Fiber-end deformation effects in enlarged-end, fiber-reinforced composites

Composite materials reinforced by fibers with enlarged ends are known to have significantly better strength and toughness than those reinforced by flat-end fibers. The objective of this study is to develop an analytical model to determine the importance of deformation of the enlarged end on the reinforcement performance of ellipsoidal enlarged-end fibers. The resisting pullout load of the fiber is composed of a component due to interfacial bond at the fiber/matrix interface and a component due to mechanical anchorage at the embedded enlarged end of the fiber. The component due to mechanical anchorage at the enlarged end is due to both mechanical interlock and deformation of the enlarged end. In the past, little has been done to account for the deformation of the enlarged end. To account for this component of the mechanical anchorage resistance at the embedded enlarged end, a spring component is introduced to connect the embedded fiber with the enlarged ellipsoid. Analytical solutions were derived to predict the effects of the rigid enlarged end shape on the pullout load and stress distribution. These solutions were then compared to finite element solutions. It is shown that the shape of enlarged end has a significant influence on the stress distribution of the short fiber. Specially, the model demonstrates that the enlarged ends deform significantly for some shapes and are not effective for long fibers.     

Analytical modeling of the bond–slip relationship at FRP-concrete interfaces for adhesively-bonded joints

The bond–slip relationship is essential to the study of the macro mechanical properties of composite materials and structures. An analytical model is developed in this work to derive the bond–slip relationship at the reinforcement-substrate concrete interface (joint) for externally bonded reinforcement. The model is applicable to both long joints (infinite bond length) and short joints. When the bond length approaches infinity, the model reverts to a well-known existing analytical model. A bond–slip relationship for short joints with a limited bond length is derived for the first time. It is concluded from the modeling that the existing model for long joints is not applicable to short joints that have a bond length that is less than the effective bond length, or at locations in long joints that are closer than the effective bond length to the free end of the reinforcement.     

环境温差下FRP-混凝土界面粘结行为分析

为明确环境温差对纤维增强聚合物(FRP)加固混凝土构件的界面粘结性能的影响,基于粘结界面的双参数内聚力指数模型,建立了FRP-混凝土粘结结点在温差作用下的界面微分平衡方程,采用边界条件叠加的方法,解析推导了界面相对滑移、界面剪应力和FRP应力-应变分布计算公式。基于解析理论模型,提出了FRP-混凝土界面最大承载温差的计算方法,分析了粘结长度、温差变化和粘结层数对界面粘结性能的影响。结果表明:该文推导出的理论公式计算结果与界面试验结果吻合良好,建立的解析理论模型能够较好地预测温差作用下FRP-混凝土界面粘结行为;界面最大承载温差随粘结长度的增加存在上限值,且由于界面粘结性能的退化,FRP温度应力的最大值出现在达到界面最大承载温差之前;界面剪应力集中在粘结端部区域,受温差变化和FRP粘结层数影响较大,且当环境温差进入胶黏剂玻璃化转变区域后影响最为明显。该结论可用于强日照和高温车间等大温差环境下桥梁和建筑加固构件的温度应力分析和界面承载力评估。     

Interface characteristics and mechanical properties of carbon fibre reinforced copper composites

Interface characteristics of carbon fibre reinforced copper matrix composites materials with various interface states and their effect on the flexural strength of composites have been studied. Interfacial states are mechanical bonding, dissolution bonding and reaction bonding. To a certain extent, raising the interfacial strength enables an increase in the flexural strength due to prevention of carbon fibre being pulled out under low stress during fracture process of composites. Raising the interfacial bondage strength, causes the brittleness of composites to increase; the fracture surface of composites is converted from a fibre pull-out model to a fibre even model. While strengthening the interface bondage, the extent of chemical reaction and dissolution at the interface must be controlled to avoid degrading the carbon fibre.     

Interface and fracture of carbon fibre reinforced Al-7 wt% Si alloy

The interface structure in an aluminium-7 wt% silicon alloy reinforced with carbon fibres has been investigated using analytical electron microscopy. Crystals of aluminium carbide (Al₄C₃) have been identified in interface regions and their structure and growth are discussed. Mechanical properties of the composite have been measured and fracture behaviour studied using acoustic emission analysis in parallel with microstructural examination. The results indicated that the aluminium carbide interfacial reaction had produced a strong fibre matrix bond, but reduced the fibre strength and embrittled the matrix. Consequently, whole fibre bundles failed in a brittle manner in the longitudinal direction with limited pull-out of individual fibres. The findings are discussed in relation to the method used to manufacture the composite.     

