Reduction of the stress concentration factor in a homogeneous panel with hole by using a functionally graded layer

This work aims at understanding the effect of a radially heterogeneous layer around the hole in a homogeneous plate on the stress concentration factor. The problem concerns a single hole in a plate under different far-field in-plane loading conditions. By assuming a radial power law variation of Young’s modulus and constant value for Poisson’s ratio, the governing differential equations for plane stress conditions, and general in-plane loading conditions are studied. The elastic solutions are obtained in closed form and, in order to describe localized interface damage between the ring and the plate, two different interface conditions (perfectly bonded and frictionless contact) are studied. The formulae for the stress concentration factors are explicitly given for uniaxial, biaxial and shear in-plane loading conditions and comparisons with interface hoop stress values are performed. The solutions are investigated to understand the role played by the geometric and graded constitutive parameters. The results are validated with numerical finite element simulations in which some simplified hypotheses assumed in the analytical model, are relaxed to explore the range of validity of the elastic solution presented. In this way the results obtained are useful in tailoring the parameters for specific applications.     

Interface characteristics of carbon nanotube reinforced polymer composites using an advanced pull-out model

An advanced pull-out model is presented to obtain the interface characteristics of carbon nanotube (CNT) in polymer composite. Since, a part of the CNT/matrix interface near the crack tip is considered to be debonded, there must present adhesive van der Waals (vdW) interaction which is generally presented in the form of Lennard-Jones potential. A separate analytical model is also proposed to account normal cohesive stress caused by the vdW interaction along the debonded CNT/polymer interface. Analytical solutions for axial and interfacial shear stress components are derived in closed form. The analytical result shows that contribution of vdW interaction is very significant and also enhances stress transfer potential of CNT in polymer composite. Parametric studies are also conducted to obtain the influence of key composite factors on bonded and debonded interface. The result reveals that the parameter dependency of interfacial stress transfer is significantly higher in the perfectly bonded interface than that of the debonded interface.     

On steady-state fibre pull-outII Computer simulation

On the basis of Part I of this paper (Zhang X, Liu, H-Y, Mai Y-W, Diaox X. On steady-state fibre pull-out Part I: stress field. Composites Science and Technology, 1999;59:2179–89) we present an extended analysis for the single-fibre pull-out process. The solutions of fibre axial stress, fibre displacement, and applied pull-out stress versus fibre displacement are obtained for the whole pull-out process. As distinct from previous work (Gao Y-C, Mai Y-W, Cottrell B. Fracture of fibre-reinforced materials. ZAMP 1988;39:550–72; Hutchinson JW, Jensen HN. Model of fibre debonding and pull-out in brittle composites with friction. Mechanics of Materials 1990;9:139–63; Hsueh C-H. Interfacial debonding and fibre pull-out stresses of fibre-reinforced composites. Materials Science and Engineering 1990;A123:1–11), a local shear strain criterion, in which the critical shear strain depends on the pull-out rate, is adopted as a more realistic interface debonding criterion. Load/displacement curves of the fibre pull-out process, which includes elastic deformation with a fully bonded interface, elastic deformation with a partially debonded interface and elastic deformation plus frictional sliding with a fully debonded interface, are obtained by computer simulations. The effects of fibre pull-out rate, thermal residual stress, friction coefficient and fibre volume fraction are also discussed.     

An improved analysis for axisymmetric stress distributions in the single fibre pull-out test

Elastic stress transfer in the fibre pull-out problem has been investigated quite extensively using various shear lag analyses. These analyses grossly underestimate the severity of the stress concentration at the fibre-matrix interface. In this study, by using the total complementary energy approach, it is found that a stress concentration zone exists at the interface near the fibre entry. Compared to shear lag analysis, the interfacial radial stress at the fibre entry is found to be much higher and the interfacial shear stress reaches a maximum not at the entry end of the fibre but in a few fibre diameters from it. It is also shown that the magnitudes of these stress peaks reduce with increasing b/a and L/a ratios. At large b/a and L/a ratios, the maximum radial and shear stresses at the interface reach a plateau and are independent of the loading methods considered. Finally, the implications of these stress concentrations on the failure of the matrix and interface and the specimen geometry in determining the interfacial shear strength are discussed. This revised version was published online in November 2006 with corrections to the Cover Date.     

