Interface end theory and re-evaluation in interfacial strength test methods

The experimental results of fragmentation, micro-indentation, pull-out and microdebond tests often exhibit large discrepancies. Since all specimens of the four test methods all have interface ends, the singularity theory of the interface end should be used to evaluate the exactness of the test methods. The eigenvalues of the specimens for the micro-indentation test, pull-out test and microdebond test are calculated and investigated. The results show that the stress singularity of the interface end depends on the Dundurs' parameters and the wedge angles. The interfacial shear strength (IFSS) obtained from the tests loses its rationality if the stress is singular at the interface end. In further analysis, for a carbon fiber-epoxy resin composite, it is found that the microdebond test gives the most reliable IFSS results, if the wedge angle of the resin droplet is less than 40°; the results from the pull-out test are dubious, due to the stress singularity at the interface end. In the micro-indentation test, there is a critical matrix stiffness value for a given fiber, above which the stress at the interface end will be non-singular. The fragmentation test assumes the interfacial shear stress on the fiber fragment of critical length is the IFSS. If debonding does not occur at the interface end, then apparently, the interfacial shear stress on the fiber fragment of critical length is less than the true value of IFSS.     

Energy release rate and stress field calculation for debonding crack extension at the fibre-matrix interface during single-fibre pull-out

For the micromechanical modelling of the macroscopic failure of fibre-reinforced composites the formulation of a critical parameter for initiation and extension of debonding cracks at the fibre-matrix interface is essential. This point is discussed for the 'fibre pull-out' specimen, a test commonly used to measure the adhesion quality of fibre-matrix systems. Some of the simplifying assumptions fundamental to shear lag theory-based models of the fibre pull-out test are compared with results from a detailed finite element (FE) model to examine their validity. The FE model strongly contradicts assumptions made with the shear lag theory that the axial stress gradient in the matrix can be neglected from the equilibrium equation. A critical interface shear strength is commonly used as a measure of adhesion quality. But for elastic materials the nature of the stress concentrations at the fibre end and interface crack-tip are singular. Therefore a fracture mechanic approach is better suited for a debonding criterion than a simple finite shear strength. The energy release rate shows a minimum for short crack lengths and may stabilize the moving crack.     

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.     

Relationship between fibre-matrix adhesion and the interfacial shear strength in polymer-based composites

A model is proposed to correlate the interfacial shear strength at the fibre-matrix interface, measured by means of a fragmentation test on single fibre composites, to the reversible work of adhesion between both solids, this quantity being defined as the sum of the dispersive and the acid-base interactions (physical interactions) between the fibre and the matrix. Whatever the nature of the fibres and the matrices, a linear relationship, passing through the origin, is established between the interfacial shear strength and the reversible work of adhesion. However, the slope of this straight line depends on the elastic properties and, more precisely, on the elastic moduli of both the fibre and the matrix. This leads us to express the reversible work of adhesion as the product of a mean intermolecular distance at the interface and an adhesive pressure related to the interfacial shear strength. The limits of the theoretical and experimental approaches leading to the establishment of such a model, as well as its domain of validity, are discussed.     

Measurement of fiber/matrix interface properties of C/C composites by single fiber and fiber bundle push-out methods

Interfacial fracture stresses of carbon/carbon composites were measured by indentation methods. Two types of test methods, namely, single fiber push-out, and bundle fiber push-out tests were conducted. Both methods successfully gave fiber/matrix interface mechanical properties, especially debonding behavior. However, when the interface was strong, the single fiber push-out test encountered technical difficulty in processing the extremely thin specimen required to realize the fiber push out. On the other hand, the bundle fiber push-out test gave a good estimation of interfacial fracture stresses.     

Evaluation of the mechanical properties of PMC interface using slice compression test — Analysis of transfer mechanism of interfacial shear stress

Properties of the fiber/matrix interface in SiO₂/epoxy and SiC/epoxy composite are investigated using the slice compression test (SCT) for the single fiber, where the specimen is loaded and unloaded between a plate which has different mechanical properties. It is found that the interfacial debonding proceeds from the polished surface at a soft plate side and that the fiber protrusion occurs after unloading. The fiber-protrusion length is directly measured at each applied stress level using a scanning electron microscope. Interfacial shear-sliding stress is obtained based on the constant shear-sliding stress analysis employing the obtained protrusion length. It is demonstrated that the value of interfacial shear-sliding stress shows good agreement with that obtained from another technique, the push-out test, on the same system. The relation between the fiber-protrusion length and applied stress is proportional to a certain extent. From this result, it is analytically pointed out that the applied stress has a limiting value in this SCT because of Poisson's effect. Also, two interfacial debonding criteria, which are determined analytically for the PMC, are discussed.     

