Modeling the Effect of a Soft Interlayer on the Stress Distribution around Fibers: Longitudinal and Transverse Loading

A model is presented which describes the effect of a soft interlayer with changing properties on the stress distribution around a fiber embedded into an infinite matrix. Transverse loading induces large deformations in the interlayer compared to the matrix and if the interphase is very soft mainly compressive deformations occur in it. Radial stress decreases considerably in this case and the stress maximum shifts to the surface of the fiber. However, stress concentration depends also on the stiffness of the interphase, increased stress concentrations may develop in the presence of interlayers having only slightly lower stiffness than the matrix. In parallel loading, deformations and shear stresses decrease in the presence of the soft interphase, the entire deformation is concentrated into a very narrow layer. Both shear yielding and debonding can take place in transverse loading, the dominating mechanism depends mainly on the properties of the interlayer. Very soft interlayers promote shear yielding. In parallel loading such interlayers result in low pull‐out forces, load transfer is impossible. Although the presence of a soft interlayer favorably changes stress concentration around the fiber, as expected, it is deleterious for reinforcement and stress transfer. The results clearly explain why soft interlayers are not employed in practice in spite of their apparent advantages.     

Interfacial shear strength studies of nicalon fibers in epoxy matrix using single fiber composite test

Interfacial properties of Nicalon (SiC) fiber in epoxy matrices of varying stiffnesses were studied using the single fiber composite test, in conjunction with stress birefringence patterns. Extensive debonding was observed with hard epoxies, but transverse matrix cracks were found in the more flexible epoxies, with the interface remaining intact. Micromechanical modeling and Monte Carlo simulation of the single fiber composite fragmentation process provided a basis to compute the interfacial shear stress from the final fragmentation length distribution. The interfacial shear stress appeared to decrease moderately with increasing matrix ductility. The large diameter Nicalon fibers create transverse cracks in the single fiber composite specimens made with flexible epoxies. Consequently, there is a high possibility of premature failure of the specimen before fiber break saturation is reached. This poses some difficulty in interpreting the results for flexible epoxies. It was also found that the interfacial shear stress values from the single fiber composite tests were always considerably higher than the ultimate shear stress values obtained from bulk epoxy (without fiber) tension tests. This effect is similar to what was seen earlier for single fiber composite tests based on graphite fibers and similar epoxy blends, though the difference between the two values was not as great.     

The interphasial regions in interlayer fiber composites

The interaction between the fiber and matrix in a fiber-reinforced material plays an important role in determining the mechanical behavior of the composite. An efficient technique to simultaneously improve fiber-matrix interfacial shear strength and impact behavior of the composite is to deposit a flexible interlayer onto the fiber. This results in the creation of three bulk phases, the fiber, matrix, and the interlayer and two interphasial regions. A phenomenological model that defines the variation of the fiber-interlayer interphase and that of the interlayer-matrix interphase has been developed. In the model, the elastic moduli of these regions vary continuously, so as to bridge the two bulk phases on either side of the interphase. The interaction between the bulk phases is also taken into consideration. The model has the potential for the use of dynamic mechanical analysis to obtain, relatively, adhesion/interaction parameters of different fiber-interlayer-matrix systems. These parameters can be used to determine the optimum interlayer thickness for improved toughness and good stress transfer efficiency.     

