Micromechanical modeling of the microbond test to quantify the interfacial properties of fiber-reinforced composites

The present study has focused on achieving a micromechanical understanding of the microbond test, which involves pulling a fiber out of a bead of matrix (i.e. droplet) through a knife-edge, in order to quantify the interfacial fracture properties of fiber-reinforced composites. According to the microbond test results for carbon-fiber and epoxy-resin system, matrix cracking occurred during the fiber pullout, in addition to the debonding at the fiber–matrix interface. Therefore, in evaluating the fracture properties of the fiber–matrix interface, we should pay attention to the coupling effects of matrix failure and interfacial debonding on the test results. Then, we discuss how to best extract the interfacial properties while excluding the influence of matrix plasticity and cracking, using numerical simulations. The key mechanism demonstrated here is that the pullout force, in the cases where the influence of matrix cracking is negligible, appears as the upper limit among the experimental data of the pullout force for a constant initial embedded length of the fiber in the matrix. For this reason, the upper-limit data all over the range of embedded fiber length in experiments can be reasonably evaluated by the simulation focusing on the debonding process with matrix plasticity. This evaluation technique is effective as a way of extracting interfacial properties appropriately from microbond test results.     

A dynamic meso-scale model of the pullout behavior for non-straight fibers and corresponding DEM3 simulation

Lots of work had been reported in the experimental investigation and modeling of the debonding and pullout behavior for straight crack-bridging fibers in brittle matrix composites, but few of them involving in the dynamic and/or non-straight fiber case. In this paper, a dynamic meso-scale model for non-straight fiber was proposed on the work of Chanvillard. The model was time-dependent and related to the impact loading through the interfacial shearing stress along the embedded part of the steel fiber, and properly setting the thresholds, the dynamic meso-damage model of the fiber's debonding and pullout process was eventually constructed. The model prediction fitted the experimental data of Chanvillard for non-straight steel fiber under static condition quite well and could demonstrate the rate sensitivity of the reinforcing effects of fibers. Then, a 3-D discrete meso-element method (DEM3) was used to simulate the dynamic pullout behavior of such fiber configurations as wiredrawn fibers from cementitious matrix with pores. Comparing to afro-mentioned model, DEM3 was more effective in simulating the complete procedures of matrix dynamic failure and fiber pullout and would be more helpful in the analyses of complicated configurations of fiber.     

Modeling long-term creep rupture by debonding in unidirectional fibre-reinforced composites

Delayed fracture due to debonding can be observed in many unidirectional fibre-reinforced composites when the fibre/matrix interface experiences creep. The aim of this work is to describe such a phenomenon within the recently proposed modeling framework of transverse isotropy that allows for a neat decomposition of the mechanical behavior into fibre-directional, transverse, and pure shear parts. Specifically, debonding is here chosen to be governed by the tension transverse to the fibres. One can then speak of a mode-I debonding if use is made of the terminology adopted in fracture mechanics. On another hand, the time-dependent response is attributed to the matrix constituent. As the role of this latter is to deform and support stresses primarily in shear, a viscoelastic behavior is introduced that affects solely the pure shear part of the behavior. We show that both characteristics can be easily embedded into the aforementioned formulation. Among others, the occurrence of tertiary creep is made possible to predict. It is otherwise found that the predicted debonding path always propagates along the direction of the fibres in agreement with many experimental observations found in the literature. On the numerical side, the algorithmic treatment of debonding is independent of the one for viscoelasticity. This renders the implementation within the context of the finite element method very easy.     

A different approach for calculation of stress intensity factors in continuous fiber reinforced metal matrix composites

In this paper, a numerical model developed for the analysis of a cylindrical element of matrix containing a single fiber is presented. A ring-shaped crack is assumed at interface of fiber and matrix. Both layers in the model are bonded perfectly with the exception of the crack faces. Contact elements, which have bonded feature, are used between fiber and matrix. Displacement correlation method is used to calculate opening-mode and sliding-mode stress intensity factors. These results obtained from the analysis help to understand the debonding phenomenon between fiber and matrix interface. Effects of the mechanical properties of fiber and matrix on direction of crack propagation are also discussed.     