Interfacial debonding behavior of composite beam/plates with PZT patch

This paper studies interfacial debonding behavior of composite beams which include piezoelectric materials, adhesive and host beam. The focus is put on crack initiation and growth of the piezoelectric adhesive interface. Closed-form solutions of interface stresses and energy release rates are obtained for adhesive layer in the piezoelectric composite beams. Finite element analyses have been carried out to study the initiation and growth of interfaces crack for piezoelectric beams with interface element by ANSYS, in which the interface element of FE model is based on the cohesive zone models to characterize the fracture behavior of the interfacial debonding. The results have been compared with analytical solution, and the influence of different geometry and material parameters on the interfacial behavior of piezoelectric composite beams have been discussed.     

Electro-mechanical load transfer from a fiber in a 1–3 piezocomposite with an imperfect interface

This paper considers the electro-mechanical interaction between a fiber and a matrix material in a 1–3 piezocomposite due to an axial load and electric charge applied to the fiber. The fiber–matrix interface is assumed to be mechanically imperfect and is represented by a spring-factor model. The interface is either electrically open- or short-circuited. The analytical general solutions corresponding to an infinite piezoelectric fiber with a vertical body force and an electric body charge are derived by using Fourier integral transforms. These solutions together with the analytical general solutions for a transversely isotropic elastic medium are used to formulate the fiber–matrix interaction problem. Selected numerical results for the fiber axial force and vertical electric field, and interfacial stresses are presented for representative 1–3 piezocomposites. The influence of the interface stiffness on the electro-mechanical load diffusion is also examined.     

Prediction of tensile capacity based on cohesive zone model of bond anchorage for fiber-reinforce dpolymer tendon

In this paper, analytical solutions based on a cohesive zone model (CZM) are developed for the bond fiber-reinforce dpolymer (FRP) tendon anchorage under axial load. With bilinear cohesive laws, the analytical solutions of tensile capacity of anchorages are derived. The concept of the minimum relative interface displacement s_m is introduced and used as the fundamental variable to express all other parameters, such as external tensile load. Experimental and analytical results show that the thickness of the anchoring material is main factor affecting tensile capacity. The characteristic bond strength depends mainly on the properties of the bonding agent-anchoring material, the geometry and surface conditions of the tendon, and the radial stiffness of the confining medium. A comparison of the calculated and experimental results showed good agreement. Formulas based on fracture energy of the tension load capacity derived in the present work can be directly used in the design of FRP tendon anchorage.     

Interfacial properties of polymer composites measured by push-out and fragmentation tests

The interfacial properties for E-glass/epoxy composites were measured using push-out tests and single fiber fragmentation tests. Theoretical models for both stress-based and energy-based criteria were used to interpret the experimental results. Fibers treated with γ-aminopropyl-triethoxysilane (γ-APS) showed higher bond strength (∼1.7 times higher) and interfacial toughness (∼1.9 times higher) than those of unsized E-glass based composites. However, the average interfacial toughness obtained from fragmentation tests was about six times higher than that obtained from push-out tests. Considering the analytical frameworks employed to interpret the values measured in the present work, the fragmentation test is a more appropriate method to obtain interfacial energy for polymeric composites, but both methods are appropriate for relative measurements of interface strength.     

Interfacial separation of fibres in fibre reinforced composites

An analytical model is proposed to predict the ultimate tensile strength of fibre-reinforced composites when the failure is governed by fibre debonding.

The analytical analysis is based on the principle of the compliance method in fracture mechanics with the presence of an interfacial crack at the fibre/matrix interface. The model is developed on the basis of the assumption that both the matrix and the fibre behave elastically and the matrix strain at a zone far from the matrix-fibre interface is equal to the composite strain. Furthermore, it is assumed that a complete bond exists between the fibre and the matrix and that the crack faces are traction free.

It is shown that the separation strain energy release rate for fibre-reinforced composites can be obtained for cases with and without the existence of an interfacial crack. Numerical examples are presented and compared with results obtained in the literature by finite element analyses and from experimental tests. The comparison demonstrates the accuracy and the convergence of the model.     