Fracture mechanics approach for a partially debonded cylindrical fibre

The mechanical behaviour of the fibre-reinforced composites depends on the properties of the matrix, the fibres and their reciprocal bonding. Degrading effects occurring in such materials under service – such as matrix–fibre detaching (debonding), fibre breaking, matrix cracking – must be taken into account in the safety assessments. In the present paper, the fibre–matrix debonding phenomenon at the fibre–matrix interface is examined through fracture mechanics concepts, since a geometric discontinuity arises at the edge of the debonded zone (between two dissimilar materials) producing a stress singularity. The mixed mode stress-intensity factors are determined, and the effects of the geometrical and mechanical parameters related to matrix and fibres are discussed.     

Monitoring the micromechanics of reinforcement in carbon fibre/epoxy resin systems

The technique of laser Raman spectroscopy (LRS) was employed to obtain the interfacial shear stress (ISS) distribution along a short high-modulus carbon fibre embedded in epoxy resin at different levels of applied stress. Up to 0.6% applied strain, the ISS reached a maximum at the bonded fibre ends and decayed to zero at the middle of the fibre. At higher applied strains, the maximum value of the ISS distribution shifted away from the fibre ends towards the middle of the fibre. At the point of fibre fracture, fibre/matrix debonding was found to initiate at the fibre breaks. Further increase of applied strain resulted also in debonding initiation at the fibre ends. Current analytical stress-transfer models are reviewed in the light of the experimental data.     

Stress transfer in the fibre fragmentation test

An improved micromechanics model has been developed of the stress transfer for a single fibre embedded in a matrix subjected to uniaxial loading. Debond crack growth is analysed based on the shear strength criterion such that when the interfacial shear stress reaches the shear bond strength, debonding occurs; and the average strength concept based on Weibull statistics is considered for fibre fragmentation. The influences of the interfacial shear bond strength and the fibre strength on the stress distributions in the composite constituents are evaluated. Depending on the relative magnitudes of these two strength parameters and given the elastic constants and geometric factors, three distinct conditions of the fibre-matrix interface are properly identified which include full bonding, partial debonding and full frictional bonding. Also quantified are the necessary criteria which must be satisfied in order for each interface condition to be valid. Finally, the mean fibre fragment length is predicted as a function of applied strain using a model composite of carbon fibre-epoxy matrix. The parametric study suggests that the critical transfer length predicted when the applied strain (or stress) required for further fibre fragmentation approaches infinity, can be regarded as a material constant, which is the sum of the bonded and the debonded lengths for the model composite.     

Stress transfer in the fibre fragmentation test: Part III Effects of interface debonding and matrix yielding

The micromechanics of stress transfer is presented for the fibre fragmentation test of microcomposites containing debonded fibre–matrix interface and yielded matrix at the interface region. Results from the parametric study are discussed for carbon fibre composites containing epoxy and polyetheretherketone (PEEK) matrices, representing respectively typical brittle debonding and matrix yielding behaviour at the interface region. The stress transfer phenomena are characterized for the two interface failure processes. The sequence of interface failure and fibre fracture as a function of applied stress are also identified. Maximum debonded and yielded interface lengths are obtained above which a fibre will fracture into smaller lengths. There are also threshold fibre fragment lengths above which fibre will fracture without interface debonding or matrix yielding. The applied stresses for these conditions are governed by three strength properties of the composite constituents, namely interface shear bond strength, matrix shear yield strength and fibre tensile strength for given elastic constants of the fibre and matrix, and the geometric factors of the microcomposite. The ineffective length, a measure of the efficiency of stress transfer across the fibre–matrix interface, is shown to strongly depend on the extent to which these failure mechanisms take place at the interface region. This revised version was published online in November 2006 with corrections to the Cover Date.     