Process of debonding in RC beams shear-strengthened with FRP U-strips or side strips

Reinforced concrete (RC) beams may be strengthened for shear using externally bonded fiber reinforced polymer (FRP) composites in the form of side bonding, U-jacketing or complete wrapping. The shear failure of almost all RC beams shear-strengthened with side bonded FRP and the majority of those strengthened with FRP U-jackets, is due to debonding of the FRP. The bond behavior between the externally-bonded FRP reinforcement (referred to as FRP strips for simplicity) and the concrete substrate therefore plays a crucial role in the failure process of these beams. Despite extensive research in the past decade, there is still a lack of understanding of how debonding of FRP strips in such a beam propagates and how the debonding process affects its shear behavior. This paper presents an analytical study on the progressive debonding of FRP strips in such strengthened beams. The complete debonding process is modeled and the contribution of the FRP strips to the shear capacity of the beam is quantified. The validity of the analytical solution is verified by comparing its predictions with numerical results from a finite element analysis. This analytical treatment represents a significant step forward in understanding how interaction between FRP strips, steel stirrups and concrete affects the shear resistance of RC beams shear-strengthened with FRP strips.     

纤维复合材料界面横向拉伸分析

以单纤维十字型横向拉伸试验为研究对象,对纤维/基体界面采用弹性-软化双线性内聚力模型,建立了纤维复合材料在横向拉伸作用下界面法向失效过程的解析模型。得到了沿纤维/基体圆周界面的法向应力分布,纤维/基体界面的状态与界面承载力和单纤维复合材料承载力的关系,以及内聚力参数和试件几何尺寸对它们的影响。结果表明:纤维/基体圆周界面在脱粘前经历全部弹性及弹性+软化两种状态;当界面为弹性状态时,界面法向应力随界面强度线性增加;当界面为弹性+软化状态时,界面软化范围随界面裂纹萌生位移的增加而增大;界面初始脱粘位置与拉伸荷载方向重合;界面初始脱粘时的界面承载力随界面强度及界面裂纹萌生位移的增加而增加,随界面裂纹生成位移的增加而降低;单纤维复合材料的脱粘荷载受基体截面尺寸的影响,当纤维体积含量相同时,沿荷载方向截面尺寸的增大对提高脱粘荷载更显著。     

Residual strength of a fiber reinforced metal matrix composite with a crack

The residual strength of a cracked unidirectional fiver reinforced metal matrix composite is studied. We propose a bridging model based on the Dugdale strip yielding zones in the matrix ahead of the crack tips that accounts for ductile deformations of the matrix and fiber debonding and pull-out in the strip yielding zone. The bridging model is used to study the fracture of an anisotropic material and its residual strength is calculated numerically. The predicted results for a SiC/titanium composite agree well with the existing experimental data. It is found that a higher fiber bridging stress and a larger fiber pull-out length significantly contribute to the composite's residual strength. The composite's strength may be more notch-insensitive than the corresponding matrix material's strength depending on several factors such as fiber-matrix interface properties and the ratio of the matrix modulus to an ‘effective modulus’ of the composite.     

Folding of fiber composites with a hyperelastic matrix

This paper presents an experimental and numerical study of the folding behavior of thin composite materials consisting of carbon fibers embedded in a silicone matrix. The soft matrix allows the fibers to microbuckle without breaking and this acts as a stress relief mechanism during folding, which allows the material to reach very high curvatures. The experiments show a highly non-linear moment vs. curvature relationship, as well as strain softening under cyclic loading. A finite element model has been created to study the micromechanics of the problem. The fibers are modeled as linear-elastic solid elements distributed in a hyperelastic matrix according to a random arrangement based on experimental observations. The simulations obtained from this model capture the detailed micromechanics of the problem and the experimentally observed non-linear response. The proposed model is in good quantitative agreement with the experimental results for the case of lower fiber volume fractions but in the case of higher volume fractions the predicted response is overly stiff.     

Prediction of overall tension behavior of short fiber-reinforced composites

The bridging stress of fibers along the crack surface plays an important role in analyzing the tension behavior of short or long fiber-reinforced composites. This paper uses the inclusion theory to obtain the expression of bridging stress for short fiber reinforced composite (SFRC) . A simplified model with periodically distributed fibers is proposed to estimate the average fiber spacings. The total fracture resistance is calculated as an energy summation including interface debonding energy dissipation, frictional sliding work between fibers and matrix, strain energy increment of fibers and matrix. The bend over point (BOP) stress is calculated by this fracture resistance. The necessary conditions of the fibers and matrix for the multiple cracking in SFRCs are discussed and the expression of ultimate external stress is derived. The critical fiber volume fraction for the strain hardening response is determined by an iteration method. In the meanwhile, the average spacing between two short fibers is proposed by a periodical distribution assumption. The theoretical prediction is compared with experimental data.     