Analytical identification of bond–slip relationship of EB-FRP joints

Bond–slip relationship of externally-bonded (EB) fiber reinforced polymer (FRP) joints can be determined by either directly or indirectly from a pull-off test. The indirect analytical method is gaining popularity and has been recommended in recent literature because of the more consistent and accurate results it yields. To date, loaded end slip vs applied load curve is used for indirect identification of the bond–slip relationship, ignoring the free end slip. This work shows that ignoring free end slip may result in significant errors in measuring the bond–slip relationship. The analytical method is used in this work to derive closed form solutions for FRP strain, interface slips, and bond strength of EB-FRP joints. The analytical solutions are validated by experimental results. Using the analytical solution, it is clearly shown in the paper that free end slip affects results and should be considered in deriving bond–slip relationship of EB-FRP joints, especially when bond length is short.     

Drug Release from Spherical Particles Under Nonsink Conditions. I. Theoretical Evaluation

Mathematical models have been developed to describe the release rate of drugs from spherical particles under nonsink conditions. Full and approximate analytical solutions have been derived for cases of solid-phase resistance only, for an additional interfacial resistance, and for membrane resistance only. These solutions provide a simple means for the determination of release characteristics of drugs from different types of formulations. It is shown that the perfect sink model     

A nonlinear bilayer beam model for an interfacial crack in dielectric bimaterials under mechanical/electrical loading

A bilayer beam model is extended to study the fracture behavior of dielectric interfacial cracks. In this model, a semi-infinite crack with an original opening value is oriented along the interface between two dielectric layers which are under mechanical/electrical loading. Taking into account the effect of the electrostatic traction on the interfacial crack, a nonlinear analytical solution is derived, along with also a developed finite element analysis method where a special constitutive equation for the capacitor element in ANSYS is utilized to simulate the electrostatic tractions. Both the analytical and numerical solutions predict the same results which further show that the elastic and dielectric mismatches can play a significant role in the interfacial cracking behavior under mechanical and electrical loading. Furthermore, the electrostatic tractions may cause hysteresis loops in the curve of crack opening versus applied mechanical displacement or versus applied electric voltage. An applied mechanical load is the driving force for the interfacial cracking, while an applied electric field retards it.     

含剪胀效应界面张力-位移关系的一种构造方法

为了研究异种材料界面的开裂过程,在Srensen等人工作的基础上,给出一种含剪胀效应张力-位移关系的构造方法。在界面受拉状态下,通过预先给定的剪胀函数及法向张力-位移关系导出切向张力-位移关系;在界面受压状态下,将切向张力分解为粘结力和摩擦力,摩擦力的大小与法向压力和粘结界面的破坏程度相关。该方法的结果解释了Srensen模型中切向张力-位移关系不连续及其不符合一致关联准则的原因。为便于进行数值计算,给出了用于三维有限元模型的界面刚度矩阵计算方法。选取了一种特定形式的剪胀函数,并将法向张力-位移关系假定为分段线性形式和指数形式,分别求得对应的切向张力-位移关系。最后给出了两个工程应用的例子,数值模拟结果与试验数据吻合较好。     

聚合物改性砂浆界面粘接特性的研究

根据聚合物改性砂浆不同的界面破坏形式,提出了表征界面粘接特性的内聚强度和界面结合强度概念,并通过二者的总体宏现效应-粘接强度试验探讨了乙烯-醋酸乙酸共聚物、双级配填料和水泥对砂浆内聚强度和界面结合强度的影响.试验表明,在本试验务件下乙烯-醋酸乙酸共聚物的最佳掺量范围为1.5%～3.5%.当聚合物掺量低于3.5%时,随着聚合物掺量的增加,聚合物改性砂浆的粘接强度增大,破坏形式为内聚破坏;当聚合物掺量高于3.5%时,聚合物改性砂浆界面的结合强度降低,导致粘接强度降低,破坏形式为界面破坏.具有合适配比的双级配填料可增强砂浆粘接强度,但大粒径填料的增加会降低砂浆与基材界面的结合强度,导致砂浆的粘接强度降低,在本试验条件下填料A/填料B的比例取1:2为宜.聚合物改性砂浆的粘接强度随水泥掺量的增加而增大,并在掺量为30%时出现拐点,故在本试验条件下水泥掺量取30%较佳.     

