Growth of interfacial debonding in notched two-dimensional unidirectional composite under stress and displacement controls

A simplified calculation method for study of the growth of interfacial debonding between elastic fiber and elastic matrix ahead of the notch-tip in composites under displacement and stress controlled conditions was presented based on the shear lag approach in which the influences of residual stress and frictional shear stress at the debonded interface were incorporated. The calculation method was applied to a model two-dimensional composite. An outline is given of the difference and similarity in the growing behavior of the debonding between the displacement and stress controls, and of the influences of the residual stresses, frictional shear stress, the nature of the final cut component (fiber or matrix) and sample length on the debonding behavior.     

Hysteresis loops of fiber-reinforced ceramic-matrix composites under in-phase/out-of-phase thermomechanical and isothermal cyclic loading

In this paper, the stress?strain hysteresis loops of fiber-reinforced ceramic-matrix composites (CMCs) under in-phase/out-of-phase thermomechanical and isothermal cyclic loading have been investigated. The thermomechanical hysteresis loops models have been developed considering synergistic effects of thermal temperature cycling, stress levels and fiber/matrix interface debonding. The relationships between thermal cyclic temperatures, peak stress, fiber/matrix interface shear stress and stress?strain hysteresis loops under in-phase/out-of-phase thermomechanical and isothermal cyclic loading have been established. The effects of fiber volume fraction, peak stress, matrix crack spacing, interface frictional coefficient, interface debonded energy and temperature range on the stress?strain hysteresis loops under in-phase/out-of-phase thermomechanical and isothermal cyclic loading have been analyzed. The hysteresis loops of cross-ply SiC/magnesium aluminosilicate (MAS) composite under in-phase/out-of-phase thermomechanical and isothermal fatigue loading have been predicted.     

Effect of interfacial debonding and matrix cracking on mechanical properties of multidirectional composites

In composites, debonding at the fiber–matrix interface and matrix cracking due to loading or residual stresses can effect the mechanical properties. Here three different architectures — 3-directional orthogonal, 3-directional 8-harness satin weave and 4-directional in-plane multidirectional composites — are investigated and their effective properties are determined for different volume fractions using unit cell modeling with appropriate periodic boundary conditions. A cohesive zone model (CZM) has been used to simulate the interfacial debonding, and an octahedral shear stress failure criterion is used for the matrix cracking. The debonding and matrix cracking have significant effect on the mechanical properties of the composite. As strain increases, debonding increases, which produces a significant reduction in all the moduli of the composite. In the presence of residual stresses, debonding and resulting deterioration in properties occurs at much lower strains. Debonding accompanied with matrix cracking leads to further deterioration in the properties. The interfacial strength has a significant effect on debonding initiation and mechanical properties in the absence of residual stresses, whereas, in the presence of residual stresses, there is no effect on mechanical properties. A comparison of predicted results with experimental results shows that, while the tensile moduli E ₁₁, E ₃₃and shear modulus G ₁₂ match well, the predicted shear modulus G ₁₃ is much lower.     

Initial damage induced by thermal residual stress and microscopic failure analysis of carbon-fiber reinforced composite under shear loading

In order to study the mechanical properties and the progressive failure process of composite under shear loading, a representative volume element (RVE) of fiber random distribution was established, with two dominant damage mechanisms – matrix plastic deformation and interfacial debonding – included in the simulation by the extended Drucker–Prager model and cohesive zone model, respectively. Also, a temperature-dependent RVE has been set up to analyze the influence of thermal residual stress. The simulation results clearly reveal the damage process of the composites and the interactions of different damage mechanisms. It can be concluded that the in-plane shear fracture initiates as interfacial debonding and evolves as a result of interactions between interfacial debonding and matrix plastic deformation. The progressive damage process and final failure mode of in-plane shear model which are based on constitute are very consistent with the observed result under scanning electron microscopy of V-notched rail shear test. Also, a transverse shear model was established as contrast in order to comprehensively understand the mechanical properties of composite materials under shear loading, and the progressive damage process and final failure mode of composite under transverse shear loading were researched. Thermal residual stress changes the damage initiation locations and damage evolution path and causes significant decreases in the strength and fracture strain.     

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.     

