Evaluation of the Effect of Thermal Oxidation and Moisture on the Interfacial Shear Strength of Unidirectional IM7/BMI Composite by Fiber Push-in Nanoindentation

Fiber push-in nanoindentation is conducted on a unidirectional carbon fiber reinforced bismaleimide resin composite (IM7/BMI) after thermal oxidation to determine the interfacial shear strength. A unidirectional IM7/BMI laminated plate is isothermally oxidized under various conditions: in air for 2 months at 195 °C and 245 °C, and immersed in water for 2 years at room temperature to reach a moisture-saturated state. The water-immersed specimens are subsequently placed in a preheated environment at 260 °C to receive sudden heating, or are gradually heated at a rate of approximately 6 °C/min. A flat punch tip of 3 μm in diameter is used to push the fiber into the matrix while the resulting load-displacement data is recorded. From the load-displacement data, the interfacial shear strength is determined using a shear-lag model, which is verified by finite element method simulations. It is found that thermal oxidation at 245 °C in air leads to a significant reduction in interfacial shear strength of the IM7/BMI unidirectional composite, while thermal oxidation at 195 °C and moisture concentration have a negligible effect on the interfacial shear strength. For moisture-saturated specimens under a slow heating rate, there is no detectable reduction in the interfacial shear strength. In contrast, the moisture-saturated specimens under sudden heating show a significant reduction in interfacial shear strength. Scanning electron micrographs of IM7/BMI composite reveal that both thermal oxidation at 245 °C in air and sudden heating induced microcracks and debonding along the fiber/matrix interface, thereby weakening the interface, which is the origin of failure mechanism.     

Improved theoretical solution for interfacial stresses in concrete beams strengthened with FRP plate

In this paper, an improved theoretical interfacial stress analysis is presented for simply supported concrete beam bonded with a FRP plate. The adherend shear deformations have been included in the present theoretical analyses by assuming a linear shear stress through the thickness of the adherends, while all existing solutions neglect this effect. Remarkable effect of shear deformations of adherends has been noted in the results. Indeed, the resulting interfacial stresses concentrations are considerably smaller than those obtained by other models which neglect adherent shear deformations. It is shown that both the normal and shear stresses at the interface are influenced by the material and geometry parameters of the composite beam. This research is helpful for the understanding on mechanical behavior of the interface and design of the FRP–RC hybrid structures.     

Finite element analysis of interfacial stresses in FRP–RC hybrid beams

The interfacial stresses in fiber reinforced plastic (FRP)–reinforced concrete (RC) hybrid beams were studied by the finite element method. The mesh sensitivity test shows that the finite element results for interfacial stresses are not sensitive to the finite element mesh. The finite element analysis then is used to calculate the interfacial stress distribution and evaluate the effect of the structural parameters on the interfacial behavior. It is shown that both the normal and shear stresses at the interface are influenced by the material and geometry parameters of the composite beam. This research is helpful for the understanding on mechanical behavior of the interface and design of the FRP–RC hybrid structures.     

含界面相效应的纤维增强复合材料桥联增韧力学分析

本文对纤维增强复合材料桥联增韧进行了详细的断裂力学分析，基于Ｃａｓｔｉｇｌｉａｎｏ＇ｓ定理和界面剪滞模型，得到了含界丰效应的复合材料桥联增专访和裂纹线开位移的控制议程；并按照第二类Ｆｒｅｄｈｏｌｍ积分方程的迭代解法，给出其数值结果，为例题于分析界面相参数对增韧效果的影响，寻求了该控制方程的近似解解析表达式，对近似解进行了误差估计，证明了解的可行性，在此基础上得到了界面剪切模量，裂纹长度。界面厚度，     

On the bidirectional stress distribution in rectangular bonded composite patches

The aim of this paper is to provide some solutions for the stress distribution in rectangular composite patches under in-plane loading. Two different cases are considered: normal stresses and shear stresses. The stress distributions in the patch, the adhesive and the substrate show evidence of some bidirectional effects, which are not accounted for by usual unidirectional solutions available in the literature.     