Bond-slip model for FRP-to-concrete bonded joints under external compression

The influence of compressive stresses exerted on FRP-concrete joints created by external strengthening of structural members on the performance of the system requires better understanding especially when mechanical devices are used to anchor the externally bonded reinforcement (EBR). The numerical modelling of those systems is a tool that permits insight into the performance of the corresponding interfaces and was used in the present study, essentially directed to analyse the effectiveness of EBR systems under compressive stresses normal to the composite surface applied to GFRP-to-concrete interfaces. The compressive stresses imposed on the GFRP-to-concrete interface model the effect produced by a mechanical anchorage system applied to the EBR system. An experimental program is described on which double-lap shear tests were performed that created normal stresses externally applied on the GFRP plates. A corresponding bond-slip model is proposed and the results of its introduction in the numerical analysis based in an available 3D finite element code are displayed, showing satisfactory agreement with the experimental data. The results also showed that lateral compressive stresses tend to increase the maximum bond stress of the interface and also originate a residual bond stress which has significant influence on the interface strength. Also, the strength of the interface increases with the increase of the bonded length which have consequences on the definition of the effective bond length.     

Interfacial crystalline structures in injection over-molded polypropylene and bond strength

This paper describes interfacial crystalline structures found in injection overmolded polypropylene components and the relationship of these structures to bond strength between the components. The combined effects of the development of hierarchical gradient structures and the particular thermomechanical environment near the interface on the interfacial crystalline structures were investigated in detail by PLM, SEM, DSC, WAXD, and infrared dichroism spectroscopy. The experimental results showed that during molding there was competitive formation of interfacial crystalline structures consisted of "shish-kebab" layer (SKL) and a transcrystalline layers (TCL). Variation in shear stress (controlled by injection pressure and injection speed) plays an important role in the formation of the SKL. The formation of TCL is influenced by the thermal environment, namely melt temperature and mold temperature. Increasing within certain limits, interfacial temperature and the thermal gradient near the interface promotes β-iPP growth. The relationship between interfacial crystalline structures and interfacial bond strength was established by lap shear measurement. The interfacial bond strength is improved by enhancing the formation of TCL, but reduced if SKL predominates.     

外贴CFRP加固混凝土梁裂缝间CFRP与混凝土界面粘结性能研究

碳纤维(CFRP)布与混凝土界面的粘结性能是影响CFRP加固构件性能的关键因素,为了更好地理解其对构件性能的影响,进行了外贴CFRP加固混凝土梁纯弯段内CFRP-混凝土界面粘结性能的研究,建立了研究相邻裂缝间CFRP-混凝土界面粘结滑移的解析模型。该模型不仅可以给出粘结界面上滑移和剪应力的分布,还可以给出外贴CFRP加固混凝土梁中相邻裂缝间各材料的应力分布,进而进行构件开裂分析等。将裂缝间CFRP应变实测分布与模型计算结果进行了比较,结果表明:由该模型导出的CFRP应变分布与试验结果吻合较好。     

纤维／聚合物基体界面性能的原位表征

建立了复合材料界面强度原位测试系统，研制出界面剪切强度有限元分析软件并探讨了影响界面剪应力分析的因素，提出了改进的微观力学模型；利用该系统，研究了表面经不同改性处理的ＣＦ增强ＰＭＲ—１５聚酰亚胺复合材料界面的微观力学性能，结果表明：有效的表面处理可使ＣＦ／ＰＭＲ—１５界面剪切强度明显提高，并与其宏观性能具有较好的对应趋势。本文还初步探讨了界面破坏的过程。     

A theory for the creep of steel fibre reinforced cement matrices under compression

The paper presents a theoretical model to predict the creep of cement matrices reinforced with randomly oriented discrete steel fibres. The theory considers the composite to be represented by an aligned steel fibre which is surrounded by a thick cylinder of the cement matrix. The fibre provides restraint to the flow component of creep of the matrix through the fibre-matrix interfacial bond strength. The delayed elastic strain component of creep is unaffected by the fibre. The fibre-matrix interfacial bond strength,, is shown to be primarily a function of the shrinkage of the cement matrix and the radial deformation caused by the sustained axial stress. In addition, the state of stress in the matrix at the interface is suggested to influence greatly the bond strength,. The validity of the theory is established by means of experimental data on concrete and mortar matrices reinforced with melt extract and hooked steel fibres, at sustained stress-strength ratios of 0.3 and 0.55. Finally an empirical expression is derived to determine the creep of steel fibre reinforced concrete, based on a knowledge of the creep in unreinforced matrices and fibre size and volume fraction.