Analytical analyses of stress transfer in fibre-reinforced composites with bonded and debonded fibre ends

The elastic stress transfer from the matrix to the fibre is analysed analytically for fibre-reinforced composites when the loading direction is parallel to the fibre axis. The fibres with bonded lateral interfaces and (1) debonded and (2) bonded ends are considered in the present study. For the case of debonded ends, the present solutions contain refinements of the previously derived analytical solutions. For the case of bonded ends, unlike the numerical solutions derived previously, the present analytical solutions are ready to be used for further analyses. The results show that the stress transfer is more effective when the fibre has higher Young's modulus or longer length. Also, compared to the debonded ends case, the stress transfer is more effective and the stress distribution is more uniform when the ends are bonded to the matrix.     

Comparison of elastic interaction of a dislocation and a crack for four bonding conditions of the crack plane

A comparison of elastic interaction of a dislocation and a crack for four bonding conditions of the crack plane was made. Four cases of single crystalline material, sliding grain boundary, perfectly bonded interface, and sliding interface were considered. The stress intensity factors arising from edge and screw dislocations and their image forces for the above four cases were compared. The stress intensity factor at a crack tip along the perfectly bonded interface arising from screw dislocation can be obtained from that in a single crystalline material if the shear modulus in the single crystalline material is replaced by the harmonic mean of both shear moduli in the bimaterial. The stress intensity factor at a crack tip along the sliding interface arising from edge dislocation in the bimaterial can be obtained from that along the sliding grain boundary in the single material if the μ/(1−ν) in the single material is substituted by the harmonic mean of μ/(1− ν) in the bimaterial where μ and ν are the shear modulus and Poisson's ratio, respectively. The solutions of screw dislocation near a crack along the sliding grain boundary and sliding interface are the same as that of screw dislocation and its mirror image. Generally, the effect of edge dislocation for perfectly bonded interface on the crack propagation is more pronounced than that for the sliding interface. The effect of edge dislocation on the crack propagation is mixed mode for the cases of perfectly bonded interface and single crystalline material, but mode I fracture for the cases of sliding interface and sliding grain boundary. All curves of Fx versus distance r from the dislocation at interface to the right-hand crack tip are similar to one another regardless of dislocation source for both sliding interface and perfectly bonded interface. The level of Fx for m=0 is larger than that for m=−1. This revised version was published online in August 2006 with corrections to the Cover Date.     

An Approach to Estimate Interface Shear Stress of Ceramic Matrix Composites from Hysteresis Loops

An approach to estimate interface shear stress of ceramic matrix composites during fatigue loading has been developed in this paper. By adopting a shear-lag model which includes the matrix shear deformation in the bonded region and friction in the debonded region, the matrix crack space and interface debonding length are obtained by matrix statistical cracking model and fracture mechanics interface debonding criterion. Based on the damage mechanisms of fiber sliding relative to matrix in the interface debonded region upon unloading and subsequent reloading, the unloading counter slip length and reloading new slip length are determined by the fracture mechanics method. The hysteresis loops of four different cases have been derived. The hysteresis loss energy for the strain energy lost per volume during corresponding cycle is formulated in terms of interface shear stress. By comparing the experimental hysteresis loss energy with computational values, the interface shear stress corresponding to different cycles can then be derived. The theoretical results have been compared with experimental data of three different ceramic composites.     

Mechanical Characterisation of Interface for Steel/Polymer Composite Using Pull-out Test： Shear-Lag and Frictional Analysis

Fibre-matrix interface is known to have contribution to the mechanical performance of fibre-reinforced composite by its potential for load transfer between the fibre and the matrix. Such load transfer is of great importance in dentistry when a post is used for fixing a ceramic crown on the tooth. In this study, a pull-out test was carried out to analyse the interfacial properties of a steel fibre embedded in a polyester and epoxy matrices. It was found that the fibre-matrix interface is debonded on the whole embedded length when the fibre stress reached the debonding stress. Then, the fibre stress fell down to the initial extraction stress required to pulling out the debonded fibre from the matrix. Both debonding stress and initial extraction stress initiated a linear increase with the implantation length after the debonding stress reached horizontal asymptotes. To analyse the fibre-matrix load transfer before debonding, an analytical shear-lag model was adopted to in this test conditions. Fitting the experimental results with the analytical model provided the interfacial shear strength. By considering the Coulomb friction at the fibre-matrix interface during the fibre extraction process, an analytical model which considers Poisson＇s effects on both fibre and matrix, was developed. In this model, knowledge of the initial extraction stress of the fibre provides the residual normal stress at the fibre-matrix interface.     