Multiple Cracking of Unidirectional and Cross-PlyCeramic Matrix Composites

This paper examines the multiple cracking behavior of unidirectional and cross-ply ceramic matrix composites. For unidirectional composites, a model of concentric cylinders with finite crack spacing and debonding length is introduced. Stresses in the fiber and matrix are found and then applied to predict the composite moduli. Using an energy balance method, critical stresses for matrix cracking initiation are predicted. Effects of interfacial shear stress, debonding length and bonding energy on the critical stress are studied. All the three composite systems examined show that the critical stress for the completely debonded case is lower than that for the perfectly bonded case. For cross-ply composites, an extensive study has been made for the transverse cracking in 90° plies and the matrix cracking in 0° plies. One transverse cracking and four matrix cracking modes are studied, and closed-form solutions of the critical stresses are obtained. The results indicate that the case of combined matrix and transverse crackings with associated fiber/matrix interfacial sliding in the 0° plies gives the lowest critical stress for matrix cracking. The theoretical predictions are compared with experimental data of SiC/CAS cross-ply composites; both results demonstrated that an increase in the transverse ply thickness reduces the critical stress for matrix cracking in the longitudinal plies. The effects of fiber volume fraction and fiber modulus on the critical stress have been quantified. Thermal residual stresses are included in the analysis.     

基体中含有随机分布裂纹的纤维增强复合材料的总体弹性常数

本文应用自洽方法计算了含随机分布裂纹的基体的等效弹性常数,然后利用GMC方法计算了复合材料的总体弹性常数.结果表明,随着裂纹密度的增加,基体的等效弹性模量和泊松比会降为零;而同时,复合材料的纤维方向的弹性模量的下降,但是仍然能达到没有裂纹时的90%.这表明当基体完全破坏的时候,纤维仍能够在纵向承受载荷.另外,当基体的等效弹性模量和泊松比会降为零时,复合材料的横向弹性模量和剪切模量都接近为零,表明这时复合材料无法承受横向的拉压力和剪切力.     

Measurement of Fiber/Matrix Interfacial Shear Stress at Elevated Temperatures

An apparatus for measurement of the fiber/matrix interfacial shear stress at temperatures up to 1100° is described. Equipment was used to measure interfacial properties as a function of temperature in two ceramic-matrix composites and one metal-matrix composite. In the composites where the thermal expansion of the matrix was higher than that of the fiber, the interfacial shear stress decreased with temperature. The opposite trend was observed in a system with low matrix thermal expansion. The change of the interfacial shear stress with temperature of all the composites studied can be fully explained by considering the fiber/matrix expansion differences.     

The single fiber pull-out test analysis: influence of a compliant coating on the stresses at bonded interfaces

The mechanical properties at the fiber/matrix interface play a significant role in controlling the fracture resistance of fiber-reinforced composites. By coating the fiber with sizing and coupling agents, these interfacial properties can be modified. The aim of the present analysis was to examine the effects of the coating thickness and modulus on the stresses at the bonded interfaces between the fiber, coating, and matrix. Using the fiber pull-out test as the analytical model, the stresses are first obtained by minimizing the total complementary energy in the coated fiber/matrix composite. The analytical results show that the interfacial shear stress between the fiber and the coating is higher than that between the matrix and the coating. Also, a thin and compliant coating reduces substantially the peak interfacial shear stress but not the interfacial radial stress due to Poisson's effect on the fiber. Furthermore, the shear stress transfer from the fiber to the matrix across the coating layer is found to be more uniform. The implications of these findings are discussed.     

Evaluation of fiber surfaces treatment and sizing on the shear and transverse tensile strengths of carbon fiber-reinforced thermoset and thermoplastic matrix composites

The mechanical performance of advanced composite materials depends to a large extent on the adhesion between the fiber and matrix. This is especially true for maximizing the strength of unidirectional composites in off-axis directions. The materials of interest in this study were PAN-based carbon fibers (XA and A4) used in combination with a thermoset (EPON 828 epoxy) and a thermoplastic (liquid crystal poymer) matrix. The effect of surface treatment and sizing were evaluated by measuring the short-beam shear (SBS) and transverse flexural (TF) tensile strengths of unidirectional composites. Results indicated that fiber surface treatment improves the shear and trasverse tensile strengths for both thermosetting and thermoplastic matrix/carbon fiber-reinforced unidirectional composites. A small additional improvement in strengths was observed as the result of sizing treated fibers for the epoxy composites. Scanning electron microscope photomicrographs were used to determine the location of composite failure, relative to the fiber-matrix interface. Finally, the epoxy composites SBS and TF strengths appear to be limited to the maximum transeverse tensile strength of the epoxy matrix, while the thermoplastic composite SBS and TF strengths are limited by the LCP matrix shear and transverse tensile strengths, respectively.     

