₁₂ and η₂₃ in fiber-reinforced composite having damage in the form of hairline debonding. Comparative studies of the various micromechanical theories/models with FEM/Strain energy method for the prediction of damping coefficients have shown consistency when both the effect of variable nature of stress and the fiber interaction is considered. Parametric damping studies for three phase composite have shown that the change in properties of fiber, matrix and interphase leads to a change in the magnitude of effectiveness of interphase, but the manner in which the interphase would affect the various loss factors depends predominately upon whether the hard or soft interphase is chosen. Analysis of the effect of damage on composite damping indicates that it is sensitive to its orientation and type of loading.     

Stress transfer efficiency in model composites under dynamic loading

The micromechanics of tension–tension fatigue loading in model single-fibre composite geometries is investigated in this paper. In an attempt to emulate the conditions encountered in full carbon fibre composites, the fibres were prestrained prior to the curing process to ensure that they were free of high residual compressive stresses as a result of resin shrinkage. The resulting specimens were grouped into two categories depending on the level of the initial fibre prestrain (case A low, case B high). The cyclic load is designed to be well below the endurance fatigue limit of the polymer matrix (∼0.6%), and to have a frequency low enough to avoid unwanted thermal post curing. Throughout the preparation procedure, as well as during fatigue loading, the fibre stress (strain) was constantly monitored by means of laser Raman spectroscopy. The fibre axial stress distributions at each fatigue step were converted to interfacial shear stress (ISS) distributions, from which important parameters such as the maximum ISS the system can accommodate, the transfer length for efficient stress built-up and the length required for the attainment of maximum ISS were obtained. The results showed that, up to 2×10⁶ loading cycles, the main parameters which affected the stress transfer efficiency at the interface were the fibre fracture process itself and the viscoelastic behaviour of the matrix material. Received: 7 November 2001 / Accepted: 22 March 2002 / Published online: 5 July 2002     

Modeling and simulation of mechanical properties of nano-particle filled materials

With the recent advances in nanoscale science and engineering, materials containing reinforcement with superior mechanical properties can be found in many advanced products. The accurate prediction of the mechanical properties of this class of composite materials is important to ensure the reliability of the products. Characterization methods based contact probe such as nano-indentation and scratch tests havebeen developed in recent years to measure the mechanical properties of the new class of nanomaterials. This paper presents a constitutive modeling framework for predicting the mechanical properties of nanoparticle reinforced composite materials. The formulation directly considers the effects of inter-nanoparticle interaction and performs a statistical averaging to the solution of the problem of two-nanoparticle interaction. Final constitutive equations are obtained in analytical closed form with no additional material parameters. The predictions from the proposed constitutive model are compared with experimental measurement from nano-indentation tests. This constitutive model for nanoparticle reinforced composites can be used to determine the volume concentration of the reinforcing nanoparticles in nano-indentation test.