Interfacial shear stress distribution in model composites: the effect of fibre modulus

The micromechanics of reinforcement have been investigated for a continuous intermediate-modulus (IM) carbon fibre embedded in an epoxy resin (MY-750). The embedded single-fibre (fragmentation) geometry was employed as the loading configuration. A laser Raman spectroscopic method was used to obtain the fibre strain distribution along the embedded fibre fragments, at various levels of applied strain. The interfacial shear stress distribution along the fibre was derived through a balance of forces analysis.A number of parameters, such as the maximum interfacial shear stress at each level of applied strain and the fibre debonded length, were evaluated. The maximum interfacial shear stress of the IM fibre system was found to increase by 80%, compared with the high-modulus fibre system examined previously, while the distance from the fibre end where the interfacial shear stress maximizes was significantly shorter. The debonded length was found to increase only marginally up to an applied strain of 1.8%, followed by a dramatic rate of increase between 1.8% and 2.5% of applied strain.     

Analysis of a modified microbond test for the measurement of interfacial shear strength of an aqueous-based adhesive and a polyamide fibre

The microbond test was used to measure the interfacial shear strength (IFSS) between a polyamide fibre and a water-based polyurethane. Due to the low viscosity of the water based polyurethane, the droplet could not be formed using a conventional preparation method. A disc shaped microbond droplet forms when an aqueous-based colloidal polymer adhesive was deposited onto the pin hole in a mounting card with a vertical polyamide fibre in the middle after drying and curing at an elevated temperature. Since the droplets were formed with a disc shape, which differs from the conventional ellipsoid, a finite element analysis of the stress distribution at the interface for these contrastingly shaped droplets were calculated and compared. The stress analysis showed that the interfacial shear stress profiles were well matched for both providing confidence that the disc-shaped droplets could be used for interfacial analysis. The microbond test using a disc-shaped droplet was used to study the influences of silane treatment and plasma treatment on the interfacial shear strength between a polyamide fibre and an aqueous deposited polyurethane. The interfacial shear strength of the fibre after plasma treatment was 10.3 MPa, much higher than that of the control and the silanised fibres, 5.2 MPa and 5.4 MPa respectively. The results showed that the microbond test could be used to investigate the interfacial properties of the polyamide fibre and water-based polymer adhesive.     

The single-filament-composite test: a new statistical theory for estimating the interfacial shear strength and Weibull parameters for fiber strength

For over two decades the single-filament-composite (SFC) test has been an important tool in the study of the failure of fibrous composites. The SFC test itself involves a single brittle fiber embedded along the center-line of a matrix specimen of both large cross-sectional area and strain to failure. With increasing strain, the fiber fractures progressively, breaking into an increasing number of shorter and shorter fragments. Surrounding each break a shielded or exclusion zone develops within which no further breaks typically occur. At some strain level ‘saturation’ occurs abruptly as the shielded zones finally occupy the whole fiber, thus leaving a final distribution of fiber fragments end-to-end. Two uses for the SFC test have emerged: one has been to estimate the interfacial shear stress, τ, in the exclusion zone, sometimes called the interfacial shear strength and usually idealized as a constant over this zone. The other has been to estimate the fiber strength distribution and in particular the Weibull shape and scale parameters, ρ and σ_l, for fiber strength appropriate to some characteristic ‘gage’ length, l, such as the mean fragmentation length. In the past, theoretical bases for these estimates have handled the statistics of shielding in ways that have led to quite large biases. The purpose of the present paper is to use some recent theoretical advances to develop more sophisticated estimation procedures for τ and the Weibull fiber strength parameters ‘ in situ’, and thus to eliminate various errors in previous methods. Straightforward computer programs (written in release 3 of Maple), which calculate the various quantities in the paper, will be provided by the first or second author on request.     