Analysis of elastic crack bridging in ceramic matrix composites

A micromechanics analytical model based on the consistent shear lag theory is developed for predicting the failure modes in fiber reinforced unidirectional stiff matrix composites. The model accounts for a relatively large matrix stiffness and hence its load carrying capacity. The fiber and matrix stresses are established as functions of the applied stress, crack geometry, and the microstructural properties of the constituents. From the predicted stresses, the mode of failure is established based on a point stress failure criterion. The role of the microstructural parameters of the constituents on the failure modes such as self-similar continuous cracking, crack bridging and debonding parallel to the fibers is assessed.     

Macroscopic strength estimates for metal matrix composites embedding a ductile interphase

The influence of an interphase region on the macroscopic strength of unidirectional fiber-reinforced metal-matrix composites (MMCs) is investigated. The three phases of the composite are supposed to be elastic-perfectly plastic and to conform with J₂-plasticity. First, theoretical bounds to the macroscopic strength are derived, according to homogenization theory for heterogeneous periodic media: the gap between these bounds is quite narrow for certain stress conditions, volumetric proportions of the constituents, and ratios of the interphase-to-matrix strength. Then, a numerical model previously developed by Taliercio (2005) is employed to predict the macroscopic response of three-phase MMCs under any 3D stress through the analysis of a single representative unit cell. The model is applied to the numerical identification of the macroscopic strength properties of MMCs under uni-, bi- and triaxial stresses, in cases where the theoretical bounds are not sufficiently close to identify the actual macroscopic yield surface. The influence of the weakening interphase on the predicted macroscopic strength is critically discussed. A decrease in interphase strength is found to affect the transverse tensile and shear strength of the composite to a moderate extent, whereas the macroscopic longitudinal shear strength is extremely sensitive to the interphase strength.     

纤维增强韧性基体界面力学行为

分析了纤维增强韧性基体的界面力学行为及其失效机理,按剪滞理论和应变理化规律研究微复合材料的弹塑性变形和应力状态,讨论了幂硬化和线性硬化基体的弹塑性变形和界面应力分布,并给出纤维应力和位移的表达式。按最大剪应力强度理论建立了纤维／基体界面失效准则,推导出弹塑性界面失效的平均剪应力随纤维埋入长度的变化关系。     

Cohesive zone modeling of interfacial stresses in plated beams

The elastic analysis of interfacial stresses in plated beams has been the subject of several investigations. These studies provided both first-order and higher-order solutions for the distributions of interfacial shear and normal stresses close to the plate end in the elastic range. The notable attention devoted to this topic was driven by the need to develop predictive models for plate end debonding mechanisms, as the early models of this type adopted debonding criteria based on interfacial stresses. Currently, approaches based on fracture mechanics are becoming increasingly established. Cohesive zone modeling bridges the gap between the stress- and energy-based approaches. While several cohesive zone analyses of bonded joints subjected to mode-II loading are available, limited studies have been conducted on cohesive zone modeling of interfacial stresses in plated beams. Moreover, the few available studies present complex formulations for which no closed-form solutions can be found. This paper presents an analytical cohesive zone model for the determination of interfacial stresses in plated beams. A first-order analysis is conducted, leading to closed-form solutions for the interfacial shear stresses. The mode-II cohesive law is taken as bilinear, as this simple shape is able to capture the essential properties of the interface. A closed-form expression for the debonding load is proposed, and the comparison between cohesive zone modeling and linear-elastic fracture mechanics predictions is discussed. Analytical predictions are also compared with results of a numerical finite element model where the interface is described with zero-thickness contact elements, using the node-to-segment strategy and incorporating decohesion and contact within a unified framework.     

正交异性光弹性应力分离的边界元法

本文对平面正交各向异性复合材料模型引入正应力线性和及边界上正应力线性和流的概念,提出从应力相容方程出发.用边界元法计算正交异性光弹性模型内任一点的正应力线性和位的方法,再与正交异性光弹性法中所给出的应力同的关系结合,即可进行正交异性光弹性应力的分离.最后,对边界元方法的精度进行了讨论.     