Stress profiles around broken fibers in unidirectional composites using influence superimposition technique

The stress transfer from broken to its unbroken adjacent neighboring fibers in unidirectional fibrous composites under a tensile loading applied in the fiber axis is analyzed using a two‐dimensional (2D) shear lag model. The numerical solutions to the governing equations is greatly simplified by the assumptions that the displacements perpendicular to the fiber direction can be ignored, and the axial displacements are uniform over the cross section of any fiber. Using an influence function superimposition technique, closed‐form analytical expressions are used to predict stress profiles in both the fiber and matrix because of any number and arbitrary array of fiber breaks in the presence of matrix shear failure. These are compared to stress concentrations predicted using the finite element analysis (FEA). It is shown that the 2D modeling presented here does generalize the governing equations to include interactions with multiple damage events. The micromechanical model is vital to develop the basic mechanics that are necessary to understand failure behavior of the composite produced by the failure of one or more of its components. POLYM. COMPOS., 2013 © 2013 Society of Plastics Engineers     

Mapping of stress distribution in woven‐fabric composites

Mapping of the stress distribution in composite materials, both at the fiber/matrix interface and in the composite constituents, is important to understand the material mechanical response. Stress mapping can help predict composite behavior under certain stresses especially failure or delamination. In this work, two analytical models were proposed to map the stress distribution at fiber, matrix and fiber/matrix interface utilizing the concept of stress superposition. The first model dealt with the fiber in the longitudinal direction considering axisymmetric conditions. The second model addressed the fiber stress distribution in the transverse direction. Experimental data from four‐point flexural tests of woven fabric composites was processed using the Graphical Integrated Numerical Analysis (pcGINA) to obtain the maximum stress in the target laminate and this value was used as the input for the two analytical models. The value for the maximum interfacial shear stress was calculated using the models and results were compared to pull‐out fiber test values obtained from literature. Good agreement was observed between the model calculations and the literature data. POLYM. COMPOS., 2008. © 2008 Society of Plastics Engineers     

An investigation into failure and behaviour of GFRP pultrusion joints

The paper investigates the failure and behaviour of metal/composite double lap shear (DLS) joints where the composite is the inner/loaded adherend, using multi-scale modelling techniques. The unidirectional (UD) composite is based on glass fibre and vinyl ester resin moulded by pultrusion. The multi-scale models include a long overlap DLS joint (macro), small shear and tensile laminate joints (meso) and fibre–matrix resin models (micro). The macro- and meso-scale joints/models were mechanically tested and numerically analysed to determine failure loads and corresponding stresses and to identify the loci of failure within the joint interfaces. In addition, the numerical modelling was extended to include micro-scale models to determine transverse tensile stresses at the fibre–matrix interface to further understand failure and behaviour. The study concluded that the failure in the bonded composite is largely governed by the maximum transverse strength at the fibre–matrix interface and its defects. Also, it was concluded that this stress might be suppressed by the longitudinal tensile stress acting on the UD composite at the surface just below the bondline.     

Elastic Properties of Laminated Calcium Aluminosilicate/Silicon Carbide Composites Determined by Resonant Ultrasound Spectroscopy

The elastic properties of unidirectional and 0°/90° crossply Nicalon-SiC-fiber-reinforced calcium aluminosilicate (CAS/SiC) ceramic-matrix composites have been measured using a resonant ultrasound spectroscopy (RUS) technique. This approach has allowed the nondestructive determination of the complete set of independent second-order elastic stiffness constants of these ceramic composites. These stiffness data have been used to obtain the orientation dependence of Young's modulus and the shear modulus. The results are in reasonably good agreement with the limited experimental data obtained from mechanical testing. The RUS measurements reveal that the unidirectional CAS/SiC composite is well modeled by transverse isotropic symmetry, indicating relatively isotropic fiber spacing in the transverse plane. The analysis indicates that the overall elastic anisotropy is also small for unidirectional and 0°/90° laminated CAS ceramic-matrix composites, a result that can be attributed to the relatively low modulus ratio of the Nicalon SiC fiber to the CAS matrix and to the moderate fiber volume fraction.     