Elastic compliance of a partially debonded circular inhomogeneity

In the present work, we predict contribution of a partially debonded circular inhomogeneity into the material overall elastic compliance. Debonding at the matrix/inclusion boundary is modeled as interfacial arc cracks. The change in the elastic compliance caused by interface cracking is estimated through the accompanying energy change that is related to the mode I and mode II stress intensity factors at the crack tips. The sum of the crack compliance and the inhomogeneity compliance (with perfect bonding) gives the total compliance of the debonded inhomogeneity. The latter is obtained in terms of the material properties and crack length. Additional analysis shows that the replacement of an interface crack with a crack in a homogenized medium is an inadequate approach when seeking approximate solutions. The paper also provides guidelines how to determine properties of a fictitious perfectly bonded orthotropic inhomogeneity that has the same contribution into the material compliance as the debonded isotropic one. This problem is of practical importance when modeling damage accumulation in composite materials by means of homogenization schemes.     

Pull-out of a ductile fibre from a brittle matrix

Pull-out of a ductile fibre from a brittle matrix has been analysed using a shear lag model. Debonding at the fibre-matrix interface and yielding of the fibre occurred during the pull-out process. Both Poisson's contraction of the fibre and Coulomb friction of the debonded interface were considered. The debond length, which consists of an elastic zone length and a plastic zone length, was also analysed. When the fibre has a finite embedded length, it was found that necking prior to full pull-out of the fibre was required to optimize the toughening of a brittle matrix due to plastic deformation of the fibres. The essential material properties to achieve this are addressed.     

超高分子量聚乙烯架桥纤维与裂缝的交互微观力学

使用拉曼光谱研究了架桥纤维与裂缝微观力学,以超高分子量聚乙烯(UHMWPE)纤维为例,将纤维搭桥试样进行微拉伸试验,着重分析架桥纤维的止裂作用和架桥纤维/环氧树脂界面的应力分布,并对不同位置架桥试样的裂缝扩展速度和应力分布进行分析,并进一步运用剪切滞后模型,对架桥纤维在不同拉伸载荷下的应力分布进行了拟合分析,结果表明:架桥纤维能够分散部分外载应力,对于裂纹扩展具有显著的止裂作用。在低于UHMWPE纤维最大应变拉伸时,发现在裂缝中心位置处架桥纤维所承受的应力最大,其应力不超过2GPa,而基体树脂的应力可达到12GPa,架桥纤维/基体界面的应力传递达不到100%。以UHMWPE为架桥的应力传递模型呈"正抛物线"型,应力分布存在于粘结区、脱粘区和架桥区。     

Deformation micromechanics in model carbon fibre-reinforced composites

Raman spectroscopy has been used to study the deformation micromechanics of the single-fibre pull-out test for a carbon fibre/epoxy resin system using surface-treated and untreated versions of the same type of PAN-based fibre. It has been possible to determine the detailed strain distribution along embedded fibres and it has been found that it varies with the level of strain in the fibre outside the resin block. The variation of interfacial shear stress along the fibre/matrix interface has been determined using the balance of forces equilibrium and this has been compared with the single values of interfacial shear strength determined from conventional pull-out analyses. It has been demonstrated that it is possible to identify situations where the interface is well-bonded, partially debonded or fully debonded and also to follow the failure mechanisms in detail. It has been found that the level of interfacial adhesion is better for the surface-treated fibre and that, for the untreated fibre, interfacial failure takes place by the cohesive failure of a weakly-bonded surface skin that appears to be removed by the surface pretreatment process.     

Modelling of the bond behaviour of tuff elements externally bonded with FRP sheets

The performance of fibre reinforced plastic (FRP) materials used for external strengthening depends strongly on the bond behaviour at the FRP-substrate interface. In this paper, the results of an analytical model and of two Finite Element (FE) models (bi-and three-dimensional) for simulating bond behaviour in FRP-strengthened masonry elements using zero-thickness interface elements are presented. The primary parameters of bilinear and nonlinear bond-slip laws were determined from experimental results of single shear bond tests that the authors conducted on masonry blocks of yellow tuff bonded with FRP carbon and glass fabrics. Several parametric analyses were conducted to estimate the effect of the primary bond law parameters on the global behaviour of the specimens and to determine the effective bonded length for the investigated masonry support.