Interfacial debonding and slipping of carbon fiber-reinforced ceramic-matrix composites under two-stage cyclic loading

In this paper, the interface debonding and frictional slipping of carbon fiber-reinforced ceramic-matrix composites (CMCs) under two-stage cyclic fatigue loading have been investigated using micromechanics approach. Under cyclic fatigue loading, the fiber/matrix interface shear stress degrades with increasing cycle number due to interface wear. The synergistic effect of interface wear and fatigue loading sequence on interface debonding and frictional slipping has been analyzed. Based on the fatigue damage mechanism of fiber slipping relative to matrix, in the interface debonded region, upon unloading and subsequent reloading, the interface debonded length and interface slip lengths, i.e. interface counter-slip length and interface new-slip length, are determined using the fracture mechanics approach. The relationships between interface debonding, interface slipping, interface wear, cycle number, and different loading sequences are determined. There are two types of fatigue loading sequences considered, i.e. (1) cyclic loading under low peak stress for N₁ cycles, and then high peak stress; and (2) cyclic loading under high peak stress for N₁ cycles, and then low peak stress. The effects of peak stress level, interface wear, cycle number, and loading sequence on interface debonding and frictional slipping of fiber-reinforced CMCs have been analyzed. The fatigue hysteresis loops of cross-ply carbon fiber-reinforced silicon carbide composite corresponding to different cycle number under two-stage cyclic fatigue loading have been predicted.     

Is there any contradiction between the stress and energy failure criteria in micromechanical tests? Part II. Crack propagation: Effect of friction on force-displacement curves

In micromechanical tests for estimating fiber-matrix interfacial properties, such as the pull-out and microbond tests, fiber debonding from a matrix is often accompanied by friction in debonded areas. In the present study, force-displacement curves, which are usually recorded in these tests, were modeled with taking interfacial friction into consideration. The friction stress was assumed, as a first approximation, to be constant across the interface. Two different approaches to interfacial failure were used: the shear-lag approach with a stress-based debonding criterion (the ultimate interfacial shear strength) and the linear elastic fracture mechanics approach using the critical energy release rate as a condition for crack propagation. The force-displacement curves derived from both models are in good agreement with each other and with experimental micromechanical data. It was shown that any pull-out and microbond experiment comprises four stages: (1) linear loading up to the point where debonding starts; (2) stable crack propagation with friction-controlled debonding; (3) catastrophic debonding; and (4) post-debonding friction. Stable crack propagation was shown to be controlled by both friction and release of residual thermal stresses. An algorithm for estimating both fiber-matrix adhesion and interfacial friction from the microbond and pull-out tests data has been proposed.     

石墨烯/柔性基底复合结构双向界面切应力传递问题的理论研究

界面力学性能是影响石墨烯/柔性基底复合结构整体力学性能的关键因素,因此对该结构界面切应力传递机理的研究十分必要.考虑了石墨烯和基底泊松效应的影响,本文提出了二维非线性剪滞模型.对于基底泊松比相比石墨烯较大的情况,利用该模型理论研究了受单轴拉伸石墨烯/柔性基底结构的双向界面切应力传递问题.在弹性粘结阶段,导出了石墨烯双向正应变和双向界面切应力的半解析表达式,分析了不同位置处石墨烯正应变和界面切应力的分布规律.导出了石墨烯/柔性基底结构发生界面滑移的临界应变,结果表明该临界应变低于利用经典一维非线性剪滞模型得到的滑移临界应变,并且明显受到石墨烯宽度尺寸以及基底泊松比大小的影响.基于二维非线性剪滞模型建立有限元模型(FEM),研究了界面滑移阶段石墨烯双向正应变和双向界面切应力的分布规律.与一维非线性剪滞模型的结果对比表明,当石墨烯宽度较大时,二维模型和一维模型对石墨烯正应变、界面切应力以及滑移临界应变的计算结果均存在较大差别,但石墨烯宽度很小时,二维模型可近似被一维模型代替.最后,通过与拉曼实验结果的对比,验证了二维非线性剪滞模型的可靠性,并得到了石墨烯/聚对苯二甲酸乙二醇酯(PET)基底结构的界面刚度(100 TPa/m)和界面剪切强度(0.295 MPa).     

Comparisons of interface shear stress degradation rate between C/SiC and SiC/SiC ceramic-matrix composites under cyclic fatigue loading at room and elevated temperatures

The interface shear stress in C/SiC and SiC/SiC ceramic-matrix composites with different fiber preforms, i.e. unidirectional, cross-ply, 2D woven, 2.5D woven, and 3D braided, under cyclic fatigue loading at room and elevated temperatures have been estimated. An effective coefficient of the fiber volume fraction along the loading direction was introduced to describe the fiber preforms. Based on fiber slipping mechanisms, the hysteresis loops models considering different interface slip cases have been developed. Using the experimental fatigue hysteresis dissipated energy, the interface shear stress degradation rates of C/SiC and SiC/SiC composites with different fiber preforms at room and elevated temperatures have been obtained and compared. It was found that the interface shear stress degradation rate is the highest for 3D braided SiC/SiC at 1300 °C in air, and the lowest for 2D woven C/SiC at room temperature under cyclic fatigue loading.     

