<Emphasis Type="Italic">In-situ</Emphasis> Full Field Measurements During Inter-Facial Debonding in Single Fiber Composite Under Transverse Load

The fibre/matrix interfacial damage mechanisms of fiber-reinforced composites (FRCs) are investigated for single-fiber composites under transverse load. A stereo microscope setup is used for 3D digital image correlation during in-situ quasi-static tests of single-fiber standard dog-bone specimens. Macro-fibers (0.9 mm diameter) with radically different interfacial bonding with the epoxy matrix are used. Damage appears to initiate with fiber debonding at the free surface along the tensile direction. The crack then propagates around the interface while slightly growing along the fiber until a lateral crack initiates on the debonded free surface, provoking specimen failure. The final failure mechanisms appears to be different for strong and weak fiber/matrix bonding. 3D DIC is used to provide precise measurements of displacements, strains, and out-of-plane displacement during the whole test. Quantitative differences in the displacement fields are measured in the cases of strong and weak bonding between the fiber and matrix. 3D DIC with macro-fibers is shown to be a promising technique to provide a better understanding of the damage mechanisms in a single-fiber composite and to determine interfacial toughness of a specific fibre/matrix couple in order to perform accurate modeling of damage in FRCs. Displacement, strain, and confidence field results for each pixel from each experiment and at each time step are also provided for detailed comparison with simulation results.     

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。     

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.     

界面脱粘对陶瓷基复合材料疲劳迟滞回线的影响

采用细观力学方法对脆性纤维增强的陶瓷基复合材料拉-拉疲劳载荷下应力-应变迟滞回线进行了研究,将拉梅公式与库仑摩擦法则相结合分析了界面脱粘区以及粘结区复合材料细观应力场.根据卸载与重新加载时纤维相对基体滑移机制,分析了加卸载纤维轴向应力分布,结合断裂力学界面脱粘准则确定了初始加载界面脱粘长度ls、卸载界面反向滑移长度y以及重新加载界面滑移长度z',讨论了界面脱粘能和界面摩擦系数对初始界面脱粘、卸载界面反向滑移、重新加载界面滑移以及加卸载迟滞回线的影响.并与Pryce-Smith模型和试验数据进行对比表明:该文模型与试验曲线吻合的较好.     

Fiber push-out study of a copper matrix composite with an engineered interface: Experiments and cohesive element simulation

The fiber push-out test is a basic method to probe the mechanical properties of the fiber/matrix interface of fiber-reinforced metal matrix composites. In order to estimate the interfacial properties, parameters should be calibrated using the measured load–displacement data and theoretical models. In the case of a soft matrix composite, the possible plastic yield of the matrix has to be considered for the calibration. Since the conventional shear lag models are based on elastic behavior, a detailed assessment of the plastic effect is needed for accurate calibration. In this paper, experimental and simulation studies are presented regarding the effect of matrix plasticity on the push-out behavior of a copper matrix composite with strong interface bonding. Microscopic images exhibited significant local plastic deformation near the fibers leading to salient nonlinear response in the global load–displacement curve. For comparison, uncoated interface with no chemical bonding was also examined where the nonlinearity was not observed. A progressive FEM simulation was conducted for a complete push-out process using the cohesive zone model and inverse fitting. Excellent coincidence was achieved with the measured push-out curve. The predicted results confirmed the experimental observations.     

A piezoelectric biaxial loading device for interfacial fracture experiments

In this paper we describe the development of a new biaxial loading device for investigating mixed-mode fracture at bimaterial interfaces. The new device makes use of piezoelectric actuators and specially arranged flexures to provide independent displacements normal and tangential to the interface. Capacitive probes and special washer load cells were used for measuring the displacements and reactive loads, respectively. A closed-loop circuit was formed with a personal computer to control the applied displacements to within 10 nm. Preliminary experiments with quartz/epoxy/aluminum sandwich specimens with cracks growing between the quartz and the epoxy found that the intrinsic toughness of this interface was 30% lower than the value for a glass/epoxy interface. Crack opening interferometry measurements having a resolution of 30 nm revealed the presence of a cohesive zone whose size was about 0.5 μm.     