BRIDGE-TOUGHENING ANALYSIS OF THE FIBER REINFORCED COMPOSITE CONTAINING INTERPHASE EFFECT

A detailed fracture mechanics analysis of bridge-toughening in a fiberreinforced composite is presented in this paper.The integral equation governing bridge-toughening as well as crack opening displacement (COD) for the composite withinterfacial layer is derived from the Castigliano's theorem and interface shear-lagmodel.A numerical result of the COD equation is obtained using the iteration solutionof the second Fredholm integral equation.In order to investigate the effect of variousparameters on the toughening,an approximate analytical solution of the equation ispresent and its error analysis is performed,which demonstrates the approximatesolution to be appropriate.A parametric study of the influence of the crack length,interracial shear modules,thickness of the interphase,fiber radius,fiber volumefraction and properties of materials on composite toughening is therefore carried out.The results are useful for experimental demonstration and toughening design includingthe fabrication process of the composite.     

Interfacial stresses in curved members bonded with a thin plate

The use of steel plates or externally bonded fibre-reinforced polymer laminates for flexural strengthening of concrete, masonry, timber or metallic structures is a technique that has become very popular. The effectiveness of this technique hinges heavily on the performance of the bond between the strengthening plate and the substrate, which has been the subject of many existing studies. In particular, the interfacial stresses between a beam and a soffit plate within the linear elastic range have been addressed by numerous analytical investigations. Surprisingly, none of these investigations has examined interfacial stresses in members with a curved soffit, despite that such members are often found in practice. This paper presents an analytical model for the interfacial stresses between a curved member of uniform section size and a thin plate bonded to its soffit. The governing differential equations for the interfacial shear and normal stresses are formulated and then solved with appropriate simplifying assumptions. Two numerical examples are presented to illustrate the effect of the curvature of the member on the interfacial stress distributions in a simply supported curved beam for the two cases of a point load and a uniformly distributed load. The analytical solution is verified by comparing its predictions with those from a finite element model.     

Precracking and interfacial delamination in a bi-material structure: Static and dynamic loadings

The behavior of a precracked bi-material structure interface under given static and dynamic axial loading is an interest object in the present paper.Firstly,it is shown that the shear-lag model is a proper tool to analyze a delamination process in a precracked bi-material structure undergoing static loading.Secondly,the"shear-lag model"is applied to the structure under dynamic loading.To solve the problem for an interface delamination of the structure and to determine the debond length along the interface,our own 2D boundary element method(BEM)code is proposed in the case of static loading,and the shear-lag model together with the Laplace transforms and half-analytical calculations are used in the case of dynamic loading.The interface layer is assumed as a very thin plate compared with the other two.The parametric(geometric and elastic)analysis of the debond length and interface shear stress is done. The results from the 2D BEM code proved the validity of analytical solutions to the shear-lag model.In the dynamic case,the influence of loading characteristics,i.e.,frequencies and amplitude fluctuations on the shear stress and the value of debond length for an interval of time,is discussed. The analysis of the obtained results is illustrated by an example of the modern ceramic-metal composite,namely cermet, and depicted in figures.     

A coated rigid elliptical inclusion loaded by a couple in the presence of uniform interfacial and hoop stresses

We consider a confocally coated rigid elliptical inclusion, loaded by a couple and introduced into a remote uniform stress field. We show that uniform interfacial and hoop stresses along the inclusion–coating interface can be achieved when the two remote normal stresses and the remote shear stress each satisfy certain conditions. Our analysis indicates that: (i) the uniform interfacial tangential stress depends only on the area of the inclusion and the moment of the couple; (ii) the rigid-body rotation of the rigid inclusion depends only on the area of the inclusion, the coating thickness, the shear moduli of the composite and the moment of the couple; (iii) for given remote normal stresses and material parameters, the coating thickness and the aspect ratio of the inclusion are required to satisfy a particular relationship; (iv) for prescribed remote shear stress, moment and given material parameters, the coating thickness, the size and aspect ratio of the inclusion are also related. Finally, a harmonic rigid inclusion emerges as a special case if the coating and the matrix have identical elastic properties.     