Micromechanical analysis of transverse damage of fibre-reinforced composites

The mechanical behaviour of fibre-reinforced composites under transverse tension, compression and shear is studied using computational micromechanics. The representative volume element is constructed for fibre’s random distribution. The Drucker–Prager model and cohesive zone model are used to simulate the matrix damage and interfacial debonding, respectively. The stress distribution along the interface is studied using the model with only one fibre embedded in the matrix. It is found that the interface tensile failure at the equators of fibre firstly occurs under transverse tension; the interface shear failure firstly occurs under transverse compression; both the interface tensile failure and shear failure occur under transverse shear. The direction of fracture plane is perpendicular to the loading direction under transverse tension, 52.5° with the perpendicular direction under compression and 7.5° with the perpendicular or vertical direction under shear, respectively.     

Theoretical analysis and numerical simulation of development length of straight steel fiber in cementitious materials

In fiber-reinforced concrete, it is important to choose an appropriate length in each fiber to develop its full yield strength without a failure in the bond strength between the fiber and the concrete. This length is called the fiber development length, L_df. The bond capacity is evaluated between the fiber and the concrete using the pull-out tests. This test evaluates the bond capacity of various types of steel fiber surfaces relative to a specific embedded length. If the steel fiber is smooth and straight, the distribution of tensile stresses will be uniform around the fiber at a specific section and varies along the anchorage length of the fiber and at a radial distance from the surface of the fiber. Pull-out tests can be performed on an embedded straight steel fiber in concrete matrix, in this case, the tensile force, P, is increased gradually and the number of cracks and their spacings and widths is recorded. The bond stresses vary along the fiber length between the cracks. The strain in the steel fiber is maximum at the cracked section and decreases toward the middle section between cracks. If the embedded length of the straight steel fiber is greater than the development length, the steel fiber may yield, leaving some length of the fiber in the concrete. The linear elastic behavior of the fiber-matrix system is interrupted by interface debonding which occurs due to overall weak bonding between the concrete matrix and the surface of the steel fiber. This paper introduces new developed shear lag model and explains simplified method to find the development length of straight steel fiber in concrete matrix using finite element model and analysis of shear lag stresses, where the maximum tension force which is applied on the steel fiber is resisted by another internal force related with the ultimate average bond stress, steel fiber diameter and its yield strength.     

Effect of Residual Stresses on Delamination Cracks in Fiber Reinforced Composites

In the processing of cross-ply fiber reinforced materials, residual stresses, as well as possible transverse cracking may arise. These affect the stress field about a delamination between two layers. In this investigation, the effect of residual stresses resulting from curing and transverse cracks is examined. A 0°/90°/0° ply system is considered with a delamination assumed between one of the 0° and 90° layers. The residual stresses along the interface without the delamination are calculated. First, this analysis is done neglecting the transverse cracks in the 90° layer. Then, the transverse cracks are included and several methods are employed to calculate the residual stresses. These include the shear lag method, a semi-analytic method and the finite element method. It is seen that the latter two methods produce similar results. By means of the superposition principle, the stress intensity factors resulting from the residual stresses are obtained for the delamination. Use is made of the conservative M-integral with tractions along the crack faces.     

Investigation of interfacial stress transfer in a PBO/polypropylene microdroplet composite using synchrotron microfocus X-ray diffraction

The micromechanics of stress transfer in a PBO/polypropylene system were followed using a microdroplet model composite and a synchrotron microfocus X-ray diffraction technique. High quality X-ray diffraction patterns were obtained from both the PBO-HM fiber and the polypropylene matrix. Diffraction patterns were obtained from the fiber inside the PP droplet by subtraction of a PP diffraction pattern from that of the composite. It was found that there was good stress transfer at the fiber–matrix interface and that significant residual stresses occurred in the fiber inside the droplet due to the cooling and crystallization of the polypropylene. The maximum residual stress of 0.55 GPa measured corresponded to an axial fiber strain of 0.2% compressive strain, similar to the literature values for compressive fiber failure.     

Evaluation on the interfacial fracture toughness of fiber-reinforced titanium matrix composites by push out test

The models for single-fiber push out test are developed to evaluate the fracture toughness G_IIc of the fiber/matrix interface in titanium alloys reinforced by SiC monofilaments. The models are based on fracture mechanics, taking into consideration of the free-end surface and Poisson expansion. Theoretical solutions to G_IIc are obtained, and the effects of several key factors such as the initial crack length, crack length, friction coefficient, and interfacial frictional shear stress are discussed. The predictions by the models are compared with the previous finite element analysis results for the interfacial toughness of the composites including Sigma1240/Ti-6-4, SCS/Ti-6-4, SCS/Timetal 834, and SCS/Timetal 21s. The results show that the models can reliably predict the interfacial toughness of the titanium matrix composites, in which interfacial debonding usually occurs at the bottom of the samples.     