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。     

Mixed-mode thermal stress intensity factors from the finite element discretized symplectic method

A finite element discretized symplectic method is introduced to find the thermal stress intensity factors (TSIFs) under steady-state thermal loading by symplectic expansion. The cracked body is modeled by the conventional finite elements and divided into two regions: near and far fields. In the near field, Hamiltonian systems are established for the heat conduction and thermoelasticity problems respectively. Closed form temperature and displacement functions are expressed by symplectic eigen-solutions in polar coordinates. Combined with the analytic symplectic series and the classical finite elements for arbitrary boundary conditions, the main unknowns are no longer the nodal temperature and displacements but are the coefficients of the symplectic series after matrix transformation. The TSIFs, temperatures, displacements and stresses at the singular region are obtained simultaneously without any post-processing. A number of numerical examples as well as convergence studies are given and are found to be in good agreement with the existing solutions.     

A New Method for Measuring Displacements of Micro Devices by an Optical Encoding System

Micro electro mechanical systems (MEMS) frequently require displacement measurements with high accuracy, a high sampling rate, and a long sensing travel. However, the available methods for measuring displacements of micro devices are typically limited in terms of at least one of these figures of merit. In this paper, we present a novel implementation of an optical encoding method for measuring displacements of micro devices that provides good capabilities in all of these figures of merit. The optical encoding system combines a commercial reading apparatus with a custom-made metal grating that can be easily produced during MEMS fabrication. Experimental tests demonstrate the ability of the system to measure displacements with a resolution of 25 nm and sampling rate of 1 MHz, under a variety of displacement rate functions.     

A direct approach to fiber and membrane reinforced bodies. Part I. Stress concentrated on curves for modelling fiber reinforced materials

An approach is outlined to the equilibrium in fiber-reinforced materials in which the fibers are modeled as curves or lines with concentrated material properties. The system of forces representing the interaction of the fibers with the bulk matter is analyzed, and equilibrium of forces is derived from global laws. The displacements of the bulk matter are assumed to have continuous extension to the fibers. This forces the set of admissible deformations superquadratically integrable. This in turn forces the energy of the bulk of superquadratic growth. The material of the bulk matrix therefore cannot be linearly elastic. The energy of fibers can have a slower growth and can be quadratic. A formal set of assumptions is given under which an equilibrium state of minimum energy exists in the given external conditions. A weak form of equilibrium equations is derived for this equilibrium state. An explicitly calculable axisymmetric example is presented with an isotropic and quadratic energy of the matrix (linear elasticity) and linearly stretchable fiber. Since the superquadratic growth assumption is not satisfied, some peculiar features of the solution arise, such as the infinite limit of the radial displacement near the fiber. Nevertheless, from the obtained solution, we can compute the normal force in the fiber and the shear stress at the interface.     

Uniform Stress Inside an Anisotropic Elliptic Inclusion with Imperfect Interface Bonding

In this paper we study the two-dimensional deformation of an anisotropic elliptic inclusion embedded in an infinite dissimilar anisotropic matrix subject to a uniform loading at infinity. The interface is assumed to be imperfectly bonded. The surface traction is continuous across the interface while the displacement is discontinuous. The interface function that relates the surface traction and the displacement discontinuity across the interface is a tensor function, not a scalar function as employed by most work in the literature. We choose the interface function such that the stress inside the elliptic inclusion is uniform. Explicit solution for the inclusion and the matrix is presented. The materials in the inclusion and in the matrix are general anisotropic elastic materials so that the antiplane and inplane displacements are coupled regardless of the applied loading at infinity. T.C.T. Ting is Professor Emeritus of University of Illinois at Chicago and Consulting Professor of Stanford University.     