先进树脂基复合材料高压微波固化工艺实验研究

先进树脂基复合材料在航空航天领域应用广泛,采用高效率、低能耗的微波固化工艺以获得令人满意的固化质量的构件,已逐渐引起学者们的关注。将高压引入树脂基复合材料的固化过程中,通过缺陷分析、显微金相、力学性能检测等手段,对先进树脂基复合材料的高压微波固化质量进行实验研究。结果表明,高压微波固化能有效实现树脂基复合材料的固化,与传统热压罐工艺相比,高压微波固化工艺可获得低孔隙、少缺陷、纤维/树脂界面结合较好的固化质量,拉伸强度提高4.82%,层间剪切强度提高10.32%。研究结果为复合材料高压微波固化技术的推广与应用提供了实验数据支撑。     

Mechanical Properties of Two Plain-Woven Chemical Vapor Infiltrated Silicon Carbide-Matrix Composites

The elastic and inelastic properties of a chemical vapor infiltrated (CVI) SiC matrix reinforced with either plain-woven carbon fibers (C/SiC) or SiC fibers (SiC/SiC) have been investigated. It has been investigated whether the mechanics of a plain weave can be described using the theory of a cross-ply laminate, because it enables a simple mechanics approach to the nonlinear mechanical behavior. The influences of interphase, fiber anisotropy, and porosity are included. The approach results in a reduction of the composite system to a fiber/matrix system with an interface. The tensile behavior is described by five damage stages. C/SiC can be modeled using one damage stage and a constant damage parameter. The tensile behavior of SiC/SiC undergoes four damage stages. Stiffness reduction due to transverse cracks in the transverse bundles is very different from cross-ply behavior. Compressive failure is initiated by interlaminar cracks between the fiber bundles. The crack path is dictated by the bundle waviness. For SiC/SiC, the compressive behavior is mostly linear to failure. C/SiC exhibits initial nonlinear behavior because of residual crack openings. Above the point where the cracks close, the compressive behavior is linear. Global compressive failure is characterized by a major crack oriented at a certain angle to the axial loading. In shear, the matrix cracks orientate in the principal tensile stress direction (i.e., 45° to the fiber direction) with very high crack densities before failure, but only SiC/SiC shows significant degradation in shear modulus. Hysteresis is observed during unloading/reloading sequences and increasing permanent strain.     

Micromechanics prediction of the transverse tensilc strength of carobn fiber/epoxy composites: The influence of the matrix and interface

Currently, there is great interest in understanding and improving the bond between the fibers and matrix in high performcance composite materials. In many recently developed systems, fiber surface treatments have been developed to improve poor bonding. These treatments are often evaluated by measureing their effect on a composite property sensitive to the interfacial bond strength, typically the composite shear strength. This paper presents an evaluation of the influence of the matrix and interface properties on the transverse tensile strength. These effects were quantified by compring transverse flexural experimental data with results from a finite element micromechanics model. The results indicate that the transverse tensile strength is significantly more dependent upon sizing than is the shear strength. Finally, the transvere flexure test appears to provide an additional and complementary test for evaluating interface bond characteristics.     

Micromechanical analysis of the kink‐band performance at the interface of a thermoplastic composite under tensile deformation

The manufacture of thermoplastic composites normally involves compression molding that generates fiber dislocations known as kink‐bands, which create stress concentrations able to cause the premature compression failure of a composite; nevertheless, the kink‐band influence over the interfacial performance or failure of a composite tested under tension is not fully understood. This work uses Raman spectroscopy as a tool to map the axial stress distribution around a kink‐band in an aramid/low density polyethylene single fiber composite. The stress distribution along the fiber was fitted to a generalized shear‐lag model to calculate the interfacial shear stress; its maximum was found around the kink‐band where the fiber interface was still bonded to the matrix, defining a localized stress concentration. POLYM. COMPOS., 31:1817–1817, 2010. © 2010 Society of Plastics Engineers.     