涂层界面结合强度检测研究(Ⅰ):涂层结合界面应力的理论分析

利用激光划痕测试法和弯曲应力理论，建立了涂层结合界面应力的理论模型，推导出结合界面剪应力、正应力和剥离应力分布公式，分析了结合界面应力产生的机理.理论分析结果表明，界面正应力主要集中在界面中心区域内，而在界面边缘附近，正应力迅速下降，在界面边缘处其值降为0；剪应力和剥离应力主要集中在界面边缘区域内，在远离界面边缘区域，剪应力和剥离应力则迅速下降；涂层中正应力和涂层厚度、基体厚度以及杨氏模量无关，界面间剪应力以及剥离应力随涂层厚度增加而增加，并且由涂层与基体厚度以及杨氏模量所共同决定.     

Analysis of single-fiber pull-out from composites by using stress birefringence

During a fiber pull-out test, it is desirable to analyze the stress profiles along the embedded fiber directly within the same time scale as the normal pull-out tests. In the present study, the axial tensile stress profiles of the fiber in a model composite are measured during the single-fiber pull-out tests by using stress birefringence of the fiber. It is concluded from the analysis of the measured stress profiles that an effective radius of matrix, i.e. a radius defining the region of the matrix where the major deformation takes place, is not constant but is an increasing function of the interfacial shear stress. By incorporating the variable values of the effective radius of matrix into the shear-lag model, the axial tensile and the interfacial shear stress profiles are calculated. To accurately estimate the interfacial shear strength, the stress distribution along the embedded fiber and the variability of the effective radius of matrix should be taken into account instead of calculating the interfacial shear strength simply from the pull-out stress and the embedded length.     

Role of weak interface to retain high strength of fiber in monofilamentary SiC fiber/titanium-aluminide composite

The tensile strength of monofilamentary weakly bonded SiC fiber/γ-TiAl intermetallic compound matrix composite, prepared by the sputtering method, was measured and analysed using a fracture mechanical technique. The main results are summarized as follows: (1) The fracture of TiAl occurred prior to that of fiber, resulting in formation of circumferential cracks on the fiber. Interfacial debonding occurred during tensile test, resulting in long pull-out of the fiber. (2) The strength of the fiber in the TiAl matrix was nearly the same as that of the bare fiber. (3) The fracture mechanical analysis showed that (i) the interfacial debonding grows unstably upon initiation and (ii) the stress distribution in the fiber in the cross-section, where the matrix is fractured, approaches to that of bare fiber with increasing debonded length. The reason why the fiber strength was maintained in spite of the formation of cracks on the fiber surface due to the premature fracture of the matrix was accounted for by the fully blunted crack-tip from the above calculation result.     

Finite element prediction of debonding onset in short fiber reinforced polymers incorporating a hybrid interphase region

A robust finite element procedure for investigating damage evolution in short fiber reinforced polymeric composites under external loads is developed. This procedure is based on an axisymmetric unit cell composed of a fiber, surrounding interphase and bulk matrix. The hybrid interphase concept involves a degraded material phase, the extent of which is material and property dependent. One of the most significant features of the model relies on establishment of variable adhesion conditions between the primary material phases. The unit cell is discretized into linearly elastic elements for the fiber and the matrix and interface elements which allow debonding in the fiber–matrix interface. The interface elements fail according to critical stress and critical energy release rate criteria. The tension and shear aspects of failure are uncoupled, although the resulting nonlinear problem is solved implicitly utilizing quasi-static incremental loading conditions. Final failure resulting from saturation and breakage is modeled by the vanishing interface element technique. Details of the propagation of interface cracks and the initiation of debonds are also observed and discussed for various shapes of fiber end. Numerical results reveal an intense effect of the fiber-end geometry on the initial fiber–matrix de-cohesion. The present finite element procedures can generate meaningful results in the analysis of fiber-reinforced composites.     

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.     

Stress field calculation around a particle in elastic–plastic polymer matrix under multiaxial loading as basis for the determination of adhesion strength

The stress distribution around a single particle coated with an elastic interphase embedded within an elastic–plastic polymer matrix under multiaxial load was considered. The specimen has a curved (necked) geometry, which causes multiaxial local stresses in the neighbourhood of the particle. The motivation for the calculations is to determine the maximum radial stress (debonding strength) at the particle surface as a function of applied load. The effect of the particle size on failure initiation is considered. Assuming that the normal stress at the interface is responsible for debonding, the adhesion strength can be determined from the critical load at debonding initiation. Because of the matrix yielding, the relation between the applied load and the maximum radial stress at the particle/interphase interface is a non-linear one. Using this relation, the determination of interfacial strength will be possible by a tensile test.