内聚力界面单元与复合材料的界面损伤分析

推导了一种基于内聚力模型无厚的界面单元,用来模拟复合材料纤维与基体之间的界面层．研究了纤维周期分布的复合材料受横向荷载时,在界面不同的强韧性条件下其界面损伤演化的规律和对复合材料整体性质的影响     

Optimization of Digital Image Correlation for High-Resolution Strain Mapping of Ceramic Composites

Digital image correlation (DIC) is assessed as a tool for measuring strains with high spatial resolution in woven-fiber ceramic matrix composites. Using results of mechanical tests on aluminum alloy specimens in various geometric configurations, guidelines are provided for selecting DIC test parameters to maximize the extent of correlation and to minimize errors in displacements and strains. The latter error is shown to be exacerbated by the presence of strain gradients. In a case study, the resulting guidelines are applied to the measurement of strain fields in a SiC/SiC composite comprising 2-D woven fiber. Sub-fiber tow resolution of strain and low strain error are achieved. The fiber weave architecture is seen to exert a significant influence over strain heterogeneity within the composite. Moreover, strain concentrations at tow crossovers lead to the formation of macroscopic cracks in adjacent longitudinal tows. Such cracks initially grow stably, subject to increasing app lied stress, but ultimately lead to composite rupture. Once cracking is evident, the composite response is couched in terms of displacements, since the computed strains lack physical meaning in the vicinity of cracks. DIC is used to identify the locations of these cracks (via displacement discontinuities) and to measure the crack opening displacement profiles as a function of applied stress.     

Dynamic fiber debonding and frictional push-out in mode composite systems: Experimental observations

In the present work a modified Split Hopkinson Pressure Bar (SHPB) system is adopted to perform dynamic fiber push-out experiments on model single fiber composite systems. A tapered punch and a support connect a monofilament composite with the incident and transmitted bars of the SHPB. The tapered punch is used to apply compressive loading to a single fiber (either steel or aluminum) embedded in a surrounding matrix material (EPON 862). The SHPB allows real time measurement of relative fiber/matrix displacement and push-out force, as the debonding and push-out event progresses. Using this technique we have studied the effect of loading rate, material mismatch, fiber length, and surface roughness on the push-out event. It was seen that maximum push-out force increases with increasing loading rate. In addition dynamic interfacial strength and toughness is highly dependent on fiber surface roughness. Results from a finite element analysis incorporating a cohesive failure model were used to extract interface strength and toughness values. It was found that the particular aluminum/EPON interface used is characterized by a dynamic shear failure strength of 48±8 MPa, a mode II fracture toughness of 160±40 N/m, and a friction coefficient of 0.2 at a sliding rate of 6 m/s. For the rates tested here these quantities were found to be approximately constant.     

A Cosserat shell model for interphases in elastic media

This study is concerned with the modeling of interphases in elastic media in general, and in composite materials in particular. The aim is to replace a boundary value problem consisting of a three-phase configuration, say that of fiber-interphase-matrix, by a simpler problem which involves the fiber and matrix only, plus certain matching conditions which simulate the interphase. The simplest of such known representations replaces a thin interphase by a “perfect contact interface” (a single surface) across which the displacements and tractions are assumed to be continuous. Another classical model replaces a thin and soft interphase by a “spring-type interface”, across which the tractions are continuous, but the displacement field undergoes a discontinuity. In the present paper, a Cosserat shell model of the interphase is derived which successfully models the original interphase in a unified manner, for the full range of its material parameters relative to those of the neighboring media. The model is derived in the setting of three-dimensional linear elasticity with small deformations and displacements. Comparisons with an existing exact solution of a coated fiber in an infinite matrix show that it performs extremely well even for moderately thick interphases.     