Application of nano-indentation, nano-scratch and single fibre tests in investigation of interphases in composite materials

Three novel experimental techniques were employed in this work in order to investigate the influence of the interphase region in polymer–glass composites on the bulk material properties: (i) the microdroplet test is a single fibre test designed to characterize the fibre–matrix bond (interface region) and to determine the interfacial shear stress in composite material; (ii) the nano-indentation test, a novel nano-hardness technique with ability to produce an indent as low as a few nanometres was employed in order to measure nano-hardness of the fibre–matrix interphase region; and (iii) the nano-scratch test, used in conjunction with the nano-indentation test for measurement of the interphase region width. The microdroplet test (MDT) has been used to characterize the interfacial bond in fibrous composite materials. The specimen consists of a fibre with a drop of cured resin pulled while the drop is being supported by a platinum disc with a hole. A properly tested specimen fails at the droplet’s tip–fibre interface, revealing the ultimate interfacial shear strength. In this study, finite element analysis (FEA) of the MDT has been focused toward simulation of the fibre–matrix interphase region. The influence of several functional variations of the material properties across the interphase layer on the stress distribution at the droplet’s tip was analysed. The results showed that the variation of the interphase properties significantly affects the stress distribution at the fibre–droplet interface, and, therefore, the stress redistribution to composite material. These results led to further experimental investigation of the interphase region, in order to obtain the material properties essential for the interfacial stress analysis. The interphase region in dry and water aged polymer–glass composite materials was investigated by means of the nano-indentation and the nano-scratch techniques. The nano-indentation test involved indentation as small as 30 nm in depth, produced along a 14 μm path between the fibre and the matrix. The distinct properties of the interphase region were revealed by 2–3 indents in dry materials and up to 15 indents in water aged, degraded materials. These results indicated interdiffusion in water aged interphase regions. The nano-scratch test involves moving a sample while being in contact with a diamond tip. The nano-scratch test, used in conjunction with the nano-indentation test, accurately measured the width of the interphase region. The results showed that the harder interphase region dissolved into the softer interphase region (both regions being harder/stronger than the matrix) expanding its width after aging in water.     

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.     

Apex exponents for polymer-probe interactions

We consider self-avoiding polymers attached to the tip of an impenetrable probe. The scaling exponents gamma(1) and gamma(2), characterizing the number of configurations for the attachment of the polymer by one end, or at its midpoint, vary continuously with the tip's angle. These apex exponents are calculated analytically by epsilon expansion, and numerically by simulations in three dimensions. We find that when the polymer can move through the attachment point, it typically slides to one end; the apex exponents quantify the entropic barrier to threading the eye of the probe.     

A review on the research progress of push-out method in testing interfacial properties of SiC fiber-reinforced titanium matrix composites

Experimental analysis of single-fiber push-out for SiC fiber-reinforced titanium matrix composites (TMCs) is complicated by the incorporation of large thermal residual stresses, strong chemical bond of the fiber/matrix interface and matrix plastic deformation. This paper summarizes the development of push-out test and the characteristics of push-out test for TMCs such as crack initiating at the bottom face and theoretical analysis of the test. Moreover, it deeply analyzes the progresses of interfacial shear strength and fracture toughness, and work focus is pointed out in future.     

Interfacial approach tod-dimensional ±J Ising models in the neighborhood of the ferromagnetic phase boundary

Two- and three-dimensional ±J Ising models in the neighborhood of the ferromagnetic phase (FP) boundary in the concentration-temperature (p-T) plane are studied, investigating the size dependence of interfacial free energies calculated by a transfer matrix method. Thep andT dependences of two stiffness exponents relevant to the FP and the nonferromagnetic ordered phase lead to the following results in two dimensions, giving a unified view. It is confirmed that the random antiphase state (RAS) exists in contact with the vertical FP boundary. Spatial fluctuations are dominant near the vertical boundary, which is separated by the Nishimori line from the remaining FP boundary governed by thermal fluctuations. The RAS is a kind of Mattis spin glass such that it changes to the FP smoothly with nonsingular physical connectivity, but with a percolation singularity of its ferromagnetic part. Universal finite-size critical amplitudes are consistent with them. Results in three dimensions give only suggestions which are similar to the two-dimensional results. These results suggest important insight into spin-glass properties in higher dimensions.     

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.     

In situ observation of interfacial debonding process induced by matrix crack propagation in two-dimensional unidirectional model composites

Interfacial debonding behavior is studied for unidirectional fiber reinforced composites from both experimental and analytical viewpoints. A new type of two-dimensional unidirectional model composite is prepared using 10 boron fibers and transparent epoxy resin with two levels of interfacial strength. In situ observation of the internal mesoscopic fracture process is carried out using the single edge notched specimen under static loading. The matrix crack propagation, the interfacial debonding growth and the interaction between them are directly observed in detail. As a result, the interfacial debonding is clearly accelerated in specimens with weakly bonded fibers in comparison with those with strongly bonded fibers. Secondary, three-dimensional finite element analysis is carried out in order to reproduce the interfacial debonding behavior. The experimentally observed relation between the mesoscopic fracture process and the applied load is given as the boundary condition. We successfully evaluate the mode II interfacial debonding toughness and the effect of interfacial frictional shear stress on the apparent mode II energy release rate separately by employing the present model composite in combination with the finite element analysis. The true mode II interfacial debonding toughness for weaker interface is about 0.4 times as high as that for a stronger interface. The effect of the interfacial frictional shear stress on the apparent mode II energy release rate for the weak interface is about 0.07 times as high as that for the strong interface. The interfacial frictional shear stress and the coefficient of friction for weak interface are calculated as 0.25 and 0.4 times as high as those for strong interface, respectively.     