固化温度对碳纤维/环氧基体界面行为影响的分析

对界面粘结性能及热残余应力影响下的单纤维复合材料的界面行为进行了分析。采用界面的弹性-软化内聚力模型,用解析法对单纤维复合材料由固化引起的热残余应力、以及单纤维碎断过程纤维的轴向应力分布进行了模拟,得到了碳纤维/环氧树脂在常温和高温固化两种情况的界面粘结性能。结果表明：与常温固化相比,高温固化后,界面的剪切强度增幅不大,界面的断裂韧性显著增加;高温固化后形成的界面,使界面的软化提前、界面的脱粘延迟;高温固化产生的纤维轴向和界面径向热残余应力对界面的软化均有延迟作用;界面径向热残余应力还对界面的脱粘有延迟作用。     

一种新的界面脱粘和纤维拔出模型

对纤维增强复合材料中界面的脱粘和纤维的拔出行为进行了研究,通过纤维间距d来考虑纤维之间的相互影响,改变脱粘段的剪切强度和粘结段的临界能量释放率,推导出了纤维拉拔荷载和纤维脱粘长度之间的变化关系,与StangH的模型进行了对比,当纤维间距较大时,纤维之间的相互影响相对较小,此时与StangH的单根纤维拉拔情况较为相符,但当纤维间距较小时,由于临近纤维的影响,使得在相同脱粘长度的情况下,纤维拉拔荷载和纤维拔出端位移有减小的趋势,改变复合材料板层的厚度,由于影响了基体的变形,界面的脱粘和纤维的拔出行为也受到了相应的影响。     

纤维增强橡胶复合材料界面力学性能有限元分析

基于剪滞理论,引入双线性内聚力模型研究了纤维与基体界面应力传递机理．采用ABAQUS模拟了非理想界面在单纤维拔出过程中的脱粘失效,分析了不同脱粘阶段界面剪应力分布情况,以及界面刚度和纤维长径比对界面应力传递和拔出载荷的影响规律．结果表明,在纤维受载失效过程中,纤维的拔出过程可分为4个阶段,即界面的完全粘结、损伤演化、逐渐脱粘、完全脱粘．界面的刚度和纤维长径比对界面应力传递与最大拔出力均有一定的影响．界面刚度、纤维长径比主要影响纤维的最大拔出载荷以及界面脱粘失效位移．     

纤维增强陶瓷基复合材料疲劳迟滞回线模型研究

纤维增强陶瓷基复合材料初始加载到疲劳峰值应力时, 基体出现裂纹, 纤维/基体界面发生脱粘. 在疲劳载荷作用下, 纤维相对基体在界面脱粘区往复滑移使得陶瓷基复合材料出现疲劳迟滞现象. 建立了纤维陶瓷基复合材料疲劳迟滞回线细观力学模型, 采用断裂力学方法确定了初始加载纤维/基体界面脱粘长度、卸载界面反向滑移长度与重新加载新界面滑移长度, 分析了4种不同界面滑移情况的疲劳迟滞回线. 假设正交铺设与编织陶瓷基复合材料疲劳迟滞回线主要受0°铺层、轴向纱线内纤维/基体界面滑移的影响, 预测了单向、正交铺设与编织陶瓷基复合材料在不同峰值应力与不同循环的疲劳迟滞回线, 与试验结果吻合.      

The cohesive law for the particle/matrix interfaces in high explosives

The debonding of particle/matrix interfaces has an important effect on the macroscopic behavior of composite materials. There are extensive analytical and numerical studies on interface debonding in composite materials based on cohesive zone models which assume a phenomenological relation between the normal (and shear) traction(s) and opening (and sliding) displacement(s) across the particle/matrix interface. However, there are little or no experiments to determine the cohesive law for particle/matrix interfaces in composite materials. In this paper, we develop a method to determine the cohesive law for particle/matrix interfaces in the high explosive PBX 9501. We use the digital image correlation technique to obtain the stress and displacement around a macroscopic crack tip in the modified compact tension experiment of PBX 9501. We use the extended Mori-Tanaka method (which accounts for the effect of interface debonding) and the equivalence of cohesive energy on the macroscale and microscale to link the macroscale compact tension experiment to the microscale cohesive law for particle/matrix interfaces. Such an approach enables us to quantitatively determine key parameters in the microscale cohesive law, namely the linear modulus, cohesive strength, and softening modulus of particle/matrix interfaces in the high explosive PBX 9501. The present study shows that Ferrante et al.'s [1982 Universal binding energy relations in metallic adhesion. In: J.M. Georges (Ed.), Microscopic Aspects of Adhesion and Lubrication, Elsevier, Amsterdam, pp. 19-30.] cohesive law, which is established primarily for bimetallic interfaces, is not suitable to the high explosive PBX 9501.     