Influence of fiber wettability on the interfacial adhesion of continuous fiber‐reinforced PPESK composite

Interfacial adhesion between fiber and matrix has a strong influence on composite mechanical performance: better interfacial adhesion can enhance composite transverse properties, flexural properties, and interlaminar shear strength, and so on. To exploit the reinforcement potential of the fibers in advanced composite, it is necessary to reach a deeper understanding on the relation between fiber wettability and interfacial adhesion. In our experiment, we study the influence of fiber wettability on interfacial properties of fiber/PPESK composites by choosing three kinds of fibers with different wettabilities. The relation between fiber wettability and surface free energy was discussed, and the influence of fiber wettability on the interfacial property of fiber/PPESK composites was analyzed. Results indicate that higher surface free energy can enhance the wettability between fiber and matrix, and the humid resistance and interfacial adhesion can be improved at the same time. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 2544–2551, 2006     

含脱粘界面纤维增强复合材料应力传递的理论分析

取具有脱粘界面的连续纤维增强复合材料的特征体积单元为研究对象,在常规剪滞模型的基础上通过引入摩擦力概念,并考虑横向泊松效应及基体径向力作用的影响,得到了纤维、基体的轴向应力及界面剪应力沿纤维方向的解析表达式。结果表明:本文所用的改进剪滞模型能较准确地反映各相介质沿纤维方向的应力分布特征,特别是较清晰地描述了脱粘界面的应力渐变以及界面粘结与脱粘临界处出现的界面剪应力跳跃现象,取得了与有限元解较为一致的结果。     

Computer simulation of the damage evolution of fiber‐reinforced polypropylene‐matrix composites with matrix defects

The damage evolution of fiber‐reinforced polypropylene‐matrix composites with matrix defects was studied via a Monte Carlo technique combined with a finite element method. A finite element model was constructed to predict the effects of various matrix defect shapes on the stress distributions. The results indicated that a small matrix defect had almost no effect on fiber stress distributions other than interfacial shear stress distributions. Then, a finite element model with a statistical distribution of the fiber strength was constructed to investigate the influences of the spatial distribution and the volume fraction of matrix defects on composite failure. The results showed that it was accurate to use the shear‐lag models and Green's function methods to predict the tensile strength of composites even though the axial stresses in the matrix were neglected. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 64–71, 2007     

Analysis of a pull-out test with real specimen geometry. Part II: the effect of meniscus

This paper continues our study on the platelet model of the pull-out specimen, in which the matrix droplet shape is approximated by a set of thin parallel disks with the diameters varying along the embedded fiber. Using this model, the fiber tensile stress and the interfacial shear stress profiles were calculated for real-shaped matrix droplets, including menisci (wetting cones) on the fibers, taking into account residual thermal stresses and interfacial friction. Then, these profiles were used to numerically simulate the processes of crack initiation and propagation in the pull-out test and to obtain theoretical force-displacement curves for specimens with different embedded lengths and wetting cone angles. Our simulations showed that the interfacial crack in real-shaped droplets initiated at very small (practically zero) force applied to the fiber, in contrast to the popular ‘equivalent cylinder’ approximation. As a result, the equivalent cylinder approach underestimated the interfacial shear strength (IFSS) value determined from the pull-out test and at the same time overestimated the interfacial frictional stress; the smaller was the wetting cone angle, the greater the difference. We also investigated the effects of the embedded fiber length and interfacial frictional stress in debonded areas on the calculated IFSS. The simulated force–displacement curves for the real-shaped droplets showed better agreement with experimental curves than those plotted using the equivalent cylinder approach.