A three-parameter elastic foundation model for interface stresses in curved beams externally strengthened by a thin FRP plate

Externally bonding of fiber reinforced polymer (FRP) plates or sheets has become a popular method for strengthening reinforced concrete structures. Stresses along the FRP–concrete interface are of great importance to the effectiveness of this type of strengthening because high stress concentration along the FRP–concrete interface can lead to the FRP debonding from the concrete beam. In this study, we develop an analytical solution of interface stresses in a curved structural beam bonded with a thin plate. A novel three-parameter elastic foundation model is used to describe the behavior of the adhesive layer. This adhesive layer model is an extension of the two-parameter elastic foundation commonly used in existing studies. It assumes that the shear stress in the adhesive layer is constant through the thickness, and the interface normal stresses along two concrete/adhesive and adhesive/FRP interfaces are different. Closed-form solutions are obtained for these two interfacial normal stresses, shear stress within the adhesive layer, and beam forces. The validation of these solutions is confirmed by finite element analysis.     

An experimental and analytical investigation of the rail shear-test method as applied to composite materials

This report presents the results from an experimental and analytical investigation of the stress distributions occurring in a rail shear test. The effects of nonuniform stresses induced by differential thermal expansion, rail flexibility and specimen aspect ratio on measured shear modulus and ultimate strength of composite laminates are shown. A two-dimensional linearly elastic finite-element model was used to analytically determine how various geometric parameters influenced the magnitude and distribution of inplane normal and shear stresses in a tensile-rail-shear specimen. Rail shear tests were conducted at room temperature and 589 K (600°F) on selected graphite-polyimide composite laminates using two titanium rail configurations. The analysis and test methods are discussed, and the results of the effects of the various parameters on shear modulus and ultimate strength are presented.     

Stress relaxation after steady shear flow in immiscible model polymer blends

Stress relaxation in immiscible blends is studied for a well defined shear history, i.e. after prolonged steady state shearing. Model systems are used that consist of quasi-Newtonian liquid polymers. Hence the relaxation is dominated by changes in the morphology of the interface. Both shear stress and the first normal stress are considered. The measurements cover the entire concentration range. For dilute blends the interfacial contribution to the stress relaxation compares well with model predictions. Deviations occur when the matrix phase is slightly elastic. In that case the similarity between the relaxation of shear and normal stresses is also lost. The latter is attributed to a wider drop size distribution.Increasing the concentration of the disperse phase results in a complex evolution of the characteristic relaxation times. The normal stresses relax systematically slower than the shear stresses and the concentration curve includes two maxima. Even for equiviscous components the concentration curves are not symmetrical. It is concluded that even a slight degree of elasticity in the matrix phase drastically affects the morphology and the interfacial relaxation of such blends.     

纤维─基体界面剪切强度与断裂韧性的表征和测定

根据单向复合材料纤维分布、剪切变形与裂纹扩展的细观分析,提出纤维一基体界面剪切强度和断裂韧性的简易细观表征与测定方法．     

纤维─基体界面剪切强度与断裂韧性的表征和测定

根据单向复合材料纤维分布、剪切变形与裂纹扩展的细观分析,提出纤维一基体界面剪切强度和断裂韧性的简易细观表征与测定方法．     

The effective properties of composites with fiber-end cracks

The paper describes use of self-consistent finite element method (SCFEM) for predicting effective properties of fiber composite with partially debonded interface. The effective longitudinal Young's modulus and shear modulus for unidirectional fiber reinforced composites with fiber-end cracks are calculated. Numerical results show that the effective properties are considerably influenced by the fiber-end cracks. The effects of microstructural parameters, such as fiber volume fraction, modulus ratio of the constituents and fiber aspect, on the effective properties of the composites were discussed. The project supported by the National Natural Science Foundation of China