Model for measurement of thermal expansion coefficient of concrete by fiber optic sensor

The existence of a coating on an optical fiber results in a difference between the strain of the matrix concrete and that sensed by the embedded fiber optic sensor. This paper deals with the theoretical model for measurement of thermal expansion coefficient of concrete by embedded fiber optic sensor. The fiber core, the coating of the optical fiber, and the matrix concrete were all supposed to be elastic. And the bonding surfaces were supposed to be intact, that is to say, there is no relative slip deformation at the interface between the matrix concrete and the coating of the optical fiber, and that between the coating and the fiber core. Based on these assumptions, a theoretical model was developed for measurement of thermal expansion coefficient of concrete. Some experiments were done to verify the validation of the theoretical model. And the comparison indicates a good agreement between the experimental and theoretical results.     

A periodic unit-cell simulation of fiber arrangement dependence on the transverse tensile failure in unidirectional carbon fiber reinforced composites

The effect of fiber arrangement on transverse tensile failure in unidirectional carbon fiber reinforced composites with a strong fiber-matrix interface was studied using a unit-cell model that includes a continuum damage mechanics model. The simulated results indicated that tensile strength is lower when neighboring fibers are arrayed parallel to the loading direction than with other fiber arrangements. A shear band occurs between neighboring fibers, and the damage in the matrix propagates around the shear band when the interfacial normal stress (INS) is sufficiently high. Moreover, based on the observation of Hobbiebrunken et al., we reproduced the damage process in actual composites with a nonuniform fiber arrangement. The simulated results clarified that the region where neighboring fibers are arrayed parallel to the loading direction becomes the origin of the transverse failure in the composites. The cracking sites observed in the simulation are consistent with experimental results. Therefore, the matrix damage in the region where the fiber is arrayed parallel to the loading direction is a key factor in understanding transverse failure in unidirectional carbon fiber reinforced composites with a strong fiber/matrix interface.     

Three-dimensional anisotropic and inhomogeneous elastic media matrix analysis for small and large displacements

Summary A matrix displacement technique for analysing three-dimensional anisotropic and inhomogeneous elastic media is given for small and large displacements. The body is idealized by an assembly of finite tetrahedra. Using the novel device of natural stresses, loads and elemental stiffness, concise expressions for stiffness of the complete system are set up. Hence small displacement solution is obtained. Extension to large displacements proceeds via an incremental technique and an additional geometrical stiffness simulating effects of change of geometry on equilibrium conditions. It is proved that geometrical stiffness of tetrahedron derives from equivalent six-bar framework. Joint presence of loads and thermal actions is included.Vollständigc Fassung, mit Ausnahme der Anwendungen, des Vortrages des Verfassers beim XI. Internationalen Kongreß für Mechanik, München, August–September 1964.     

Numerical solution of three-dimensional static problems of elasticity for a body with a noncanonical inclusion

A boundary-element scheme is proposed for the numerical determination of the stress-strain state of a three-dimensional composite body, which is an elastic inclusion of arbitrary shape perfectly bonded to an infinite elastic matrix. The scheme involves the reduction of the original problem to six boundary integral equations for the components of interfacial displacements and forces and the boundary-element parametrization and discretization of these equations using generalized Gaussian integrals and topological maps with regularizing Jacobians. Numerical results are obtained for a cylindrical inclusion with rounded ends in a matrix subject at infinity to constant forces acting along this fiber. The influence of the length-to-radius ratio of the fiber and the ratio of the elastic moduli of the matrix and fiber on the stresses is examined __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 27–35, April 2007.     

A cracked sliding interface between anisotropic bimaterials

A general solution for the stresses and displacements of a cracked sliding interface between anisotropic bimaterials subjected to uniform tensile stress at infinity is given by using the Stroh’s formulation. Horizontal and vertical opening displacements on the interface, stress intensity factors, and energy release rate are expressed in real form, which are valid for any kind of anisotropic materials including the degenerate materials such as isotropic materials. It is observed that stresses exhibit the traditional inverse square root singularities near the crack tips, and the vertical opening displacement and energy release rate are intimately related to a real parameter λ determined by the elastic constants of the anisotropic bimaterials.