INVESTIGATION ON FATIGUE HYSTERESIS LOOPS MODELS OF FIBRE-REINFORCED CERAMIC-MATRIX COMPOSITES

纤维增强陶瓷基复合材料初始加载到疲劳峰值应力时, 基体出现裂纹, 纤维/基体界面发生脱粘. 在疲劳载荷作用下, 纤维相对基体在界面脱粘区往复滑移使得陶瓷基复合材料出现疲劳迟滞现象. 建立了纤维陶瓷基复合材料疲劳迟滞回线细观力学模型, 采用断裂力学方法确定了初始加载纤维/基体界面脱粘长度、卸载界面反向滑移长度与重新加载新界面滑移长度, 分析了4种不同界面滑移情况的疲劳迟滞回线. 假设正交铺设与编织陶瓷基复合材料疲劳迟滞回线主要受0°铺层、轴向纱线内纤维/基体界面滑移的影响, 预测了单向、正交铺设与编织陶瓷基复合材料在不同峰值应力与不同循环的疲劳迟滞回线, 与试验结果吻合.     

Micromechanical modelling and simulation of chopped random fiber reinforced polymer composites with progressive debonding damage

The aim of the present paper is to provide a quantitative prediction of the elastic-damage behaviour of randomly oriented fiber polymer composites. A constitutive model based on micromechanical considerations is presented. The nucleation and growth of voids induced by progressive fiber debonding is combined with the constitutive relationship. Failure resulting of excessive damage accumulation is captured by a critical void volume criterion and a vanishing element technique. Experimentally, damage accumulation in random glass fiber–polyester composites was monitored by a videoextensometry technique able to control the local strain rate. Good agreement of model predictions with experimental data is pointed out. The model was implemented into a finite element program and numerical applications on composite structures (a tensile specimen and a plate containing a central hole) are presented to illustrate the capability of the approach. Digital image correlation method was also used to measure the full-field strain in a notched specimen under tensile loading. The simulated results compared favourably with those obtained from experiments.     

Debonding and fiber pull-out in reinforced composites

In order to evaluate the strength of fiber-reinforced composites, there is first the need to investigate the interfacial debonding and the pull-out of fibers in a fractured composite with intact fibers. This type of problem in crack bridging has been investigated by several authors based on different models and assumptions [1–7]. In this study, we will consider a three-dimensional model of a single fiber of finite length bonded by a finite cylindrical matrix with an initial crack existing in a portion of the interface. In the model, one end of the cylinder is so constrained that the axial component of displacement vanishes. A tensile stress is applied to the fiber at the other end. The aim is to determine the pull-out of the fiber and the critical condition for interfacial debonding. Both the fiber and the matrix are treated as elastic materials. Analysis is made based on a method using Papkovich-Neuber displacement potential functions for the problem of an elastic solid subjected to axisymmetrical boundary conditions. Solutions are found by means of the technique of trigonometrical series. Effects of initial misfit strains and frictional sliding between the fiber and the matrix over the interfacial crack are also included in the study.     

The uniaxial tension of particulate composite materials with nonlinear interface debonding

Debonding of particle/matrix interfaces can significantly affect the macroscopic behavior of composite material. We have used a nonlinear cohesive law for particle/matrix interfaces to study interface debonding and its effect on particulate composite materials subject to uniaxial tension. The dilute solution shows that, at a fixed particle volume fraction, small particles lead to hardening behavior of the composite while large particles yield softening behavior. Interface debonding of large particles is unstable since the interface opening (and sliding) displacement(s) may have a sudden jump as the applied strain increases, which is called the catastrophic debonding. A simple estimate is given for the critical particle radius that separates the hardening and softening behavior of the composite.     

一种新形式的钢纤维混凝土冲击动态本构关系及材料参数的确定

采用?75 mm大口径SHPB系统进行了钢纤维体积率为0%、0.75%、1.5%三种混凝土材料动态性能实验,得出了不同钢纤维含量、不同应变率下的材料应力-应变关系曲线,实验结果表明:随着纤维含量及应变率的增加,钢纤维混凝土材料的峰值应变、峰值应力都随之提高,并在峰值应力之后出现应力的应变软化现象。以此实验结果为基础,提出了一种依赖于应变和应变率相关函数的新型非线性黏塑性动态本构关系,并通过对实验曲线的三步逐次最小二乘优选模拟,得到了相应的材料参数。结果表明,该本构关系对实验数据的模拟效果较好。     

A continuum model for fiber reinforced materials with debonding

A continuum theory for a fiber-reinforced material with debonding between the constituents is presented. The debonding phenomenon is simulated by imposing the continuity of the normal displacements at the fiber-matrix interfaces while allowing free tangential slip there. The derived theory is of the lowest order and is obtained by using a first order expansion in the displacements in the fiber and matrix phases. The theory is applied to investigate the effect of debonding on the propagation of waves in a boron/epoxy fiber reinforced material. It is shown that an additional mode of propagation is obtained as compared with the usual case of perfect bonding