Polypropylene-natural fibre composites. Analysis of fibre structure modification during compounding and its influence on the final properties

The final properties of composite materials are highly dependent on the residual geometrical parameters (length, diameter, aspect ratio), orientation and distribution of the fibres in the matrix, which in turn are related to the processing conditions. This study analysed the fibre structure variation during the processing of a polypropylene matrix reinforced with cellulose flax pulp for different reinforcement concentrations. The fibre's geometrical parameters, length, diameter and aspect ratio have been measured and their statistical distributions have been assessed for each concentration. Furthermore, the effect of the microstructure variation on the final mechanical properties was analysed. In particular, changes in the interfacial area were evaluated based on the hypothesis that the fibres were cylindrical in shape and considering the average values of the diameters and the lengths calculated using a statistical distribution approach. The fibre interfacial area after the process decreases as the fibre concentration increases and this evaluation explains how the adhesion methods that are used for fibre surface modification fail because of the decrement in the modifier interfacial density. The Halpin–Tsai approach was used to model the experimental data obtained from tensile tests for different composites, so as to confirm the effect of fibre parameters, such as aspect ratio and interfacial area values, in the PP/cellulose blends final properties.     

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.     

Microstructure and mechanical properties of continuous Al2O3 fibre reinforced Ni45Al45Cr7.5Ta2.5 alloy (IP75) matrix composites

Single crystalline Al₂O₃ fibres (sapphire), coated with the NiAl alloy IP75 by physical vapour deposition (PVD), were assembled to fabricate composites by means of diffusion bonding. The microstructure and chemistry of both as-coated fibre and as-diffusion bonded composites were investigated by electron microscopy and microanalysis. The interface shear stress for complete debonding was measured by fibre push-out tests at room temperature, and the composite tensile strength was measured at 900°C and 1100°C. An amorphous layer with a thickness of about 400?nm formed between the fibre and the matrix during the PVD process and was maintained during diffusion bonding. A Laves phase precipitated along NiAl grain boundaries in the IP75 matrix. This caused a lower tensile strength of the IP75/Al₂O₃ composite at high temperatures compared to as-cast monolithic IP75 and rendered the composite useless for structural applications.     

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     

Influence of mesoscale three-phase parameters to the tensile behavior of concrete

In the mesoscopic level, concrete is regarded as three-phase composite material with cement matrix, aggregate, and the interfacial transition zone (ITZ) between them. The mechanical properties of ITZ are regarded weaker than those of the cement matrix and aggregate. In this study, a mesoscale mechanical model based on the interface specimen with a single aggregate is established to study the influence of three-phase parameters on the interface specimen under quasi-static and dynamic direct tensile loading. Besides, the loading rate effect is also considered in this study to further analyze the dynamic performance of ITZ and the whole interface specimen. According to the numerical results, it is indicated that the ITZ properties (elastic modulus and strength) play significant roles in the performance of the interface specimen under quasi-static direct tensile loading. However, the cement matrix is dominant to the mechanical properties of interface specimen under dynamic tensile loading. Moreover, the properties of ITZ (elastic modulus, strength, and DIF values) and the ITZ thickness have some influence on the dynamic performance of ITZ and the whole interface specimen under dynamic tensile loading. In contrast, the Poisson’s ratio and density of ITZ have little influence on the dynamic behavior of the whole interface specimen. Additionally, the aggregate diameter is influential to the time reaching peak stress of ITZ and the whole interface specimen, and the loading rate only influences the time to reach the peak stress of ITZ under dynamic tensile loading.     

Determination of interfacial parameters in fiber-polymer systems from pull-out test data using a bilinear bond law

We propose a new model for characterization of strength properties of fiber-polymer interfaces by means of a single fiber pull-out test. Our model is based on shear-lag analysis using a bilinear bond law (stress–slip relationship) which, in turn, is a simplified representation of the true stress behavior as a function of strain for cold-drawing polymers. According to this law, the fiber-polymer interface is subjected to the following successive processes: (1) linear loading within the elastic region; (2) yielding and subsequent bond strengthening with increasing strain; (3) local debonding and interfacial crack propagation along the interface; (4) post-debonding friction. Both crack propagation and extension of the yielded zone can be stable and unstable, depending on the values of interfacial parameters and the load applied to the free fiber end. The procedure of construction of theoretical force–displacement curves for a pull-out test is described in detail. Theoretical curves exhibit such features as multiple kinks and non-linear regions, whose positions and shape are related to interfacial parameters. By fitting experimental curves with theoretical ones, these parameters can be determined for each separate pull-out specimen. Practical examples are provided for basalt fiber–polypropylene and glass fiber–polypropylene specimens.